Chemistry of the Climate System: Volume 1 Fundamentals and Processes [3rd, completely revised and extended Edition] 9783110561265, 9783110559750

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Detlev Möller Chemistry of the Climate System

Also of Interest Chemistry of the Climate System. Volume 2: History, Change and Sustainability Möller, 2019 ISBN 978-3-11-055985-9, e-ISBN 978-3-11-056134-0

Drinking Water Treatment. An Introduction Worch, 2019 ISBN 978-3-11-055154-9, e-ISBN 978-3-11-055155-6

Biomass and Biowaste. New Chemical Products from Old Balu, García (Eds.), 2019 ISBN 978-3-11-053778-9, e-ISBN 978-3-11-053815-1

Chemistry for Environmental Scientists. Möller, 2015 ISBN 978-3-11-040999-4, e-ISBN 978-3-11-041001-3

Detlev Möller

Chemistry of the Climate System | Volume 1: Fundamentals and Processes 3rd, completely revised and extended Edition

Author Univ.-Prof. Dr. rer. nat. habil. Detlev Möller Brandenburgische Technische Universität Platz der Deutschen Einheit 1 03046 Cottbus Germany This book has 115 figures and 130 tables.

ISBN 978-3-11-055975-0 e-ISBN (PDF) 978-3-11-056126-5 e-ISBN (EPUB) 978-3-11-055992-7 Library of Congress Control Number: 2018956972 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2019 Walter de Gruyter GmbH, Berlin/Boston Cover image: Gabiixs/iStock/Getty Images Typesetting: le-tex publishing services GmbH, Leipzig Printing and binding: CPI books GmbH, Leck www.degruyter.com

| To my known (Andreas, Stefan, and Eleni) and still unknown descendants to whom the future belongs and to all people who love nature, life, and science.

Nothing in nature makes sense except in the light of evolution Adapted from Theodosius Grygorovych Dobzhansky (1900–1975; born in Ukraine, emigrated to the United States in 1927). In: The American Biology Teacher 35 (1973) 125–129

Nicht die Wahrheit, in deren Besitz irgend ein Mensch ist, oder zu seyn vermeynet, sondern die aufrichtige Mühe, die er angewandt hat, hinter die Wahrheit zu kommen, macht den Wert des Menschen. Denn nicht durch den Besitz, sondern durch die Nachforschung der Wahrheit erweitern sich seine Kräfte, worin allein seine immer wachsende Vollkommenheit besteht. Der Besitz macht ruhig, träge, stolz – It is not the truth which a man possesses, or thinks he possesses, but the sincere endeavour which he has used to come to truth, makes the worth of a man. For not through the possession of truth, but through the search for it, are those powers expanded in which alone his ever-growing perfection consists. Possession makes restful, indolent, proud – Gotthold Ephraim Lessing (Eine Duplik, 1778) [Lessing 1883, English version from Rolleston 1889, pp. 200/201]

Preface to the first edition Half a century ago, Christian Junge, the founding “father” of atmospheric chemistry, summarized the existing knowledge in his field of research. In 1960, Junge counted only 75 research articles dealing with atmospheric chemistry and radioactivity (Junge 1958, 1963). At present, the publication rate and number of researchers in atmospheric chemistry are orders of magnitude greater. Many major advances have been made since then. For example, in the early 1970s, the role of OH radicals in oxidizing gases, leading to their removal from the atmosphere, was discovered. The necessary ingredients to produce OH are ozone, water vapor, and ultraviolet B (UV-B) solar radiation. The catalytic role of NO in producing ozone was also recognized in the early 1970s. Until that time it was generally believed that tropospheric ozone was produced in the stratosphere and transported downward into the troposphere. The feedstocks for the creation of ozone are CO, CH4 , and many biogenic gases. Both natural and anthropogenic processes are responsible for their emissions. Although the main photochemical chain reactions are reasonably well known, their quantification needs much further research. They all are parts of the biogeochemical cycles of carbon, nitrogen, and sulfur. They can also play a role in climate, as does particulate matter (PM), which, contrary to the greenhouse gases (CO2 , CH4 ), tends to cool the Earth and atmosphere. In his book, Detlev Möller gives a thorough overview of the main chemical processes that occur in the atmosphere, only a few of which were mentioned earlier. The novel title of this book, Chemistry of the Climate System, should direct the attention of the reader to the fact that understanding atmospheric chemistry is incomplete without considering interfacing neighboring reservoirs such as the hydrosphere, lithosphere, and biosphere. An overview of the topics treated is provided in the introduction. It emphasizes that drawing strong borderlines between disciplines makes no sense; this is also valid for the various systems because they overlap and the most important processes can happen at their interfaces. Therefore, chemistry of the climate system combines atmospheric with water, soil, and biological chemistry. Another general approach of this book lies in the incorporation of historical facts: despite the orders of magnitude more publications each year at present than in the past, we should not forget that careful observations were made and serious conclusions drawn by many of our scientific ancestors. The text has its roots in a book written in German, entitled Luft and published by De Gruyter in 2003. Although the text was entirely rewritten and many chapters were replaced, the main emphasis on regarding the atmosphere as a multiphase system is essentially unchanged. Moreover, by adding interfacial chemistry, the system is enlarged into a multireservoir system, encompassing the climate system. Ultimately, however, the central focus is chemistry. The author avoids using the term environhttps://doi.org/10.1515/9783110561265-201

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mental chemistry, emphasizing that substances having specific physical and chemical properties can modify (chemical) systems in various directions depending on the mixture and initial conditions. Specialists in physics, chemistry, and biology, as well their many subdisciplines, need to understand what their disciplines can bring to the subject of climate system chemistry. This book is about fundamental aspects of (chemical) climate change, but it does not attempt to review all of the research on this topic. At many places in the book, a list of “Further Reading” is provided referring the reader to more specialized textbooks. The book comprises three large fundamental chapters on chemical evolution, physicochemical fundamentals and substances, and chemical reactions. Following the introduction, the chapter “Chemical Evolution” gives a brief history from the Big Bang to the Anthropocene, the human-influenced Earth system. Möller describes the historical dimension in connecting the past with future developments. Changing chemical air composition is based on three pillars: land-use change, burning of fossil fuels, and agricultural fertilization, all caused by the rising global population. The resulting air chemical “episodes” (acid rain, ozone, PM) are fairly well understood, and end-of-pipe technologies to control air pollution were introduced. The remaining future challenge, limiting global warming through reduced emission of CO2 , however, can be achieved only by moving the anthroposphere into a solar era, as suggested in Chapter 2.8.4. Hence, Möller defines global sustainable chemistry as a coupling of biogeochemical cycles with anthropogenic matter cycles, proposing a global carbon dioxide cyling (CO2 economy). Chapter 4 provides a brief overview pf the physical and chemical principles of transporting and transforming substances in natural reservoirs, again with an emphasis on multiphase and interfacial processes. The texts on chemical reactions, multiphase processes, atmospheric removal, and characteristic timescales are well written and easy to read, even for nonchemists. The third main chapter treats “Substances and Chemical Reactions in the Climate System” according to the elements and their compounds, depending on the conditions of reactions and whether the given substance exists in the gaseous or condensed phase. The structure is adapted from “classical,” substance-oriented textbooks in chemistry: hydrogen, oxygen, nitrogen, sulfur, phosphorus, carbon, and halogens. Many excellent figures summarize chemical pathways under different natural conditions and make it easy to understand complex chemical processes. The various appendixes provide useful information on abbreviations, quantities, units, and the Earth’s geological time scale. The respect brought to the history of science is reflected by the inclusion of nice biographical sketches, including of some notso-well-known scientists. In short, this well-written and useful book fills a gap in the attempt to provide books written from the perspective of a particular discipline (chemistry) on an inter-

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disciplinary subject (the climate system) for readers and scientists from different disciplines to learn (or teach) some chemistry outside of the laboratory retort or industrial vessel. Paul Crutzen, Mainz 2009 Nobel Prize in Chemistry 1995

Author’s preface to the third edition The entire focus in all previous editions of the Chemistry of the Climate System was on a chemical understanding of the climate system in the light of changes, from early times to the present and even into the future. Hence, insights into the evolution (or history) of the Earth and the atmosphere became key for understanding processes under changing conditions. It was the idea of De Gruyter to issue a third edition. Unfortunately, we are living in a time when the infinitesimal period between today and tomorrow is is virtually the only thing that interests people. Holding onto the past seems to be a hobby for only a few passionate individuals and looking far into the future is of interest only to a few solitary individuals. Students ask for textbooks that are no older than 2 years, not knowing that (good) textbooks, being decades old, already contain 90% of basic knowledge for understanding natural processes (in chemistry, physics, and biology) today. Nevertheless, books always get better with each new edition, even if only mistakes are corrected. It goes without saying that mistakes have been corrected in the present text as well. My deep gratitude goes to the publishers, who granted me an extension and allowed me to fully restructure the second edition of Chemistry of the Climate System into two volumes, now in the present third edition. Volume 1 now comprises the physical-chemical basics (fundamentals and principles) of the chemistry of the climate system. Volume 2 treats the system with respect to its evolution (or history) and how it has changed, as well as its sustainability. Volume 1 contains carefully corrected, fully restructured, and partly enlarged chapters from the second edition concerning the fundamentals of physics (kinetic gas theory and radiation budget), physicochemistry (thermodynamics, equilibrium, properties of water and solutions, multiphase processes), chemistry (substances and reactions, enlarged by metalloids and metals that are environmentally important), and global cycling in the climate system. All historical remarks are now – more systematically – integrated in Volume 2. The transport and transformation of chemical species are continuous, ongoing processes in the atmosphere. Air constituents (gases, solid and liquid particles) change perpetually through chemical reactions, transfers among physical states, and transfers to (deposition) and from (emissions) the Earth’s surface. Direct solar radiation and scattered and reemitted radiation interacts with air constituents, resulting in changes to energetic states and photochemical conversions. This volume mainly focuses on the physicochemical fundamentals of the climate system. As I will often mention in this book, we cannot separate chemical and physical processes. Hence, it is inevitable to outline briefly the physical fundamentals in this regard. However, there are many excellent books on atmospheric physics and meteorology on the market, and the reader is referred to them in connection with the following topics: atmospheric physics and thermodynamics (Peixoto and Oort 1992, Andrews 2000, Zdunkowski and Bott 2004, Hewitt and Jackson 2003, Tsonis 2007), atmospheric dynamics (Gill 1982, https://doi.org/10.1515/9783110561265-202

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Holton 2004, Vallis 2006, Marshall and Plumb 2007), meteorology (Garratt 1992, Kraus 2004, Wallace and Hobbs 2006, Ackerman and Knox 2006, Ahrens 2007, Lutgens et al. 2009), and radiation (Kyle 1991, Zdunkowski et al. 2007, Wendisch and Yang 2012). Great scientific progress was made in the nineteenth century. The twentieth century saw explosive scientific growth. What do we expect in the present century? The growth of science or “growth of knowledge,” a term coined by Karl Popper (1902–1994), was shown to have “an exponential curve” by the sociologist William Fielding Ogburn (1886–1959) in 1922¹ (Popper 1962, Ogburn 1922), based on data compiled by Darmstaedter (1908) on discoveries and inventions. Basil Bernstein (1924–2000) said, “the theory, however primitive, has always come before the research. Thus by the time a piece of research was initiated the theory has already been subject to conceptual clarification as it engages with the empirical problem. And by the time it has finished there were further conceptual developments.” (Bernstein 2000, p. 93). By the evolution of the Earth and the climate system we will simply understand their historical development from earliest times until the present. Theories on how the atmosphere and ocean formed must begin with an idea of how the Earth itself originated (Kasting 1993). An understanding of our atmosphere and the climate system is incomplete without going into the past. “The farther backward you can look the farther forward you can see” (Winston Churchill). “Evolution is God’s, or Nature’s, method of creation. Creation is not an event that happened in 4004 BC; it is a process that began some ten billion years ago and is still under way” (Theodosius Grygorovych Dobzhansky). “Progress is not an objective fact of nature and cannot therefore be used to justify a normative ethic” (Ruse 1999, p. 221). Despite important achievements in our understanding of key aspects of aerosols, clouds, and precipitation chemistry and physics, clouds and aerosols remain the largest source of uncertainty in the two most important climate change metrics: radiative forcing and climate sensitivity (IPPC 2007, 2013). This uncertainty is the “manifestation of the lack of our understanding of how aerosol–cloud–precipitation processes act in the climate system” (Heintzenberg and Charlson 2009). An understanding of this complex matter requires an interdisciplinary and integrated approach. Contemporary science has had to adopt a new way of thinking because of the emergence of a rapid accumulation of knowledge at different levels. It seems, however, that progress in understanding nature is slow and infinite. Wise adages illustrate this predicament: “Nature is simple, but scientists are complicated,” said Spanish cardiologist Francisco Torrent-Guasp (1931–2005), and Jean-Jacques Rousseau asserted, “Nature never deceives us; it is we who deceive ourselves” (references from Buckberg 2005). Albert Einstein said that “everything should be made as simple as possible, but not simpler.” 1 Ogburn wrote, “When the material culture was small inventions were few, and now when the material culture is large the inventions are many” or in other words, the greater the number of inventions, the greater the number of new inventions generated. Ogburn’s exponential curve was criticized regularly throughout history; see for example Schmookler (1966).

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Stewart and Cohen (1994) also stated: “The role of science is to seek simplicity in a complex world. This is a comfortable picture, which encourages a view of the relation between laws and their consequences – between cause and effect –that might be characterized as ‘conservation of complexity’. That is, simple rules imply simple behaviour, therefore complicated behaviour must arise from complicated rules.” Today, an innumerable sites devoted to the study of air chemistry exist that are often only active for short periods, with sometimes barely more than a dozen samples collected and analyzed for whatever purpose. Josiah Charles Stamp (1880–1941) wrote: “We are so obsessed with the delight and advantage of discovery of new things that we have no proportionate regard for the problems of arrangement and absorption of the things discovered” (Stamp 1937, p. 60). I hope that this history, at least since the systematic monitoring in the second half of the nineteenth century – which is certainly unknown to most modern air chemists – will not only encourage respect for our scientific predecessors but will help to avoid many scientifically meaningless studies of the kind that have appeared over the last few decades. The endeavor remains to learn from previous studies to ask the appropriate open questions and draw the right conclusions for further studies. We learn from history that all kinds of people have been interested in our subject from a philosophical perspective or with respect to the application of techniques (engineering) but always motivated by specific problems (e.g., pollution) of their era. We also hold deep respect for our scientific forebears for the brilliant conclusions they drew based on experiments using very simple techniques and limited quantitative measurements. The great interest in historical data from the era before fossil fuel combustion lies also in the deduction of background concentrations, in other words, the natural reference concentrations for assessing human-influenced changes in chemical air composition. On the other hand, recognition of pervasive urban air pollution in the past would also provide a scale for a more realistic assessment of present air pollution, often still referred to as serious by politicians and administrators. English chemist Colin Archibald Russell (1928–2013) wrote, “Science without its history is like a man without a memory. The results of such collective amnesia are dire” [In: Whigs and professionals. Nature (1984) 308, 777–778]. A chemist who has spent 40 years studying atmospheric chemistry and air pollution wrote this book. When I began learning what air chemistry was about, it was the era of sulfur dioxide pollution, the 1970s. It was soon clear to me – and first shown by Junge and Ryan (1958) – that aqueous-phase chemistry dominates in the overall conversion of SO2 to sulfuric acid, i.e., chemical reactions in clouds, fog, and raindrops (Möller 1980). Being fascinated from the first publication on complex chemistry in raindrops (Graedel and Weschler 1981), we began to study acid deposition (Marquardt et al. 1984) and to develop the first extensive model on aqueous-phase chemistry for raindrops and rain events in Europe (Mauersberger and Möller 1990). Soon after, we learned that chemical conversion in rain is negligible compared to chemistry in clouds in the development of a cloud chemistry model (Möller and Mauersberger 1992). Fol-

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lowing the motto of Gottfried Wilhelm Leibniz (1646–1716) “theoria cum praxis” we constructed a mountain cloud chemistry station at Mount Brocken of the Harz mountain range (Möller et al. 1993), in continuous operation until 2010. Now, more than 5 years after my retirement and at the end of my scientific career, I would like to thank more people than just my former staff members (see preface to the second edition). First, I thank history (very special East German circumstances) that I had the freedom to decide in late 1974 to become an atmospheric chemist. It was the time of the so-called cold war, dividing the world into East (former “socialist” countries) and West (“capitalistic” countries), antagonized at all fronts. However, air pollution knows no borders, nor does science. Before the fall of the Wall in late 1989, despite some invitations from Western countries (my special thanks go to Henning Rodhe and Hans-Walter Georgii), my “area of distribution” remained the East before 1990. I am very happy to know all those individuals in the Eastern bloc (the number was limited) who worked at the same time as I did in the field of atmospheric chemistry and air pollution. It also makes me happy that I became one of the very few specialists in the field in the former Eastern bloc in the 1980s. The most renowned scientists from the East at that time, who were also of international repute, I name here: Ernö Mészáros (Budapest), Alexey Ryaboshapko (Moscow), Mark Evseevič Berljand (†), and Rimma Lavrinenko and Valerij Isidirov (Leningrad and St. Petersburg, respectively), and in addition Bedřich Binek (Prague), Dušan Závodský (Bratislava), Lászlo Hórvath, Lászlo Bózo, Lászlo Haszpra and Gabriella Várhelyi (Budapest), Stefan Godzik (Katowice), Dalia Shopauskine (Vilnius), Zhao Dianwu (Beijing), and a few more with whom I was in constant contact and was engaged in very fruitful discussions. Unfortunately, I never met the great Olga Petrovna Petrenchuk (Leningrad), a pioneer in aerosol and cloud research. Another person I never met owing to his untimely death but whom I hold in the highest regard is Hans Cauer (1899–1962), the German pioneer of chemical climatology – my intellectual father. The dream, however, of establishing a research station at Mount Brocken became a reality only after the fall of the Berlin Wall in early spring 1990. Hence, I would also like to thank many leading West German scientists for supporting me and my project ideas in the early 1990s: Paul Crutzen, Meinrath Andreae, Adolf Ebel, Hans-Walther Georgii (†), Hans Pruppacher, Dieter Kley, Dieter Ehhalt, Ruprecht Jaenicke, Reinhard Zellner, Dieter Klockow (†), Wolfgang Jaeschke, Wolfgang Seiler, Ullrich Schurath, Peter Warneck, Gode Gravenhorst, Peter Winkler, Karl-Heinz Becker, Ulrich Platt, Jürgen Kesselmeier, and many others. I am very happy to have met Christian Junge in 1992. My special thanks go again to Volker Mohnen, who flew me in his Cessna airplane in 1991 from Albany to Lake Placid, New York, visiting the Whiteface Mountain Field Station, which served as the inspiration for my Brocken station. Without the extensive international cooperation or idea exchange in the 1990s, the Brocken station and our large mobile measuring equipment (we participated in 12 international field campaigns at many sites throughout Europe between 1990 and 2008 and 13 joint national and 17 institutional field campaigns) would not have been developed to such a so-

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phisticated degree. I would like to thank (in alphabetical order) Hajime Akimoto, Helen ApSimon, Greg Ayers, Len Barrie, Axel Berner, Peter Brimblecombe, Peter Builtjes, Robert Charlson, Nadine Chaumerliac, Tom Choularton, Jeff Collett, Tony Cox, Robert Delmas, Bob Duce, Sandro Fuzzi, Ian Galbally, Hiroshi Hara, Manabu Igawa, Peter Liss, Tony Marsh, John Miller, Stuart Penkett, Pascal Perros, Hans Puxbaum, Robert Rosset, Steve Schwartz, Jack Slanina, Chris Walcek, and many others. Last but not least, I thank my East German colleagues and partners without whom I would not have been able to build my research profile in the 1980s: Karl-Heinz Bernhardt, Hans-Günther Däßler, Wolfgang Rolle (†), Eberhard Renner, Wolfgang Warmbt (†), Uwe Feister, Wolfgang Marquardt (†), Herbert Mohry, Herbert Lux, Günther Flemming, Ulrich Damrath, Manfred Zier, Günther Herrmann, Bernd Schneider, Eberhard Hüttner, Peter Ihle, Christian Hänsel (†), Kurt Schwinkowski, Wolfgang von Hoyningen-Huene, Rudolf Kind, and others. Unfortunately, I never had the opportunity to meet Helmut Mrose (†), a pioneer in air chemistry at Wahnsdorf (DDR) in the early 1950s (in addition to W. Warmbt). I cannot name everyone, but I have forgotten no one. Detlev Möller Berlin, August 2018

Author’s preface to the second edition Now, 4 years after the publication of the first edition of Chemistry of the Climate System, we see continued growth in the scientific literature and in particular new insights in the field of atmospheric aerosol (fine PM and especially the role of biological material) but also in HNO2 and OH chemistry; however, it is not my aim to consider them all in the second edition, giving an actual review. My intention is, rather, to provide the reader a monograph textbook for a deeper understanding of physicochemical processes in a very complex system composed of different states of matter (gas, liquid, and solid) within different reservoirs, specifically the atmosphere, hydrosphere, lithosphere, and biosphere (the climate system). Scientific progress is measured in large strides in the fundamental sciences – laboratory and theoretical studies. Nevertheless, studying complex environmental processes by “outdoor” studies (field experiments) – and even extending one reservoir or phase – became extremely complicated and was carried out in the decade or two only in large projects that included many institutes and scientists. Our knowledge also increased and feedback for detailed laboratory work was produced. Better understanding of the climate system acquired by a deeper consideration and coupling of subsystems, most of all the atmosphere with the oceans (for example, explaining the discrepancy between a further rise in atmospheric CO2 and stagnant air temperature). In addition, the biosphere was revealed to be much more complex in its feedbacks to atmospheric changes (the still unanswered question of where all the CO2 remains). Unfortunately, controlling our climate system is much more far off compared to our understanding 4 years ago. Economics largely disregards results from climate research. Visible, human-caused catastrophes, such as the Fukushima Daiichi nuclear disaster, did result in any forward-looking changes to the energy mix or a transition to solar technologies but led backward to coal combustion, exacerbating the CO2 problem. Climate change is likely not a catastrophe in a traditional way; rather, it is a slow process with winners and losers (humans, animals, and plants). I hope that this new edition of Chemistry of the Climate System will find new readers who want to learn more about our climate system. Knowledge is the key to sustainable development and to realizing that the benefits accruing to winners will pale by comparison to the penalty the losers will pay. Needless to say, (I hope) all errors have been corrected, information (especially monitoring and emission data) have been updated, many figures have been improved, several paragraphs were rewritten for clarity, and new key knowledge has been added in this edition. Moreover, two new sections on “chemical climatology” have been added: precipitation and cloud chemistry monitoring. The chapter on atmospheric trace species was enlarged to include a discussion of hydrochloric acid, nitrous acid, and nitric acid with its salty PM.

https://doi.org/10.1515/9783110561265-203

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Last but not least, I would like to express my profound gratitude to my coworkers who accompanied me over many years, even decades, in atmospheric chemistry; without them this book would have been impossible [I corrected the periods with this 3rd edition]: Karin Acker (1988–2014), Wolfgang Wieprecht (1982–2019), Günther Mauersberger (1985–2006), Renate Auel (1987–2008), Gisela Hager (1987–1997), Jürgen Hofmeister (1988–2017), and Dieter Kalass (1992–2018). Many others, not named here, were part of my group for “only” a few years. We had a great time, with many highlights in atmospheric chemistry in the 1980s and 1990s. Detlev Möller Berlin, February 2014

Prologue Ten years ago the publishing house De Gruyter asked me to write a book titled Luft (Air), which was published in 2003. Paul Crutzen said that it was written in the wrong language. It was written in German, my mother tongue. I took it as a compliment that they wanted me to reach more international readers. My first thank you goes to De Gruyter, who offered me the opportunity to write another book on air in English about 3 years ago. The German book Air belongs to a planned series on water, air, and soil (the last one has not been written yet), which means that there were certain restrictions and wishes that came from the editor. However, for this new book I had absolute freedom to choose my own content; therefore, I would like to express a second thank you to De Gruyter. The only wish from the editor was that this book should contribute to the discussion on climate change. This new book is not a (revised) translation of Air – I have only used a few fundamental issues such as physicochemistry and basic air chemistry, which has become fundamental knowledge in any textbook. I am a chemist; my original background is physical chemistry, but for 35 years I have been dealing with air chemistry (and air pollution studies). Chemistry is the science of matter, and matter distributes and cycles through nature. The climate system is a part of this, and the atmosphere is another part. The Earth’s climate system provides a habitable zone. I agree with those scientists who argue that human beings, as a part of nature, have altered the “natural system” to such an extent that we are now unable to reverse the present system back to a preindustrial or even prehuman state. Nevertheless, the key question at present is how to maintain the functioning of our climate system in such a way that enables the sustainable survival of humans. We can state that humans have become a global force in chemical evolution with respect to climate change by interrupting naturally evolved biogeochemical cycles. However, humans also have all the capacities to turn the “chemical revolution” into a sustainable chemical evolution. An understanding of how the climate system works is provided by the natural sciences (physics, chemistry, and biology). This book focuses on the chemistry of the climate system, but differentiating precisely between physics and chemistry makes absolutely no sense when trying to understand that system. However, without an understanding of biological laws – and we could probably include social laws here as well, considering that the biosphere was long ago transformed into the noosphere – we will neither understand climate change nor find solutions to climate control. Maybe this book will provoke people by bridging state-of-the-art textbook knowledge with ideas or opinions beyond “pure” chemistry. Without a paradigm change in the next two to three decades (for example, carbon dioxide cycling), we will have little chance to control climate.

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XX | Prologue

My knowledge is limited; therefore, specialists will find gaps and missing pieces in my book. A few weeks ago, I attended a lecture by Professor Norimichi Takenaka (Japan), who studied the decomposition of ammonium nitrite in drying dew droplets by the formation of N2 – a disproportioning and fascinating pathway for atmospheric NH3 and NOx . Unfortunately, I did not know about this reaction, even though it was already known in the nineteenth century, and it is a key example of interfacial chemistry, which is a focus of my book and has been a special interest of mine in the last few years after having studied multiphase chemistry for many years. I believe that interfaces (or heterogeneous systems) at certain places in natureprovide special conditions for chemical reactions and therefore result in the turnover of matter. Our knowledge about what happens in atmospheric multiphase chemistry, despite much progress over the last two decades, remains limited (I hope that some of that knowledge is summarized in this book). However, interfacial chemistry may be more important (and almost more interesting) for controlling the climate system at the interfaces between the atmosphere and the Earth’s surface, including, for example, natural waters, soils, plants, and microorganisms. Special thanks go to Professor Volker A. Mohnen, to whom I owe important scientific suggestions over the last 20 years, including the impulse to write this book. Finally, I would like to thank my coworkers who accepted my frequent absence at the institute throughout the last 2 years (and who kept things running smoothly); I wrote this book in my office at my home in Berlin (day and night, weekdays and weekends – special thanks go to my wife Ursula and my family), surrounded by hundreds of books on the chemistry (but also the history, physics, and biology) of the climate system published in the last 200 years (and a few older ones). This book, to my knowledge, is the first ever to be titled Chemistry of the Climate System, and I hope – no, I am sure – that it will not be the last. It stands between “special” and “generic”; it is part textbook, part monograph (and might even appear to be an ecopamphlet). Hence, the book is recommended to any and all who like nature and chemistry or who want to learn more about climate system chemistry. Detlev Möller Berlin and Cottbus, November 2010

Contents Preface to the first edition | VII Author’s preface to the third edition | XI Author’s preface to the second edition | XVII Prologue | XIX List of principal symbols | XXVII 1 1.1 1.2 1.3 1.4

Introduction | 1 Chemistry and the climate system | 2 Air and atmosphere: a multiphase and multicomponent system | 9 Principles of chemistry in the climate system | 14 Substances in climate system | 16

2 Fundamentals of physics in the climate system | 21 2.1 Meteorological basics | 21 2.1.1 Scaling and structure of the atmosphere | 21 2.1.2 Meteorological elements | 26 2.1.2.1 Air pressure | 27 2.1.2.2 Air temperature | 28 2.1.2.3 Air humidity | 29 2.1.3 Hydrometeors | 29 2.1.3.1 Clouds | 30 2.1.3.2 Fog, mist, and haze | 36 2.1.3.3 Precipitation | 38 2.1.4 Dew, frost, rime, and interception | 39 2.2 Climatological basics | 42 2.2.1 Climate | 42 2.2.2 Climate system | 45 2.2.3 Chemical climate | 48 2.3 Optics of the atmosphere: Radiation | 51 2.3.1 Solar radiation | 52 2.3.1.1 The Sun and its radiation output | 52 2.3.1.2 Solar radiation transfer through the atmosphere | 53 2.3.2 Absorption and emission of light | 61 2.3.2.1 Absorption (Lambert–Beer law) | 62 2.3.2.2 Emission (Planck’s law and Stefan-Boltzmann law) | 63

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2.3.3 2.4 2.4.1 2.4.1.1 2.4.1.2 2.4.1.3 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.6 2.6.1 2.6.2 2.7

Terrestrial radiation and radiation budget | 65 Atmospheric dynamics | 67 Fluid characteristics | 68 Effective atmospheric forces | 68 Atmospheric flow: Laminar and turbulent | 70 Fluid characteristics: Wind speed and direction | 73 Properties of gases: The ideal gas | 75 Gas laws | 75 Mean free path and number of collisions between molecules | 79 Viscosity | 82 Diffusion | 82 Atmospheric removal: Deposition processes | 84 Dry deposition | 86 Wet deposition | 92 Characteristic times: Residence time, lifetime, and turnover time | 94

3 Fundamentals of physicochemistry in the climate system | 101 3.1 Chemical thermodynamics | 101 3.1.1 First law of thermodynamics and its applications | 102 3.1.1.1 Internal energy | 102 3.1.1.2 Molar heat capacity | 104 3.1.1.3 Thermochemistry: Heat of chemical reaction | 105 3.1.2 Second law of thermodynamics and its applications | 107 3.1.2.1 Entropy and reversibility | 107 3.1.2.2 Thermodynamic potential: Gibbs–Helmholtz equation | 109 3.1.2.3 Chemical potential | 111 3.1.2.4 Chemical potential in real mixtures: Activity | 112 3.2 Equilibrium | 114 3.2.1 Chemical equilibrium: The mass action law | 115 3.2.2 Phase equilibrium | 116 3.2.2.1 Gas-liquid equilibrium: Evaporation and condensation | 117 3.2.2.2 Gas-liquid equilibrium: Special case of droplets (Kelvin equation) | 118 3.2.2.3 Absorption of gases in water: Henry’s law | 119 3.2.2.4 Solubility equilibrium: Solid–aqueous equilibrium | 123 3.2.2.5 Adsorption and desorption | 124 3.3 Steady state | 126 3.4 Water: Physical and chemical properties | 128 3.4.1 Water structure: Hydrogen bond | 130 3.4.2 Water as solvent | 132 3.4.3 Water vapor | 133 3.4.4 Water properties in relation to the climate system | 136

Contents | XXIII

3.5 3.5.1 3.5.2 3.5.3 3.5.4 3.6 3.6.1 3.6.2 3.6.2.1 3.6.2.2 3.6.3 3.6.4 3.6.5 3.6.5.1 3.6.5.2 3.6.5.3 3.6.5.4

Properties of solutions and droplets | 137 Surface tension and surface-active substances | 138 Vapor pressure lowering: Raoult’s law | 139 Freezing point depression | 142 Diffusion in solution | 143 Heterogeneous processes: Multiphase chemistry in the climate system | 143 Aerosols, clouds, and precipitation: The climate multiphase system | 146 Gas-to-particle formation: Homogeneous formation of CCNs | 149 Classical nucleation theory | 149 Formation of secondary organic aerosols | 154 Atmospheric aerosols and the properties of aerosol particles | 156 Formation of cloud droplets: Heterogeneous nucleation | 163 Scavenging: Acommodation, adsorption, and reaction (mass transfer) | 166 Mass transfer: General remarks | 166 Adsorption | 172 Surface chemistry: Kinetics of heterogeneous chemical reactions | 172 Mass transfer into droplets with chemical reaction | 174

4 Fundamentals of chemistry in the climate system | 179 4.1 State of matter | 179 4.1.1 Atoms, elements, molecules, compounds, and substances | 180 4.1.2 Pure substances and mixtures | 181 4.1.3 Radicals, groups, and nomenclature | 182 4.1.4 Units for chemical abundance: Concentrations and mixing ratios | 185 4.2 Theory of chemical reactions | 191 4.2.1 Chemical bonding | 191 4.2.2 Types of chemical reactions | 197 4.2.3 Chemical kinetics: Reaction rate constant | 198 4.3 Catalysis | 206 4.4 Electrochemistry | 207 4.4.1 Electrolytic dissociation | 208 4.4.1.1 Acids, bases, and the ionic product of water | 209 4.4.1.2 pH value | 213 4.4.1.3 Hydrolysis of salts and oxides | 214 4.4.1.4 Buffer solutions | 215 4.4.1.5 Complex ions | 216 4.4.1.6 The CO2 –carbonate system | 217 4.4.2 Oxidation–reduction reaction (redox process) | 228

XXIV | Contents

4.4.3 4.5 4.5.1 4.5.2 4.5.3 4.6 4.6.1 4.6.2 4.7

Hydrated electron: A fundamental species | 233 Photochemistry | 237 Photoexcitation: Electronic states | 238 Photodissociation: Photolysis rate coefficient | 240 Photocatalysis: Photosensitization and autoxidation | 243 Environmental relevance of acidity | 246 Atmospheric acidity | 248 pH averaging | 254 Isotopes in atmospheric chemistry and geochemistry | 255

5 Substances and chemical reactions in the climate system | 261 5.1 Hydrogen | 261 5.1.1 Natural occurrence | 261 5.1.2 Compounds of hydrogen | 263 5.1.3 Chemistry | 264 5.2 Oxygen | 268 5.2.1 Natural occurrence | 271 5.2.2 Oxygen, dioxygen, and ozone: O, O2 , and O3 | 271 5.2.3 Reactive oxygen species I: OH, HO2 , and H2 O2 (Hx Oy species) | 275 5.2.3.1 Atmosphere, free of trace species | 275 5.2.3.2 Atmosphere with trace species | 280 5.2.4 Reactive oxygen species II: RO, RO2 , and ROOH | 284 5.2.5 Aqueous-phase oxygen chemistry | 287 5.2.5.1 Water chemistry | 289 5.2.5.2 Dioxygen and superoxide ion chemistry | 293 5.2.5.3 Hydrogen peroxide chemistry | 297 5.2.5.4 Ozone and hydroxyl radical chemistry | 300 5.2.5.5 Hydrogen polyoxides | 304 5.2.6 Multiphase oxygen chemistry | 307 5.2.6.1 Hydrogen peroxide | 311 5.2.6.2 Ozone | 314 5.2.7 Stratospheric oxygen chemistry | 317 5.3 Nitrogen | 322 5.3.1 Natural occurrence and sources | 326 5.3.2 Thermal dissociation of dinitrogen (N2 ) | 327 5.3.3 Ammonia (NH3 ) | 328 5.3.4 Dinitrogen oxide (N2 O) | 332 5.3.5 Inorganic nitrogen oxides and oxoacids (NOy ) | 332 5.3.5.1 Gas-phase chemistry | 333 5.3.5.2 Aqueous and interfacial chemistry | 338 5.3.6 Organic nitrogen compounds | 357 5.3.6.1 Amines, amides, and nitriles | 358

Contents | XXV

5.3.6.2 5.4 5.4.1 5.4.2 5.4.3 5.4.3.1 5.4.3.2 5.4.4 5.5 5.6 5.6.1 5.6.2 5.6.3 5.6.3.1 5.6.3.2 5.6.4 5.6.5 5.6.6 5.6.6.1 5.6.6.2 5.6.7 5.6.8 5.6.9 5.7 5.7.1 5.7.2 5.7.3 5.7.4 5.8 5.8.1 5.8.2 5.8.3 5.8.4 5.8.5 5.8.6 5.8.7 5.8.8 6 6.1 6.1.1

Organic NOx compounds | 361 Sulfur | 363 Natural occurrence and sources | 365 Reduced sulfur: H2 S, COS, CS2 , and DMS | 366 Oxides and oxoacids: SO2 , H2 SO3 , SO3 , and H2 SO4 | 371 Gas-phase SO2 oxidation | 373 Aqueous-phase sulfur chemistry | 373 Multiphase sulfur chemistry | 382 Phosphorus | 384 Carbon | 387 Organic carbon and chemistry | 389 Elemental carbon and soot | 394 Inorganic C1 chemistry: CO, CO2 , and H2 CO3 | 397 Gas-phase chemistry | 397 Aqueous chemistry | 397 Hydrocarbon oxidation and organic radicals | 401 Organic C1 chemistry: CH4 , CH3 OH, HCHO, HCOOH | 404 C2 chemistry: C2 H6 , CH3 CHO, C2 H5 OH, CH3 COOH, and (COOH)2 | 408 Gas-phase chemistry | 408 Aqueous chemistry | 410 Alkenes, alkynes, and ketones | 414 Aromatic compounds | 417 Is the atmospheric fate of complex organic compounds predictable? | 420 Halogens (Cl, Br, F, and I) | 420 Chlorine in the environment | 424 Formation of sea salt and chlorine degassing | 428 Gas-phase chemistry | 432 Aqueous and interfacial chemistry | 441 Metals and metalloids | 449 General remarks | 449 Alkali and alkaline earth metals: Na, K, Mg, and Ca | 452 Iron: Fe | 453 Mercury: Hg | 454 Cadmium: Cd | 457 Lead: Pb | 458 Arsenic: As | 459 Silicon (Si) and aluminum (Al) | 459 Biogeochemistry and global cycling | 461 The hydrosphere and the global water cycle | 461 The hydrological cycle and the climate system | 463

XXVI | Contents

6.1.2 6.1.3 6.1.4 6.1.5 6.1.5.1 6.1.5.2 6.1.5.3 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.3 6.3.1 6.3.2 6.3.2.1 6.3.2.2 6.3.3 6.3.3.1 6.3.3.2 6.3.3.3 6.3.4 6.3.4.1 6.3.4.2

Soil water and groundwater: Chemical weathering | 466 Surface water: Rivers and lakes | 467 The oceans | 469 Atmospheric waters (hydrometeors): Chemical composition | 470 Clouds | 472 Fog | 474 Rain (precipitation) | 474 Biogeochemical cycling | 478 Photosynthesis: Nonequilibrium redox processes | 482 Primary production of carbon | 490 Nitrogen cycling | 495 Sulfur cycling | 500 Natural sources of atmospheric substances | 505 Source characteristics | 506 Biological processes | 507 Continental | 507 Oceanic | 511 Geogenic processes | 514 Soil dust | 515 Sea salt | 517 Volcanism | 519 Chemical processes | 524 Lightning | 524 Secondary atmospheric processes | 526

A

List of acronyms and abbreviations used in this volume | 531

B

Quantities, units, and some useful numerical values | 535

References | 539 Name Index | 595 Subject Index | 597

List of principal symbols Note all variables (with the exception of Acy, Alk, LWC, and those written in capital Greek letters) are in italics, and constants, indices, and symbols are nonitalic (roman); some symbols are used several times. a A ads ap aq Acy Alk α α α β c c cD c(m) c(n) c N , c(N) Cp CV chem coll d D des diff div dry ∇ e eff el eq E E E EA ε ε ε

acceleration area adsorption (index) apparent (index) aqueous (index) acidity alkalinity dissociation degree Bunsen’s absorption coefficient mass accommodation process Ostwald’s solubility concentration speed of light drag coefficient mass concentration molar concentration number concentration molar heat capacity at constant pressure molar heat capacity at constant volume chemical conversion (index) collision (index) diameter diffusion coefficient desorption (index) diffusion (index) divergence dry deposition (index) nabla operator ionic (or electric) charge effective (index) electrical (index) equivalent (index) energy irradiance electrical potential activation energy emission of light general physical quantity fraction (0...1) of scavenged (washout) aerosol particles in air

https://doi.org/10.1515/9783110561265-205

η η θ θ F F F f f g g g G γ γ Γ H H H0 h h het i I IK j J k k kg K Kf Kn Ksp Kz κ κ l L LWC

number density dynamic viscosity solar zenith angle surface coverage degree (0...1) flux molar free energy (Helmholtz energy) Faraday constant force free energy (Helmholtz energy) gaseous (index) standard gravity (gravity of Earth) free enthalpy (Gibbs energy) molar free enthalpy surface tension uptake coefficient transport coefficient Henry’s law constant molar enthalpy Hammet function Planck’s constant (reference) height heterogeneous (index) specific object (index) radiant intensity solar constant photolysis rate emittance Boltzman constant reaction rate constant mass transfer coefficient equilibrium constant cryoscopic constant Knudsen number solubility product turbulent vertical diffusion coefficient coefficient for absorption (a) or scattering (s) Karman constant mean free path radiance liquid water content

XXVIII | List of principal symbols

λ λ m m m mm M M μ ν ν n n n0 n(r) N NA N(r) ox 0 ⊖ π PM p p Q Q Q r r r r2 ra rb rc R R R R Re red rem rev RH ρ ρm

wavelength scavenging coefficient mass molality mass (index) mass of molecule molar mass third body chemical potential frequency kinematic viscosity number of moles (amount) (given) number of objects Loschmidt constant differential number size distribution number (of objects or subjects) Avogadro constant cumulative number size distribution oxidation or oxidized (index) zero – reference concerns time or distance (index) index for standard conditions number Pi particulate matter pressure particulate (index) (molar) heat radiant energy source term (as flux) radius reaction rate resistance coefficient of determination aerodynamic resistance quasi-laminar resistance surface resistance rate precipitation amount (rainfall rate) reaction (index) gas constant Reynolds number reduction or reduced (index) removal (index) reversible (index) relative humidity density mass density

σ σ s s S S S S S Sc sm sol S T t τ τ τc τt U u u∗ v v vd V V Vm vap w W wet x x y z z z z0 φ φ Φv Φ Φ Ω ω ∞

Stefan-Boltzmann constant absorption cross section solid (index) space (vector field x, y and z) actinic flux molar entropy salinity sink term (as flux) solubility Schmidt number smelting (index) dissolution / solution (index) saturation ratio temperature time residence time shear stress characteristic time turnover time molar inner energy wind speed friction velocity velocity velocity (vector field u, v, and w) dry deposition velocity volume volume (as index) molar volume evaporation (index) water (index) (molar) work wet deposition (index) mixing ratio displacement (horizontal) displacement (horizontal) displacement (vertical) collision number number of elementary charges roughness length of surface azimuth angle fluidity luminous flux quantum yield radiant power steariant (solid angle) angular velocity “far from” (index)

1 Introduction Our understanding of complex systems is naturally limited, for three main reasons. First, the number of parameters, processes, and compartments is always larger than our facilities to observe them simultaneously and continuously (otherwise it would not be a complex system). Second, research has historically developed within distinct disciplines. Leibniz and Humboldt were two of the last great polymaths,¹ and nobody at present is able to recognize (and to understand) different scientific fields at a consistently high level. Third, the necessity of subdividing the sciences (as a tool for understanding nature) led to an increasing misunderstanding among scholars due to the use of different (scientific) language. An anonymous reviewer² of Charles Lyell’s “Principles of Geology” (published in 1835 and subtitled “An attempt to explain the former changes of the earth’s surface by reference to causes now in operation”) wrote to the point: Just as the dairy-maid believes the moon to be a great cheese, so the astronomer fancies our globe a condensed nebula; the chemist, an oxidized ball of aluminum and potassium; the mineralogist, a prodigious crystal – “one entire chrysolite”; and the zoologist, an enormous animal – a thing of life and heat, with volcanoes for nostrils, lava for blood, and earthquakes for pulsations.

Out of the recognized complexity of nature arose the three natural sciences³: physics, chemistry, and biology. Further progress in understanding natural processes created numerous subdisciplines and cross-disciplines, named using a variety of prefixes and combinations, often creating misunderstandings unless careful definitions were used. As discussed later, there is no need in principle to use prefixes such as “environmental,” “geo-,” or “bio-” because the aim of these sciences is a priori the study of matter and life or, in other words, nature. Insofar as “life” is quite different from just a simple application of physics and chemistry, biology seems to be a science naturally based on physical and chemical laws but additionally having “biological” laws. Therefore, to draw a sharp border between physics and chemistry makes absolutely no sense in the attempt to understand the climate system. However, without understanding biological laws – and we can probably enlarge that concept by including social laws when we consider that the biosphere was long ago transformed into the noosphere – we will neither understand climate change nor find solutions to climate control.

1 The term “polymath“ (an artificial word) was surely unknown at the time of Leibniz, and the German word Universalgelehrter expresses this facility much better. 2 Principles of Geology: An attempt to explain the former changes of the earth’s surface by reference to causes now in operation. London Quarterly Reviews, Vol. LIII, April 1835, pp. 213–235 (at p. 217). 3 It is remarkable that the English term science includes the sciences in general and the natural sciences (it is different in the German language, for example, where the analogous term only means science in general). https://doi.org/10.1515/9783110561265-001

2 | 1 Introduction

To overcome disciplinary borders, a new super-science was established, Earth system science, to study the Earth as a system, with an emphasis on observing, understanding, and predicting global environmental changes involving interactions between land, atmosphere, water, ice, biosphere, societies, technologies, and economies. We will define the climate system as a part of the Earth system, with an emphasis on the atmosphere but involving interactions between land, atmosphere, water, ice, biosphere, societies, and so forth. Hence, “chemistry of the climate system” is neither simply air nor environmental chemistry. Humans – by decoupling their life cycle from natural conditions – have altered “natural” biogeochemical cycles. The Russian geochemist Vladimir Ivanovich Vernadsky understood by noosphere (called the anthroposphere by Paul Crutzen) a new dimension of the biosphere, developing under the evolutionary influence of humans on natural processes (Vernadsky 1926); consequently, Crutzen and Stoermer (2000) proposed to name the present epoch the Anthropocene. Antoine Lavoisier, who revolutionized the science of chemistry in the eighteenth century and replaced the mythical “phlogiston” with the term (and concept) of oxygen, clearly understood the importance of accurate definitions. In his words: “We cannot improve the language of any science without at the same time improving the science itself; nor can we, on the other hand, improve a science without improving the language or nomenclature” (Lavoisier 1798).

1.1 Chemistry and the climate system This book will treat the chemistry of the climate system according to the elements and their compounds depending on the conditions of reactions. Furthermore, we separate the compounds by whether they exist in the gaseous or condensed (aqueous and solid) phase (Figure 1.1) but considering their transfer in the sense of multiphase chemistry. The chemistry of the climate system is more than simply air or atmospheric chemistry; it is to a large extent atmospheric chemistry. The atmosphere is the only reservoir connecting all other reservoirs, such as the biosphere (life), hydrosphere (waters), and pedosphere (soils). As chemistry is the science of matter, we consider substances moving through the climate system. Table 1.1 classifies how chemical regimes meet in the climate system. We see that almost so-called normal conditions occur and extreme low and high temperatures border the climate system. The chemistry described in the following chapters concerns these almost normal conditions of the climate system. We focus on the troposphere and the interfaces between reservoirs. For example, aqueous-phase chemistry in cloud droplets does not differ principally from surfacewater chemistry (aquatic chemistry), and much of soil chemistry does not differ from aerosol chemistry (colloidal chemistry). Plant chemistry (biological chemistry), however, is different, and only by using the generic terms of inorganic interfacial chemistry can we link it with atmospheric chemistry (Chapter 6.1.2). The chemistry of the atmo-

1.1 Chemistry and the climate system | 3

air cloud

gas

aerosol

precipitation

plant

soil

water

earth surface Fig. 1.1: Chemical reservoirs and mass transfers in climate system. Tab. 1.1: Chemical regimes in climate system characterized by temperature T , pressure p, H2 O vapor pressure, radiation (wavelength λ in nm), and trace concentrations. T

p

H2 O

λ

Traces

Regime

Low: < 200 °C

Very low

Very low

< 300

Very low

Stratosphere and upper atmosphere

Normal: ∼ 285 ± 30 °C

Normal

Normal

> 300

Normal

Troposphere, waters, and plants

High: ∼ 1000 °C

Normal

Large

–

High

Biomass burning

Very high: > 1300 °C

Normal-high

Normal

> 300

Normal

Lightning

sphere is widely described (Seinfeld 1986, Brimblecombe 1996, Wayne 1996, 2000, Seinfeld and Pandis 1998, 2012, Warneck 1988, 2000, Hobbs 2000, Finlayson-Pitts and Pitts 2000, Visconti 2001, Brasseur et al. 1999, 2003, Brasseur and Jacob 2017, Ritchie 2017), and the branches in atmospheric chemistry are well defined (cf. Figure 1.2). To clarify the meaning of the chemistry of the climate system (the chemical climate system), we must discuss these terms further. It seems likely that in the past, as in the present, difficulties of language gave rise to many of the misconceptions upon which alchemical practice was based and later environmental studies were carried out. In early chemistry, it was the practice to give names to substances before their precise chemical nature had been ascertained. In modern environmental research, it seems similarly common to have defined disciplines before the complexity of nature had been approximately understood. In this way, many of the so-called environmental disciplines tended not to see the forest for the trees but to become lost in details (even

4 | 1 Introduction

though it is important to study them) without seeing how the system functioned. A “classic” example may be the enlargement of our view from ecosystem to Earth system research. The existing sciences devoted to studying and understanding nature are physics, chemistry, and biology – and that’s all. The system of sciences is pyramidal. To understand just the physics of systems, chemistry and biology are not needed, but to describe the chemistry of a system, we also need physics (physical chemistry), and to gain insights into biology, we cannot exclude physics and chemistry (biophysics and biochemistry). However, it makes sense to establish scientific disciplines and subdisciplines simply to limit the area of interest (the discipline itself). Complications arise by establishing separate languages and causing misunderstandings among scientists from different disciplines. “To look for definitions, to separate physics and chemistry fundamentally is impossible because they deal with the very same task, the insight into matter,” wrote the German chemist Jean D’Ans (1881–1969) in the preface to his Einführung in die allgemeine und anorganische Chemie (D’Ans 1948). There is no need to prefix the sciences (e.g., environmental, ecological, geo-, air, hydro-). “Other” sciences, such as geology and meteorology, for example, can be included in the natural sciences. It is worth noting the linguistic roots of “geo” and “meteor.” In Greek γή (ge) means earth, land, and ground, poetically γαία, (gaia).⁴ In the composition of words, the Greek γέα (gea), γης (ges), γην (gen), and γεο (geo) occur. Already before 600 BC, the Greek word μετέορος (metéoros) was in use, meaning “a thing in the air, altitude, or above ground.”⁵ Until the late eighteenth century, μετέορος denoted all celestial phenomena, including those that are aqueous, vaporous, solid, and light. Aristotle’s Meteorologia (Chapter 2.1.1.2, Volume 2) is a book on natural philosophy (Earth science, as it is known today). Hence, in a more narrow (historical) sense, the geosciences (e.g., geology, geography, geochemistry, geophysics) deal with the subject of the solid Earth (the geosphere). Geochemistry studies the composition and alterations of the solid matter of the Earth; geology is the scientific study of the origin, history, and structure of the Earth; geography studies the Earth and its features and the distribution of life on Earth, including human life and the effects of human activity (Saukov 1953, Mason and Moore 1982). Geography (which is an old discipline, founded as a modern science by Humboldt) is thus the science of the Earth’s surface – physical and human landscapes, the processes that affect them, how and why they change over time, and how and why they vary spatially. In other words, geography is an interfacial science between the solid and the gaseous Earth (the atmosphere); in-

¯ (in the sense of celestial body) and “terra” 4 The Latin words for earth, land, and ground are “tellus” (in the sense of matter). 5 μετέορολογια [metéorologia] means the “science of celestial, heavenly things” but also “vague talk” and “philosophical shenanigans” (Benselers Greek–German School Dictionary (Griechisch–Deutsches Schulwörterbuch, Leipzig and Berlin 1911).

1.1 Chemistry and the climate system |

5

deed, some geographers consider climatology to be a subdiscipline of geography (and, conversely, some meteorologists do not include climatology in meteorology). Finally, the liquid Earth (the hydrosphere) is the subject of hydrology.⁶ It is important to note that gaseous water (vapor) in the atmosphere is not considered an object of study in hydrology, but liquid water in the atmosphere is. Logically we now can state that the science of studying the “gaseous Earth” (atmosphere) is meteorology. Older (synonymous) terms for the science of the study of Earth’s atmosphere are aerology and atmospherology. For example, meteorology was defined as the physics and chemistry of the atmosphere (Scharnow et al. 1965) but also reduced to just the physics of the atmosphere (Liljequist and Cehak 1984). Some definitions restrict meteorology to weather processes and forecasting (which surely was the focus in the early stages of that science). A satisfactory definition of meteorology is “the study dealing with the phenomena of the atmosphere, including the physics, chemistry, and dynamics extending to the effects of the atmosphere on the Earth’s surface and the oceans.”⁷ Hence, meteorology is more than “just” the physics and chemistry of the atmosphere. At present the term atmospheric sciences is also used to summarize all the subdisciplines required to explain atmospheric phenomena and processes. To return to chemistry, (atmospheric) chemistry is just one of the sciences used to understand the (chemical) processes in the atmosphere (see following discussion for definition of atmospheric chemistry). What we see is that all disciplines overlap. The original focus of geology as the science of the (solid) Earth, hydrology as the science of liquid water, and meteorology as the science of the atmosphere is still valid and should not be undermined but the modern study of Earth sciences looks at the planet as a large, complex network of physical, chemical, and biological interactions (Sammonds and Thompson 2007). This is known as a systems approach to the study of the Earth. The systems approach treats the Earth as a combination of several subsystems, each of which can be viewed individually or in concert with the others. These subsystems are the geosphere, the atmosphere, the hydrosphere, and the biosphere. As mentioned earlier, this book will treat the chemistry of the climate system according to the elements and its compounds depending on the conditions of reactions and whether the substance exists in the gaseous or condensed (aqueous and solid)

6 In Greek ϋδορ (idor) means originally rainwater and generally water; it appears in composite words as ύδρο (idro). This is the derivation of the prefix “hydro” (the pronunciation of Greek letter ϋ and ύ is like “hy”). In Latin, water as a substance is “aqua,” but natural waters are referred to as “unda,” derived from the Greek “hy-dor” (ϋδωρ); ϋδρα (Greek) and hydra (Latin) are the many-headed water snake in Greek mythology. From Gothic “vato” and Old High German “waz-ar” are clearly seen the roots of English “water” and German “Wasser.” 7 Definition by the Department of Defense (USA), DOD Dictionary of Military and Associated Terms, 2017, p. 151 (http://www.dtic.mil/doctrine/new_pubs/dictionary.pdf).

6 | 1 Introduction

phase. Without initially defining how we should understand a climate system (Chapter 2.2.2), we will set it within a chain of subsystems: Cosmic system → solar system → Earth system → climate system → subsystems (e.g., atmosphere). In other words, each system to be defined lies in another “mother” system, the surrounding or environment, where an exchange of energy and material is realized via interfaces. Consequently, there is no fully closed system in our world. As shown earlier, the climate system is a subsystem of the Earth system. The chemistry of the Earth system – when not considering life – is geochemistry. The term geochemistry, like many other scientific terms, has variable connotations. If geochemistry means simply the chemical study of the Earth or parts of the Earth, then geochemistry must be as old as chemistry itself and dates from the attempts of Babylonian and Egyptian metalworkers and potters to understand the nature and properties of their materials (Tomkeiev 1944). It is self-evident that biochemistry deals with chemical processes in organisms and, thus, chemical interactions that occur between organisms via geochemical processes; consequently, biogeochemistry is the chemistry of the climate system that we have defined as that part of the Earth system affecting life. Subdividing the geogenic part of the climate system into “other” systems gives us the atmosphere, hydrosphere, cryosphere, and lithosphere; thus, atmospheric, aquatic, and soil chemistry would be the subdisciplines of geochemistry. Traditionally we may also subdivide the climate system into the atmosphere, lakes and rivers, the oceans, soil, minerals, and volcanoes, consisting of gases, liquids, and solids. Organisms – plants and animals – are distributed among these areas. We study the chemistry of a natural system by chemical quantitative analysis of the different materials. On the basis of innumerable analyses, we need to obtain a three-dimensional distribution of the concentration of specific substances or, in other words, the chemical composition of the climate system. This is the static approach to obtain an average chemical composition over a given time period, depending on the lifetime of the substances, the climatological mean. However, concentration changes occur with time because of transportation (motion) and transformation (chemical reactions). Hence, we need a dynamic approach, too. Studying chemical reactions – which means establishing their kinetics and mechanisms – is possible only in the laboratory under controlled (and hence replicable) conditions in a large variety of so-called smog chambers. Many attempts to acquire kinetic data from field experiments have been unsuccessful because the number of degrees of freedom in a natural system is always larger than the number of measurable parameters. Chemical climatology seeks to establish the four-dimensional concentration field in space and time. The timescale can show variations and trends. Variations can be characterized stochastically and periodically. It was not until the 1970s that scientists recognized the occurrence of global changes. It is worth mentioning that already in the Roman epoch, 2000 years ago,

1.1 Chemistry and the climate system |

7

mining and smelting of ores led to the hemispheric distribution of heavy metals, which were detected in Greenland ice cores. The rapid reduction of European forests from more than 80% cover 2000 years ago to about 25% at present surely had a significant influence on air chemistry (due to emissions, deposition, and climatic changes), but it is not something that can be quantified. Local pollution was order(s) of magnitude higher in medieval cities than it is today, and consequently “urban air chemistry” must have been quite different. Efforts at pollution control and legislative measures were applied from that time forward. Emission of chemically reactive substances (SO2 , NO x , VOC) on a scale from the local to the regional began with the exponential increase of fossil fuel use (coal after 1870 and oil after 1950). Presently, after the successful introduction of end-of-pipe technologies for the reduction of these substances, we have observed a drastic decrease of many trace species in air and subsequent changing chemistry (in terms of acidity, oxidation potential, and deposition patterns) that often is not “linear” with emission changes. For example, the number of days with excessive ozone concentrations in Germany fell practically to zero in the late 1990s, but increases in annual means of ozone concentration are still observed at many sites. This suggests that different processes determine ozone formation and distribution, since the abatement strategy reduced only the short-lived so-called ozone precursors. It is worth noting here that many chemical features such as acidity and redox potential are quantified from budgets (acid–bases, oxidant–reductants). Hence, the same difference results from concentrations at a low level and vice versa. However, low-level or high-level concentrations of individual substances may lead to other effects. The matter (in terms of physics and chemistry) of the climate system is extremely complex. With the focus of many disciplines in science and engineering on our environment, many new subdisciplines have arisen, such as biometeorology, bioclimatology, environmental chemistry, ecological chemistry, atmospheric environmental research, environmental meteorology, and environmental physics, among others. Atmospheric chemistry cuts into the subsubdisciplines (cf. Figure 1.2) of tropospheric chemistry, stratospheric chemistry, cloud chemistry, precipitation chemistry, particle chemistry, polar chemistry, marine chemistry, and so on. It is not the aim here to validate the sense or nonsense of such subdisciplines. Basic research is progressing with individuals and in small groups on limited topics and, hence, with growing understanding (learning) and specialization results in establishing “scientific fields.” There is no other way to proceed in fundamental science. However, the complexity of the climate system (and even just of the atmosphere) calls for an interdisciplinary approach, and we have learned that, especially at the “interfaces” between biological, physical, chemical, and geological systems, crucial and key processes occur that determine the function of the whole system. Consequently, a chemist without an understanding of the fundamental physical processes in the atmosphere (and vice versa) can only work on discrete research topics and will not be able to describe the climate system.

8 | 1 Introduction

e.g. polar air chemistry

e.g. tropical air chemistry

continental air chemistry

maritime air chemistry

laboratory studies

horizontal stratospheric chemistry

instrument development

methods

region

remote air

vertical

air chemistry

tropospheric chemistry pollution

phase

gas phase chemistry

multiphase chemistry cloud chemistry

heterogeneous chemistry

gas/solid

polluted air

aerosol chemistry

fog chemistry precipitation chemistry

gas/liquid Fig. 1.2: Subdisciplines of atmospheric chemistry.

Six core areas have been identified for future research in atmospheric chemistry (National Academies 2016); however, these areas had already been identified in the late 1980s (Galbally 1989a, Borrel and Borrel 2000)⁸ and framed global research activities of climate system chemistry (CACGP 2002):

8 The Commission on Atmospheric Chemistry and Global Pollution (CACGP), one of the commissions within the International Association of Meteorology and Atmospheric Sciences (lAMAS), founded in 1957 as the Commission on Atmospheric Chemistry and Radioactivity (CACR) and renamed the CACGP in 1971, organized a meeting under the title “Planning and Formation of the International Global Atmospheric Chemistry Program (IGAC)” in Dookie, Australia, November 7–11, 1988 (the author was elected member of the CACGP in 1985 but was able to participate at meetings only after 1989). At the same time, the International Geosphere Biosphere Programme (IGBP) was planned. In Europe, the European Experiment on Transport and Transformation of Environmentally Relevant Trace Constituents in the Troposphere over Europe (EUROTRAC) project was first announced in 1985, and projects were implemented in 1988; a first EUROTRAC symposium was held in Garmisch-Partenkirchen in 1990. The author’s group was able to participate from 1991 on several projects within EUROTRAC.

1.2 Air and atmosphere: a multiphase and multicomponent system

– – – – – –

| 9

Human activities and natural processes govern the emissions that determine the chemical composition of the atmosphere. Chemical transformations affect the spatial and temporal variability of gases and particles. Atmospheric oxidants control the lifetimes, distribution, and products of emitted species. Chemical processes interact with atmospheric dynamics to control the distribution of trace gases and particles. Particle chemical and physical properties affect cloud and aerosol particles’ radiative properties, cloud microphysics, and precipitation processes. Atmospheric trace gases and aerosol particles impact and alter global biogeochemical cycles.

1.2 Air and atmosphere: a multiphase and multicomponent system It makes even more sense to define the atmosphere as a reservoir (space) surrounding our (and any) planet, and air as a mixture of substances filling the atmospheric space. With this in mind, the term air chemistry is more adequate than atmospheric chemistry. From a chemical point of view, it is possible to say that air is the substrate that fills the atmosphere. This is in analogy to the hydrosphere, where water is the substance. Furthermore, air is an atmospheric suspension containing different gaseous, liquid (water droplets), and solid (dust particles) substances and, therefore, provides a multiphase and multicomponent chemical system. Solar radiation is the sole primary driving force in creating gradients in pressure, temperature, and concentration, which result in transport, phase transfer, and chemical processes (Figure 1.3). The physical and chemical status of the atmosphere is what we call climate. Considering that incoming solar radiation shows no trend over several hundred years (despite periodic variations), and accepting the fact that natural biogenic and geogenic processes vary but likewise show no trends on these timescales, it is only human influence on land use and emissions into the atmosphere that changes air chemical composition and, thus, the climate. Human activities have an influence on natural processes (biological, such as plant growth and diversity, and physical, such as radiation budget), resulting in a cascade of consequent physical and chemical developments (feedbacks). Without going into detail the biological and physical processes of the climate system in this book, knowledge of the chemical composition of the atmosphere and its variation over time and space, as well as its trends, is essential for an understanding of climate change. Atmospheric substances with their physical and chemical properties will have many effects on the climate system; we list the most important among

10 | 1 Introduction

solar radiation

atmosphere chemical system: composition and reactivity

emission

physical system: motion, dynamic and energy

deposition

agriculture industry traffic municipal

technology (anthroposphere)

soil water fauna/flora

nature (biogeosphere)

Fig. 1.3: Physicochemical interactions between atmosphere, biosphere, and anthroposphere (the climate system).

them here together with impacts (there are many more impacts, parallel and synergistic effects): – formation of cloud condensation nuclei (CCNs) and subsequent cloud droplets: hydrological cycle, – so-called greenhouse gases (GHGs): radiative interaction (warming the atmosphere), – ozone-depleting substances (ODSs): radiative interaction (increasing UV radiation penetration into the lower troposphere), – formation of atmospheric aerosol: radiative interaction (cooling the atmosphere), – oxidation capacity: lifetime of pollutants, – acidity: chemical weathering, – toxicity: poisoning the environment (affecting life functions), – nutrition: bioavailability of compounds essential for life. We see that the climate system has physical and chemical components, interacting and (at least partly) determining each other. Physical quantities in the climate system show strong influences on chemical processes:

1.2 Air and atmosphere: a multiphase and multicomponent system |

– – –

11

temperature and pressure: reactions rate and (chemical and phase) equilibria; radiation (wavelength and intensity): photochemistry; motion: fluxes of matter (bringing substances together for chemical reactions).

Table 1.2 shows the present composition of our air. It shows that the concentration range from the main constituents to the trace species covers more than ten orders of magnitude. Each component in air has a “function” in the climate system and in biogeochemical cycling (Chapter 6.1.1). Changes in the chemical composition of air caused by humans are termed air pollution. The terms air pollution and pollutant require some commentary. To start with, the term pollutant should be used only for human-made (anthropogenic) emitted substances, despite the fact that most of them are also of natural origin. Air pollution represents a deviation from a natural chemical composition of air (representing a reference level) at a given site and period (note that climate change and variation are ongoing natural processes). Depending on the residence time of a pollutant, we can Tab. 1.2: Composition of dry remote atmosphere (global mean concentrations 2015–2016); note that the concentration of water vapor in the air is highly variable, from less than 0.5% in saturated polar continental air to more than 3% in saturated (i.e., 100% humidity) tropical air (see also Figure 3.3). Substance Nitrogen Oxygen Argon Carbon dioxide Neon Helium Methane Krypton Hydrogen Dinitrogen monoxide Carbon monoxide Xenon Ozone Particulate matter Carbonyl sulfide Nitric acid b Radicals c Hydroxyl radical

Formula

Mixing ratio (ppm)

Comment

N2 O2 Ar CO2 Ne He CH4 Kr H2 N2 O CO Xe O3 – COS HNO3 – OH

780,825 a

Constant Constant Constant Increasing Constant Constant Increasing Constant Constant Increasing Increasing Constant Variable Variable Increasing Variable Highly variable Highly variable

209,432 a 9,339 a 404 18.18 5.24 1.845 1.14 0.5 0.328 0.120 0.087 0.03 0.01 d 0.00066 ≤ 0.001 < 0.00001 0.0000003

Related to “clean” atmosphere O2 + N2 + Ar + CO2 (= 100%); note with increasing CO2 content the concentration of main gases decreases. b And many other trace substances (e.g., NH3 , NOx , HCl, nonmethane volatile organic carbon (NMVOC), H2 O2 , dimethyl sulfide (DMS), chlorofluorocarbons (CFCs)). c For example, HO , NO , Cl. 2 3 d Corresponds to 10–20 μg m−3 . a

12 | 1 Introduction

characterize the scale of pollution from local via regional to global. Air pollution at present is a global phenomenon because some long-lived pollutants still increase at given sites around the globe. Remote air just means that the site is located far away from the sources of emissions and, consequently, this air has lower concentrations of short-lived (reactive) substances compared with sites close to sources of pollutants. Although polluted air is human-influenced air, clean air is not synonymous with natural air. The natural atmosphere no longer exists; it was the chemical composition of air without human-made influences. However, this definition is also not exact because humans are part of nature. In nature, situations may occur, such as volcanic eruptions, sand storms, and biomass burning, where the air is being “polluted” (rendered unwholesome by contaminants) or, in other words, concentrations of substances of natural origin are increased. Therefore, the reference state of natural air is a climatological figure representing a mean value with its variations. The term clean air is also used politically in air pollution control as a target, i.e., to make our air cleaner (or less polluted) in the sense of pollutant abatement. A clean atmosphere is a political target; it represents an air chemical composition (defined in terms of time and scale) that should permit sustainable development. The largest difficulty, however, lies in the definition of sustainable. This term comprises the whole range of categories from simple scientific questions (for example, impact threshold) to political decisions (global ecomanagement) and to philosophical questions (for example, what human life needs). Therefore, air pollution in terms of changing chemical composition of the atmosphere must be identified through a problem, not simply by measured concentrations. The problem lies between “dangerous” and “acceptable” impact on climate, humans, and so forth, a definition that is beyond the direct role of the scientific community despite the fact that scientists have many ideas about it (Schneider 2006). Doubtless, the air of settlements and towns was extremely polluted in the past. Heavy metals were found in Greenland ice cores dating back to the Roman Empire, demonstrating that metallurgical operations of immense volume took place in that era. The modern quality of air pollution, since the Industrial Revolution of the nineteenth century, is best characterized by a continuous worldwide increase in emissions with the advent of the era of fossil fuel combustion (Volume 2, Chapter 4.2.2). In the last 150 years, serious air pollution problems (Volume 2, Chapter 2.5) have been described, analyzed, and solved (to an extent by end-of-pipe technologies), such as soot, dust, and smoke plagues, winter and summer smog, and acid rain. The chemicals (or emitted compounds) behind these phenomena are soot, sulfur dioxide (SO2 ), nitrogen oxides (NO x ), and volatile organic compounds (VOCs) – all short-lived species, but because of the global use of fossil fuels, the pollution problem becomes distributed globally. However, it was not until the 1970s that scientists recognized the occurrence of global changes. Some air pollution problems connected with long-lived compounds – now in terms of persistent compounds, such as agricultural chemicals (food chain ac-

1.2 Air and atmosphere: a multiphase and multicomponent system

| 13

Tab. 1.3: Increase of some climate-relevant gases in air (ppb). Substance

1850

Present (2017)

Increase (ppb)

Increase (%) a

Carbon dioxide, CO2 Methane, CH4 Dinitrogen monoxide, N2 O Ozone, O3

280,000 700 300 10

408,000 1,845 328 34

108,000 1,145 28 24

46 164 10 240

a

The value for 1850 corresponds to 100%.

cumulation) and halogenated organic compounds (ozone layer destruction) – were solved by legislation banning their use.⁹ Unfortunately, some long-lived emitted compounds, the so-called GHGs, have increased significantly in global mean concentration¹⁰ (Table 1.3). Ozone is not a long-lived species, but globally it is a secondary product of methane oxidation (Chapter 5.2.3.2). CH4 and N2 O (mainly byproducts of agriculture) as well as CO2 (a byproduct of fossil fuel combustion) are coupled with the two pillars of human existence: food and energy. There is no doubt that we can solve the CO2 problem only through sustainable technological change (Volume 2, Chapter 5.3). It should be noted that these three pollutants (CO2 , CH4 , and N2 O), even with much higher atmospheric concentrations, are harmless to life (they are in fact key substances in biogeochemical cycles, see Chapter 6.1.1), but there is also no doubt that these three substances contribute to about 90% of global warming. In addition, N2 O acts as an ozone-depleting substance in the stratosphere and CH4 contributes to O3 formation in the troposphere and is probably responsible for up to 80% of the global O3 increase. Air pollution control in the future will be synonymous with climate control and must be focused on CO2 , CH4 , and N2 O. Let us now return to the atmosphere as a multiphase system. While gases and particles (from molecules via molecular clusters to nano- and microparticles) are always present in the air, although with changing concentrations, condensed water (hydrometeors) is occasionally present in air, depending on the presence of so-called CCNs and water vapor supersaturation at the site of fog and cloud formation. With the formation, transportation, and evaporation of clouds, huge amounts of atmospheric energy transfers take place. This results in a changing radiation transfer and, thus, “makes” the weather and, on a long timescale, the climate. Furthermore, clouds provide an effective “chemical reactor” and transport medium and cause the redistribution of trace

9 The decrease of halogenated substances in the stratosphere is very slow, so recovery of the ozone layer will also still require several decades; fortunately, the “ozone hole” has not expanded since the 1990s. 10 In my opinion, the atmospheric CO2 due to fossil-fuel combustion is the last unresolved air pollution problem; fortunately it is soluble, if the political will exists to make the transition to the so-called solar era (Möller 2012).

14 | 1 Introduction

species after evaporation. When precipitating, clouds remove trace substances from the air (we call this wet deposition) to the Earth’s surface. Therefore, apart from the continuous process of dry deposition, clouds may occasionally lead to large inputs of trace substances into ecosystems. The amount of condensed water in clouds and fog is very small, with around 1 g ⋅ m−3 of air or, in dimensionless terms, a liquid-water content of 1 ⋅ 10−6 (identical to 1 ppb). Thus, 99.99% or more of total atmospheric water remains in the gaseous phase of an air parcel. Hydrometeors may be solid (ice crystals in different shapes and forms) or liquid (droplets ranging from a few μm up to some tens of μm). We distinguish the phenomenon of hydrometeors into clouds, fog, and precipitation (e.g., rain, drizzle, snow, hail). This atmospheric water is always a chemical aqueous solution where the concentration of dissolved trace matter (related to the bulk quantity of water) is up to several orders of magnitude higher than in the gaseous state of air. This analytical fact is the simple explanation for why the collection and chemical analysis of hydrometeors began much earlier than gas-phase measurements. Due to continuous motion, specifically advection and turbulent diffusion, having stochastic characteristics on different time and spatial scales, it is extremely complicated to model chemistry and transport (so-called chemistry-transport models, CTM, which are also a basis for climate modeling) in space and time. At the earth-air interface, exchange of matter occurs, emission as well as deposition.

1.3 Principles of chemistry in the climate system Earlier, we stated that chemistry was the science of matter, and we consider substances moving through the climate system. The chemical composition of air depends on the natural and artificial sources of its constituents (their distribution and source strength over time and space) as well the physical (e.g., radiation, temperature, humidity, wind) and chemical conditions (other trace species) that determine its transportation and transformation. Thus, atmospheric chemistry is not a pure chemistry and includes other disciplines that are important for describing the interaction between the atmosphere and other surrounding reservoirs (e.g., biosphere, hydrosphere). Measurements of chemical and physical parameters in air will always contain a “geographical” component, i.e., the particularities of the given locality. That is why the terms chemical weather and chemical climate were introduced. For example, the diurnal variation of the concentration of a substance may occur for different reasons. Therefore, the transfer of conclusions and results to other sites should be done with caution. On the other hand, it is a basic task in atmospheric chemistry not only to present the local results of chemical composition and its variation over time but also to find general relationships between pollutants and their behavior under different conditions.

1.3 Principles of chemistry in the climate system

| 15

We describe elementary chemical reactions definitely by a mechanism and a kinetic law, which are therefore applicable to all regimes in nature if the conditions (temperature, radiation, pressure, concentration) for reactions correspond to those of a natural reservoir. For example, the photolytic decay of molecules is only possible in the presence of adequate radiation. Hence, in darkness, no photolysis takes place, and in the troposphere, there is no O2 photolysis because of the lack of radiation smaller than a wavelength of 300 nm. The approach of this book is to use the classical chemical textbook concept based on the elements and their compounds. However, it is not the aim of the book to include as many substances and reactions as possible. Two criteria always help make the chemistry as simple as possible. First, we only consider the main reactions of a species A, having competitive chemical pathways; all reactions that contribute less than 1% to species A’s conversion are neglected.¹¹ Let us consider an example of two reactions where A = O(3 P): (O3 P) + O2 → O3 3

and

(O P) + SO2 → SO3 .

(a) (b)

Hundreds of reactions of O(3 P) have been described,¹² but under normal conditions in the climate system (Table 1.1), pathway (a) is the only relevant reaction because the overall rate is many orders of magnitude larger than all other competitive reactions due to the magnitude of the oxygen concentration compared with all other trace gas concentrations. Second, we only consider a limited number of chemical species that play a significant role in the climate system. We do not regard the huge number of organic compounds of different origins and different fates in the environment (this is a special task for environmental chemistry). It is possible to understand the climate system’s chemistry by “lumping” together characteristic groups with specific “roles.” A key question, however, is their specific or significant role in the climate system. We focus here on chemical species contributing to – acidity/alkalinity (atmospheric acidifying potential), – oxidizing/reducing agents (atmospheric oxidation capacity), – PM formation (global cooling), – greenhouse effect (global warming) and – ozone depletion (UV radiation effects). Biogeochemical cycling drives climate system chemistry; the emissions from plants and microorganisms in terms of rate and substances specify the chemical regime.

11 This condition is reliable because any quantification of fluxes, budgets, and pool concentrations in the climate system has a large uncertainty; an error of only 10% is an excellent result. 12 See, for example, the IUPAC subcommittee for gas kinetic data evaluation (Atkinson et al. 2004, 2006, 2007, 2008; http://www.iupac-kinetic.ch.cam.ac.uk/).

16 | 1 Introduction

Tab. 1.4: Chemical interactions.

Multiphase

{ { { { { { Homogeneous { { { { { { { { { { { { { { { { Heterogeneous { { { { {

Gas phase { { { Aqueous phase { { { {Solid phase {Gas–solid { { Gas–aqueous { { { {Solid–aqueous

Hence the chemistry in the boundary layer with interfaces to soils, waters, and plants is of crucial importance. According to the scheme shown in Table 1.4, we classify this as multiphase chemistry. Discussing the fate, transport, and transformation of chemicals in soils, water, and plants is the task of biogeochemistry (Schlesinger 2003), for instance, marine biogeochemistry (Turner and Hunter 2002, Hansell and Carlson 2002, Fasham 2003, Libes 2009), aquatic chemistry (Stumm and Morgan 1995, Jensen 2015), trace elements (Braids and Cai 2002, Prasad et al. 2005, Huang and Gobran 2005), wetlands (Bianchi 2006, Reddy and DeLaune 2008), soils (Bohn et al. 2001, Sposito 2008, Konya and Nagy 2009, Tab 2010), soils and water (Langmuir 1997, Essington 2003, Franzle 2009), water chemistry (Gianguzza et al. 2002, Jensen 2003, Yves 2006, Kuwajima et al. 2009), and plant chemistry (Haas and Hill 1929, Heldt 2004). The upper border of the atmosphere could be influenced by space chemistry (Lewis 2004, Rehder 2010).

1.4 Substances in climate system Life determines the global biogeochemical cycles of the elements of biochemistry, especially C, N, P, and S (Schlesinger 1997, 2003), but the key process of plant life is the process of splitting water into H and O (Chapter 6.1.2) and thereby creating oxic (oxidizing) and anoxic (reducing) environments. Figure 1.4 shows schematically the three principal groups of compounds and their biogeochemical cycles. Hydrides (methane, ammonia, hydrogen sulfide, and water) represent the lowest oxidation state of the elements C, N, S, and O because they bond in biomass and are then released into abiogenic surroundings (soil, water, and air). In air, these substances (and many more, such as hydrocarbons, amines, and sulfides) oxidize, ultimately to oxides of C, N, and S. Many oxides represent anhydrides and form oxoacids and, subsequently, salts (such as carbonate, sulfate, and nitrate) when reacting with water. This last group provides the stock chemicals for the biosphere that reduce them back to hydrides and close the cycle. There are other important elements. First, hydrogen, which in its molecular form (H2 ) is relatively nonreactive but exists atomically as short-lived transient and stable hydronium ions in solutions. Its role alters between water, hydrides, and acids.

1.4 Substances in climate system

| 17

emission and atmospheric oxidation

group / period

group / period

4 2

3

CH4

5

6

NH3

OH2

2

SH2

3

hydrides

4

5

6

COx

NOy

OOx

oxides

x = 1, 2 y = 1, 2, 3 z = 2, 3

SOz

group / period 4

transfer to the biosphere and biological reduction

5

6

2

H2CO3

HNOx

H2Oy

3

oxoacids and salts

x = 2, 3 y = 1, 2 z = 3, 4

H2SOz

oxidation and dissolution, phase and reservoir partitioning

Fig. 1.4: Characteristic groups for C, N, O, and S and their role in biogeochemical cycling.

Second, phosphorus is also a key bioelement. It has few and unstable volatile compounds and plays only a minor role in atmospheric chemistry but likely, according to recent findings, in the formation of PM. Moreover, some halogens (F, Cl, Br, I) could also be included in Figure 1.4 because they form hydrides (acids such as HCl), oxides (e.g., ClO), and oxoacids (e.g., HOCl). The role of organic chlorine compounds in soils is very complex and not yet understood (see also Chapter 5.7.1). Finally, many trace elements are biogeochemically important (Chapter 5.8), either because of their roles as redox elements or as bioelements with very specific properties. However, some trace elements (e.g., Cd and Hg) have no (known) biological functions but are extremely poisonous. Table 1.5 shows the distribution of the main compounds in the climate system among different states of matter. It is remarkable that only one substance (H2 O) exists in all three phases. Not all gases exist in dissolved form in the aqueous phase, but the main inorganic compounds (essential for life such as sulfurous, nitrous, carbonaceous, chlorine, ammoniacal) exist in gaseous, dissolved, and particulate forms. All dissolved species also exist in PM. All insoluble species exist either only as gases or as particulates. Insoluble but oxidable substances exist in dissolved form and, hence, in PM too. However, some organic substances transform into solids (homogeneous nucleation process) but must not be soluble.

18 | 1 Introduction

Tab. 1.5: Principal compounds in climate system. PM – particulate matter, SOA – secondary organic aerosol, OA – (primary) organic solid matter (biogenic), EC – elemental carbon, reduced S – H2 S, COS, CS2 , DMS, and others. Liquid

Dissolved a

Solid

H2 O

H2 O (water)

H+

H2 O (ice, snow)

CO2 HCl NH3 NOy SO2 red. S NMVOC – – –

– – – – – – – – – –

H+ + HCO−3 H+ + Cl− NH+4 + OH− H+ + NO−2 /NO−3

CH4

–

Gas

+ OH−

} H+ + HSO−3 /HSO−4

} } } } } } } } } } } } } } }

NMVOC b OA b – Na+ + Cl−c K+ + Ca2+ + Mg2+ d

SOA OA EC + BC (soot) sea salt (NaCl) c dust e

–

–

PM (chloride, ammonium, carbonate, nitrate, sulfate)

} } } } } } } } } } } } } } } } } } } } } PM } } } } } } } } } } } } } } } } } } } } } }

a

Partly after oxidation. If soluble, organic acids protolyzed. c About 90% NaCl but including other compounds (sulfate, magnesium, calcium, potassium, and many others). d And many others, including anions (carbonate, sulfate). e Insoluble main components: Si, Al. b

Excluding novel gases, the number of gaseous elements is very limited: N, O, H, Cl (Table 1.6). All these elements form many gaseous compounds. It is remarkable that the number of aditional elements (which are not gaseous) forming gaseous compounds is also limited: C, S, Br, and I (Table 1.6). Table 1.6 lists more elements (Si, P, Tab. 1.6: Main-group elements in gaseous compounds in climate system (and Hg from transition elements). Note in air only elementary novel gases exist: nitrogen (N2 ), oxygen (O2 ), hydrogen (H2 ); in traces chlorine (Cl, Cl2 ); and atomic oxygen (O), bromine (Br), and iodine (I) exist only in extremely small concentrations.

1 2 3 4 5 6

4

5

6

7

8

C Si

N P As

O S Se

H F Cl Br I

He Ne Ar Kr Xe Ra

1.4 Substances in climate system

| 19

Tab. 1.7: Principal educts and products (simplified). Element/group

Educts and intermediates

Final products

Oxygen Inorganic carbon Sulfur Nitrogen Chlorine a Organic carbon

O3 , OH, HO2 , H2 O2 CO, CO2 H2 S, DMS, COS, CS2 , SO2 NO, NO2 , NO3 , N2 O5 , HNO2 Cl2 , Cl, HCl RCH3 , RCHO

O2 , H2 O CO2 , H2 CO3 , HCO−3 H2 SO4 , SO2− 4 HNO3 , NO−3 HCl, Cl− RCOOH, RCOO−

a

Representative for other halogens (F, Br, I).

As, Se) that also form gaseous compounds but play no role¹³ in the climate system. In addition, many compounds and a few other elements (such as Br, I, and Hg) can be detected as gaseous in the atmosphere despite having boiling points exceeding the temperature at the Earth’s surface and having volatile properties. The number of primarily emitted important substances, intermediates, and final products is relatively limited (excluding organic compounds) (Table 1.7). All kinetic data given in this book are from the IUPAC Subcommittee on Gas Kinetic Data Evaluation unless otherwise indicated (also Atkinson et al. 2004, 2006, 2007, 2008, Baulch et al. 1980).

13 P may be an exception (Chapter 5.5).

2 Fundamentals of physics in the climate system The fundamental law of nature is the law of conservation of matter. Matter occurs in two states: flowing energy and cycling material. The climate system, however, is an open system and in continual exchange with its surrounding Earth system and, thus, space. Therefore, we generally expect changes and variations of internal energy and mass over time. From a chemical point of view, the interest lies in the quantification of the amount – in terms of the number of particles and, thus, mass – of different chemical species in a volume regarded. This quantity, called density (an equivalent term to concentration) is investigated as a function of time and space. Hence, mass, time, and distance are the fundamental quantities of the climate system, all of whose quantities can be expressed in terms of meters, kilograms, and seconds (Appendix B). The basic science of the atmosphere is the meteorology, defined and discussed in the introduction. We emphasized earlier that physics and chemistry cannot be sharply separated while studying the climate system. In this book, we describe physical fundamentals only insofar as they are important for an understanding of chemical processes.

2.1 Meteorological basics I like to follow the definition of meteorology given by the National Geographical Society: the study of the atmosphere, atmospheric phenomena, and atmospheric effects on our weather. As an umbrella term covering all studies of the atmosphere, the term atmospheric science is used. Another subdiscipline of atmospheric sciences, climatology, focuses on how atmospheric changes define and alter the world’s climates (Volume 2, Chapter 3.3). Aeronomy is the study of the upper parts of the atmosphere, where unique chemical and physical processes occur. Meteorology focuses on the lower parts of the atmosphere, primarily the troposphere, where most weather takes place.

2.1.1 Scaling and structure of the atmosphere The structure of the atmosphere dictates the way the atmosphere behaves and controls how weather develops near the surface of the Earth. Hence it is inherently a reactor for chemical processes determining the transport, mixing, turnover, and removal of chemical substances. All atmospheric processes proceed in space and time (Table 2.1). The timescale of a process describes the magnitude of its lifespan, the duration from initiation until completion of a process. Atmospheric processes include not only chemical transformation but also transport, clouds, and all other atmospheric phenomena. With respect to subhttps://doi.org/10.1515/9783110561265-002

22 | 2 Fundamentals of physics in the climate system

Tab. 2.1: Scale of atmospheric processes (examples) (approximate order of magnitude). Process

Timescale

Space scale (km)

Chemical elementary reaction Dissipation eddies Formation and destruction of OH Microturbulence Clouds Cloud systems Cyclone Oxidation of SO2 Oxidation of CH4 Oxidation of CFCs

10−9 s

10−12 (10 Å) 10−5 10−3 0.1 1–10 100–1000 1000 1000 10,000 10,000

1s 1s 1 min 1h 1d 1–3 d 4–5 d 8 yr 100 yr

Note: A spatial scale of 1000 km corresponds to a regional and 10,000 km to a global scale.

stances, it is simply called the lifetime or residence time, occasionally also turnover time (see Chapter 2.7 for further details). The magnitude of the spatial dimensions of the process refers to the spatial scale. The range of atmospheric time and spatial scales enfolds many magnitudes, from 10−10 m (1 Å – molecular range) up to 107 m of the circumference of the Earth and from 10−9 s (chemical elementary process) up to the age of the Earth (1015 s). Local processes (smaller than 1 km) range between nanoseconds (molecular interaction) and minutes (turbulence and cloud microphysical processes). At the upper range of the scale are global processes, beginning with a timescale of 1 year but open at the top of the timescale (geological and cosmic processes). From the point of view of air pollution, 100 years is about the open end of the degradation of climate-relevant gases. However, some gases have a residence time of thousands of years, for example, CO2 – not relating to technical abatement strategies – or SF6 , a minor climate gas, insignificant in terms of its contribution to climate forcing due to small concentrations. Chemical elementary reactions, i.e., electronic interactions between molecules, are not a primary object of atmospheric research but essential to study in the laboratory to obtain kinetic and mechanistic information for atmospheric modeling. Very short-lived species, such as OH and other radicals, have a spatial range (transport distance) of a few meters only. This is of importance for studying impacts on materials and plants and the chemistry nearby. In chemistry-transport modeling (CTM), with a grid size in the kilometer range, the transport term of these short-lived species is neglected and only formation and destruction must be considered. On the other hand, with short-distance transport processes (almost dry deposition in the meter range near the Earth’s surface), fast reactions must be considered in measurement and modeling of vertical gradients; this is essential for NO, NO2 , and O3 .

2.1 Meteorological basics

|

23

In meteorology, a horizontal spatial scale is used, where the Greek letters α, β, and γ (not listed here) further subdivide the macro- and mesoscales: – macroscale (or global scale): x > 2000 km; – mesoscale: 2000 km > x > 2 km; – microscale: x < 2 km. In the background of climate research, horizontal scaling arises, apart from process time, also from type and extension of different Earth surfaces (Table 2.2). The type of surface on the Earth determines the parameters, such as albedo, evaporation, emission, and deposition, that are important for the physics and chemistry of the atmosphere and, hence, the climate. The atmosphere consists of four layers: troposphere, stratosphere, mesosphere, and thermosphere (Figure 2.1). The temperature profile characterizes the vertical structure of the atmosphere. Temperature (Chapter 2.1.2.2) is a thermodynamic term that results from the specific processes occurring in the corresponding layer. Penetrating solar radiation substantially controls physical and chemical processes (Chapter 2.3.1.2). The chemical composition of the atmospheric layer and available radiation determine the photochemistry. In the lower layer, the troposphere, additional absorption, and emission of radiation from the Earth’s surface determine essential weather phenomena. Tab. 2.2: Global areas, volumes, and masses in climate system, after Holland (1984). Mass of atmosphere Mass of troposphere (up to 11 km) Volume of troposphere (up to 11 km) Volume of ocean (density 1.036 kg L−1 )

5.2 ⋅ 1021 g 4.0 ⋅ 1021 g 5.75 ⋅ 1018 m3 1.37 ⋅ 1018 m3

Areas

1014 m2

%b

Ocean Northern Hemisphere ocean Southern Hemisphere ocean

3.64 1.54 2.10

– – –

Continents Northern Hemisphere continents Southern Hemisphere continents a

1.49 1.03 0.46

– – –

Antarctica Forests Tundra and bush land Deserts Grassland (savanna and steppes) Miscellaneous (e.g., semidesert, swamps, ice) Cultivated land

0.23 0.48 0.08 0.24 0.24 0.06 0.16

– 38 6 19 19 5 13

a b

Including Antarctica. Without Antarctica.

24 | 2 Fundamentals of physics in the climate system

10

250

10

-9

heterosphere thermosphere

150

100

0

10

-8

10-4

10-7

10-3

10

-6

-2

10

-5

10-1

10

-4

1

10-3

10

50

-5

10

10-2

100

10-1

1000

1

100

200

meteorites

mesopause

turbopause

mesosphere

stratopause

ozone layer

10

homosphere (turbosphere)

diffusion

air pressure (in mbar) -9 10

dissociation

polar light

air density (in kg m-3)

200

altutide (in km)

cosmic radiation

-6

turbulent mixing

10

-6

stratosphere

tropopause

troposphere 300

400

500

600

700

800

900

1000

temperature (in °C)

Fig. 2.1: Vertical structure of atmosphere; adapted after Liljequist and Cehak (1984).

The troposphere, the lowest atmospheric layer, is characterized by a temperature decrease with altitude (0.5–1 K per 100 m), strong mixing, and cloud and precipitation formation. Sometimes, particularly under the influence of high pressure, the temperature does not decrease with height at certain altitudes but remains constant or even increases. This situation is called inversion, which results in stable layers without vertical mixing. One distinguishes between ground inversion (radiation inversion due to nighttime cooling of the Earth’s surface) and height inversion (falling inversion due to large-scale descending air masses within a high-pressure area or turbulence inversion due to strong mixing in a friction layer). The lowest layer of the troposphere is called the boundary layer, characterized by interactions between the Earth’s surface and air, specifically friction and exchanges of matter and energy. The height of the boundary layer varies widely and depends on location and time, showing a pronounced diurnal and annual cycle. In Central Europe, the height of the boundary layer in winter is a few hundred meters and in summer 1.5–2 km. At the Earth’s surface, a laminar sublayer exists that comprises only a few centimeters and determines the molecular transport processes of momentum, heat, and humidity. Above the small laminar sublayer is the actual ground layer, the Prandtl layer (20–60 m), characterized by a (height-independent) turbulent exchange of momentum, sensible heat, and latent heat. Some 50–70% of friction-free wind reaches the upper edge of the Prandtl layer. The next layer, the Ekman layer, describes the range where turbulent exchange becomes height independent. Finally, the tropopause

2.1 Meteorological basics

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25

STRATOSPHERE

T

O RO P

T RO

SE P AU

10 km

FRE E

TROPO

POPA

USE

SPHERE

POLAR NIGHT

POLAR DAY BOUNDARY LAYER

90° winter

mid/latitudes

subtropics 0°

subtropics

mid/latitudes

90° summer

equatorial zone

Fig. 2.2: Structure of atmosphere, horizontally and vertically.

is the top edge of the troposphere, characterized by no further decrease in temperature but even remaining constant or even increasing. This is a result of radiation and vertical exchange. The tropopause height reaches 16 km in the tropics, whereas it decreases poleward, making a “jump” at about 30° N and S (Figure 2.2). In the tropics, cumulonimbus convection is a mechanism contributing to more than half of the energy budget of the Hadley circulation. Air rises at high speed (2–3 m s−1 ) near the equator (together with air pollutants) and flows poleward at 10–15 km above the surface, descending in the subtropics and then returning equatorward near the surface. This circulation creates the trade winds, tropical rain belts and hurricanes, subtropical deserts, and jet streams. Large-scale circulation in the free troposphere is ongoing in accordance with certain physical laws. Generally, circulation is anticyclic around the hemispheres, where warm air flows polward and cold air returns back to the equator. In this way, the global distribution of trace substances occurs. The stratosphere is characterized mainly by the ozone layer based on what radiation, with wavelengths smaller than about 300 nm, cannot penetrate into the troposphere due to the absorption of smaller wavelengths through oxygen and ozone. The maximum ozone concentration was found to be between 17 and 25 km in height, depending on the season and geographic location. Temperature increase and temperature maximum in the stratosphere are a result of solar radiation absorption by ozone. Owing to the extremely low water vapor, no clouds exist there.

26 | 2 Fundamentals of physics in the climate system

On the other hand, many transport and radiation processes in the stratosphere determine tropospheric properties. Of high importance is the stratosphere–troposphere exchange (STE) for the chemistry in both layers. From the troposphere, substances slow to react and having a lifetime of more than 1 year (e.g., N2 O, CFCs) enter the stratosphere and are photochemically destroyed, almost by the consumption of ozone. Conversely, huge amounts of ozone are transported down into the troposphere, initiating there photochemical processes. However, generally the tropopause works as a barrier layer like an inversion. Mixing in the troposphere (a few months in the hemisphere and around 1 year between both hemispheres) is much faster than exchanging the whole troposphere with the stratosphere (about 18 years). The STE lasts only 2 years because of the much lower mass of the stratosphere. At an altitude of about 50 km, the stratopause, characterized by a temperature maximum (about 0 °C), represents the transition to the mesosphere. Above the stratopause, temperature decreases up to a minimum, which characterizes the mesopause (at about 85 km height). Up to this height, the dry air remains a mixture of constant chemical composition due to sufficient mixing. Temperature again increases up to 1000 K at an altitude of 400 km and remains constant. Because the low pressure and the mean free path of molecules are several orders of magnitude larger, the temperature can be regarded only in the sense of a kinetic energetic term and not be compared with the temperature close to Earth’s surface. Molecules are almost dissociated and ionized in that layer (plasma formation) and show a high electrical conductivity, which is important for the formation of rare noctilucent clouds. Above 800 km exists the exosphere (or magnetosphere), where uncharged atoms, such as hydrogen, overcome gravity and escape to outer space. The vast majority of particles are charged and determine the magnetic properties of this layer, reaching up to 6000 km (magnetopause). Then there is a region of solar winds, consisting of fast protons and neutrons coming from the solar corona. The magnetopause characterizes the upper top of Earth’s atmosphere with an extension of ten Earth radii.

2.1.2 Meteorological elements Meteorological elements are the parameters of atmospheric conditions, which determine the weather and the climate. They are identical with climate elements; the only difference is the timescale of observation (Chapter 2.2.1). Meteorological elements are observed at aerological and meteorological (weather) stations and at meteorological observatories using aerological and meteorological instruments. The German Weather Service includes temperature, pressure, wind (speed and direction), precipitation, cloudiness, visibility, sunshine duration, and radiation (if applicable divided into solar, long-wave terrestrial, and atmospheric radiation). Other phenomena, such

2.1 Meteorological basics

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27

as thunderstorms and snowstorms, may be included as meteorological elements. Variations in meteorological elements are the result of atmospheric processes. Doubtless the most important are temperature, pressure, and humidity, which we address in the following subsections. Other elements, such as clouds, precipitation, and radiation, are treated in separate chapters. 2.1.2.1 Air pressure Air or atmospheric pressure, also called barometric pressure, is force per unit area exerted by an atmospheric column (that is, the entire body of air above the specified area): f p= . (2.1) q Hence the dimension is equal to 1 N m−2 = 1 Pa (Pascal) = 10−5 bar. Meteorologists like to express atmospheric pressure in hectopascals (hPa): 1 hPa = 100 Pa = 1 mbar. Under the influence of gravity, air exerts a hydrostatic pressure (heavy pressure), which depends on the amount of air above the level being considered: p=

f = gρh , q

(2.2)

where g is the gravity of Earth (standard gravity), ρ is air density, and h is the height of the atmospheric layer. 1 bar is equal to about the normal atmospheric pressure at sea level: 1 atm = 1013 mbar. If the air were everywhere as dense as at sea level, the atmosphere could attain a height of only h=

p 1.013 ⋅ 105 N m−2 ≈ 8 km . = gρ 9.81 m s−2 1.29 kg m−3

According to the Boyle–Mariotte law (Chapter 2.5.1), density must decrease proportionally with pressure at constant temperature. Equation (2.3) is therefore valid only for a small layer. With increasing height dz, pressure changes by dp = −gρ dz, i.e., ∂p = −gρ ∂z

and

1 ∂p +g=0. ρ ∂z

(2.3)

The application of a partial derivative ∂p/∂z expresses that we only consider changes with altitude. The so-called static basic equation, eq. (2.3), claims that air pressure decreases with height and that this decrease is proportional to gravity and density. The right-hand equation of eq. (2.3) expresses an equilibrium between two forces, specifically the vertical part of the pressure gradient (note it is a vector) and gravity. Acceleration of gravity is a vector based on Newton’s gravity and the centrifugal force resulting from Earth’s rotation (more information on forces in the atmosphere can be found in Chapter 2.4.1.1).

28 | 2 Fundamentals of physics in the climate system Expressing density ρ now by means of the gas law, i.e., n/V = ρ = p/RT (Chapter 2.5.1), it follows that¹ ∂p p =− g. (2.4) ∂z RT Assuming with good approximation that g is constant with height, on the further assumption of constant temperature, the barometric formula for an isothermal atmosphere is p = p0 exp (−

g(z − z0 ) ) RT

or

h=

RT p0 ln , g p

respectively ,

(2.5)

where h = z − z0 . Using eq. (2.5), a mean temperature of the layer considered is assumed. We already stated that the temperature decreases approximately linearly with height; adopting a relationship T(z) = T0 − ψz, it follows from eq. (2.5) that g

T0 − ψz R p = p0 ( ) . T0 − ψz0

(2.6)

The equation, which is concerned with the height dependency of pressure shows that for pressure arbitrary units can be chosen because of the dimensionless ratio p/p0 . Using the barometric formula, it is possible to calculate the difference in height between two points when the air pressure and air temperature are known for both points. This is useful in measurements of vertical concentration profiles by balloons. 2.1.2.2 Air temperature The air or atmospheric temperature is a measure of the mean kinetic energy of air molecules and, therefore, heat. Besides pressure, temperature is the most important variable thermodynamic state function (Chapter 3.1). The most general and complete definition of temperature, when only considering translation energy Etrans , is Etrans =

1 2 3 mv = kT , 2 2

(2.7)

where v2 is the mean square velocity of molecules having mass m, and k is the Boltzmann constant. From eq. (2.7) it follows that an absolute zero point of temperature exists, i.e., E and T become zero. From this point the absolute or Kelvin temperature is counted. It follows from eq. (2.7) that the mean molecule velocity² increases with T: √v2 = √ 3kT . m

(2.8)

Hence, air with T = 20 °C shows a molecular velocity of 500 m s−1 . Hydrogen molecules move due to their smaller mass – 3.8-fold times faster than air molecules 1 It is important to consider the dimensions in detail. Density is generally [mass/volume], but n/V means [mole/volume], whereas mass m is m = n/M (M = molar mass). 2 There are different definitions of mean molecular speed or velocity (Chapter 2.5.2).

2.1 Meteorological basics

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Tab. 2.3: Characteristic point of different temperature scales; C – Celsius, K – Kelvin, F – Fahrenheit, R – Roemer. C K F R a b

−273.15 0 –a –b

−40 233.15 −40 –b

−17.78 255.37 0 –b

−12.6 260.55 9.35 0

0 273.15 32 7.5

37 310.15 98.6 22.5

100 373.15 212 60

Beyond the range used. Unknown range of temperature.

(N2 + O2 ). Measurement of temperature requires scaling, introduced by Anders Celsius (1701–1744) in 1742 based on the phase transition of water. Another scale introduced by Fahrenheit uses different characteristic points of temperature, among other the body temperature. However, Daniel Gabriel Fahrenheit (1686–1736) met Olaus Christensen Roemer (1644–1710), a Danish astronomer who had developed a temperature scale, almost forgotten, based on the temperature of a healthy body (37 °C) and that of melting ice (0 °C) (Middleton 1966). Table 2.3 shows different characteristic fixing points of various scales. Recalculation between Celsius and Fahrenheit is possible by TC =

5 (TF − 32) 9

and

TF =

9 TC + 32 , respectively. 5

(2.9)

2.1.2.3 Air humidity Air contains different amounts of water vapor (0 up to 4 Vol-%, here given as a mixing ratio). The concentration of water vapor (g m−3 ) is termed absolute humidity. The significant role of water vapor in the atmosphere is described elsewhere (Chapter 3.4.3). Different measures of humidity and the role of water vapor in atmospheric processes are treated in Chapter 3 (Sections 3.4.3 and 3.4.4). Wet and dry airs have different densities because water vapor is a constituent of the gaseous mixture of air. Due to the lower density of water vapor, wet air has a smaller density than dry air at the same T and p. At the same pressure, dry air has a somewhat higher T than wet air so that the densities are equal. This higher T is called the virtual temperature.

2.1.3 Hydrometeors The World Meteorological Organization (WMO) defines hydrometeors as liquid or solid water particles. They may be suspended in the atmosphere (clouds, fog, haze, mist), fall through the atmosphere (precipitation), or be blown by wind from the Earth’s surface (spray). Snow or water on the ground is, by convention, not considered a hydrometeor. Hence, water deposited on other objects (frost, rime, dew) is not treated as a hydrometeor.

30 | 2 Fundamentals of physics in the climate system

2.1.3.1 Clouds Clouds are an intermediate form in the water cycle between vaporized water from the surface and precipitation back to the surface. Clouds also serve several important functions in air chemistry: transportation, removal and redistribution of atmospheric compounds, and the radiation budget (Figure 2.3). At any given time, about 60% of the Earth’s surface is masked by clouds in some form or other (Summer 1988). Despite its relatively low spatial occupancy of the troposphere, clouds provide an aqueous-phase medium for surface and bulk chemical reactions for unique transformations. The formation of clouds and fog droplets requires two conditions: first, the presence of aerosol particles acting as CCNs for water vapor condensation (Chapter 3.6.4) and, second, a slight supersaturation. The ability of a particle to act as a CCN depends strongly on its size and chemical composition, which implies that the knowledge of both parameters would suffice to provide an accurate prediction of ambient CCN concentrations (Andreae and Rosenfeld 2008). Particle hygroscopicity plays a key role in understanding the mechanisms of haze formation and particle optical properties. As demonstrated in Figure 3.3, an air parcel with given absolute humidity can increase its relative humidity (RH) and finally become supersaturated only by cooling. Air temperature normally does not decrease spontaneously. Uplift of air in the atmosphere causes a drop in temperature. There are three ways to initiate this uplift. Air, becoming hot at Earth’s surface, will continue to rise (we call this process convection) as long as its temperature remains higher than that of the air surrounding it. Second, air may be forced to rise by barriers such as mountains. Third, air passing over rough surfaces will become turbulent, causing an exchange of warmer surface air with cooler air above. These three categories will clearly act at different scales and, most importantly, involve uplift at different rates. The clouds associated with these different scales and types of processes vary in their morphology (Table 2.4). In determining their ability to nucleate clouds, the chemical composition of aerosol particles is much less important than their size, a result that will clarify aerosol effects on climate (Rosenfeld 2006). This is what we expect from theory because the radius-to-volume ratio determines molecular transfer from the gas phase, whereas the hygroscopicity (surface characteristics of CCNs) determines the uptake coefficient (Chapter 3.6.5). The other very important parameter for cloud formation is the CCN number, determining the cloud droplet number. Behind this relationship is the so-called Twomey effect (Twomey 1974), which describes how CCNs from anthropogenic pollution may increase the amount of solar radiation reflected by clouds (Figure 2.4).

2.1 Meteorological basics

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hQ hQ' enhancement of photochemistry above clouds

liquid phase chemistry and cloud processing

hQ´´ redistribution of pollutants

transport

influence on radiation budget and photochemistry below clouds

acceleration of dry deposition (for rain clouds)

removal from the atmosphere (wet deposiiton)

earth surface Fig. 2.3: Role of clouds in climate system: influencing transport and mixing, removal, chemical transformation, and radiation budget.

Tab. 2.4: Cloud types (after Summer 1988 and WMO 1992). Category

Type

Base height (km)

Depth (km)

Typical base temperature (°C)

LWC (g m−3 )

High

Cirrus (Ci) Cirrocumulus (Cc) Cirrostratus (Cs)

5–13 5–13 5–13

0.6 0.6 0.6

−20 to −60 −20 to −60 −20 to −60

0.05

Medium

Altocumulus (Ac) Altostratus (As)

2–7 2–7

0.6 0.6

+10 to −30 +10 to −30

0.1 0.1

Low

Nimbostratus (Ns) Stratocumulus (Sc) Stratus (St)

1–3 0.5–2 0–0. 5

2

0.5

0.5

+10 to −15 +15 to −5 +20 to −5

Cumulus (Cu) Cumulonimbus (Cb)

0.5–2 0.5–2

1 6

+15 to −5 +15 to −5

1.0 1.5

Vertical

0.25

32 | 2 Fundamentals of physics in the climate system

emission increase

more atmospheric aerosol

more CCN

smaller cloud droplets

less precipitation

more cloud water

higher albedo

bigger optical thickness

Fig. 2.4: The so-called Twomey effect.

As a well-known example, Charlson et al. (1987) established a self-controlling cycle between marine sulfur emissions and air temperature, illustrating the Gaia hypothesis,³ spurring much useful air chemical and climate research (Figure 2.5). As shown originally by Twomey (1991) and recently reviewed by Lohmann and Feichter (2005), the sensitivity of climate to CCN number density is nonlinear, with the effect being much stronger at low particle numbers. In a preindustrial model scenario by Pringle et al. (2010), the particle hygroscopicity tends to be higher over marine regions and lower over continents because the anthropogenic PM is on average less hygroscopic than sea spray but more hygroscopic than natural continental background aerosol (dust and or-

3 The Gaia hypothesis is an ecological hypothesis proposing that the biosphere and the physical components of Earth (atmosphere, cryosphere, hydrosphere, and lithosphere) are closely integrated to form a complex interacting system that maintains the climatic and biogeochemical conditions on Earth in a preferred homeostasis, originally proposed by James Lovelock as the Earth feedback hypothesis (Lovelock and Margulis 1974, Lovelock 1979). In short, the biosphere itself is an organism; it acts much like an organism and appears to be internally controlled (Crutzen 2002). Gaia is the “invisible hand” of biogeochemistry. Lovelock suggests that life processes regulate the radiation balance of Earth to keep it habitable.

2.1 Meteorological basics

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sun

radiation budget –

cloud albedo

CCN anthropogenic aerosol

global temperature –

+ aerosol

climate feedback

+

+

SO2

+

± (?) greenhouse gases

+

precursor emission

DMS

+

+

continent

atmosphere

+ continent

DMS

ocean

± (?) phytoplankton (availibity/specification)

marine ecosystem ± (?)

run-off (+)

– sea pollution

Fig. 2.5: Relationship between marine sulfur emission (as DMS), climate, and feedback, including human perturbation as an example of the Gaia hypothesis, called the CLAW hypothesis; modified after Charlson et al. (1987).

ganic matter (OM)). In regions influenced by desert dust, the particle hygroscopicity has increased strongly due to mixing of air pollutants with mineral particles. The chemical composition of CCNs determines the water chemistry (Chapter 3.6.4) of individual droplets and the ability to absorb gases. In a short period (on average about 1 h) of existence of drops of different sizes and chemical composition, the chemical composition of the interstitial gas phase and that of the droplet phase changes. Depending on the cloud microphysics and cloud dynamics, the droplets can have one of two fates: either they evaporate or they precipitate. Only in one out of ten cases, on average, does a cloud precipitate. Subsequent evaporation and condensation again until final dissipation back to water vapor is the more frequent process, called cloud processing. During that process, the aerosol particles, acting as nuclei in the beginning and ending as residues, are generally growing and becoming more water-soluble (e.g., Henning et al. 2014). The cloud amplifies production of CCNs. Recent research suggests that clouds are able to take up water-soluble organic molecules, which then

34 | 2 Fundamentals of physics in the climate system

oxidize and form SOA after evaporation of cloud droplets (Ervens et al. 2008). The term cloud chemistry is considered here to comprise – cloud water chemical composition (Chapter 6.1.5.1), – reactions that take place in cloud water droplets (aqueous chemistry) and – reactions that take place in the gas (interstitial) phase between droplets (gasphase chemistry). Therefore, cloud chemistry (such as aerosol chemistry) is also known as multiphase chemistry. Even though the volume fraction of the liquid water content (LWC) in clouds rarely exceeds 10−6 (1 mL in 1 m3 air, Fig. 2.7), the fundamental role of cloud droplets as a medium for chemical reaction has long been recognized. Clouds influence the photochemistry of the atmosphere and the radiation budget and redistribute emitted trace compounds to other regions and from the boundary layer to the free troposphere (Figure 2.3). In cloud droplets, chemical transformations occur that would otherwise not take place or would proceed at much slower rates. Cloud processes are responsible for more than 70% of sulfate formation from gas-phase SO2 (Chapter 5.4.4). More and more, it is accepted that clouds also influence the ozone budget regionally and even global between 10% and 30% (Chapter 5.2.6.2). Despite the short lifetime of single cloud droplets, cloud systems may exist for many hours and even a few days and transport pollutants over distances of several hundred kilometers. Finally, clouds produce precipitation, which acts as a very efficient removal mechanism of chemical substances (Chapter 2.6.2). For a description of cloud chemical climatology, the most important cloud parameters are as follows (Table 2.5): – radius and size distribution of droplets or ice particles, – liquid or ice water content (if possible as vertical profile), – base height and top height, – chemical composition of cloud water (if possible size-resolved), – interstitial gas-phase chemical composition in cloud, – frequency and duration of cloud events and degree of cloud cover and – type of cloud and weather situation. The main results of cloud chemistry monitoring at Mount Brocken, one of the longest time-series worldwide, are summarized in Chapter 4.2.5.3 of Volume 2. Many attempts, though limited because of the experimental difficulties, have been made to study the chemistry of clouds in single droplets and in different size fractions. The literature is huge, and it is beyond the scope of this book to review the results; in Volume 2, Chapter 2.4.8, the reader will find a review of the history of cloud studies. Cloud modeling is one of the most important and effective means of investigating cloud processes with sophisticated representations of cloud microphysics, and it can reasonably well resolve the time evolution, structure, and life cycles of a single cloud and its systems (Barth et al. 2003).

2.1 Meteorological basics

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Tab. 2.5: Cloud droplet characteristics including standard deviation, low-level stratiform clouds. Observational data from Miles et al. (2000). Parameter Droplet number Mean droplet diameter Effective droplet diameter a Liquid water content

(cm−3 )

N d (μm) d eff (μm) LWC (g m−3 )

Marine cloud

Continental cloud

74 ± 45 14.2 ± 3.4 5.8 ± 2.0 0.18 ± 0.14

288 ± 159 8.2 ± 3.9 3.1 ± 1.2 0.19 ± 0.21

a

The effective diameter of cloud droplets is usually derived from measurements of droplet size distribution measured by particle measuring system (PMS) probes. For imaging probes, the effective diameter (μm) is calculated according to the following definition (the geometric cross-sectional area A of water drops (μm2 ) per unit volume (μm3 ), density ρ (equal to 1 g m−3 )): d eff =

3 LWC 2 4 Aρ

From aircraft measurement it has long been known that LWC increases linearly from the cloud base up to 80% of the cloud thickness and then declines strongly, which is shown in Figure 2.6 from the author’s own measurements using a cable car and a sensitive LWC instrument. A correlation exists between LWC and visibility (Chaloupecky et al. 2007, Acker et al. 2010). Ice particles found within polar stratospheric clouds (PSCs) and upper tropospheric cirrus clouds can dramatically affect the chemistry and climate of Earth’s 600

400

200

0 0

50

100

150 LWC (in mg

200

250

300

350

m-3)

Fig. 2.6: Profile of liquid water content (LWC, mg m−3 ) through a stratiform cloud, measured using a cable car at Mount Grünten (Bavaria) on November 5, 1993 (summit 1738 m a.s.l. and valley 750 m a.s.l.), after Wieprecht and Junkermann, unpubl.

36 | 2 Fundamentals of physics in the climate system

relative frequency (in %)

25

20

15

10

5

0 50

150 250 350 450 550 650 750 850 950 1050 1150

liquid water content (in mg m-3) Fig. 2.7: Arithmetic mean of LWC for different classes of LWC at Mount Brocken (mg m−3 ) based on 1-h averages (n = 32, 661) derived from 30-s data 1993–2009 in frost-free period (note that the number of data is considerably higher than that of cloud water samples).

atmosphere. The formation of PSCs and the subsequent chemical reactions that occur on their surfaces are key components of the massive ozone hole observed each spring over Antarctica. Cirrus clouds also provide surfaces for heterogeneous reactions and significantly modify Earth’s climate by changing the visible and infrared (IR) radiation fluxes. Although the role of ice particles in climate and chemistry is well recognized, the exact mechanisms of cloud formation remain unknown, and thus it is difficult to predict how anthropogenic activities will change cloud abundance in the future. Besides the role of clouds in atmospheric chemistry and the water cycle, their most important impact on the climate system is probably through influencing solar and terrestrial radiation. Counteracting the role of GHGs in absorbing terrestrial radiation, clouds act by scattering and reflecting incoming solar radiation. For details on cloud, aerosol, and climate interactions, see Hobbs (1993), Crutzen and Ramanathan (1996), and Heintzenberg and Charlson (2009), and for details on cloud (and precipitation) physics, see Summer (1988), Pruppacher and Klett (1997), Strangeways (2007), and Lohmann et al. (2016). 2.1.3.2 Fog, mist, and haze The atmosphere becomes “milky” through light scattering on particles in a size range between 50 and 200 nm. The WMO uses for atmospheric obscuration the following terms: fog, ice fog, steam fog, mist, haze, smoke, volcanic ash, dust, sand, and snow. With the exception of smoke, volcanic ash, dust, and sand (all these are particles belonging to atmospheric aerosol) (see also Chapter 3.6.3), the other particles are considered hydrometeors. Snow is precipitation (see the next section, Chapter 2.1.3.3) as

2.1 Meteorological basics

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the ultimate fate of cloud development, whereas fog, mist, and haze are particles (in that order) with decreasing water content. Fog is a cloud that is in contact with the ground. Fog is distinguished from mist only by its density, as expressed in the resulting decrease in visibility: Fog reduces visibility to less than 1 km, whereas mist reduces visibility to no less than 2 km. Before fog (or clouds) and mist are formed through heterogeneous nucleation, aerosol particles that can act as CCNs must be activated, i.e., they become moistened at RH depending on the so-called deliquescence point (around 60% RH). These particles are almost⁴ secondary, produced from various organic (biogenic terpenes, NMVOC) and inorganic (SO2 , NH3 , NO x ) gaseous precursors. Haze particles form when water condenses on dry particles (Heintzenberg et al. 1998). Some texts differentiate between dry and wet haze, but usually (and this is recommended) haze is the term for moistened particles that will probably become CCNs. Dry haze is simply dust and smoke (each particle in the atmosphere contains more or less water) in a size range below about 100 nm. A well-known phenomenon is blue haze: SOA from plant organic emissions (Chapter 3.6.2). A hazy condition often occurs in summer and affects large areas from cities to mountains. Such a haze is often caused by excessive amounts of pollutants resulting from combustion (smog and smoke). Depending on their size, the particles produce different optical effects. Continuation of this condensation leads to the formation of fog. The formation of a fog layer occurs when a moist air mass cools to its saturation point (dew point). This cooling can be the result of radiative processes (radiation fog), advection of warm air over cold surfaces (advection fog), evaporation of precipitation (precipitation or frontal fog), or air being adiabatically cooled while being forced up a mountain (upslope fog). Another type of fog is so-called valley fog. This fog forms in air being radiatively cooled, during the evening, on the slopes of topographical features. This air, becoming denser than the surrounding air, starts going down the slope. This results in the creation of a pool of cold air at the valley floor. If the air is cold enough to reach its dew point, fog forms. Generally, we distinguish between warm (> 0 °C) and cold (< 0 °C) fog. Globally, warm fog is dominant (about 80% of all events). Compared with other cloud types, a fog droplet is generally smaller, although great variability in size distributions of fog droplets has been observed. In some instances, larger than expected fog droplets were observed (Gerber 1991). Also, in contrast to other cloud types, fogs have a low LWC. Most fog has LWC ranging from 0.05 to 0.5 g m−3 . Fogs forming in polluted areas act as efficient mechanisms for the deposition of some chemical species on vegetation (wet deposition) (Lovett and Kinsman 1990). Aqueous-phase chemical reactions take place in fog droplets (e.g., Facchini et al. 1992, Bott and Carmichael 1993, Acker and Möller 2007), and when these drops evaporate after settling on vegetation, they leave behind concentrated chemicals that may be detri-

4 An exception of primary particles is due to finest sea salt particles.

38 | 2 Fundamentals of physics in the climate system

Tab. 2.6: Precipitation forms; rain, showers, drizzle, snow, and hail are distinguished by the magnitude of precipitation; d – diameter. Form

Description

Rain Drizzle Freezing rain Freezing drizzle Snowflakes Snow pellets Snow grains Ice pellets Ice prism Hail

Water drops, d > 0.5 mm Fine drops, d < 0.5 mm and close together Supercooled water drops, freeze after impact with surfaces As freezing rain but d < 0.5 mm Loose aggregates of ice crystals > −5 °C White, opaque ice grains, d = 2−5 mm Small ice grains, d < 1 mm Frozen raindrops, melted and refrozen snow, d < 5 mm Ice crystals in the form of needles at very low temperature Balls or pieces of ice, d = 5–50 mm, sometimes greater

mental to vegetation growth. In addition, fog water represents an important resource for people living in arid regions (Amedie 2001). Different fog-water collectors are available so that fog can be used as a source of irrigation and drinking water (Klemm et al. 2012). Consequently, knowing and understanding the chemical composition of fog water is important for health and agricultural productivity issues. 2.1.3.3 Precipitation We stated that not all clouds precipitate. Indeed, from only a very small proportion of clouds does precipitation actually reach the ground surface. The basic problem is that cloud water droplets or ice particles are frequently too small to fall from the cloud base or to survive on the way to the ground because they evaporate. Whereas a cloud droplet is on average 8 μm in diameter, a raindrop is between 500 and 5000 μm (0.5–5 mm); this means that a small raindrop is as large in volume as 240,000 cloud droplets. Assuming 240 cloud droplets cm−3 (cf. Table 2.5), there is only one raindrop in 1 L of air. Several microphysical processes occur in clouds depending on the temperature, vertical resolution, dynamic, and other parameters that result in the growth of a particle (Figure 2.8) and different precipitation forms (Table 2.6). In a pioneering work, Mason and Ludlam (1951) wrote: “While the rate of spontaneous nucleation in water vapor is inappreciable until the supersaturation reaches about 400%, the presence of foreign nuclei [now called CCNs] in the atmosphere allows cloud formation with supersaturation of only about 0.1%.” Earlier theories of cloud-droplet growth by diffusion and by coagulation cannot explain the formation of raindrops (so-called precipitation elements). Three different processes (Figure 2.8), coalescence (liquid on liquid), aggregation (solid on solid) and accretion (liquid on solid) describe the collision between particles. The process of coalescence is the only process occurring in warm clouds, and the process of aggregation is the only process that may occur where cloud temperature is below −39 °C. This is the temperature of

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spontaneous freezing of supercooled drops. In mixed clouds, where both supercooled droplets and ice particles coexist, ice particles tend to grow at the expense of adjacent supercooled water droplets due to different vapor pressures (the Bergeron–Findeisen process). The crystals grow by vapor deposition at a rate (maximum of around −12 °C) that produces individual snow crystals in some 10 to 20 min. The modern practice of cloud seeding (to initiate precipitation artificially) is mostly based upon the introduction of artificial ice nuclei to supply more of the ice particles. Similarly, the seederfeeder mechanism works especially in orographic clouds: there are vertical layers of warm and cold clouds, where the warm (feeder) cloud acquires falling ice crystals from the upper cold (seeder) cloud to initiate particle growth. This mechanism also explains why the raindrops collected at ground level for chemical analysis contain much fewer substances (they are diluted) than cloud water. In warm clouds, not only coalescence may cause rain formation. In cumulus clouds, a small number of either wet hailstones or giant salt nuclei may initiate a water-drop chain reaction; in tropical clouds the presence of the latter may render the intervention of ice crystals unnecessary. The processes of rain formation are not completely understood even today. The chemical composition of precipitation is a result of three different processes, summarized as wet deposition (Chapter 2.6.2): – Nucleation scavenging: the chemical composition of the CCNs determines the initial cloud (fog) composition (dissolved and suspended material). – In-cloud scavenging: in a cloud, aerosol particles (of minor importance) and gases are taken up; chemical reactions occur in droplets. – Subcloud scavenging: falling raindrops (or snowflakes) absorb gases and take up particles. For a description of precipitation chemical climatology, the most important rain parameters are as follows (see Chapter 4.2.5.4 in Volume 2 for long-term precipitation chemistry): – precipitation intensity (rainfall depth per hour, mm h−1 ), – precipitation rate (rainfall depth per time unit), – precipitation amount (total amount of precipitated water in L), – frequency and duration of precipitation events (including time without precipitation), – distribution of drop sizes, – precipitation water chemical composition (event-based) and – precipitation form (Table 2.6).

2.1.4 Dew, frost, rime, and interception In the last three sections, we considered hydrometeors, drops, and ice particles in clouds, fog, mist, and precipitation. This section deals with the formation of inter-

40 | 2 Fundamentals of physics in the climate system

H2O + •

 condensation (heterogenous nucleation) 

cooling (< 0°C ... –39°C)



freezing (< -39°C)

H2O +



deposition (gas sticking)

+



collision (accretion, riming)

+



collision (aggregation)

+



collision (coalescence)



melting

mixed cloud



CCN

small and

+

drop breakup

large water droplet (warm, > 0°C)

supercooled water droplet (< 0°C) small and

large ice crystal

Fig. 2.8: Droplet growth and dynamic in a mixed cloud (containing droplets and ice particles).

facial water, from either water vapor (dew and frost) or hydrometeors (rime and interception). These forms of atmospheric water require contact with a surface: soils and vegetation, but also artificial surfaces. Some meteorologists classify these phenomena (in the sense of deposition) (Chapter 2.6) as belonging to precipitation; we will not. Precipitation is physically a sedimentation process due to gravitational force; see Figure 2.9 for the different deposition processes. Condensation of water vapor occurs when the dew point is undershot on cooler surfaces, resulting in a subsequent diffusion process in the direction of the surface (that is dry deposition, similar to the surface removal of molecules other than H2 O, but these are ad- or absorbed onto the surface – only water can condense into liquid in the Earth’s climate system). When the temperature is above 0 °C, liquid drops (not film) are formed on the surface – most likely on condensation or crystallization centers – and we call this dew. If T < 0 °C, water vapor is transformed into ice on the surface (frost) in different sizes and forms, mostly depending on temperature and wind; on trees, filigreed ice needles and structures are formed (hoar frost). Droplets in clouds, fog, and mist are in continuous motion because of the dynamic processes but also due to the advective motion of air. In this way, they can affect surfaces such as trees, towers, and buildings, and, due to the adhesive properties of water, the droplets stick. When the temperature is higher than 0 °C, the impacted drops

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evaporation

gaseous precursors

(< 0°C)

gas-to-particle conversion

nucleation

cloud, fog, mist

CCN

rime

impaction

interception (> 0°C) dry deposition

emission

condensation

precipitation

mountain surface

evaporation

water vapor

(< 0°C)

condensation

frost

(> 0°C)

dew

wet deposition ground surface

Fig. 2.9: Simplified scheme of atmospheric water forms, transfers, and removal (deposition); note that the different scavenging processes are not shown in their entirety.

can grow by collision and finally flow down; this process⁵ is called cloud-droplet interception. At temperatures below 0 °C, the supercooled droplets will freeze on surfaces to form rime. Riming can lead to severe problems on mountaintops (Figure 2.10). Cloud-water (and rainfall) interception is a hydrological process of particular interest in tropical mountain cloud forests. Studies in these systems have shown the important contributions of cloud/fog water to the hydrological balance (Gomez-Peralta et al. 2008). Interest in dew formation, as well as its physics and chemistry, rose after 1960 for several reasons: first, due to amplified dry deposition onto moistered surfaces (Chang et al. 1967, Brimblecombe and Todd 1977); second, in the last two decades because of ecological considerations (dew as a source of moisture for plants, biological crusts, insects, and small animals) (e.g., Jacobs et al. 2000) and its potential use as potable water (Beysens et al. 2006, Muselli et al. 2006); and finally, from an air chemical point of view, now also termed interfacial chemistry (Rubio et al. 2006, Acker and Möller 2007).

5 Foresters and hydrologists call the interception of rain drops by leaves and needles of trees rainfall interception (or sometimes canopy interception; however, this term does not distinguish between cloud and fog interception, and should therefore not be used). Because of evaporation, interception of liquid water leads to a loss of precipitation for the drainage basin.

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Fig. 2.10: Riming of meteorological instruments in winter 1992/1993 at the Cloud Chemistry Monitoring Station, Mount Brocken (Harz, Germany, 1142 m a.s.l.).

2.2 Climatological basics 2.2.1 Climate The term climate is currently often used in connection with climate change (a term widely popularized in recent years). The synonymous expression climate alteration (a more scientific term) is used. In the United Nations Framework Agreement on Climate Change, which was signed by 34 countries and ratified in New York on May 9, 1992, climate change is defined as “changes in climate, that are directly or indirectly attributable to anthropogenic activities, which change the composition of the atmosphere and which add up to the natural climatic changes observed over comparable periods of time.” This definition is circumscribed, as natural processes are included in the sense of climate change but not in the sense of climate alteration. However, it can only be observed that climate change is due to all factors. Possible anthropogenic factors having an effect on climate (and therefore on its alteration) are manifold and range from an alteration in the use of land (altered surface properties) to emissions, whereas direct energetic influences (e.g., warmth islands) are at most only of local importance. Thus, a climatic change is the difference between two states of climate. A state of climate is described through the static condition of the climatic system. A cli-

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matic fluctuation can therefore be described as a periodic climatic change, independent of the corresponding timescale. Climate is a function of space and time – and is continuously changing (Schneider-Carius 1961). The climate system is too complex to be clearly mathematically described. In all likelihood, this observation will hold true in the future as well. Our knowledge about many isolated processes in this system is still imperfect. Nevertheless, immense progress has been made in the past 20 years, and the description of the principal processes is considered definitive (Hansen et al. 2007). Both climate researchers and historians of climate science have conceived of climate as a stable and well-defined category, but such a conception is flawed. In the course of the nineteenth and twentieth centuries, the very concept of climate changed considerably. Scientists came up with various definitions and concepts of climate that implied different understandings, interests, and research approaches. Understanding of climate shifted from a timeless, spatial concept at the end of the nineteenth century to a spaceless, temporal concept at the end of the twentieth. Climatologists in the nineteenth and early twentieth centuries considered climate to be a set of atmospheric characteristics associated with specific places or regions. In this context, while the weather was subject to change, climate remained largely stable. Of particular interest was the impact of climate on human beings and the environment. In modern climate research, at the close of the twentieth century, the concept of climate lost its temporal stability. Instead, climate change became a core feature of the understanding of climate and a focus of research interest. Climate has also lost its immediate association with specific geographical places and become global. Interest is now focused on the impact of human beings on climate (Heymann 2009). In Volume 2, we will discuss the history of the climate system; to summarize, the following major phases in the evolution of Earth can be identified: 1. The accretion of Earth and its primitive atmosphere from the primordial solar nebula. 2. The differentiation of the interior of the planet and the associated outgassing of volatile materials. 3. The chemical era of abiotic photochemical transformation of the primordial atmosphere and oceanic water to form the organic molecules from which life could arise. 4. The microbial era during which the first simple life forms evolved, proliferated, and forever modified the atmosphere and environment. 5. The geological era in which the physical reconfiguration of oceans and continents caused major deviations in the evolution of life and the atmosphere. 6. The recent age, when humans appeared with the intelligence to exploit fully their capability to alter significantly the global atmosphere and environment. Each of those epochs started with rapid climate change and (with the exception of phase 1, which ended soon after Earth’s formation) continued with more gradual

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change due to the progressive evolution of an adaptive climate system. To some extent, the disturbances of biogeochemical cycles caused by anthropogenic activities since the Industrial Revolution have already exceeded the natural flow of matter, but many of those disturbances remain in a state of natural variability of air composition over geological epochs. The time periods of natural variability and changes, however, are far beyond the dimensions of the last 150 years. Our atmospheric environmental problem – climatic change – is therefore a matter of adaptation over time of various subsystems with the global system in the first place. The humans causing alterations may disappear, but another climate and climate system will remain. Using the definition that “climate is the entirety of the properties of the climate system” (Hantel et al. 1987, Hantel 2001), it is logical to define climate change as any change in the condition of the climate system. According to Bärring (1993), the distinction between the terms climate change, climate variation, climate fluctuation, and climate variability remains unclear, or was in 1993. He argued that this, perhaps, is not a problem in the scientific community but that difficulties may arise when climatological information is interpreted by nonspecialists, for example, in a political or socioeconomic context. Already a hundred years ago (Hann 1908, Alt 1916) the term climate change(s)⁶ had been divided into changes ongoing continuously of the same tenor and others varying over more or less long periods around a mean value, called periodic variability. Climate variations within a defined period (e.g., 30 years) are not climate change but belong to the climate value, expressed as the periodic mean and its variance, including statistics of extreme values. Human societies are highly adapted to the ordinary annual rhythms of climate, which we call the seasons. Moreover, almost all climates display interannual differences, which have hitherto appeared to be unpredictable (Hare 1985). Climate change is said to occur when the differences between successive averaging periods exceed what variance can account for, i.e., when a distinct signal exists that is visible above the variance. There are three principal causes of climate change and variability: – changing solar radiation, specifically the solar constant (due to solar activities or astronomical factors), – changing chemical composition of the atmosphere (due to emission changes) and – changing characteristics of Earth’s surface (due to land-use changes or geological and biological changes). This also includes catastrophic events such as volcanic eruptions and the impact of celestial bodies. It is beyond the focus of this book to describe the physics of these alterations. However, with an understanding of the chemical evolution of the climate system (Volume 2), it is evident that different chronological processes are superposed and that the different causes are interlinked in the sense of climatic feedbacks, which 6 In German: Klimaänderungen.

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make it very difficult to quantify climate changes and variations. Temperature and precipitation, as the most important climatic factors, are interrelated, but they are also interrelated with atmospheric composition and surface characteristics, which again are interrelated.

2.2.2 Climate system Within climatology, as the rather descriptive science of climate, the meteorological definition of climate has proved itself reliable. For an understanding of the dynamics of climate, that is, the processes that determine the average state and the variability of the atmosphere over longer periods, the meteorological definition is inadequate, as over longer periods changes in the atmosphere are considerably affected by interdependencies of the atmosphere, ocean, vegetation, and ice masses (Claußen 2006). For this reason, in climate dynamics, climate is defined by the state and the statistical behavior of the climate system, as discussed in modern textbooks on meteorology and climate physics (e.g., Peixoto and Oort 1992, Berdowski at al. 2001, Kraus 2004, Lutgens et al. 2009). Claußen (2006) distinguishes between a meteorological and a system-analytical definition. Note that it is essential to incorporate statistics into the idea of climate, i.e., climate means not simply the “mean weather.” It follows that – Climate is a function of space and time. – Climate cannot be described as a single unit. With our increasing understanding of global environmental processes, it was concluded that the mean atmospheric status (over several years) not only depends on processes occurring in the atmosphere itself but also oceanic circulation, glacier movements, the spread of vegetation, and others. Consequently, Gates (1975) defined climate on the basis of three categories, specifically the climate system, climate states, and climate change. The climate system consists of the atmosphere, hydrosphere, cryosphere, lithosphere, and biosphere. A climate state is determined by the full description of the statistics of the inner climate system. A climate change is the difference between two climate states of same kind. In human history and the history of exploration of air and the atmosphere, the concept of climate was subject to change, but various descriptions have also existed at the same time. It is beyond the scope of this book to address them here. For our purposes, we may say that different definitions of climate are also in use. A priori, this is a contradiction, as there is only one climate system on Earth. Obviously, this results from a pragmatic approach to the cognition and description of the climatic system by 1. diverse disciplinary points of view, 2. different objectives (e.g., description of subsystems) and 3. differentiated knowledge of system relationships.

46 | 2 Fundamentals of physics in the climate system

The climate system (Figure 2.11) consists of various subsystems: the atmosphere, the hydrosphere (which includes oceans, rivers, lakes, rain, groundwater), the cryosphere (ice sheets, sea ice, snow, permafrost), the marine and terrestrial biosphere, soil, and – when considering the development of climate over many millennia –Earth’s crust and the upper mantle. Basically, this classification is carried out by means of the matter involved (gaseous, liquid, and solid) and the timescales that can be observed for typical changes in the subsystems. The subsystems are linked to each other through flows of energy, momentum, and matter. To the flow of matter the transport of chemical substances and the processes of their transformation need to be added, insofar as these substances – for example, GHGs or nutrients of the biosphere – are directly or indirectly related to the energy budget. The definition of the climate system is not derived from superior principles but is a pragmatic restriction of the subject to be examined by classification in subsystems and interpretation of the corresponding system environment. In this way, the climate system is separated from its environment because no significant flow of matter between the system and its environment occurs on timescales relevant for examination.

solar radiation

atmosphere

energy (physical processes)

material (chemical processes)

climate system

anthroposphere

biosphere / geosphere

earth system Fig. 2.11: The climate system (cf. also Figure 1.1).

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For Kraus (2004), the anthroposphere, the world of human action, belongs to the climate system as well. On one hand, this seems to be reasonable, as humans, being a part of nature, have altered the “natural system” dramatically. On the other hand, it is not pragmatic, as human action, especially culture and psychology, elude thermodynamic description. In the literature, the total of the climate system and anthroposphere is defined as the Earth system (Schellnhuber and Wenzel 1998, Schellnhuber 1999, Claußen 1998, 2001). Hantel (2001) presents a very pregnant definition: The climate is not a subject-matter but a property. Its carrier is the climate system. The climate is the entirety of the properties of the climate system.⁷

The climate system can be described (and widely quantified through measurements) by 1. the natural energy system, 2. the hydrological cycle, 3. the carbon cycle and 4. the other biogeochemical cycles. In a broader sense, the climate system can be seen as an interlayer in Earth’s system, buffering a habitable zone from uninhabitable physical and chemical conditions by altitude (upper atmosphere) and depth (deep lithosphere) (Figure 2.12). In a more narrow sense, the human-habitable zone is limited to the gas–solid interface (Earth–

space

upper atmosphere

cosmos habitable zone

climate system

earth system

deeper lithosphere

Fig. 2.12: Layer structure of climate system.

7 Original text in German: Das Klima ist kein Gegenstand, sondern eine Eigenschaft. Ihr Träger ist das Klimasystem. Das Klima ist die Gesamtheit der Eigenschaften des Klimasystems.

48 | 2 Fundamentals of physics in the climate system

surface/atmosphere) with a very small extension of a few tens of meters. The anthroposphere (or noosphere), however, is permanently spatially expanding – also out of the climate system – due to the fact that humans are creating inhabited and uninhabited closed habitable systems in uninhabitable surroundings.

2.2.3 Chemical climate By now we have seen that the term climate inevitably includes chemistry and that the climate system “works” because of chemical processes. Chemistry (in terms of chemical compounds and reactions) and transport are inextricably linked with each other. Physics (in terms of energy conversions) is the driving force of chemical processes. However, the climate system does not work without biology (in terms of biochemical processes); Vernadsky introduced the term biogeochemical potential (Chapter 3.2.2.5, Volume 2). Predicting the changing chemical state is an essential task of climate research, and without long-term chemical monitoring (concentrations of chemical compounds in air, within PM, rain, and cloud water) we have no insight into climatological processes and no opportunity to validate adequate mathematical models. Climatologists agree that climate refers to the long-term state of the atmosphere (characterized by its mean as well as by variations thereof). Atmosphere is in turn characterized by air (in the sense of a mixture of substances) and the processes occurring therein. It follows that, in the attempt to describe the atmosphere, a separation between chemistry and physics would be fatuous. The chemical composition of air includes among its main components (nitrogen and oxygen) and its minor components (noble gases and water) a virtually “unlimited” number of trace gases and solid components (aerosol particles) as well as (temporarily) dissolved substances (in hydrometeors). In analogy to the meteorological definition of weather, Lawrence et al. (2005) define chemical weather as the . . . local, regional, and global distribution of important trace gases and aerosols and their variabilities on time scales of minutes to hours to days, particularly in light of their various impacts, such as on human health, ecosystems, the meteorological weather, and climate.

Certainly, the alert observer will instantly notice that (in hydrometeors) dissolved trace matter is missing, and then the question arises as to what the important and unimportant trace matter is. The term weather (which describes the short-term timescale of the state of the atmosphere) with respect to effects on life – actually unavoidably – includes a priori atmospheric chemical species. Hence, without further discussion, atmospheric chemistry can be incorporated into the definition of weather (although in all likelihood no meteorologist would have thought so). Thus, the definition of Lawrence et al. (2005) can be adjusted to The chemical state of the atmosphere mainly with respect to. . .

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When we leave out the short-term timescale, that is, we use the latter sentence concerning the definition of climate, we arrive at a formal definition of chemical climate (location-related) as follows: The synthesis of chemical weather conditions in a given area, characterized by long-term statistics (e.g., mean values, variances, probabilities of extreme values) of the chemical substances in that area.

Instead of “meteorological elements”⁸ we have “chemical substances.” When – as implicitly mentioned earlier – meteorology feels responsible as a discipline for providing a description of the chemical state of the atmosphere, the list of “meteorological elements” can simply be expanded to accommodate all relevant chemical variables as well. So as not to cause misunderstandings, extending the term climate allows us to address chemical aspects, not so with “chemistry,” just as climatology is not a subdiscipline of physics. The variation over time (e.g., intraday, trend) of the concentration of an atmospheric trace matter is not chemistry. Chemistry deals with the transformation of trace substances and the corresponding atmospheric conditions, that is, it investigates – in analogy to the physics of the atmosphere – the process and changes of states. Here chemical substance (e.g., temperature as a physical “element”) is understood as a “state variable” in the sense of a geographical (time-space dependence) and a meteorological (atmospheric-phenomenological) property. I would like to define climate in a general sense as follows: Climate describes the mean status of the atmosphere at a given site of Earth’s surface, represented by the total statistical properties (e.g., mean values, frequencies, durations) of a long enough time period.

It is understood (and therefore no differentiation between a meteorological and a system-related definition of climate according to Claußen shall be undertaken) that the atmosphere is only one part of the climate system, and therefore climate can only correctly be described in a physical-chemical manner taking into consideration material and energetic interdependencies with other subsystems. Advantageously, climatic state (i.e., the scientific, broadly mathematical description of the climate) can be defined as follows: A climate state is given by the whole description of the statistical status of the internal climate system.

Why – apart from an academic point of view – is the inclusion of “chemical dimension” in the description of climate so important? Why is the observation of a “chemical weather” phenomenon of no or only slight importance? The current state of the atmo-

8 The term element is used here in the sense of “component” and not chemically.

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sphere (weather) in relation to its physical dimension has an enormous relevance for humans and society, and any further rationale is superfluous. Using the definitions of chemical weather given earlier, the meaning is limited to selected so-called weather elements, like the chemical composition of select species, for example, ozone concentration concerns exceeding threshold values (ozone forecast and daily information). Some institutions prepare forecasts of “chemical weather.” This makes little sense, as trace gas concentrations are presently (barring some accident) almost below acute impact levels, and there is neither a way nor a need to respond to chemical weather. This information only makes sense when (a) a possible hazard is associated with it and (b) the possibility of prevention and response, respectively, exists. An effective acute countermeasure is not known (e.g., bans or restrictions on driving in particular cities were shown to be ineffective – which with deeper knowledge of atmospheric and chemical processes should have been known beforehand). However, prior warning (e.g., of winter and summer smog)⁹ would be important to enable sensitive individuals to stay indoors. The acute potential of chemical variables in the atmosphere to affect humans (see subsequent discussion), compared with physical variables, is negligibly low and therefore of only marginal importance to society. The record of the current chemical state of the atmosphere (that is, chemical weather) is a condition that precedes the long-term record, which makes it possible to establish a chemical climatology. The alteration of the chemical composition of the atmosphere has become a continuous process since the Industrial Revolution.¹⁰ Only with the concept of sustainability (which brought about the need for “green” chemistry and solar power as technological alternatives) can the resource and energy industries be integrated into (anthropogenically strongly modified) biogeochemical cycles and – as we hope – lead to the stability of the chemical composition of the atmosphere. The alteration of the chemical composition (GHGs and aerosols, to mention just two components) of the atmosphere is generally cited as the cause of ongoing climate change. With our new, comprehensive definition, the alteration of that chemical composition itself is climate change. The awareness that certain chemical substances (which are in a relationship of interdependency with radiation and, thus, change the energetic balance of the atmosphere) alter the physical components of climate by internal feedback reflects the scientific understanding of a “simple” interrelation. Conversely, changed physical variables (cloud coverage and radiation, among others) will change reaction conditions, chemical turnover (spatiotemporal concentration distribution), and, thus, the chemical setting. Climate is then determined by internal feedback in the atmosphere as well

9 For the sake of completeness, the necessity of warnings related to chemical disasters should be mentioned as well. 10 More exactly, since the start of large-scale forest clearing.

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Tab. 2.7: Climatic elements (examples – incomplete). Atmospheric-physical

Atmospheric-chemical

Radiation and heat (temperature) Humidity (absolute and relative) Cloudiness Precipitation Wind (direction and speed)

Atmospheric aerosol (e.g., number, mass, size) Concentration (of gaseous compounds) Oxidation capacity Acidity potential Deposition

as by external feedback with processes in other subsystems (which, from the point of view of the climate system, can be seen as internal relations as well). From the viewpoint of the Earth system, extraterrestrial as well as magmatic influences can also be seen as external feedback. The record of chemical components in climate (i.e., the development of a chemical climatology) is of great importance for societies. Long-term forecasts of the chemical climate are extremely important due to the close interaction between the physical and chemical systems (climate change) and due to the fact that any feedback response to establish abatement strategies will require many years and even decades to take effect. Climate modelers have realized recently that only a better description of chemical processes will lead to greater soundness of important physical statements (e.g., concerning the water cycle). On the other hand, a description of changes in the chemical composition of the atmosphere (recall that we understand this as a component of climate) is a self-contained value, for example, concerning the toxic potential of the atmosphere (continued rising mean ozone concentrations cause stress for plants), the oxidative potential (decomposition rates of harmful trace matter), and the acid-base balance (geochemical erosion, availability of nutrients, mobility of heavy metals). These slowly moving, ongoing changes require extensive global and careful monitoring, analysis, and evaluation, as well as (only possible on a long-term basis) technological changes and adaptations with the aim of securing sustainable development. The parameters shown in Table 2.7, which is not exhaustive, will be included in the list of climatic elements.

2.3 Optics of the atmosphere: Radiation All chemical reactions require energy for activation (Chapter 4.2.3) independent of whether they are exothermic or endothermic. Deep in the Earth, heat and pressure are thermodynamic quantities initiating chemical reactions (Volume 2). In the atmosphere and at the Earth’s surface, however, the only available energy to promote chemical reactions is direct solar radiation. The fundaments of photochemical processes are described later (Chapter 4.5); in this chapter the radiation transfer and physical processes in relation to it are briefly summarized. Beside initialization of chemical

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reactions, solar energy determines the Earth’s temperature regime (heat and subsequent pressure gradients) allowing transportation of matter in fluid systems such as the atmosphere and hydrosphere. The mean surface temperature of the Earth is 288 K (varying between 222 K and 321 K); without the present atmosphere, the mean surface temperature would be only 255 K. This narrow temperature regime allows phase transfer of water and the coexistence of its solid, liquid and gaseous phase, which surely is the main condition for our habitat/biosphere. Beside the distance from the planet to the sun (which determines the solar constant and hence the habitable zone in the solar system) the planetary atmospheric composition determines the radiation transfer and budget through the atmosphere.

2.3.1 Solar radiation 2.3.1.1 The Sun and its radiation output For each second of the solar nuclear fusion process, 700 Mt of hydrogen converts into the heavier atom helium. Since its formation, approximately 4.6 Gyr ago, the Sun has used up about half of the hydrogen found in it. The solar nuclear fusion process also creates immense heat, which causes atoms to discharge photons. Temperatures at the core are about 1.5 ⋅ 107 K. Each photon created travels about 1 μm before being absorbed by an adjacent gas molecule. This absorption then causes the heating of the neighboring atom and reemits another photon that again travels a short distance before being absorbed by another atom. This process then repeats itself many times over before a photon finally emits to outer space at the Sun’s surface. For the last 20% of the journey to the Sun’s surface the energy is transported more by convection than by radiation. It takes a photon approximately 105 years, or about 1025 absorptions and reemissions, to make the journey from the core to the Sun’s surface. The journey from the Sun’s surface to the Earth takes about 8 min. The irradiative surface of the Sun, or photosphere, has an average temperature of about 5800 K. Most of the electromagnetic radiation emitted from the Sun’s surface lies in the visible band centered at 500 nm, although the Sun also emits significant energy in the UV and IR bands, and small amounts of energy in the radio, microwave, X-ray, and gamma ray bands. The total quantity of energy emitted from the Sun’s surface is approximately 6.3 ⋅ 107 W m−2 . The energy emitted by the Sun passes through space until planets, other celestial objects, or interstellar gas and dust intercept it. A physical law known as the inverse-square law determines the intensity of solar radiation striking these objects. This law merely states that the intensity of the radiation emitted from the Sun varies with the squared distance from the source. For example, the intensity of radiation from the Sun to Mercury is 9140 W m−2 but only 1370 ± 5 W m−2 to Earth – a threefold increase in distance results in a ninefold decrease in intensity of radiation. This quantity is called the solar constant IK (not a constant in the physi-

2.3 Optics of the atmosphere: Radiation | 53

cal sense). It is important to note that this quantity is related to a plane perpendicular to the radiation beam. Therefore, Earth receives solar radiation only hemispherically (IK πr2earth ) and on a global average of IK /4 (343 W m−2 ). The solar cycle, or the solar magnetic activity cycle, is the main source of periodic solar variation driving variations in space weather. The cycle is observed by counting the frequency and placement of sunspots visible on the Sun. Samuel Heinrich Schwabe (1789–1875) discovered the solar cycle in 1843. Rudolf Wolf (1816–1893) compiled and studied Schwabe’s and others’ observations, reconstructing the cycle back to 1745, eventually pushing these reconstructions to the earliest observations of sunspots by Galileo and contemporaries in the early seventeenth century. Starting with Wolf, solar astronomers have found it useful to define a standard sunspot number index, which continues to be used today. Several periodic cycles are evident, most notably the 11year (131 ± 14 month) cycle. Every solar proton event will generate nitrogen monoxide (NO) in the upper atmosphere (see also Chapters 5.3.2 and 6.3.4.1) and consequent ozone depletion (Chapter 5.2.7) (Jackman et al. 2000). Only major large-scale events (those with > 30 MeV) will generate sufficient NO y to be observable above this terrestrial background. An ultra-high-resolution nitrate analysis of ice cores from Greenland shows an impulsive nitrate deposition, relatively consistent with those of the last five solar cycles (Smart et al. 2007). 2.3.1.2 Solar radiation transfer through the atmosphere Radiation describes any process in which energy is emitted by a body traveling through a medium or through space, ultimately to be absorbed by another body. Radiant energy is the energy of electromagnetic waves. Sunlight (solar radiation), in the broad sense, is the total spectrum of the electromagnetic waves given off by the Sun. On Earth, sunlight is filtered through the atmosphere, and solar radiation is evident as daylight when the Sun is above the horizon. The World Meteorological Organization defines sunshine as direct irradiance from the Sun measured on the ground of at least 120 W m−2 . Direct sunlight has a luminous efficiency of about 93 lumens per watt of radiant flux, which includes IR, visible, and UV light. Bright sunlight provides luminance of approximately 106 candelas per square meter (cd m−2 ) at the Earth’s surface. There are many systems of units for optical radiation, and Table 2.8 summarizes the radiometric, purely physical quantities used to describe photophysical and photochemical processes. In Chapter 4.5.2, more information is presented on photodissociation, whereby spectral and actinic related quantities are of interest. Actinic radiation (and, hence, related quantities such as actinic flux) is solar radiation that can initiate photochemical reactions. The radiant energy Q denotes the radiation transported by solar light to a surface or emitted from the surface. The radiant power Φ (also termed radiant flux as energy per unit of time) may be the total emission from a source (exitance) or the total landing

54 | 2 Fundamentals of physics in the climate system

Tab. 2.8: Radiometric quantities (note different symbols are used in the literature). Quantity

Symbol

Dimension

Radiant energy Radiant power a Radiant intensity b Radiance c Irradiance d Radiant exitance e

Q Φ = dQ/ dt I = dΦ/ dΩ = ∫ L dΩ L = dΦ/(cos θ dA dΩ) = dI/ dΩ E = dΦ/ dA J = dΦ/ dA

J W (J s−1 ) W sr−1 W m−2 sr−1 W m−2 W m−2

a

Also called radiant flux (dimension: energy/time). Spherical radiant flux (dimension: energy/time ⋅ unit angle). c Radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area; sometimes also confusingly called “intensity” (dimension: energy/time⋅area⋅unit angle). d Radiant flux received by a surface per unit area. e Radiant flux emitted by a surface per unit area. Also called (old) emittance (light emission). b

(irradiance) on a particular surface (dA) of an emitting or reflecting body: Φ=

dQ = ∫ I(Ω) dΩ [J ⋅ s−1 or W] . dt

(2.10)

The radiant power Φ of a light source is given by its total emitted radiation (energy) and contains no information on the spectral or directional distribution of the source output. The radiant intensity I describes the radiant power of a source emitted in a certain direction (into a unit solid angle Ω in a particular direction): I=

dΦ [W ⋅ m−2 or J ⋅ s−1 ⋅ m−2 ] , dΩ

(2.11)

where Ω steradiant (cf. Figure 2.13), defined as a solid angle, is expressed in a dimensionless unit by the symbol sr, called a steradian. The total solid angle (steradiant) Ω of a sphere is given by 4π ⋅ sr, and therefore it follows that 1 sr = Ω/4π. With the area of a sphere (A = 4π ⋅ r2 ), (Ωtotal /1 sr) = A/r2 is valid. For a partial area of a sphere it follows that ∆A = (1 sr/1 sr)r2 = r2 , and thus 1 sr is a solid angle (steradiant) when the partial area is equal to the square of the radius (r2 ). It is important to distinguish between radiation transfer through a plane and a spherical surface. Hence, the spherical radiant flux, denoted radiance L, is described (Figure 2.13) by L=

dΦ dΦ dΦ = = , dA cos θ dΩ cos θ dΩ sin θ cos θ dφ dθ

(2.12)

where θ is the angle between the emitting surface element dA and the direction for which the radiant intensity I is calculated. Hence, dI = L cos θ dA. In eq. (2.12) the area (dA) is given by dA = r sin θ ⋅ r sin φ, and because ds = r2 dΩ, it follows that dΩ = sin θ ⋅ dφ ⋅ dθ (cf. Figure 2.13). The factor cos θ = h/L(θ solar zenith angle)

2.3 Optics of the atmosphere: Radiation |

55

Fig. 2.13: Geometry of irradiation; θ solar zenith angle, Ω solid angle, φ azimuth direction angle.

in eq. (2.12) operates so that the radiation is always regarded as perpendicular to the direction of arrival of light along the line L (Figure 2.13). Irradiance E is the total amount of radiant flux incident upon a point on a surface from all directions above the surface. Radiant exitance J is the total amount of radiant flux leaving a point on a surface in all directions above the surface. The solar constant represents the solar irradiance. The previously discussed radiometric quantities are defined without reference to the wavelength, which is essential for describing photochemical reactions (Chapter 4.5.2). All quantities can be expressed “spectrally,” which simply means that a quantity is measured per wavelength λ per interval (Table 2.9). For example, the spectral radiant power is defined as a radiant power per wavelength interval as a function of wavelength: dΦ = dΦ λ (λ) d λ (dimension: W nm−1 ). The actinic flux is the quantity of light available to molecules at a particular point in the atmosphere and that, on absorption, drives photochemical processes in air. It is calculated by integrating the spectral radiance E(λ, θ, ϕ) over all directions of incidence of the light.¹¹ The radiant flux can also be described by photons – a more usual approach to describing photochemical processes. The photon is the matter symbol of the electro-

11 The actinic flux has had many names (e.g., flux, flux density, beam irradiance, actinic irradiance, integrated intensity), which has caused some confusion. It is important to distinguish the actinic flux from the spectral irradiance, which refers to energy arrival on a flat surface having fixed spatial orientation (J m−2 nm−1 ). The actinic flux does not refer to any specific orientation because molecules are oriented randomly in the atmosphere. This distinction is of practical relevance: the actinic flux (and therefore a j-value) near a brightly reflecting surface (e.g., over snow or above a thick cloud) can be a factor of three higher than that near a nonreflecting surface.

56 | 2 Fundamentals of physics in the climate system

Tab. 2.9: Spectral distribution of extraterrestrial solar radiation; definition according to WMO (1986). Light range

Wavelength (nm)

Radiant flux density (W m−2 )

UV-C light UV-B light UV-A light Total UV light Visible light Infrared light

100–280 280–315 315–400 100–400 400–760 760–106

7.0 16.8 84.1 107.9 610.9 648.2

0.5 1.2 6.2 7.9 44.7 47.4

total

100–106

1367.0

100.0

Percentage of total flux (%)

magnetic wave. Since the velocity of a photon is given by the speed c of light (c = 2.998 ⋅ 108 m s−1 in a vacuum), the speed of light is proportional to the refractive index of the medium and is in the air only slightly less than c. We can therefore describe the energy of a photon by the quantity hν (h is Planck’s constant); frequency ν and wavelength λ are combined by λ = c/ν. 1369

solar irradiance (in W m -2)

1368

1367

1366

1365

1364

1363 1975

1980

1985

1990

1995

2000

2005

2010

year Fig. 2.14: Composite database of solar irradiance compiled from many satellite TSI data 1978–2014 (daily means). I acknowledge the receipt of the data set from PMOD/WRC (Physical Meteorological Observatory and World Radiation Centre in Davos, Switzerland) and acknowledge unpublished data from the Variability IRradiance Gravity Oscillation (VIRGO) Team (e.g., Fröhlich and Lean 1998).

2.3 Optics of the atmosphere: Radiation | 57

Photometric quantities (luminance and derived luminous quantities) are used to describe light in the visible range in relation to the human eye. Luminous flux (Φ v ) is energy per unit of time (dW/ dt) that is radiated from a source over visible wavelengths. More specifically, it is energy radiated over wavelengths sensitive to the human eye, from about 330 to 780 nm (Table 2.9). Thus, luminous flux is a weighted average of the radiant flux in the visible spectrum. It is a weighted average because the human eye does not respond equally to all visible wavelengths. The lumen is the standard unit for the luminous flux of a light source. It is an SI-derived unit based on the candela. It can be defined as the luminous flux Φv emitted into a unit solid angle (1 sr) by an isotropic point source (cf. Figure 2.13) having a luminous intensity (I v ) of 1 cd. The unit lumen (lm) is then equal to cd ⋅ sr. For general purposes, the energy output of the Sun can be considered constant. This, of course is, not entirely accurate. Scientists have shown that the output of the Sun is temporally variable (Figure 2.14). Some researchers have also suggested that the increase in the average global temperature over the last century is a result of solar activity. This statement, however, is difficult to prove because accurate data on solar output of radiation go back only to about 1978. The incoming solar flux (solar constant) is distributed among all wavelengths (cf. Table 2.9) extraterrestrially above the Earth’s atmosphere perpendicular to the source with a mean distance between the Sun and Earth of 1496 ⋅ 108 m. The light range sensible to human eyes lies between 400 and 750 nm (visible light); light < 400 nm is called UV, and light > 750 IR. Only about 30% of the solar energy intercepted at the top of Earth’s atmosphere passes directly through to the surface (cf. Figure 2.15). On the way through the atmosphere, direct solar radiation undergoes scattering, absorption, and reflection on molecules and suspended particles, such as dust particles and cloud droplets (Figure 2.16). The atmosphere reflects and scatters some of the received visible radiation. Gamma rays, X-rays, and UV radiation less than 200 nm in wavelength are selectively absorbed in the upper atmosphere by oxygen and nitrogen and turned into heat energy. Most of the solar UV radiation with a range of wavelengths from 200 to 300 nm is absorbed by ozone (O3 ) and oxygen found in the stratosphere. IR solar radiation with wavelengths greater than 700 nm is partially absorbed by carbon dioxide, ozone, and water present in the atmosphere in liquid and vapor forms (Figure 2.17). Hence, only radiation with wavelengths greater than about 290–300 nm can penetrate into the troposphere initiating photochemical processes there (Chapter 4.5). As discussed in Chapter 3.2.2, Volume 2, this was a precondition for the evolution of life on Earth’s surface. Photochemical reactions only occur with radiation < 750 nm (ozone photolysis into O3 P). Its range of 240–790 nm encompasses the three relevant ozone absorption bands (named after their discoverers, Hartley, Huggins, and Chappuis). Another band, called the Wulf band (near IR > 750 nm), is only of photophysical interest, for instance, for observing ozone from space. The process of scattering is elastic and occurs when small particles and gas molecules diffuse part of the incoming solar radiation in random directions with-

58 | 2 Fundamentals of physics in the climate system

IK/4 | 343 W m-2 ( A 100%)

15

T

20

IRp

6

Rp

30

Ip

30 40

Ie

20

Ic

Rc

35

IRc

4

space

Re

(+ 3)

(+16)

atmosphere

A AB

Dp

15 99 95 114

terrestrial radiation - 19

heat radiation

Dc 8 30

17

SH 4

LH 5

27

earth surface

55

solar transmission

+ 51

solar absorption

- 32

turbulent fluxes

Fig. 2.15: Radiation and heat balance of Earth-atmosphere system. Percentages are given in relation to incoming solar radiation (100% = ̂ 343 W m−2 ). I interception of solar radiation by molecules/ particles (p), clouds (c), and Earth’s surface (e), D diffuse radiation by molecules/particles (p) and clouds (c), R reflexion (albedo) by molecules/particles (p), clouds (c), and Earth’s surface (e), IR infrared dissipation to space by molecules/particles (p) and clouds (c), T terrestrial radiation back to space (without absorption), A absorption of terrestrial radiation by molecules, AB atmospheric back radiation, SH sensible heat, LH latent heat.

out any alteration to the wavelength of the electromagnetic energy, i.e., no energy transformation results. Hence, scattering reduces the amount of incoming radiation reaching Earth’s surface. The sky is bright also from directions from which there is no direct sunlight because of scattering; such light is called diffuse solar radiation (skylight). Scattering occurs on particles when their diameter is similar to or larger than a wavelength (Mie scattering) and on molecules generally much smaller than the wavelength of the light (Rayleigh scattering). The sky has a blue appearance in the daytime because Rayleigh scattering is inversely proportional to the fourth power of wavelength, which means that the shorter wavelength of blue light will scatter more than the longer wavelengths of green and red light. When the Sun is near the horizon, the light travels a greater distance through the atmosphere and red light remains after scattering out of blue light.

2.3 Optics of the atmosphere: Radiation |

59

Fig. 2.16: Solar radiation transfer through Earth’s atmosphere; θ solar zenith angle, h height of atmosphere, L length of radiation beam through atmosphere.

Fig. 2.17: Solar spectrum at top of Earth’s atmosphere (1) and at Earth’s surface (2); absorbing gases are identified.

60 | 2 Fundamentals of physics in the climate system Tab. 2.10: Earth radiation budget as a percentage of incoming solar radiation (100% = 343 W m−2 ). ⇊ input, ⇈ output, IR infrared radiation. Where Top of atmosphere

⇊

⇈

Atmosphere ⇊

⇈

Earth’s surface ⇊

%

Type of radiation / interaction

sum

100

Solar radiation (solar constant)

100

20 6 4

Albedo (clouds) Albedo (particles) Albedo (Earth’s surface)

30

35 20 15

IR from clouds IR from molecules IR from Earth’s surface

70

99 40 30 32

Absorption of terrestrial radiation by molecules Reflexion/scattering of solar radiation by clouds Reflexion/scattering of solar radiation by particles Latent and sensible heat

20 6 25

Albedo (clouds) Albedo (particles) Diffuse radiation (particles and clouds)

35 20 95

IR from clouds IR from molecules Atmospheric back radiation to Earth’s surface

30 17 8

Direct solar radiation Diffuse radiation (clouds) Diffuse radiation (particles)

55

95

Atmospheric back radiation

95

4 ⇈

15 99 5 27

Albedo of solar radiation (transmission to space) Terrestrial radiation (absorption by molecules) Terrestrial radiation (transmission to space) Sensible heat Latent heat

budget ∆ = ±0

201 ∆ = ±0 51

150

4

∆ = ±0

146

Absorption is defined as a process by which solar radiation is retained by a substance and converted into heat energy or, in other words, into inner energy (rotation, vibration, and translation) but also into dissociation (photolysis, Chapter 4.5.2). The absorbed light will finally be emitted as long-wave radiation (dissipated heat). The wave is spherical, or, in other words, the emission is uniform in all directions. Reflection is the third process of altering direct solar radiation through the atmosphere where sunlight is redirected 180° after it strikes very large particles (cloud droplets, liquid and frozen) and Earth’s surface. The angle of incidence equals the angle of reflection. This redirection causes a 100% loss of insolation. Sunlight reaching Earth’s surface unmodified by any of the aforementioned atmospheric processes is called direct solar radiation. Roughly, 30% of the Sun’s visible radiation (wavelengths from

2.3 Optics of the atmosphere: Radiation |

61

400 to 700 nm) is reflected back to space by the atmosphere or Earth’s surface (cf. Table 2.10). The reflectivity of Earth or any body is referred to as its albedo, defined as the ratio of light reflected to the light received from a source, expressed as a number between zero (total absorption) and one (total reflectance) (Figure 2.15). The reflectivity or albedo of Earth’s surface varies with the type of material that covers it. For example, some surface-type reflectivities are – clouds, 40 to 90% – fresh snow, up to 95% – dry sand, 35 to 45% – broadleaf deciduous forest, 5 to 10% – coniferous forest, 10 to 20% – grass -type vegetation, 15 to 25% Therefore, and due to global averaging (IK /4), only 240 W m−2 reaches Earth’s surface, varying with time and site (further reading: Lenoble 1985, Liou 1992, Thomas and Stamnes 1999, Wendisch and Yang 2012).

2.3.2 Absorption and emission of light Thermal equilibrium means that a body (molecule, particle, surface) receives from its environment as much energy as it emits. The higher the temperature of the body, the higher is the radiant flux density of emitted (thermal) radiation. The percentage of absorbed radiation, called absorptivity (or absorbance), is given as degree ε, thus the reflectivity is 1 − ε (note absorbance = emissivity). complementary to the reflectivity (1−ε). For each temperature, the emitted radiation is linear to the absorption degree to obtain the thermal equilibrium. In other words, the more a surface absorbs, the more it emits. This is valid for each frequency. A black surface is defined by ε = 1. With this, the radiant exitance (J) of all surfaces can be related to that of black bodies/surfaces (Jb ): J(λ) = ε(λ)J b (λ) . (2.13) This is called Kirchhoff ’s law. Hence, a body that does not absorb the radiation of a given wavelength cannot emit at this wavelength either. The emissivity of Earth’s atmosphere varies according to cloud cover and the concentration of gases that absorb and emit energy in the thermal IR (i.e., wavelengths around 8 to 14 μm). These gases are often called GHGs, from their role in the so-called greenhouse effect. The main naturally occurring GHGs are water vapor, carbon dioxide, methane, and ozone. The human problem lies in an increase of the latter gases in the troposphere. The major constituents of the atmosphere, N2 and O2 , do not absorb or emit in the thermal IR.

62 | 2 Fundamentals of physics in the climate system

Thus, the Earth obtains energy from solar radiation and loses it (to maintain a thermal equilibrium) by reflection, emission, and terrestrial radiation; the temperature of the Earth’s surface and atmosphere thus corresponds to the thermal budget. 2.3.2.1 Absorption (Lambert–Beer law) Due to the interaction of solar radiation with molecules and particles of the atmosphere, the radiant flux decreases with the path x through the atmosphere (Figure 2.13). Johann Heinrich Lambert (1718–1777) showed in 1760¹² that the reduction of light intensity is proportional to the length of path x (or layer thickness) and the light (radiant flux) itself, ∆Φ = x ⋅ Φ, from which we derive the equation dΦ = −m󸀠 ⋅ Φ , dx

(2.14)

where m󸀠 is the extinction module. The minus sign denotes that the radiation decreases. Now, expressing the path x by the solar zenith angle θ, we obtain x = h ⋅ sec θ and, finally, Φ = Φ0 exp (−m ⋅ sec θ) , (2.15) where m = m󸀠 ⋅ h. For θ > 60°, eq. (2.15) must be corrected due to the curvature of the Earth. August Beer (1825–1863) found in 1848 that the extinction of light further depends on the concentration of substances in an irradiated medium, i.e., m = κ ⋅ c, where κ is the extinction coefficient (fraction of light lost due to scattering and absorption per unit distance in a participating medium). The extinction coefficient, depending on wavelength, is further separated into coefficients for absorption and scattering gas particle gas particle for molecules as well as particles: κ = κ abs + κ abs + κ scat + κ scat . Combining Lambert’s and Beer’s relationships, we obtain the Lambert–Beer law: Φ = Φ0 exp (−κ ⋅ c ⋅ sec θ) .

(2.16)

The amount of light absorbed by a substance, depending on the wavelength, can be calculated according to Φabs (λ) = Φ(λ)σ(λ) ⋅ c . (2.17) The absorption cross section σ, depending on wavelength and temperature and specific to each substance, characterizes the effective area of a molecule for scavenging a photon. Equation (2.17) is used to calculate the photolysis rate (Chapter 4.5.2). Between 0.3–0.7 μm (visible range) and 8–12 μm, with the exception of ozone bands, there is virtually no absorption in the atmosphere, so these ranges are called atmospheric windows; solar and terrestrial radiation can penetrate the atmosphere unopposed. Between 1–8 μm H2 O (2.5–3.5 μm and 4.5–7.5 μm) and CO2 (2.2–3.5 μm and

12 Photometria, siva, De mensura et gradibus luminis colorum et umbrae (Photometry, or, On the Measure and Gradations of Light, Colors, and Shade), Augsburg 1760

2.3 Optics of the atmosphere: Radiation | 63

4–4.5 μm as well as 15–20 μm) absorb terrestrial radiation partially, and at > 15 μm nearly completely. 2.3.2.2 Emission (Planck’s law and Stefan-Boltzmann law) Max Planck (1858–1947) first found in 1900 that none of the known thermodynamic and electrodynamic laws could explain the spectrum of black body radiation; thus, he proposed quantum theory. This suggests that energy in a radiation field is not exchanged continuously but only as integer multiples of the so-called energy quantum hν (now often termed Planck’s quantum). Planck’s law gives the intensity radiated by a black body as a function of frequency (or wavelength) (Figure 2.18), here written as the specific emission per area dA and frequency dν or wavelength dλ (note that in some formulas instead of 2h it is written 8πh, which is related to the whole spherical emission): J(ν, T) d A dν =

ν2 2hν dA dν , c2 exp ( hν ) − 1

(2.18a)

1 2hc2 dA dλ . λ5 exp ( hν ) − 1 kT

(2.18b)

kT

J(λ, T) d A dλ =

Note that λ = c/ν and dν = (c/λ2 ) dλ, c is the speed of light, and k is the Boltzmann constant. A simplification was formerly known for large frequencies (hν ≫ kT) as Wien’s law: 2hν3 hν exp (− ) dA dν , 2 kT c hν 2hc2 J(λ, T) d A dλ ≈ 5 exp (− ) dA dλ . kT λ J(ν, T) d A dν ≈

(2.19a) (2.19b)

The Planck curves for different T proceed such that those for lower T always lie below the curves for higher T – in other words, the curves never intersect. The radiation maximum displaces with increasing T to shorter wavelengths (Wien’s displacement law). From eq. (2.19) with dI/ dν = 0 Wien’s displacement law can finally be derived (using an approximate solution because only a numerical solution is possible), the statement that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature: νmax =

2.82 kT = 5.88 ⋅ 1010 T h

or expressed in wavelength

λmax =

b , T

(2.20)

where b is Wien’s displacement constant (b = 2.898 ⋅ 106 nm ⋅ K). The total energy emitted from a black body corresponds to the area below the Planck curve ∞

Jtotal = ∫ J(ν, T) d ν , 0

(2.21)

emission

64 | 2 Fundamentals of physics in the climate system

2000°C 1750°C 1500°C 1250°C 1000°C

0

1

2

3

4

5

6

7

wavelength (in μm) Fig. 2.18: Planck curves showing spectral radiation distribution of black bodies for different temperatures (in K).

from which the Stefan–Boltzmann law is derived: J total =

2π5 k4 4 T = σT 4 15 c2 h

(2.22)

where σ = 5.67 ⋅ 10−8 W ⋅ m−2 ⋅ K−4 (Stefan–Boltzmann constant). This means that the total emitted black body radiation only depends on its temperature (of the fourth power). According to Kirchhoff ’s law (eq. (2.13)), the emission of a body for a given T and λ is in a definite ratio to its absorptivity, where this ratio is independent of the material of the body and identical with the black body radiation. Therefore, the emission can also be calculated for nonblack bodies (with ε(λ) < 1) using Planck’s law. The emission for very low frequencies (large wavelength), or in other words for a body that emits to the far left of the radiation maximum (hν ≪ kT), can be calculated using the socalled Rayleigh–Jeans approximation with exp(hν/kT) ≈ 1 + hν/kT in application to eq. (2.18): 2ν2 2c J(ν, T) d ν = 2 kT dν and J(λ, T) d λ = 4 kT dλ . (2.23) λ c

2.3 Optics of the atmosphere: Radiation | 65

The specific emission at temperature T is the same as for a black body according to Kirchhoff’s law at temperature T 󸀠 : J = β ⋅ T = ε ⋅ Tblack = β ⋅ T 󸀠 ,

and it follows that

T = ε ⋅ T󸀠 ,

(2.24)

where β summarizes 2ν2 k/c2 or 2ck/λ4 . With this, the temperature of the (cold) emitting nonblack body is by a factor ε (absorption degree) smaller than the temperature of the comparable black body. Analogously, it follows for hot emitters (hν ≫ kT) from eq. (2.19) that the true temperature T is higher than the black body temperature T 󸀠 , 1 k 1 − 󸀠 = ln ε , T T hν

(2.25)

where for ε = 1 it follows that T = T 󸀠 .

2.3.3 Terrestrial radiation and radiation budget As already mentioned, 30% of incoming solar radiation is reflected back into space (without changing the wavelength, almost all in the visible range), mostly by clouds, which contribute 2/3 to this percentage (Table 2.10 and Figure 2.15). Hence, clouds play a dominant role in regulating climate, i.e., the temperature of the atmosphere. Several parameters, such as coverage, depth, liquid water content, and cloud droplet size, make up so-called cloud climatology. These are important quantities considered in the radiation budget but are difficult to monitor or to model. Therefore, climate models contain a large uncertainty in this regard. Of the remaining 70% of solar radiation (corresponding to 240 W m−2 ), however, less than half (30%) actually reaches Earth’s surface directly. The remaining 40% is scattered by clouds and particles in the atmosphere, from which a part of the diffuse radiation (25%) transmits to Earth’s surface. The total of direct solar radiation and diffuse sky radiation received by a unit horizontal surface is termed global radiation. Naturally, the radiation budget at the borders of the atmosphere (in the upper reaches and at Earth’s surface) is balanced, i.e., ±0 (Table 2.10 and Figure 2.15); all percentages are climatological means and based on the incoming solar radiation at the top of the atmosphere. Insofar as the energy fluxes of irradiation and emission are equal, it results in a certain temperature according to Planck’s law. The temperature remains constant if the fluxes do not change. Otherwise, T may increase (flux > 150%) or decrease (flux < 150%). A valid equation (a = mean global albedo) is J+ =

IK IK 4 = J − = σTearth +a 4 4

and

4 σTearth = (1 − a)

IK . 4

(2.26)

With an albedo of 0% and a radiation flux of 343 W m−2 , an equilibrium temperature of 6 °C results, almost unrealistically. When a = 30% and then 240 W m−2 , Tearth = −18 °C results. This is exactly the global mean temperature at an altitude of around

66 | 2 Fundamentals of physics in the climate system

5000 m or 550 hPa. This quantity is termed the effective radiation temperature of Earth (255 K or −18 °C). It is worth noting here that in these cases no life would exist on Earth. Fortunately, the global mean temperature close to Earth’s surface (at an altitude of 1 m) is about 15 °C (280 K), i.e., 33 K higher than the effective radiation temperature. This natural effect is due to the absorbance of some trace gases (H2 O, CO2 , CH4 , N2 O, and others, now known as GHGs) in the atmosphere that absorb IR terrestrial radiation and emit the energy in a more IR range (remember: in all directions and, thus, partly back to Earth’s surface), termed atmospheric back radiation. The anthropogenic effect lies in increasing the atmospheric concentration of these GHGs owing to various activities (Volume 2). This effect is termed the greenhouse effect, but it does not correspond to the effects in a greenhouse, only to the impact of warming (for different physical reasons). The shortwave radiation budget of Earth’s surface amounts to 51% (Table 2.10 and Figure 2.15), i.e., +0.51 ⋅ IK /4 = ̂ 175 W m−2 (solar absorption). This energy is transformed into terrestrial radiation (budget −19%) and turbulent fluxes of latent and sensible heat (−32%). The latter energy in the form of turbulent fluxes (110 W m−2 ) is then transferred through cloud processing and finally dissipated as IR radiation back to space (35% corresponding to 120 W m−2 ). The difference of −3% (10 W m−2 ) is balanced by the positive budget of shortwave solar radiation, i.e., +3% is the net absorbance of clouds, resulting in atmospheric heating. More net absorbance, however, results from the absorption of solar radiation through molecules and particles (+16% = ̂ 55 W m−2 ). The energy budget of the two groups of interactors (molecules/ particles and clouds) with radiation, both shortwave as well as longwave, is naturally zero: ±72% for clouds and ±129% for molecules/particles, respectively. In the terrestrial radiation (budget −19%) at Earth’s surface, one must consider a split between the absorption of terrestrial radiation by molecules (99%) and so-called atmospheric back radiation (95%), while 20% radiates back into space. The budget (−4%) must be added to the transmission of the 15% of terrestrial radiation that can pass through the atmosphere without absorption (through the atmospheric windows) to space. This back radiation is the reason why Earth’s surface has a higher temperature than would be expected from the effective radiation temperature, as mentioned earlier. A part of the solar transmission absorbed by Earth’s surface transfers into heat, a different form of energy compared with thermal radiation. Latent heat transport occurs through water. Water (surface water and soil humidity) evaporates by taking up the enthalpy needed for evaporation. Consequently, Earth’s surface cools down. Through vertical turbulent transport of water vapor, it finally condenses into clouds while releasing the heat back to the atmosphere. The latent heat transport goes through heated air due to a temperature gradient from the surface to higher altitudes. To balance the ascending heated air (consequently there is a density gradient), at another site cooler air sinks down. This turbulent heat (32%) finally – together with the 3% of shortwave radiation stored in clouds – dissipates as far-IR back to space (35%). In contrast to the global mean values used in discussing the energy budget of Earth’s atmosphere, the “true” geographic budgets are different (because of the dif-

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ferent characteristics of Earth’s surface and the solar zenith angle) and depend on the time of day and season as well. It is logical to mention that these differences drive the weather on Earth. What follows are some typical annual means of global radiation: – 168 W m−2 global mean – 130 W m−2 Central Europe – 200 W m−2 Spain – 280 W m−2 Sahara

2.4 Atmospheric dynamics In physics, mechanics is concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The bodies in air are gaseous (molecules), liquid (droplets), and solid (particles). In atmospheric physics, specifically meteorology, however, this science is known as atmospheric dynamics. Even more specifically, it is fluid dynamics, studying flows, where the mathematical equations are identical for gases and liquids. Mechanics is based on three axioms by Isaac Newton (1643–1727): 1. Inertia principle (law of inertia): Any mass point remains in a state of rest or rectilinear uniform motion until this state is terminated by the action of other forces (i.e., by the transfer of forces). This is a special case of the second axiom, that is, mv = constant if f = 0. 2. Action principle (fundamental equation of dynamics): When one body with mass m exerts a force f , the body is accelerated at rate a = f/m (the inertia principle is a special case of the action principle with f = 0). 3. Reaction principle (interaction law): When one body exerts a force f on a second body, the second body simultaneously exerts a force –f equal in magnitude and opposite in direction on the first body. Newton used these to explain and investigate the motion of many physical objects and systems. Note that two or more vectors can be added together to determine the resultant vector. Newton showed that the momentum mv changes when a force f is exerted on a body so that d(mv)/ dt = f . Newton’s equations follow, describing the motion of bodies: (

d v⃗ 1 ) = ⋅f dt m m

and

(

1 dm ) = ⋅f dt v⃗ v⃗

and

d (m v)⃗ = ∑ f i = ma , dt i

(2.27)

where m is mass, t is time, v⃗ is velocity (as a vector), a is acceleration, and f is force. The last equation of motion (m v⃗ is momentum) characterizes a fluid atmosphere (force = mass⋅acceleration = power/velocity and work = power⋅distance). Force is the change in energy over some distance (1 J m−1 = 1 N = 1 kg m s−2 ). Energy is the capacity to do work (or produce heat); there are different kinds of energy: energy ≡ heat ≡ radiation ≡ work (1 J = 1 N m = 1 kg m2 s−2 ). Heat is the transfer of thermal energy from one

68 | 2 Fundamentals of physics in the climate system object to another. Power is the rate of energy change (1 J s−1 = 1 W = 1 kg m2 s−3 ). −2 Climate forcing is expressed by the energy flux (1 W m−2 = 1 J s−1 m ). The rate R is a ratio between two measurements, normally per unit of time: R = ∆ε/∆t. However, a rate of change can be specified per unit of length (∆l) or mass (∆m) or another quantity, for example ∆ε/∆x, where ∆x is the displacement (the shortest direct distance between any two points). In chemistry and physics, the word “rate” is often replaced by (or synonymously used with) speed (see subsequent discussion on the difference with velocity) and can be the distance covered per unit of time (i.e., acceleration, the rate of change in speed) or the change in speed per unit of time (i.e., reaction rate, the speed at which chemical reactions occur (Chapter 4.2.3). In physics, velocity v⃗ is the rate of change in position. This is a vector physical quantity, and both speed and direction are required to define it. The scalar absolute value (magnitude) of velocity is speed. The average velocity v⃗ of an object moving through a displacement (∆x) during a time interval (∆t) is described by v = ∆x/∆t. A flux F is defined as the amount of a quantity that flows through a unit area per unit of time: F = ∆ε/A∆t (A area). Flux in this definition is a vector. However, in general “flux” in Earth system research relates to the movement of a substance between compartments. This looser usage is equivalent to a rate (change of mass per time); sometimes, the term specific rate is used in the more exact sense of time- and arearelated flux. Generally, the terms “rate” and “flux” as well as “velocity” and “speed” are often not distinguished in the literature in such an exact physical sense but are used synonymously. The gradient of a scalar field ε (e.g., air temperature, wind speed, density) is a vector field (whose components are the partial derivatives of ε) that points in the direction of the greatest rate of increase of the scalar field and whose magnitude is the greatest rate of change. The gradient (or gradient vector field) of a scalar function ⃗ where ∇⃗ (the nabla symbol¹³) denotes the vector ε(x1 , x2 , . . . , x n ) is denoted by ∇ε, differential operator (del). The notation grad (ε) is also used for gradient. That is, ⃗ = ( ∂ε , . . . , ∂ε ) ≡ grad ε . ∇ε ∂x1 ∂x n

2.4.1 Fluid characteristics 2.4.1.1 Effective atmospheric forces In the atmosphere, the action principle is very important, conveying information on timely changes of a motion quantity, the momentum mv, and acceleration a: d (m v)⃗ = ∑ f i = ma dt i

or

a=

dv 1 = ∑ fi . dt m i

13 In English also called “del”: ∇⃗ or simple ∇. Note ∇p = grad p and ∇ v⃗ = div v.⃗

(2.27)

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With this, the motion equation of a fluid atmosphere, more exactly an air parcel, is given. With constant mass, it follows the timely change of wind speed v if the force f is known. For each air parcel (partial volume), Newton’s eqs. (2.27) are valid. Acceleration is equal to the sum of exerting forces divided by the mass of the air parcel. The following primary forces must be considered: – pressure gradient force fp (results from high- and low-pressure systems in the atmosphere; air will tend to move from high pressure to low pressure), – friction ff (drag exerted on air by Earth’s surface), – gravitational force fg (keeps molecules in atmosphere from moving into space), – Coriolis force (force resulting from Earth’s rotation) and – centrifugal force (tendency for a body to resist a change in direction). The attraction of the Earth’s mass (gravitation) for all bodies near its surface is always directed to the Earth’s center and must therefore be formulated as a vector quantity, 1 (2.28) fg ≡ g = 0 ⋅ i + 0 ⋅ j + (−g)k , m where g is the standard gravity. However, the centrifugal force pulls all bodies outward from the axis of planetary rotation; the effective gravity is therefore the vector sum of these two forces. Bodies (molecules and particles) in air acquire acceleration due to the pressure gradient force fp directed in opposition to the pressure gradient (note density ρ = m/V): 1 1 dfp = − grad p dV and fp = − grad p , (2.29) m ρ where the power density of the pressure force is defined as dfp / dV = − grad p ≡ −∇p. Friction transforms kinetic energy (ordered motion) into heat (disorderly movement). Frictional forces appear in air between aerosol particles and surrounding molecules, between Earth’s surface and air flowing over it, and with wind shears. Slower air parcels will accelerate due to faster air parcels that will be slowed down. Consequently, a momentum flows. A distinction is made between Stokes friction (viscous friction) and Newton friction wherein viscous friction is negligible compared with inertia effects. The Stokes law gives the force of viscosity on a small sphere (particle) moving through a viscous fluid: ff = 6πηrv ≡ ma = m

dv , dt

(2.30)

where η is the dynamic viscosity (dimension: mass/time ⋅ distance), r the radius of the particles, v the speed of the particles, m the mass of particles, and a the particle acceleration within time interval dt. Internal friction between two moving small air layers having area A results in a gradient of velocity v in the z direction (vertical to the flow), described also by (viscose) shear stress τ: ff = ηA

∂v ∂z

and

τ=η

∂v ff = . ∂z A

(2.31)

70 | 2 Fundamentals of physics in the climate system

The differential quotient ∂v/∂z describes a shear rate. The dimension of shear stress also produces a momentum flux density: [τ] = [momentum]/(m2 s). Hence, from Newton’s equation, after insertion of the different relationships for the forces and acceleration, follows the Navier–Stokes equation (cf. eq. (2.45) concerns vectorial components such as the velocity) a=

dv ∂v 1 1 ⃗ = − ∇p + ff + g − 2ωv . = + v∇v dt ∂t ρ m

(2.32)

All terms on the right-hand side of this equation denote acceleration terms: acceleration by the pressure gradient, acceleration by the friction force, acceleration by gravity, and acceleration by the Coriolis force. It must be noted that Newton’s laws are valid only for a coordinate system fixed in space (inertial motion), not for motions in our atmosphere since Earth is moving underneath. To use Newton’s laws in the atmosphere, even with a rotating frame of reference, we need two apparent forces (also termed inertial forces), centrifugal force and the Coriolis force. Once air is set in motion by the pressure gradient force, it undergoes an apparent deflection from its path, as seen by an observer on Earth. This apparent deflection is termed the Coriolis force and is a result of Earth’s rotation. As air moves from high to low pressure in the Northern Hemisphere, the Coriolis force deflects it to the right. In the Southern Hemisphere, the Coriolis force deflects air moving from high to low pressure to the left. The centrifugal force is directed away from the axis of rotation that appears to act on all objects when viewed in a rotating frame of reference. Both forces are important for an understanding of global circulation processes. 2.4.1.2 Atmospheric flow: Laminar and turbulent When visualizating a three-dimensional moving air mass, each air parcel should produce a short line characterized by its length and direction the current flow or wind speed v. The total flow is described by the sum of all these vectors, the vector field v(s, t) with the rectangular coordinates u, v, and w in space field s (eq. (2.42)). The velocity vectors v, at an adequate point’s visualization, combine to streamlines (trajectories). Setting a frame with area A perpendicular to the flow direction, an air volume Av dt having mass ρAv dt passes the frame (with an equal wind velocity assumed). The flux through the area is (dimension: mass per unit of time) F = ρvA .

(2.33)

The vector F/A = ρv denotes the flux density or specific flux (dimension: mass per units of area and time). This flux equation is valid also for all other transportable quantities such as heat and momentum. The mass balance of an air parcel with volume dV = dx dy dz flowing in the x direction is given by sources (influx) and sinks

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(outflux) as partial fluxes: dF+ = ρu(x) dy dz

and

dF− = ρu(x + dx) dy dz = ρ (u +

∂u dx) dy dz . ∂x

(2.34)

The difference between input and output (flux balance) is equal to dF = ρ (

∂u ∂v ∂w + + ) dV ∂x ∂y ∂z

or

dF = ρ ⋅ div v ⋅ dV ,

resp.,

(2.35)

where the term in parentheses, which is crucial for all vector fields, is called the divergence¹⁴ v(s). A flux that is described by its internal friction is termed laminar flux, and eq. (2.31) applies. Thus, one air layer floats on top of another without mixing, i.e., the air parcels not overflow from one layer into another. Only air molecules move due to thermal motion (molecular diffusion) in the direction of a negative concentration gradient or, if there is no such gradient, equally in all directions. By contrast, in turbulent motion, a continuous exchange of air parcels occurs in all directions with nonstationary arbitrary motion. This turbulent diffusion is orders of magnitude more effective than molecular diffusion. Turbulence transfers (or transports) concern all characteristic properties of an air parcel. In the atmosphere there exists only a very small (a few millimeters) laminar boundary layer (not to be confused with the planetary boundary layer, or PBL) directly at the Earth’s surface, also called a molecular viscous layer. In this layer, there exists a linear gradient of flux rate to the surface; at the surface, the velocity becomes zero. This laminar layer limits heat and matter exchange (e.g., between a leaf and the circumambient air) due to the much lower molecular diffusion compared with turbulent exchange. Each air parcel (partial volume) follows Newton’s equations (eq. (2.27)), and the acceleration is described by eq. (2.32). If the sum of all impacting forces becomes zero, equilibrium occurs and there is no more acceleration. Neglecting the apparent forces, from eq. (2.32), using eq. (2.31) for the frictional force, where ∂v/∂z = ∆v/l2 was simplified, it follows that 1 ρa = − grad p + 2 η∆v . (2.36) l The arithmetic product ρa [mass ⋅ acceleration ⋅ volume−1 ] denotes the density of inertial force [force ⋅ volume−1 ]; eq. (2.36) is a relationship between the inertial, pressure, and frictional force density. Neglecting the inertial force (ρa = 0, it follows that grad p = η∆v/l2 ), the flow transfers to laminar motion. Furthermore, neglecting friction (grad p ≫ η∆v/l2 ) the ideal flow follows. A change in velocity (acceleration) occurs at distance l within time t, and t ≈ l/v, follows; hence, a ≈ v2 /l. We assume that

14 Divergence (div) is the flux density, the amount of flux entering or leaving a point [flux/volume]: 3 1 2 div = ∂ϵ + ∂ϵ + ∂ϵ . ∂x ∂y ∂z

72 | 2 Fundamentals of physics in the climate system

the pressure gradient proceeds at the same distance l, so eq. (2.36) may be rewritten in the form v2 p v (2.37) ρ =− +η 2 . l l l As a criterion for the flow characteristic, the Reynolds number Re is defined: 2

ρv ρvl inertial force Re = = vl = , frictional force η l 2 η

(2.38)

where the critical Reynolds number Rec denotes the transfer between laminar and turbulent motion (for air, typically Rec = 1400): – Re < Rec laminar flow, – Re > Rec turbulent flow. For atmospheric particles and droplets, Re is similarly defined: Re =

vr , η

(2.39)

where r is the particle radius and v the particle velocity. Atmospheric particles with r < 10 μm have Re < 1. The movement of these particles can be described without the inertial term and is called Stokes flow: grad p = η∆v/l2 . Turbulent flow exerts on spherical bodies a drag force, which is by definition the force component in the direction of the flow velocity, 1 (2.40) f = cD ρAv2 , 2 where cD is the drag coefficient, A the particle cross section, and v the air (wind) velocity. With a change from laminar into turbulent flow, the flow resistance increases substantially due to the formation of eddies; see also eq. (2.42) for turbulent transport. In the atmosphere, transport is always turbulent with the exception of a small laminar layer near the surface. Thermal and dynamic processes generate turbulence. The magnitude of turbulence increases with wind velocity, roughness of the surface, and vertical negative T gradient (thermal stratification). In contrast to molecular diffusion, the turbulent diffusion coefficient is not a physical constant. The theory of turbulence remains incomplete¹⁵. Besides the transport of mass, convective heat transfer (heat transfer by radiation was dealt with in Chapter 2.3.1.2) is another phenomenon of turbulence. Flow is

15 “Turbulence is probably the most important and yet least understood problem in classical physics” wrote Tom Mullin in “Turbulent Times For Fluids” (New Science, 11 Nov 1989) and cited the British mathematician and physicist, Horace Lamb (1849–1934), who said on a meeting of the British Association for the Advancement of Science in 1932: “I am an old man now, and when I die and go to Heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am really rather optimistic.”

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induced by local T differences and thereby differences in density. Analogously to Newton’s equation, heat flux FQ is given by (using the equation of diffusion, eq. (2.87)) FQ = −k Q

dT , dz

(2.41)

where k Q is the molecular heat conduction coefficient. 2.4.1.3 Fluid characteristics: Wind speed and direction The velocity of moving air, more exactly of an air parcel, is the wind velocity. It is not the velocity of molecules and particles contained in the air. Wind is another term for flow. The wind velocity v⃗ is a vector given by a norm (wind speed) and a direction in space (wind direction).¹⁶ An air parcel is a volume large enough to allow a statistically macroscopic consideration of the gas; this can even be given for a small volume of about 1 mm in diameter. In the Cartesian (rectangular) coordinate system (in an atmosphere where the direction of the x-axis is east, the y-axis north, and the z-axis upward), the wind velocity is divided into three directions, u, v, and w: v⃗ = u ⋅ i ⃗ + v ⋅ j ⃗ + w ⋅ k⃗ ,

(2.42)

where i,⃗ j,⃗ and k⃗ are the unit vectors in the x-, y-, and z-directions. The wind speed (absolute value of velocity) follows from 󵄨󵄨 ⃗ 󵄨󵄨 √ 2 󵄨󵄨v󵄨󵄨 = u + v2 + w2

or

󵄨󵄨 ⃗ 󵄨󵄨 √ 2 󵄨󵄨v󵄨󵄨 = v x + v2y + v2z .

(2.43)

Because of the time-dependent wind velocity, the wind vector is described by a compli⃗ y, z, t) with the components u(x, y, z, t), v(x, y, z, t), cated four-dimensional field v(x, and w(x, y, z, t). The vertical component is much smaller (by a factor of 103 to 104 ) than the horizontal components, and the typical wind speed at 1 km altitude is 10 m s−1 . Velocity describes the motion of an air parcel, i.e., the distance l ⃗ that is traveled in time dt: d l ⃗ dx ⃗ dy ⃗ dz ⃗ k. (2.44) = i+ j+ v⃗ = dt dt dt dt This means that dx/ dt = u, dy/ dt = v, and dz/ dt = w are the directional components of wind velocity and that any property ε of this air parcel can be described as dε ∂ε ∂ε ∂ε ∂ε ∂ε ⃗ . = +u +v +w = + v⃗ ⋅ ∇ε dt ∂t ∂x ∂y ∂z ∂t

(2.45)

16 In physics, velocity is the rate of change of displacement (position). It is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is speed. However, in colloquial language, “velocity” and “speed” are sometimes used interchangeably. In meteorology, wind speed is always denoted by the symbol u, which is identical to flow ⃗ velocity v (but not the vector v or v).

74 | 2 Fundamentals of physics in the climate system

This is the total derivative of ε over time, where the partial derivatives were included. The quantity changed (e.g., velocity, density, or momentum) is expressed through a mean value (convective transport) and a jitter (turbulent transport): ε(t) = ε(tR , ∆t) + ε󸀠 (t) .

(2.46)

Turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes as a self-organizing process; information entropy serves as a criterion for the degree of its self-organization. The degree of turbulence (Tu) in a fluid characterizes the ratio between the velocity jitter and averaged speed u; it is a parameter for transition from laminar to turbulent flow. Tu =

√ 13 (u 2 + v2 + w2 ) u

.

(2.47)

The change along a particle path, i.e., the trajectory of the air parcel, is termed Lagrangian. By contrast, the Eulerian approach considers changes at a given site or fixed volume element, i.e., local changes in ∂ε/∂t. The transport of mass and convective heat is a phenomenon of turbulence. Flows are triggered through local temperature differences and thereby density differences. Near the Earth’s surface, the logarithmic wind law holds: u∗ z u= ln , (2.48) κ z0 where u ∗ = √τ/ρ is the friction velocity¹⁷ (also called shear-stress velocity) and z0 the roughness. Equation (2.45) can be rewritten in terms of a general balance equation: dε = −v∇ε − ∇v󸀠 ε󸀠 + Q . dt

(2.49)

This equation says that a mean local change in quantity ε is due to the advection of ε by the mean wind speed, by the divergence of turbulent flux densities of ε, and by existing source terms Q. The first term on the right-hand side is called the inertial term. Despite the dominant turbulent transport in the atmosphere, it is necessary to know the molecular fundamentals of motion, kinetic energy, and molecular diffusion for an understanding of chemical processes (Chapter 4.2) and in particular the processes of particle growth and mass transfer (Chapter 3.6).

17 This expressions follows from eq. (2.27), where only velocity in the z-direction (vertical to the flow), with dz = l, is considered (dv/ dt) = ff /m = v2 /l, and eq. (2.31) after rearrangement follows (dv/ dt) = v2 /l = τ/ρ ⋅ l; τ is the shear stress.

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2.5 Properties of gases: The ideal gas Without a doubt, one of the most important models in physical chemistry is that of an ideal gas, assuming the gas to be the congregation of particles existing in omnidirectional stochastic motion.

2.5.1 Gas laws The gas laws developed by Robert Boyle (1627–1691), Jacques Charles (1746–1823), and Joseph Gay-Lussac (1778–1850) are based upon empirical observations and describe the behavior of a gas in macroscopic terms, that is, in terms of properties that a person can directly observe and experience. The kinetic theory of gases describes the behavior of molecules in a gas based on the mechanical movements of single molecules. A gas is defined as a collection of small particles (atom- and molecule-sized) with mass m i (subscript i denotes a defined substance): – occupying no volume (that is, they are points), – where collisions between molecules are perfectly elastic (that is, no energy is gained or lost during collisions), – having no attractive or repulsive forces between the molecules, – traveling in straight-line motion independently of each other and not favoring any direction and – obeying Newton’s laws. While colliding the particles exchange energy and momentum. Collisions lead macroscopically to the viscosity of a gas and diffusion of molecules. Considering only the translation of particles (the aim of the kinetic theory of gases), there is no need for a quantum mechanical description. However, when describing rotation and vibration in molecules (the other parts of internal energy), quantum mechanics is essential. The size and speed of molecules with a mass mm can be different. Therefore, gas is considered macroscopic by averaging individual quantities. The molecule number density cN is defined as the ratio between the number of gas molecules N and the gas volume V, cN = N/V (we will later see that cN in pure ideal gases denotes the Loschmidt constant n0 ). Please note that in the scientific literature, the number density is normally denoted by n, but here such notation would be confused with the number of moles n. Let us now consider the motion of a molecule in the x-direction onto a virtual wall. Because of the three spatial directions and each positive and negative direction, the particle density in each direction amounts to cN /6. For these molecules v = v x is valid because the speed in all other directions (y, z) is zero (by convention they only move in the x-direction). In time dt a molecule travels distance v dt. At a wall with area A, a total of cN qv d t/6 molecules collide. Therefore, each molecule transfers momentum 2mm v because of the action-reaction principle (to and from the wall). All collisions,

76 | 2 Fundamentals of physics in the climate system

given by the collision number z (the collision frequency or rate is z/ dt), transfer in a given time period dt a momentum that generates the force f according to eq. (2.27): f =

z ⋅ 2mm v cN 1 = Av ⋅ 2mm v = cN A ⋅ mm v2 . dt 6 3

(2.50)

For pressure p (force/area) this results in p=

1 f = cN ⋅ mm v2 . A 3

(2.51)

With the definition of gas density ρ as a product of particle density cN and molecular mass mm , the fundamental equation of the kinetic theory of gases follows: p=

1 2 ρv . 3

(2.52)

Expressing gas density ρ as the ratio between total mass m (m = Nmm ) and gas volume V the Boyle–Mariotte law then follows. pV represents the quantity of energy, or more specifically the pressure-volume work of this gaseous system: pV =

1 m ⋅ v2 = constant . 3

(2.53)

Empirically, it was found that (T is the absolute temperature) pV = constant . T

(2.54)

This is the combined gas law that combines Charles’s law (V = constant ⋅ T, where cN , p = constant), Boyle’s law (pV = constant, where cN , T = constant), and Gay-Lussac’s law (p/T = constant, where m, V = constant). Avogadro’s law expresses that the ratio of a given gas volume to the amount of gas molecules within that volume is constant (where T, p = constant): V = constant . (2.55) cN Combining eqs. (2.54) and (2.55) leads to the ideal gas law, where R is the universal gas constant. We will express the amount of gas molecules by the number of moles n = m/M (M molar mass): pV = nRT . (2.56) Now we can derive an expression for the work W done by the gas volume (that is equivalent to the kinetic energy). Using the definitions f = dW/ dx, a = dv/ dt, and v = dx/ dt it follows from eq. (2.27) that Ekin

x

x

v

v

0

0

0

0

dx 1 dv = ∫ mm v dv = mm v2 . = ∆W = ∫ f dx = ∫ mm a dx = ∫ mm dt 2

(2.57)

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Now, combining eqs. (2.52) and (2.56) and taking into account that ρ = m/V and n = m/M, we derive an important relationship for the mean velocity of molecules: vmean = √

3p √ 3RT 3kt . = =√ ρ M mm

(2.58)

More precisely, the velocity derived in eq. (2.58) is the root-mean-square velocity vrms (eq. (2.78)). Remember that mm is the molecular mass and k is the Boltzmann constant, which is in the following relationship to the gas constant (hence, equations with k are related to averaged single molecule properties and those with R to the gas being the collection of molecules): k mm 1 = = . (2.59) R M NA where NA is the Avogadro constant¹⁸ (in the past called number), that is, the number of “elementary entities” (usually atoms or molecules) in one mol, and is (from the definition of mole; see Chapter 4.1.4) the number of atoms in exactly 12 grams of C12 , which is about 6.023 ⋅ 1023 . From eqs. (2.58) and (2.57) another expression for the kinetic energy of molecules follows (remember that M = mm NA ): Ekin =

1 1 M 2 3 RT 3 v = = kT . mm v2 = 2 2 NA 2 NA 2

(2.60)

The average kinetic energy of a molecule is 3kT/2, and the molar kinetic energy amounts to 3RT/2. It is important to distinguish between molecular and molar quantities. Furthermore, the following expression holds (Vm is the molar volume): p n 1 . = = RT V Vm

(2.61)

Another (original) expression for the gas law then follows: pVm = RT =

1 kt . NA

(2.62)

The Loschmidt constant n0 is the number of particles (atoms or molecules) of an ideal gas in a given volume V (the number density) and is usually given at standard temperature and pressure (0 °C and 1 atm to be 2.687 ⋅ 1025 m−3 ): n0 =

p p N NA = = NA = . V kT RT Vm

(2.63)

From eqs. (2.56), (2.59), (2.62), and (2.63) the following gas equations are derived: pV =

m kT mm

and

p = n0 kT .

(2.64)

18 Johann Josef Loschmidt (1821–1895) first calculated the value of Avogadro’s number; often referred to as the Loschmidt number in German-speaking countries (Loschmidt constant now has another meaning).

78 | 2 Fundamentals of physics in the climate system

The model of an ideal gas can be applied with sufficient accuracy¹⁹ to air with a mean pressure of 1 bar (variation of about 0.65–1.35 bar) and a mean temperature near the Earth’s surface of 285 K (variation of about 213–317 K). For a description of air as a gas mixture, Dalton’s law (also termed Dalton’s law of partial pressures) is important. This law states that the total pressure p exerted by a gaseous mixture is equal to the sum of the partial pressures p i of each individual component in a gas mixture: p = ∑ p i . It follows that V = ∑ V i and n = ∑ n i . The gas density ρ (note the difference from the number density η and n0 , respectively) can also be expressed by several terms: ρ=

m N pM = ηmm = mm = . V V RT

(2.65)

In a gas mixture, we can now introduce all equations related to a specific compound (molecule) i or to the sum of all gases; hence, m = ∑ m i also holds. A useful quantity for describing mixtures (not only gaseous) is the mole (or molar) fraction x i = n i /n, which generally characterizes a mixing ratio (Chapter 4.1.4). From the different forms of the gas law it follows (the subscript i denotes partial quantities) that xi =

ni Vi pi mi ρi = = = = . n V p m ρ

(2.66)

A mean molar mass M of air (or generally a gas mixture) can be defined based on moleweighted fractions of individual molar masses: M=

∑ ni Mi = ∑ xi Mi . ∑ ni

(2.67)

Equation (2.65) states that the molar mass of a gas is directly proportional to its densities in the case of the same pressure and temperature. Based on standard values (normally 0 °C and 1 bar), the density for different pressures and temperature can be calculated according to p T0 ρ T,p = ρ 0 . (2.68) p0 T Furthermore, it is practicable to introduce a relative density ρ r , which is the ratio of a gas density to the density of a gas selected as standard (ρ s ) because the ratio of densities does not depend on pressure and temperature. Oxygen and dry air are often selected as standards, which have the following densities (at 1 bar and 273.15 K): ρ O2 = 0.001429 g cm−3 , ρ air = 0.0012928 g cm−3 .

19 Because of the complexity of air, which is a multicomponent and multiphase system, we are only able to roughly model this system. It makes no sense to describe single processes with a complexity several orders of magnitude greater than the process with the lowest accuracy.

2.5 Properties of gases: The ideal gas

| 79

The relative density is also equivalent to the ratio of the relevant molar masses: ρr =

ρ M = . ρs Ms

(2.69)

Air has a mean relative molar mass of Mr,air = Mr,O2 ⋅ ρ air /ρ O2 = 28.949.

2.5.2 Mean free path and number of collisions between molecules To understand heat conduction, diffusion, viscosity, and chemical kinetics, the mechanistic view of molecular motion is of fundamental importance. The fundamental quantity is the mean free path, i.e., the distance of a molecule between two collisions with any other molecule. In Chapter 2.5.1 we derived the number of collisions between a molecule and a wall to be z = cN Av d t/6. Similarly, we can calculate the number of collisions between molecules from a geometric view. We say that all molecules have a mean speed v, and their mean relative speed with respect to the colliding molecule is g. When two molecules collide, the distance between their centers is d; in the case of identical molecules, d corresponds to the effective diameter of a molecule. Hence, this molecule will collide in time dt with any molecular center that lies in a cylinder of diameter 2d with area πd2 and length g dt (it follows that the volume is πd2 g dt). The area πd2 , where d is the molecule (particle) diameter, is also called the collisional cross section σ (σ = πd2 is only valid for like molecules). This is a measure of the area (centered on the center of the mass of one of the particles) through which the particles cannot pass each other without colliding. Hence, the number of collisions of a certain molecule A is zA = cN πd2 g dt. A more correct derivation, taking into account the motion of all other molecules with a Maxwell distribution (see below), leads to the same expression for z but with a factor of √2. We must consider the relative speed, which is the vector difference between the velocities of two objects A and B (here for A relative to B): 2 (g)2 = ( vA⃗ − vB⃗ ) = vA⃗ 2 − 2vA⃗ vB⃗ + vB⃗ 2 = vA⃗ 2 + vB⃗ 2 ≈ 2v⃗2 . (2.70) Since vA⃗ vB⃗ must average to zero, with the relative directions being random, the average square of the relative velocity is twice the average square of the velocity of A + B, and therefore, the average root-mean-square velocity is increased by a factor of √2 (remember that √v⃗ 2 = v), and the collision rate is increased by this factor (g = √2v). Consequently, the mean free path decreases by a factor of √2 when we take into account that all the molecules are moving: zA = √2 cN πd2 v dt .

(2.71a)

To determine the distance traveled between collisions, the mean free path l, we must divide the mean moleculur velocity by the collision frequency or, in other words, the

80 | 2 Fundamentals of physics in the climate system

mean traveling distance v dt by the number of collisions. Furthermore, we must find an expression for the collision frequency (ν = z/ dt) and the mean free time (τ = 1/ν): v dt 1 = , zA √2 cN πd2

l=

l=τ⋅v,

(2.72a) (2.72b)

where τ = 1/(√2cN πd2 v). Replacing cN = n0 with p/kT (eq. (2.63)) we get kT . √2πd2 p

l=

(2.72c)

The total number of collisions in a given volume V in time dt is obtained from the number of collisions of a certain molecule A (eq. (2.71a)), multiplied by the half number of molecules in the volume (cN )V/2: z=

√2 2

V(cN )2 πd2 v dt .

(2.17b)

That fraction of gas molecules is of interest, having a velocity within v and v + dv. This fraction f(v) d v is time-independent of the exchange with other molecules. The Boltzmann distribution states that at higher energies (> kT) the probability of encountering molecules is exponentially lower: f(v) d v = const ⋅ exp (−

m m v2 Mv2 ) dv = const ⋅ exp (− ) dv . 2kT 2RT

(2.73)

The Maxwell distribution describes the distribution of the speeds of gas molecules at a given temperature: f(v) d v = √

2 mm 2 2 mm v2 ( ) v ⋅ exp (− ) dv . π kT 2kT 3

(2.74)

The fraction f(v) d v denotes the probability dW and is also represented by dz/z (= dln z): dz f(v) d v = dW = . (2.75) z To find the most probable speed vpr of molecules, which is the speed most likely to be possessed by any molecule (of the same mass mm ) in a system (in other words, it is the speed of maximum likelihood), we calculate df(v)/ d v from eq. (2.74), set it to zero, and solve for v, which yields vpr = √

2kt √ 2RT = . mm M

(2.76)

2.5 Properties of gases: The ideal gas

|

81

By contrast, the mean speed follows as the mathematical average of the speed distribution, equivalent to the weighted arithmetic mean of all velocities (N number of molecules): N

∞

0

0

∞

2 mm 2 1 mm v2 ) ∫ exp (− ) v3 dv v = ∫ v dN = ∫ vf(v) d v = √ ( N π kT 2kT =√

3

0

8kT √ 8RT . = πmm πM

(2.77)

The root-mean-square speed vrms is the square root of the average squared speed: 1 2

∞

vrms = ( ∫ v f(v) d v) = √ 2

0

3kT √ 3RT = . mm M

(2.78)

All three velocities are interlinked in the following ratios: vpr : v : vrms = √2 : √

8 : √3 . π

(2.79)

Now we can combine expression (2.77) for the mean molecular velocity and eq. (2.71a) for the mean molecular number of collisions z: z = 4cN πd2 dt√

RT M

or collision frequency

ν = 4cN πd2 √

RT . M

(2.80)

Note that all these equations are valid only for like molecules. In the case of air, many different (unlike) molecules must be considered with different radii or diameters, molar masses, and molecular speeds. For the example of gas mixtures A and B, the following expressions must be applied for the mean molecular diameter and mass: dAB = (dA + dB ) /2 ,

(2.81)

mAB = mA mB / (mA + mB ) .

(2.82)

From eq. (2.17b) follows now eq. (2.83) for the number of collisions between different molecules A and B replacing the mean molecular velocity by eq. (2.77), where MA and MB the molar mass of molecule A and B, respectively: zAB = V(cN )A (cN )B d2AB dt√8πRT (

1 1 + ). MA MB

(2.83)

In air, the mean free path has an order of 10−7 m and does not depend on temperature but is inversely proportional to pressure. The expressions given for collision number and mean free path are useful for understanding chemical reactions (see collision theory in Chapter 4.2.3) but have only limited value for applications because the molecular diameter (or radius) is not directly measurable. However, the molecular diameter is typically determined from viscosity measurements.

82 | 2 Fundamentals of physics in the climate system

2.5.3 Viscosity Air is a viscose medium; hence, we observe friction or drag. Friction converts kinetic energy into heat. The internal friction between two moving thin air layers in the xdirection results in a gradient of speed v in the y-direction (perpendicular to the flow); ff is the frictional force (ff /A = τ denotes a force per unit of area, also termed stress) and A the area between the moving layers: ff = Aη

dv =A⋅τ, dz

(2.31)

where η is the dynamic or absolute viscosity (dimension kg m−1 s−1 ). Kinematic viscosity ν is defined as the ratio of the dynamic viscosity to the density of the fluid: ν = η/ρ. When compared with Newton’s eq. (2.27), the meaning of τ is clearly seen to be a flux density of momentum. The momentum flows between moving layers in the direction of decreasing shear velocity (from higher layers down to the Earth’s surface). More exactly, the frictional force must be regarded in all directions, i.e., since it is a vector. The viscosity of a gas is in direct relation to the mean free path (Gombosi 1994)²⁰; gas density ρ = m/V = Nmm /V = cN mm (note the difference with the number density): η =

1 1 2 1 √ mm kT ρ ⋅ vl = cN mm vl = . 3 3 3 √2πd2 π

(2.84)

However, this equation is an approximation; with respect to intramolecular interactions, a more exact relation, η = 0.499ρ m vl, is obtained. Viscosity is independent of pressure but decreases with increasing temperature because of rising molecular speed. The temperature dependence of viscosity is described by an empirical expression; the Sutherland constant C and the constant B follow from eq. (2.84): η=

B√ T . 1 + C/T

(2.85)

2.5.4 Diffusion In summarizing, we can state that no preferential direction exists in molecular motion. Hence, there is no transport of any quantity (Brownian motion). Any flux (transport of material, heat, or momentum) is caused either by turbulent diffusion (air parcel advection) or by laminar diffusion. Diffusion (in chemistry this term refers only to laminar transport) is the flux (dn/ dt) due to concentration gradients (dc/ dz). These concen-

20 From eqs. (2.30) and (2.31) it follows that η =

m ∂z A ∂t

⃗ ≈ ρ ⋅ vl.

2.5 Properties of gases: The ideal gas

| 83

tration gradients occur near interfaces very close to Earth’s surface (see dry deposition in Chapter 2.6.1) and between air gases and solid aerosol or aqueous particles (cloud and raindrops) through phase transfer processes (Chapter 3.6.5). Physically, diffusion means that the mean free path of molecules (or particles²¹) increases in the direction of decreasing number concentration; therefore, diffusion is directed Brownian motion. The diffusion flux Fdiff = dn/A dt (mole per unit of time and area) is proportional to the concentration gradient dc/ dx; D is the diffusion coefficient, V volume (A ⋅d z), and n number of moles, known as Fick’s first law: Fdiff =

1 dn 1 dn dc = −D = −D . A dt V dz dz

(2.86)

Combining the basic Newton’s eq. (2.27) with eq. (2.83) in terms of the general quantity ε (eq. (2.45)), which can be a molecular mass mm , velocity v, heat, and so forth, and where β means a proportionality coefficient, namely a characteristic transfer coefficient, it follows that F=

1 dε dε = −β ⋅ ε ≡ −βff = −β ⋅ η . A dt dz

(2.87)

This is a general flux equation for material, energy, and momentum (e.g., β = 1/m for motion). The negative sign indicates a decrease in the quantity ε in the direction of the gradient dε/ dz (z is for the vertical direction and x, y for any horizontal one). In terms of velocity from eq. (2.86), an expression for the fluidity φ = 1/η follows (τ shear stress, see eq. (2.31), mm molecule mass): dv dv 1 =− mm = −φ ⋅ τ , dz η⋅A dt

(2.88)

where (dv/ dz) is the velocity gradient perpendicular to the flow direction x. Hence, viscosity means the transport of momentum against a velocity gradient, and diffusion is the transport of material against a concentration gradient. Combining eqs. (2.72b), (2.77), and (2.84) generates a simple expression for the gas diffusion coefficient Dg (which is different from the liquid-phase diffusion coefficient); ρ is gas density: Dg ≡

4kT η 1 1 1 1 √ . = vl = ρ 3 3 √2πd2 ρ π ⋅ mm

(2.89)

A typical diffusion coefficient for a molecule in the gas phase is in the range of 10−6 to 10−5 m2 s−1 . Table 2.11 summarizes the most important quantities for describing molecular kinetics.

21 The diffusion of large particles (PM) compared with molecules is described in a different way. The term particle here involves molecules, atoms, and molecule clusters.

84 | 2 Fundamentals of physics in the climate system

Tab. 2.11: Useful quantities in molecular kinetics (V – gas volume, d – molecule diameter, A – square). Quantity

Meaning

Description

mm m M n N NA n0 ρN ρm c Vm p k R

Molecular mass Mass Molar mass Number of moles Number of molecules Avogadro constant a Loschmidt constant Density, number related b Density, mass related c Concentration Molar volume Pressure Boltzmann constant Gas constant

= M/NA = Nm m = NA m m = m/M = M/m m = N/V (ideal gas and standard conditions) = N/V = m/V = n0 m 0 = m/V = n0 m 0 = V/n = f/A = n0 kT = nRT = ρ m v 2 /3 = k(M/m m ) = kNA = R(m m /M) = R/NA

v

Mean molecular velocity d

2 = √ v rms

v rms

Root-mean-square speed

= √3kT/m m

a f Fdiff

Acceleration Force Diffusion flux

= dv/ dt = p ⋅ A = m m (dv/ dt) = v(dm/ dt) = ma = dn/ dt

z

Collision number

= √2n0 πd 2 v dt

l

Mean free path

= v dt/z = 1/ (√2n0 πd 2 )

η

(Dynamic) viscosity

= (1/πd 2 )√m m kT/6

D

Diffusion coefficient

= (v ⋅ l)/3

a

Identical to a number density. Identical to a number concentration. c Identical to a mass concentration. d Also transport velocity. b

2.6 Atmospheric removal: Deposition processes Deposition is the mass transfer from the atmosphere to Earth’s surface; it is the opposite of emission (the escape of chemical species from Earth’s surface into the air). It is a flux given in mass per unit of area and unit of time. According to the various forms and reservoirs of atmospheric chemical species (molecules in the gas, particulate, and liquid phases), different physical and chemical processes are distinguished: – sedimentation of matter because of Earth’s gravitational force (this is valid only for particles larger than a certain size), – sorption of molecules and small particles at Earth’s surface with subsequent vertical transport process, termed dry deposition,

2.6 Atmospheric removal: Deposition processes | 85

– –

sorption of molecules and impaction of particles by falling hydrometeors, termed wet deposition and impaction of particles from an airflow at surfaces.

Gravitational settlement is only of interest for large particles in the upper range of the coarse mode (Chapter 3.6.3). In addition, hydrometeors (raindrops, hail, and snow particles) settle because of gravitation, but we do not consider water to be deposited (it is physically sedimented, but we call this process precipitation, see Chapter 2.1.3.3). Wet deposition only concerns the scavenged and dissolved chemical trace species within hydrometeors. Therefore, we consider three reservoirs of trace substances: gaseous (molecules), atmospheric aerosol particles, and substances dissolved in hydrometeors. Despite the fact that sedimentation and impaction can be important removal processes under specific conditions, they play no significant role in the regional and global budget of fluxes in the climate system. On local sites, however, these removal processes can be important, for example, fog droplet impaction by animals (e.g., Stenocara beetle) and montane cloud forests, and the sedimentation of dust after volcanic eruptions or soil dust after storm events. For details, see Mark (1999), Pahl (1996), Herckes et al. (2002). Particle removal is often parameterized as being not sharply distinct between dry deposition and sedimentation but including deposition processes such as turbulent transfer, Brownian diffusion, impaction, interception, gravitational settling, and particle rebound (Zhang et al. 2001). Unfortunately, in the scientific literature the term “dry” for all “nonwet” deposition processes is widely used. Figure 2.19 shows the removal process of gases and particles from the atmosphere (impaction is not shown, but it is a simple collision impaction of solid particles and cloud droplets). Without further comment, it is clear that dry deposition also occurs during precipitation; for soluble gases, dry deposition velocity increases because of the reduced soil resistance (see subsequent discussion). Total deposition onto Earth’s surface (normally in the sense of an artificial collector surface) is termed bulk deposition: Bulk deposition = dry deposition + wet deposition + sedimentation . From a measurement point of view, there are difficulties in approaching the physically correct removal processes. Dry deposition strongly depends on surface characteristics; correct estimation is only possible by flux measurements (eddy correlation and gradient methods). Any so-called deposition sampler can be installed with a wet-only/dryonly cover plate to avoid bulk sampling, but it is never possible to avoid the collection of sedimentation dust in dry-only samplers or dry deposition or sedimentation by wet-only samplers. However, with enough accuracy all other deposition processes contribute negligibly to the deposition flux under wet-only and dry-only conditions.

86 | 2 Fundamentals of physics in the climate system

scavenging particles

heterogeneous scavenging

homogeneous nucleation

cloud (in-cloud scavenging)

scavenging gases scavenging

sedimentation

dry deposition

precipitation (sub-cloud scavenging)

wet deposition

Fig. 2.19: Deposition processes.

2.6.1 Dry deposition Dry deposition is a generic term describing turbulent transport of molecules and small particles (where gravitational settlement is negligible) vertically downward toward lower concentrations at Earth’s surface that takes them up by different sorption processes. The situation, however, is complicated by the possible upward flux of the same substance due to plant and soil emissions. Only the net flux is measurable (Foken et al. 1995). The case where downward and upward fluxes (so-called bidirectional trace gas exchanges) are equal (Fdry = FQ ) is termed the compensation point. It depends only on the concentration gradient (ch − c0 ). Additionally, fast gas-phase reactions in a diffusion layer might influence the net flux (not treated here) (e.g., Kramm et al. 1995, 1996). Let us now consider the surface as sink, independent of the specific process, which can be – surface adsorption, – interfacial transfer (absorption including chemical reaction) and – stomatal uptake. Chamberlain (1953) first introduced the concept of dry deposition; the dry deposition flux is considered to be of first order with respect to atmospheric concentration (Slinn 1977), Fdry = −vd c , (2.90)

2.6 Atmospheric removal: Deposition processes |

87

where vd is the dry deposition velocity (dimension: distance per unit of time). Because c is a function of the height z, vd must also be related to a reference height h at which c is specified and from which the dry deposition flux starts. It also holds that Fdry =

dc 1 dn V dc A ⋅ h dc = = =h = −vd c . A dt A dt A dt dt

(2.91)

The rate of dry deposition is then Rdry = (

vd dc ) =− c. dt dry h

(2.92)

The reference height h can be regarded as a mixing height (there are other meteorological definitions): ∞

1 h = ∫ c(z) d z . c

(2.93)

0

The advantage of introducing deposition velocity is to avoid a microphysical treatment of vertical diffusion and surface interfacial processes in a single mass transfer coefficient, which is measurable. The limiting application of eq. (2.91) is because of the dependence of vd on various parameters and states of the atmosphere and Earth’s surface. Besides eq. (2.91), the general diffusion equation is valid (cf. eq. (2.86)): Fdry = Kz (

dc = vd c , ) dz z=h

(2.94)

where Kz is the turbulent vertical diffusion coefficient. From this equation it can be seen that vd is experimentally quantifiable through vd = Kz (dln c/ dz). The dry deposition process consists of three steps: – aerodynamic (turbulent) transport through the atmospheric surface layer to the molecular (diffusion) boundary layer close to the surface, – molecular diffusion transport onto the surface (quasi-laminar sublayer) and – uptake by the surface as the ultimate process of removal. Each step contributes to vd or the dry deposition resistance r = 1/vd . On the basis of the three layers, the total resistance r is given by the partial resistances (Figure 2.20), the aerodynamic ra , the quasi-laminar rb , and the surface resistance rc : 1 = r = ra + rb + rc . vd

(2.95)

This equation follows from the flux through different layers under steady-state conditions with the boundary condition c0 = 0, rearranging after c1 , c2 , and c3 : F=

c3 − c2 c2 − c1 c1 − c0 c3 − c0 = = = . ra rb rc r

(2.96)

88 | 2 Fundamentals of physics in the climate system

Fig. 2.20: Resistance model of dry deposition. ra – aerodynamic resistance, rb – quasi-laminar resistance, rc – soil resistance, rcw – soil resistance (water), rcg – soil resistance (other ground), rcf – foliar resistance (weighted by leaf area index), rcs – stomatal resistance, rcc – cuticular resistance, rcm – mesophylic resistance.

However, the overall resistance is always the sum of all individual or specific resistances (Figure 2.20) in different layers: n

r(z) = ∑ r i (z i ) .

(2.97)

1

The limitation of the resistance model lies in its application only to sufficiently homogeneous surfaces such as forests, lakes, and grasslands. Therefore, in dispersion models, dry deposition is often described using partial areas or weighted partial areas in a grid. The aerodynamic resistance through the upper layer can be calculated using eq. (2.94) and an approach for the turbulent diffusion coefficient (eddy diffusivity)

2.6 Atmospheric removal: Deposition processes

| 89

Kz = κu ∗ z (valid only for neutral conditions) z3

−1

∂c dz c3 − c2 Fa = = Kz = (c3 − c2 ) (∫ ) ra ∂z κu ∗ z

,

(2.98)

z2

where κ is the von Karman constant (∼ 0.4), u ∗ is the friction velocity, and Fa is the partial aerodynamic flux. The integral in eq. (2.98) is evaluated from the bottom of the constant flux layer (at z0 , the roughness length of the surface) to the top (z, the reference height implicit in the definition of vd ); therefore, it follows that ra (z3 , z2 ) =

1 z ln . κu ∗ z0

(2.99a)

The roughness length varies from 0.003 m for a flat uncovered surface to 1–6 m for forests and 1.5–10 m for urban areas (Oke 1987). Using the logarithmic wind law eq. (2.48), it follows from eq. (2.99a) that ra (z3 , z2 ) =

u(z0 ) . u 2∗

(2.99b)

The aerodynamic resistance grows proportionally with wind speed at the reference height and decreases with increasing roughness of the surface. The quasi-laminar resistance rb is based on the idea that close to the surface a molecular diffusion sublayer exists where the transport only depends on the diffusivity of the molecule and the surface characteristics of the surface but not on atmospheric parameters (such as wind speed). The flux under steady-state conditions is parameterized by (B dimensionless transfer coefficient) Fb = Bu ∗ (c2 − c1 ) . (2.100) A useful expression for the quasi-laminar resistance rb in terms of the Schmidt number (Sc = ν/Dg ) is the one proposed by Wesely (1989): rb =

5Sc2/3 . u∗

(2.101)

The surface or canopy resistance rc is almost the dominant resistance in dry deposition and depends on vegetation characteristics, building materials, soil, water, and snow surface with different humidity, pH, and reactivity related to the deposited substance (Table 2.12) (Hosker and Lindberg 1989). It is the most difficult of the three resistances to describe (Weseley 1989). Baldochi (1991) defined the plant canopy as a complex consisting of a plant community, plant litter located on the soil surface and incorporated into the upper layers of the soil, and the rhizosphere consisting of roots, soil OM, microbes, and soil fauna. The canopy control of trace gas exchange operates on the interconnected vegetation-litter-soil complex. According to Figure 2.20, three parallel surface resistances exist: plant (or foliar), water, and ground resistance (the resistances in eq. (2.95) are in series): 1 1 1 1 = + + . rc rcf rcw rcg

(2.102)

90 | 2 Fundamentals of physics in the climate system Tab. 2.12: Averaged surface resistances rc (s m−1 ) for different gases during the day; stomatal resistance rcb is also given (after Erisman and Pul 1997).

rc

rcb a b

SO2 NH3 NO2 O3 HNO3

Wet and moderate temperature

Dry and summer

Coniferous forest

Coniferous forest

Grassland

a

Grassland a

1 1a 320 320 1a

1 1a 100 100 1a

300 500 b 240 240 1a

50 500 b 80 80 1a

200

60

150

50

Zero but set to 1 to avoid high v d at low ra and rb . Under these conditions NH3 will be emitted by vegetation.

The foliar resistance consists again of two parallel resistances, the cuticular resistance rcc and the stomatal resistance rcs , which are in series with the mesophyll resistance rcm : 1 1 1 = + . (2.103) rcf rcs + rcm rcc Investigations show that mass transfer through the cuticle can be neglected in comparison to stomatal exchange (Kerstiens et al. 2006). The stomata are leaf openings used in photosynthesis and respiration. The air spaces in leaves are saturated with water vapor, which exits the leaves through the stomata (known as transpiration). Therefore, plants cannot acquire carbon dioxide without simultaneously losing water vapor. Stomatal resistance can, therefore, be calculated from the transpiration rate and humidity gradient. Afterwards the mesophyll (the layer between the upper and lower epidermis) resistance is the final step in gas uptake. In the mesophyll, the palisade cells are exposed directly to the air spaces inside the leaves, which is the primary site of photosynthesis in a plant’s leaves. The gas transfer through the stomata is by molecular diffusion. An inverse dependence on molecular diffusivity is generally accepted (Grünhage et al. 2000). The surface resistance reduces to a particular resistance in the following cases (Erisman and Pul 1997): – water surface: rc = rcw – bare soil: rc = rcg – snow cover: rc = rsnow The detailed processes in trace gas exchange based on the photosynthesis budget equation are as follows: Fphotosynthesis/net = Fphotosynthesis/sun + Fphotosynthesis/shadow + Frespiration/sun + Frespiration/shadow .

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| 91

Tab. 2.13: Averaged dry deposition velocities for SO2 (cm s−1 ) for summer (Su) and winter (Wi) (after Möller 2003).

Wet Dry Snow

Farmland

Grassland

Mixed forest

Coniferous forest

Urban

Water

Wi

Su

Wi

Su

Wi

Su

Wi

Su

Wi

Su

Wi

Su

1.0 0.7 –

1.0 0.5 0.1

1.0 0.6 –

1.0 0.4 0.1

3.0 1.5 –

1.5 0.5 0.2

2.0 0.7 –

2.0 0.5 0.2

1.0 0.1 –

1.0 0.1 0.1

0.5 0.5 –

0.5 0.5 0.1

Tab. 2.14: Averaged dry deposition velocities (cm s−1 ) above land (after Möller 2003). Substance

SO2

NO

NO2

HNO3

O3

H2 O2

CO

NH3

vd

0.8

< 0.02

0.02

3

0.6

2

< 0.02

1

Grünhage and Haenel (2008) provided an explicit parameterization. For reviews on dry deposition see Sehmel (1980), Voldner et al. (1985), Hanson and Lindberg (1991), Padro (1996), Wesely and Hicks (2000), and Petroff et al. (2008). Pioneering work was done by Chamberlain (1953), Hicks and Liss (1976), Slinn (1977), Wesely and Hicks (1977, 2000), Garland (1978), Weseley (1989), and many others. Table 2.13 shows the averaged dry deposition velocities for sulfur dioxide for several surface conditions and Table 2.14 the typical vd for several gases on land. A special case of high importance is dry deposition onto water surfaces, especially oceans (for details see Danckwerts 1970, Hicks and Liss 1976, Liss and Slinn 1983, Schwartz 1986). The dry deposition flux is described by (see eq. (3.181) in Chapter 3.6.5.4) caq (Fdry )aq = k g (c − (2.104) ) , H where c and caq are the concentrations in the gas and liquid phases, close to the surface, respectively, and H is the dimensionless Henry’s law constant. It is evident from eq. (2.104) that for there to be a deposition flux, and caq must be less than cHeff . For caq → 0, this equation leads to eq. (2.94): F = k g c ≡ vd c. In analogy to the gas transfer described in Chapter 3.6.5, we can consider three fluxes: gas-phase diffusion (diff) close to the water surface, interfacial transfer (int), and dissolution including chemistry (sol) in water body. The index “int” denotes the concentrations immediately adjacent to the interface, and the coefficient β represents mass transfer enhancement due to chemical reactions in water; when there is no reaction β = 1: (Fdry )diff = k diff (c − cint ) , 1 (Fdry )int = αv (cint − cint aq ) , 4 (Fdry )sol = βk sol (cint aq − c aq ) .

(2.105) (2.106) (2.107)

92 | 2 Fundamentals of physics in the climate system

Under steady-state conditions, the flux is constant and equal in both media and across the interface. By equating the several expressions (2.104)–(2.107) for the flux, one obtains the overall mass transfer coefficient k g as the inverse sum of the mass transfer coefficients in two media and the interface: 1 1 4 1 + = + . k g k diff αv βk sol H

(2.108)

According to Schwartz (1986), large magnitudes of mass transfer coefficients appear sufficient when the interfacial resistance is negligible in the natural environment. In the absence of an aqueous phase, the chemical reaction of the dissolved gas β = 1, and it follows for nonreactive gases that 1 1 1 . = + k g k diff k sol H

(2.109)

There follows a critical value for the Henry’s law constant Hcrit = k diff /k sol , where the gas and liquid phase resistances are equal. For H ≪ Hcrit , the liquid-phase mass transport is controlling and dry deposition flux depends linearly on H. For H ≫ Hcrit , the gas-phase transport is controlling and the dry deposition flux is independent of H. For reactive gases, the dry deposition flux is enhanced, and it is βH that is compared with Hcrit .

2.6.2 Wet deposition As seen in Figure 2.19, wet deposition is a complex process beginning with heterogeneous scavenging during cloud droplet formation, cloud processing (in-cloud scavenging), and precipitation (subcloud scavenging, sometimes called below-cloud scavenging). Hence, several microphysical processes and chemical reactions must be considered. It is remarkable that wet deposition is extremely difficult to model, in contrast to dry deposition, but is easier to measure by rain gauges (water sampling and analyzing the dissolved substances), whereas dry deposition measurements (vertical flux quantifications) are laborious. The number of precipitation chemistry measurements is uncountable; a huge number of networks has existed since the 1950s. In contrast to dry deposition, wet deposition is occasional. In remote areas, the average fluxes in dry and wet deposition are of comparable magnitude. However, because precipitation occurs for only 5–10% of the year, event-based wet flux is considerably larger than dry flux within a comparable time. Table 2.15 shows characteristic data of cloud and rain events. Despite the complexity of the specific steps in obtaining wet deposited substances, we can parameterize the wet deposition flux Fwet , similar to the approach to dry deposition: dc Fwet = − ( ) = k wet c . (2.110) dt wet

2.6 Atmospheric removal: Deposition processes |

93

Tab. 2.15: Averaged values characterizing wet deposition or precipitation typical for Germany (after Möller 2003). Parameter

Deep clouds

Rain

duration of event (h) Duration of dry period (h) Volume occupying mixing layer (%) Rain amount (mm yr−1 ) LWC (mg m−3 ) Lifetime of droplets (min) Droplet radius (μm) Droplet number

6.6 14 34 – 0.3 60 5 2 ⋅ 105

2 30 100 800 0.05 10 500 0.03

By contrast, it holds from the simple balancing of deposited rainwater that Fwet = R ⋅ caq ,

(2.111)

where caq is the rainwater concentration of the substance (dimension: mass per liter) and R is the rainfall amount (dimension: liter per unit of time and unit of area). From both equations is derived the scavenging coefficient λ (dimension: time−1 ): k wet =

Rcaq ≡λ. c

(2.112)

Older literature is full of “experimental estimations” of λ, also termed the washout coefficient, by measurements of simultaneous gas and rainwater concentrations of soluble gases. However, that approach is wrong because (a) λ is a function of height (the vertical gas-phase concentration profile should be measured, not the surface concentration) and, more importantly, (b) a dominant part of the dissolved matter arises from in-cloud scavenging. For subcloud scavenging, assuming the washout process is a first-order process (dc/ dt) = λc, we can describe the subcloud process for gases as well as particles; indexes g and p denote the gas and particle, respectively: ∞ g

(2.113)

p

(2.114)

Fsub (g) = ∫ λsub (z, t)c(x, y, z, t) d z , 0 ∞

Fsub (p) = ∫ λsub (r, z, t)cN (r, x, y, z) d z . 0

Seinfeld (1986) defined the wet deposition velocity as vsub =

Fsub . c(x, y, 0, t)

(2.115)

94 | 2 Fundamentals of physics in the climate system Tab. 2.16: Mean scavenging coefficients λ (10−4 s−1 ) of H2 O2 depending on SO2 gas-phase concentration c (ppb), calculated from a cloud model with coupled gas-aqueous chemistry (after Möller 1995b).

Species

c(SO2 ) and λ(SO2 , H2 O2 ) 0.1 ppb

H2 O2 SO2

4.1 27.9

1.0 ppb

2.0 ppb

13.5 8.8

69.0 3.6

5.0 ppb 269.0 0.8

For the homogeneous distribution of gases in a subcloud layer of height h we derive h

vsub = ∫ λ(z, t) d z = hλsub =

Fsub . c(x, y, 0, t)

(2.116)

0

An in-cloud scavenging coefficient follows by using eqs. (3.179) and (3.181); tc is the lifetime of the cloud: tc

λin-cloud = RT ⋅ LWC ∫

F aq (t) dt . c(t)

(2.117)

0

Table 2.16 shows the relationship between λ values for SO2 and H2 O2 as an example of enhancement due to chemical reactions. Now considering the raindrop distribution, we obtain an averaged scavenging coefficient for the rain event: ∞

λsub = RT ⋅ LWC ∫ πr2 λr ⋅ N(r) d r .

(2.118)

0

2.7 Characteristic times: Residence time, lifetime, and turnover time The residence time (often interchangeable with the term lifetime, but later we will distinguish between the two) is the average amount of time that a particle spends in a particular system. This definition is adapted to fit with groundwater, the atmosphere, glaciers, lakes, streams, and oceans. It was first introduced by Barth (1952) as the ratio of the total amount m of an element in the ocean to the rate of input (flux) F to the ocean τ = m/F. Junge (1963, 1974), Bolin and Rodhe (1973), and Bolin et al. (1974) first applied this conception to atmospheric trace gases. We now consider the various flux equations in the general form (the removal flux from the atmosphere at a given site is expressed by different specific processes such as deposition, decomposition, or transportation): Frem = k r c = − (

dc 1 dm M dn ) =− ( ) = − ( ) ≡ ∑ Fi = ∑ ki c , dt r V dt r V dt r i

(2.119)

2.7 Characteristic times: Residence time, lifetime, and turnover time |

95

where k r is the removal coefficient (dimension: time−1 ) and c is the concentration (recall that we always regard substance A and do not use the subscript cA to avoid confusion with other subscripts). The flux, therefore, has the dimension mass per unit of time and unit of volume, corresponding to the rate definition in chemistry. The reciprocal removal coefficient denotes a characteristic time τc : 1 . kr

(2.120)

c . Frem

(2.121)

τc = Formally, it leads to τc =

It is important to note that c(t) is not constant over time, and thus the removal flux depends on time (it decreases over time if c is decreasing) or, in other words, τ depends on the concentration or mass of the substance in the reservoir. Moreover, the removal coefficient is not necessarily constant, i.e., k r (t) leads to τ(t). Only in the case of constant k r (we call it the first-order removal process) does it follow from eq. (2.119) that t c = c0 exp (− ) , (2.122) τc from which we define turnover time τt as τt = − ln (

c ) τc . c0

(2.123)

From eq. (2.122) it follows that c → 0 for t → ∞. At t = τc , c/c0 = ln(−1) ≈ 0.37 is valid or, in other words, the initial amount of A in the volume (or reservoir) decreases to about 37% (1/e), where e is Euler’s number. We have seen that the condition c = 0 is undefined because of the exponential removal law. However, we can set the condition c ≪ c0 , and it follows for c = 0.01 ⋅ c0 that τ t = 4.6 ⋅ τc . The turnover time of a substance denotes that time when substance A in the volume becomes “practically” zero. Only in the case of a zero-order removal process, i.e., the removal rate is constant over time and does not depend on the concentration, does τ t mark exactly the time when c = 0. The basic eq. (2.119) changes into (note that the removal coefficient k 0r becomes identical to the removal flux and acquires another dimension) dc 1 dm M dn Frem = k 0r = − ( ) = − ( )=− ( ) . (2.124) dt V dt V dt The solution of eq. (2.124) is c0 − c = Frem t .

(2.125)

V is the reservoir- or volume-based flux in mass per unit of time) It follows that (Frem

τt =

c0 1 m0 m0 = = V . Frem V Frem Frem

(2.126)

96 | 2 Fundamentals of physics in the climate system The often used equation²² in the form τ = m/F referring to the “lifetime” and here given in terms of eq. (2.126) with constant m and F represents the turnover time for zero-order removal (constant removal rate); it is not a residence time! However, when we consider time-dependend mass and flux, we will later see that it corresponds to the residence time: dt m(t) m(t) ≡ dt = . τ= F(t) dm dln m The mass of A in a reservoir is given by the three-dimensional concentration distribution in the reservoir: xx yy zz

m = ∫ ∫ ∫ c(x, y, z) d x dy dz .

(2.127)

0 0 0

The residence time τ is generically defined as the average time a substance spends in a specified region of space, such as a reservoir. We now define τ as the arithmetic mean of the individual lifetimes of all molecules of substance A in a reservoir. It must be noted that there is much confusion in the scientific literature over the different characteristic times. The lifetime τ of a molecule (it is similar to life expectancy at birth of a biological species) is the time the molecule spends in the reservoir from entering to leaving it: 0

1 τ= ∫ t dN . N0

(2.128)

N0

The specific expression for residence time depends on the kinetic law applicable to N(t). In the simple case of the (pseudo-)first-order law dN = −k r N0 exp(−k r t) d t and replacing the number with the concentration (N ∼ c), it follows that ∞

τ = k r ∫ t ⋅ exp (−k r t) dt .

(2.129)

0

The solution²³ is τ=

1 . kr

(2.130)

Compared with eq. (2.120), we conclude that the characteristic time τc corresponds to the residence time τ for removal processes of the first-order rate. Using the residence time distribution approach, we define ∞

τ = ∫ t dfA (t) ,

(2.131)

0

22 We use m instead of M for mass to avoid confusion with the molar mass. 23 Because ∫ x ⋅ exp(ax) dx =

exp(ax) (ax a2

󵄨󵄨∞ r t) − 1), it follows that τ = kr exp(−k (−kr t − 1)󵄨󵄨󵄨󵄨 = k2r 󵄨0

kr k2r

.

2.7 Characteristic times: Residence time, lifetime, and turnover time

| 97

∞

where fA denotes the normalized distribution function ∫0 fA (t) d t = 0 of the age of the molecules of A, which is in the following relationship to the concentration: fA =

c0 − c(t) c(t) = 1− . c0 c0

(2.132)

With dfA (t) = − c10 ( dd ct ) dt, a general definition of residence time, not dependent on the specific kinetic law of concentration decrease (depletion of A), follows from eq. (2.131): ∞

τ = −∫t( 0

dc 1 dt . ) dt c0

(2.133)

From eq. (2.133) follows eq. (2.129) when using a first-order rate law (dc/ dt) = −k r c0 exp(−k r t), and therefore τ = 1/k r . With the logical assumption that c(t) → 0 for t → ∞, eq. (2.133) simplifies to (the second term becomes zero) ∞

∞ ∞ dc 1 dc 1 dc 1 󵄨󵄨󵄨󵄨∞ dc 1 dt = ∫ ( ) dt − ( ) t󵄨󵄨 = ∫ ( ) dt . τ = −∫t( ) dt c0 dt c0 dt c0 󵄨󵄨0 dt c0 0

0

(2.134)

0

α Now we assume the general time law ddc(t) t = −k r c(t) ; for α < 1 it follows a hyperbolic characteristic or, in other words, c → 0 for t → ∞ (infinite time), and for α > 1 it follows parabolic characteristics, i.e., c → 0 is obtained in a finite time. For these cases, the following solutions from eq. (2.134) are valid:

α > 1:

c(t) =

α > 1:

c(t) =

ϑ α

,

α

,

(tg + t) α−1 ϑ (tg − t) 1−α

−1

where ϑ = (|α − 1|k r ) α−1 and tg = (c0α−1 |α − 1|k r )−1 . In both cases, the solution of the integral results as α < 2 to ∞

τ=∫ 0

c1−α c(t) 0 dt = . c0 (2 − α)k r

(2.135)

This equation represents the general expression for the residence time for 1 ≤ α ≤ 2. The case α = 1 represents the first-order rate law as already described and eq. (2.133) becomes identical to eq. (2.130). Now we see that the residence time is independent of time only if k r is constant. With Frem = −(dc/ dt) and k r = Frem /c it follows that τ=

dt c(t) ≡ . Frem (t) dln c

(2.136)

98 | 2 Fundamentals of physics in the climate system

1000 Mace Head

[CH3CCl3] in ppt

Cape Grim

100

10

1 1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

year Fig. 2.21: Historical record of methyl chloroform (CH3 CCl3 ) in logarithmic relationship; data from Cape Grim (July 1978–September 2013) and Mace Head (January 1987–September 2013). Data source for Cape Grim data: CSIRO Marine & Atmospheric Research, Cape Grim Baseline Air Pollution Station/Australian Bureau of Meteorology, and the Advanced Global Atmospheric Gases Experiment (AGAGE); see also Prinn et al. (2005). Data source for Mace Head: ALE/GAGE/AGAGE global network program (see also Reimann et al. 2004): http://cdiac.ornl.gov/ndps/alegage.html.

An example of the application of eq. (2.136) is shown in Figure 2.21, where the longterm measurement of CH3 CCl3 data (Chapter 4.4.5, Volume 2) results in a linear function lg c = f(t). It follows from the diagram that dln c/ dt = 0.315, and therefore τ = 3.2 years. According to the resistance model, we must consider parallel and serial removal processes. Without consideration of source terms (see subsequent discussion), we have the budget equation (first-order law) of Frem = (

n n dc dc ) = ∑ ( ) = ∑ ki c , dt r i=1 dt i i=1

(2.137)

from which a relationship between the overall residence time τ and process-specific residence times τ i follows, for example in terms of dry deposition τd , wet deposition τ wet , and chemical reactions τ chem : n 1 1 . =∑ τ i=1 τ i

(2.138)

2.7 Characteristic times: Residence time, lifetime, and turnover time | 99

In the case of subsequent (in series) processes, the residence times sum up as m

τ = ∑ τj

(2.139)

j=1

when the fluxes branch out and pass several reservoirs (number 0) parallel to the fluxes F i , where ∑ F i = Frem ; the residence time follows as the weighted mean τ=

1 Frem

0

∑ Fi τi .

(2.140)

i=1

In all cases, it holds that the overall residence time is the total mass (or mean concentration) divided by the total removal flux (eq. (2.136)) at a given time. The removal flux normally splits into dry and wet removal as well as chemical transformation. These flux equations were shown in previous chapters, and we now use the reciprocal characteristic mass transfer coefficients in the sense of specific residence times in connection with dry deposition, wet deposition, and chemical decomposition: Frem = k r c = Fdry + Fwet + Fchem = (

kd + k wet + ∑ k i ) c . h i

(2.140)

We are often interested in determining the relative importance of different sinks contributing to the overall removal of a species. For example, the fraction f i removed by process i is given by Fi fi = . (2.141) Frem So-called wet events such as wet deposition and aqueous-phase chemistry in clouds and precipitation are episodic, i.e., the specific residence time during the dry period is not defined (flux is zero). To average over longer periods containing several alternating dry periods and wet events, Rodhe (1978) developed an expression for the averaged wet removal residence time: τwet = τ a

τa τb + τa + τwet = A + Bτ wet . τa + τb τa

(2.142)

The subscripts a and b characterize the mean time of dry periods (nonrainy or cloudyfree) and wet periods (clouds, rain), respectively. τwet represents the residence time during a wet event, either according to eq. (2.111) for wet deposition or eq. (3.177) for aqueous-phase chemistry. The constant A corresponds to a fractional time of the dry period time τ a , which becomes smaller when the ratio between the dry and wet periods decreases. The coefficient B is normally larger than 1 (if τa > τb ). Most likely τ a ≫ τb , but if τ ≪ τb , it follows that τ → τa . Equation (2.142) represents the flow through two reservoirs according to eq. (2.139), first a space without wet events (dry

100 | 2 Fundamentals of physics in the climate system

Tab. 2.17: Mean residence times of gaseous and dissolved SO2 (after Möller 1995a, b and 1996b). Chemical regime

Residence time

Gas phase related to OH oxidation Averaged over 1 year Sunny days (daytime)

∼ 20 d ≤ 4d

Liquid phase In droplets (daytime) Averaged over mixing layer Cloud Rain Averaged over 1 year Cloud Rain Overall average over 1 year

∼ 2 min ∼ 3h ∼ 6h ∼ 0.8 d ∼ 2.9 d 1–2 d

period) and then a space with a wet event. For a given atmospheric volume, we might also define a transport residence time as τ advection =

2u , x

(2.143)

where u is the mean wind velocity and x is the length of the atmospheric reservoir. It follows for the overall atmospheric residence time of a substance that 1 1 1 1 1 + + + . = τ τg τdry τwet + τaq τadvection chem chem

(2.144)

Similarly to eq. (2.141), we can calculate the fractions of specific removal processes by fi =

τ τi

(2.145)

because ∑(τ/τ i ) = 1. Table 2.17 lists as an example different, i.e., process-related, residence times for sulfur dioxide.

3 Fundamentals of physicochemistry in the climate system The transport and transformation of chemical species is ongoing in the environment, within soils, waters, and air, as well as by crossing reservoir interfaces. As already stated, the atmosphere is the global reservoir, characterized by the highest rates of turnover. The Earth’s surface (soils, waters, and vegetation) is the source of atmospheric constituents but also a disposal site of air pollutants (after deposition) and direct pollution from wastewater, landfills, agrochemicals, and other human activities. Physicochemistry describes particulate phenomena in chemical systems in terms of laws and concepts of physics. Hence, we describe here the state of systems, thermodynamics and equilibrium, properties of water and solutions, and, finally, heterogeneous processes.

3.1 Chemical thermodynamics Thermodynamics was originally the study of energy conversion between heat and mechanical work, but now it tends to include macroscopic variables such as temperature, volume, pressure, internal energy, and entropy. In physics and chemistry, and thus the environment and more generally the climate system, thermodynamics includes all processes of equilibrium between liquid, gas, and solid phases. These processes occurring in energetic changes are the key factor in understanding atmospheric states and, thus, climate changes. Changes in heat and kinetic energy can be measured in work carried out. Specifically, chemical thermodynamics¹ is the study of the interrelation of heat and work by chemical reactions or physical changes of state. The structure of chemical thermodynamics is based on the first two laws of thermodynamics. Starting from the first and second laws of thermodynamics, four equations, known as the “fundamental equations of Gibbs,” can be derived. From these four a multitude of equations, relating the thermodynamic properties of a thermodynamic system, can be derived using relatively simple mathematics. Thermodynamics deals with four types of system: 1. Isolated system: Neither energy (work and heat) nor matter is exchanged with the surroundings. 2. Adiabatic isolated system: Neither heat nor matter is exchanged with the surroundings; other kinds of energy (work) may be exchanged. 1 Unfortunately, teachers like to introduce many disciplinary terms such as technical thermodynamics, not to confuse students but to make their own field more important. In my understanding, there is only thermodynamics, which you can apply to many (physical) systems (including chemical ones). https://doi.org/10.1515/9783110561265-003

102 | 3 Fundamentals of physicochemistry in the climate system

3.

Closed system: Energy exchange with the surroundings is possible, but matter is not exchanged. 4. Open system: In contrast to the closed system, all kinds of exchange with the surroundings are allowed. In previous chapters, we introduced the following state functions: temperature T, pressure p, volume V, and amount n. In the following chapters, we introduce additional state functions to describe the energetic state of a system: internal energy U, entropy S, enthalpy H, free energy F (Helmholtz energy), and free enthalpy G (Gibbs energy). State functions are values that depend on the state of the given substance and not on how that state was reached. State functions are also known as state variables and state quantities.

3.1.1 First law of thermodynamics and its applications The first law of thermodynamics is a special case of the law of energy conservation. This law says that within an isolated system, the sum of all kinds of energy remains constant. Energy can be transformed from one form to another, but cannot be created or destroyed. 3.1.1.1 Internal energy Rudolf Julius Emanuel Clausius (1822–1888) coined the term internal energy. Note that thermodynamic functions in capital letters (U) refer to molar quantities (indicating one mol of substance) and small letters (u) to a given amount: u = nU. The internal energy of a system or body (e.g., a unit of air or water volume) with well-defined boundaries, denoted by U, is the total kinetic energy due to the motion of particles (translational, rotational, and vibrational) and the potential energy associated with the vibrational and electrical energy of atoms within molecules or any matter state. This includes the energy in all chemical bonds and that of free electrons (e.g., hydrated electrons in water and photons in air). The change ∆U = U2 − U1 as a result of a state change means, according to the law of energy conservation, that energy is either taken up by the environment (∆U > 0) or released into the surroundings (∆U < 0). The first case is termed endothermic (e.g., the evaporation of water) and the second case exothermic (e.g., oxidation). Heat Q occupies a special place among different kinds of energy² (which are summarized by the term work, W). Hence, change in internal energy (we can only measure the change 2 Work, energy, and heat are well-defined quantities in physics and should not be confused with the equivalent terms use in daily life. In physics, the term energy is defined as the amount of work carried out by a physical system. Performing work by a body increases its energy content. Hence, energy is “stored work.” Work is a process or body quantity, whereas energy is a state quantity. To carry out

3.1 Chemical thermodynamics

|

103

but not the absolute value of internal energy) is defined by ∆U = W + Q

or in differential form

dU = dW + dQ .

(3.1)

Equation (3.1) is the mathematical expression of the first law of thermodynamics: The change in internal energy of a system is equal to the sum of gathered or released energy in the form of work and heat. In a closed system, the internal energy remains constant. In the gas phase, work is carried out primarily³ as pressure-volume work (in the condensed phase such as droplets and solid particles; surface work, electrical work, and expansion work also occur). A change in volume occurs at a constant pressure (isobaric change of state), and so it holds that − W = p∆V .

(3.2)

If no other work is carried out, the differential change in internal energy is described by dU = dQ − p dV . (3.3) The internal energy of an ideal gas⁴ depends only on temperature (the Gay-Lussac law). During isothermal expansion, when air performs positive work by overcoming external pressure, it must take up an equivalent amount of heat to meet a constant temperature (−W = Q > 0). If there is no heat exchange with the surroundings (Q = 0), this is defined as an adiabatic change of state. Consequently, the gas (air) cools and the internal energy decreases by an amount equivalent to the work performed (−W = −∆U). In air parcels, pressure and volume change with each shift in height. As the air rises, the volume increases (expansion) and pressure decreases. As long as there is no

work, we need power (recall: energy = work ⋅ power). We distinguish between mechanical and electrical work. Again, mechanical work is subdivided into acceleration work, displacement work (this includes lifting work, volume work, surface work, and elastic work), and frictional work. Different forms of energy are distinguished: kinetic energy (stored acceleration work) and potential energy (stored displacement work). Belonging to potential energy (in the sense of a positioning energy) are also electrical energy (motion of electrically charged particles, analogous to lifting energy), magnetic energy, and gravitation energy. Potential energy can be regarded as the capability to carry out work. Energy producing through frictional work is random microscopic motion energy called heat. Heat cannot be transformed fully into other forms of energy, in contrast to mechanical energy. Transferred heat ∆Q is a process quantity such as work. Heating means that work is dissipated. When frictional work (heat) appears, then the real work carried out at the system is larger, in other words, the usable work is lower than the reversible work. Radiation energy (electromagnetic wave) is a mixture of electrical and magnetic energy. The only energy coming to the Earth is solar radiation energy, which is transformed into all other forms of energy. Large amounts of heat are stored in Earth’s interior because of planetary formation and continuous ongoing nuclear reactions (radioactive decay). 3 Further transformed into accelerational and frictional work. 4 For real gases, the internal energy also depends on volume.

104 | 3 Fundamentals of physicochemistry in the climate system

heat exchange with the surrounding air, the internal energy remains constant and the altitude change is adiabatic. Therefore, adiabatic air mass changes are an important condition for the condensation of water vapor onto CCNs. Adiabatic, rising air cools by 0.98 °C per 100 m; this is called the dry adiabatic lapse rate (DALR), or dT/ dz. As soon as the air parcel is saturated by water vapor, it partly condenses and is then heated by the released heat. Then a wet adiabatic temperature gradient (lapse rate) is observed, which lies between 0.4 °C at high temperatures and 1 °C at low temperatures. During adiabatic changes, the potential temperature remains constant, i.e., an air parcel with 10 °C at 1000 m altitude contains about the same heat as a near-surface air parcel at 20 °C. The temperature gradient determines the atmospheric layering. This is known as a stable atmospheric boundary layer⁵ (SBL) if the air temperature decreases less with altitude than in the case of adiabatic layering. The rising air becomes cold faster than its environment and sinks down again so that only small vertical displacements occur. By contrast, if the air temperature decreases faster than the adiabatic lapse rate (the rising air is warmer than the environment), another buoyant force evolves – it becomes a labile layering. 3.1.1.2 Molar heat capacity In an isochoric process (no volume change), the heat needed to heat one mol of a gas, water, or solid body by 1 K (°C) is called the molar heat capacity CV , defined as dQ = CV dT. At constant volume, work cannot be carried out (p∆V = 0), so dU = dQ = C V dT, or ∆Q ∆U (3.4) CV = ( ) =( ) . ∆T V ∆T V However, most processes proceed not at constant volume but at constant pressure (isobaric process), and we define the molar heat capacity Cp as dQ = Cp dT. Using eqs. (3.3) and (3.4) and taking into account that p dV = R dT (from eq. (2.56)), it follows that Cp dT = dU + R dT . (3.5) Because isobaric processes are frequent in chemistry, to calculate the change in internal energy at constant pressure and the performed work, a new state function, H, called enthalpy, was introduced, H = U + pV = U + nRT ,

(3.6a)

dH = dU + p dV + V dp .

(3.6b)

or, in differential form,

5 The boundary layer is the lowest part of the troposphere in contact with Earth’s surface and therefore determined by extensive exchange processes and friction.

3.1 Chemical thermodynamics

| 105

The last equation can be integrated for isobaric changes (dp = 0): ∆H = ∆U + p∆V = Q

dH = dU + p dV = dQ .

or in differential form

(3.6c)

The heat capacity at a constant pressure is thus defined as Cp = (

∆Q ∆H ) ≡( ) . ∆T p ∆T p

(3.7a)

It follows, using eq. (3.6b) for constant pressure (V dp = 0) and eq. (3.3) for constant volume (p dV = 0) and taking into account that p dV = R dt, that Cp = (

dU dQ )+R =( ) + R = CV + R . dT dT V

(3.7b)

The gas constant R is equal to the volume work of an ideal gas (Cp − CV ) when heating one mol by 1 °C at constant pressure. The change in enthalpy is equal to the change in heat in processes at constant pressure. From eq. (3.7a) we can derive the relationship between the change in enthalpy and the (infinitesimal) change in temperature at a constant pressure in the case of constant heat capacity within a certain temperature range (note, however, that molar heat depends on T; consult specialized books on physical chemistry): T2

∆H = ∫ Cp dT .

(3.8a)

T1

However, if within ∆T a change of state occurs (melting, evaporation), the associated heat from melting or evaporation must be considered (Tu temperature of change, ∆Hu enthalpy of change): Tu

T2

∆H = ∫ Cp dT + ∆Hu + ∫ Cp dT . T1

(3.8b)

Tu

3.1.1.3 Thermochemistry: Heat of chemical reaction Thermochemistry is the study of heat associated with chemical reactions. A reaction may release (exothermic) or absorb (endothermic) energy. A general form of a chemical reaction is given by eq. (3.9), ν1 A1 + ν2 A2 + . . . → ν m+1 Am+1 ν m+2 Am+2 + ⋅ ⋅ ⋅ ,

(3.9)

where Ai with i = 1. . .m are the parent substances and the products with i = m+1 . . . n and ν i stoichiometric coefficients. In terms of thermodynamics, the reaction may also be written 0 = ∑ νi Ai . (3.10) i

106 | 3 Fundamentals of physicochemistry in the climate system

This is called the first thermochemical law, i.e., the molar amount of energy evolved or absorbed during a chemical change always remains the same for the same quantities of reacting substances. The change in internal energy is then given by ∆U = ∑ ν i U i .

(3.11)

i

The reaction heat is given by the difference in internal energy before and after the chemical reaction. More frequently, reactions proceed at constant pressure, and we can describe the energy change as a change in enthalpy (eq. (3.6c)): ∆H = ∆U + ∆nRT .

(3.12)

According to the first law of thermodynamics, a change in internal energy does not depend on the path, and transforming that on chemical reactions, we state that the reaction enthalpy is always the same, independent from the reaction path of the parent compounds to the products (initial and terminal status). This is called Hess’s law: the reaction heat is equal to the sum of the reaction heats of all subsequent partial reactions, starting from the same parent compounds to the same products. In other words, this law states that the total enthalpy change during the complete course of a chemical reaction is the same whether the reaction proceeds in one step or in several steps. Many chemical conversions in the climate system are multistep processes. Based on this law, we can calculate reaction heats whose measurement is impossible or even extremely complicated. It makes sense to introduce a standard state function, related to the standard state (1 bar and 298.15 K). The standard enthalpy H ⊖ of reaction eq. (3.9) is now given by ∆H ⊖ = ν m+1 HX⊖m+1 + ν m+2 HX⊖m+2 − ν1 HX⊖1 − ν2 HX⊖2 = ∑ ν i H ⊖i .

(3.13)

i

H ⊖i is the standard enthalpy of formation for compound Ai , listed in specialized tables. A similar procedure is possible for all changes in state, for example, evaporation, melting, condensation, crystallization, dissolution, ionization, dissociation, and neutralization. From eq. (3.8a) follows the temperature dependency of enthalpy (without phase transfer): T2

H(T2 ) = H(T1 ) + ∫ Cp dT .

(3.14)

T1

This equation can be applied to each compound participating in the chemical process; written in standard enthalpies of formation, it is called Kirchhoff ’s law⁶: T2

∆R H ⊖ (T2 ) = ∆R H ⊖ (T1 ) + ∫ ∆R Cp dT , T1

6 Not to be confused with the radiation law of the same name.

(3.15)

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107

where ∆R Cp = ∑i ν i Cp,i . As an example, for a gas-phase reaction (in parentheses is the standard enthalpy of formation in kJ/mol), CO (−110.5) + H2 O (−241.8) 󴀘󴀯 CO2 (393.5) + H2 (0) , it follows for the reaction enthalpy that ∆R H298 = (−393.5 + 110.5 + 241.8) kJ/mol = −41.2 kJ/mol.

3.1.2 Second law of thermodynamics and its applications With the first law of thermodynamics, we have learned that heat and work are mutually convertible. Nevertheless, there was no statement about whether this conversion has unlimited potential. Moreover, no information about the direction of chemical processes was provided. To describe chemical conversions, this question is of crucial importance. The second law of thermodynamics is an empirical finding that was accepted as an axiom of thermodynamic theory. Using this law we can calculate the state of equilibrium and, hence, the chemical yield of a reaction. The basic empirical finding is that all spontaneously natural processes go in a specified direction, the simplest being that heat will naturally flow from a hotter to a colder body (and never the reverse). All processes (changes of state and chemical reactions) can be subdivided into reversible and irreversible processes. All voluntary processes in a given direction are irreversible. For example, the volcanic eruption of SO2 into the air leads through diffusion to mixing – a separation of SO2 from air is per se impossible but only when processing outer work. 3.1.2.1 Entropy and reversibility The quantities ∆U and ∆H might also be expressed as heat because all kinds of energy, which the system exchanges with its surroundings, can be completely transferred to heat, in accordance with the law of energy conservation. The general driving force can be quantified as entropy. With these qualifications, it is possible to study whether a process runs voluntarily. Voluntary processes in the environment are of crucial interest because it is nearly⁷ impossible to trigger desired changes in pressure and temperature. Only voluntary chemical processes can be observed in nature. The finding that all processes can be grouped into voluntary and involuntary processes leads to the second law of thermodynamics. It is impossible to carry out a process with an uptake of heat from a reservoir and its complete transfer into work (there is no perpetuum mobile). In slightly different

7 It is not impossible, for example in weather modification (rainmaking, hail prevention, and fog dissipation), but only through “catalytic” triggering.

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phrasing, heat is low-grade energy, i.e., whereas heat always degrades, heat of a lower grade will always remain (e.g., in the form of IR radiation). This “loss” can be termed dissipated work. The “value” of heat is determined by the temperature of the system; the higher the temperature, the more heat that is transferable to work (useful energy). This property of heat is characterized by entropy, which is a state function and, hence, independent of the way in which the process is carried out: dS =

dQrev . T

(3.16a)

In the case of isothermal processes, we can rewrite it as follows: ∆S =

Qrev . T

(3.16b)

Qrev is reversible heat taken up by the system at a given temperature. In a closed system,⁸ the total energy remains constant, and so the direction of a process is associated with the redistribution of energy. Experience has shown that voluntary processes always result in a larger disorder of the system (∆S > 0). This is a condition for an irreversible process, which cannot return the system or surroundings to their original conditions. Consequently, a reversible process in an adiabatic isolated system is characterized by ∆S = 0. This is an ideal abstraction because all processes in nature are spontaneous and, hence, voluntary and irreversible. This does not exclude cycling processes, for example biogeochemical material cycles where all single processes are irreversible but directed in a cycle, not returning the system to its original condition but maintaining a steady state. This also does not exclude small intermediate steps that are reversible. The Nernst heat theorem (also termed the third law of thermodynamics)⁹ says that the entropy of all pure solid bodies goes to zero at absolute zero (0 K): lim S = 0 .

T→0

(3.17)

Hence at each T (T > 0) S must be greater than 0. The absolute value of S is calculated according to T

S = ∫ Cp

dT . T

(3.18)

0

Considering spontaneous processes from the view of probability f (with a range of values 0. . . 1), irreversible processes operate as transfers from a less probable to a more 8 In nature, a closed system is a fiction or a model approximation. The atmosphere is open to space and the Earth’s surface. The Earth system is open regarding energy flux and only apparently closed regarding mass, when not considering cosmic epochs. 9 Discovered in 1905 by Walther Herman Nernst (1864–1941) while lecturing in the Walther-NernstHörsaal (lecture hall) of the “Institut für Physikalische Chemie” at Bunsenstrasse 1, Berlin, where the author (DM) attended lectures on physical chemistry in the years 1968–1969.

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probable state. Ludwig Boltzmann (1844–1906) derived the equation S = k ⋅ ln f + constant ,

(3.19)

where k is Boltzmann constant. With the assumption by Max Planck (1858–1942) that the constant is equal to zero, eq. (3.19) can also be written ∆S = k ⋅ ln

f2 , f1

(3.20)

where f1 and f2 denote the probabilities of the initial and final states, respectively. 3.1.2.2 Thermodynamic potential: Gibbs–Helmholtz equation The equilibrium condition for an isolated system is dS = 0, i.e., a change in entropy is zero in equilibrium. During the reaction, the entropy increases to a maximum when approaching equilibrium. Isolated systems (no exchange of energy and matter with the surroundings), however, do not occur in nature. For nonclosed systems, we need another condition of equilibrium. For isothermal and isobaric processes the total entropy, that is, the entropy of the system dS and that of the surrounding dSenv , remains constant: dSenv = − dS. Because we use for the reversible heat change Qrev the enthalpy H, we get − d S = dH/T, respectively d H+T dS = 0. The temperature is constant (isothermal process), so we can write the difference in the form d(H − TS) = 0 .

(3.21)

This is the condition for equilibrium under isotherm-isobaric conditions; the function (H−TS) reaches a minimum at equilibrium (but its change is zero) and was introduced as the thermodynamic potential or free enthalpy G (also termed Gibbs energy): G = H − TS .

(3.22)

Equilibrium condition: dG = 0 (T = constant, p = constant, G minimum). Rearranged, eq. (3.22) reads H = G + TS, i.e., the enthalpy is the sum of free enthalpy G and a bonded energy TS. Free enthalpy is that part of enthalpy that can be fully transformed during a reversible process into any other kind of energy, i.e., the maximum work carried out. Bonded energy TS cannot be extracted from a system at constant temperature. To characterize the equilibrium condition for an isothermal-isochoric process (constant volume), the free energy (also termed Helmholtz energy) F was introduced in a similar way: F = U − TS . (3.23) Changes in the state at a constant temperature can be written dF = dU − T dS

and

dG = dH − T dS .

110 | 3 Fundamentals of physicochemistry in the climate system With the condition of “voluntariness” of the process, that is, dS ≥ 0, another important thermodynamic condition follows: dF T,V ≤ 0

and

∆G T,p ≤ 0 .

In a spontaneous operating process, the change in free energy is negative, whereas in equilibrium dW T,V = 0 holds. The change in free energy corresponds to the maximum possible work that can be carried out (dW = −p∆V). A more general criterion for the “voluntariness” of processes, however, is the attempt to acquire a maximum from the sum of entropy changes in the system (dS) and the surroundings (− dU/T) or, in other words, to obtain a small total entropy. The criterion ∆G T,p ≤ 0 means in chemistry that a chemical reaction at constant temperature and constant pressure is connected with a decrease in free enthalpy. Hence, it makes sense to introduce free standard enthalpies ∆R G⊖ to calculate reactions and equilibria: ∆R G⊖ = ∆R H ⊖ − T∆R S⊖ .

(3.24)

It is logical to treat a change in free enthalpy as a function of p and T: dG = dH − T dS − S dT .

(3.25)

Because H = U + pV, we have dH = dU + p dV + V dp and using the fundamental equation dU = T dS − p dV, it follows finally that dG = V dp − S dT .

(3.26)

The free enthalpy is a function of pressure and temperature G(p, T), i.e., dG = ∂G ( ∂G ∂p )T dp + ( ∂T )p dT, and it follows that (

∂G ) = −S ∂T p

and

(

∂G ) =V. ∂p T

(3.27)

Because S takes positive values, G must decrease if T is increasing in a system at constant pressure and constant composition. In gases, G responds more sensibly to pressure variation than in condensed phases (because gases have a large molar volume). From eq. (3.27) the temperature dependency of free enthalpy can be derived. Owing to S = (H − G)/T, after a few steps we get the well-known Gibbs–Helmholtz equation: (

∂ G H ( )) = − 2 . ∂T T p T

(3.28)

Relating this equation to the initial and final states of a chemical reaction or physical change of state, it follows that, because ∆G = G2 − G1 , (

∂ ∆G ∆H ( )) = − 2 . ∂T T T p

(3.29)

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3.1.2.3 Chemical potential Chemical potential denotes how the free enthalpy of a system changes with changing chemical composition. The driving force of all voluntary processes is the existence of a gradient, such as temperature, pressure, concentration, electric charge, and so forth, gaining equilibrium. The thermodynamic potential of a pure substance depends only on T and p. In mixtures, another state function, the amount n must be considered: G(T, p, n1 , n2 . . .). In a binary system, the differential change is given by dG = (

∂G ∂G ∂G ∂G dp + ( dT + ( ) dn1 + ( ) dn2 . ) ) ∂p T,n1 ,n2 ∂T p,n1 ,n2 ∂n1 T,p,n2 ∂n2 T,p,n1

The first and second differential quotients (pressure and temperature gradients, respectively) we already know; the last two differential quotients (∂G/∂n) of any chemical species are termed partial molar thermodynamic potential (partial free enthalpy) or, according to Gibbs, chemical potential μ. Therefore, equilibrium of all kinds can be clearly described, especially in mixtures or multiphases. A substance between two phases (e.g., aqueous/dissolved and gaseous) has a certain chemical potential in each phase – equilibrium is reached when μ 1 = μ 2 or ∆μ = 0. For pure substances (because dn i = 0) it holds that μ = G = H − TS. The molar free enthalpy for solids and liquids depends slightly on pressure, but for gases, this dependency is large. The total derivative dG follows from eq. (3.25) with consideration of the gas equation for molar quantities (V = RT/p; note that V denotes here the molar volume Vm ): dG = V dp = RT ln p , (3.30) where dp/p = dln p (= dln(p/p0 ) more precisely); p0 is set to 1 bar but might gain any reference value. After integration and μ = G we get the important equation μ = μ ⊖ + RT ln p , μ⊖

(3.31)

denotes the chemical standard potential. The difference μ − μ0

where is equal to the molar work when the ideal gas is reversible and isothermally transferred from standard pressure to pressure p. In an open system – its chemical composition does not need to be constant – a change in G must be described with a variation in p and T as well with n, the composition. Besides the terms (∂G/∂p)T,n = V and (∂G/∂T)p,n = −S, it further follows eq. (3.32) as a general definition of the chemical potential that (

∂G ) = μi . ∂n i p,T,nj

(3.32)

The constancy of the chemical composition is expressed by n j (in addition to p and T). From the thermodynamic fundamental equation, it now follows for H and U: μi = (

∂U ) ∂n i S,V,nj

and

μi = (

∂H ) , ∂n i S,p,nj

resp.

(3.33)

112 | 3 Fundamentals of physicochemistry in the climate system

In an ideal mixture, i.e., the components do not interact through intermolecular forces, and the chemical potential of each component is equal to that of the pure component if its pressure is identical to the partial pressure in the composition (valid in air): μ i = μ ⊖i + RT ln p i . (3.34) Because of p i = p ⋅ x i it follows that μ i = μ⊖i + RT (ln p + ln x i ) = [μ ⊖i ] + RT ln x i .

(3.35)

where [μ ⊖i ] denotes a new standard potential of the pure gas i at total pressure p, whereas μ ⊖i denotes the standard potential for the pure gas i at a pressure of 1 atm. As with gases for diluted solutions (otherwise activities a j must be used; see eq. (3.41)) we write μ i = μ⊖i + RT ln c i , (3.36) where μ ⊖i denotes the standard potential of the dissolved compound i at a concentration of 1 mol L−1 . With the presence of a multiphase system (e.g., droplets or particles in air, particles in water), several new types of energy increase the inner energy U of the system (eq. (3.3)). The mixing work μ dn, surface work γ dA, and electrical work E dQ (for charge Q, see eqs. (4.101) and (4.102)) are the most important forms: dU = T dS − p dV + μ dn + γ dA + E dQ + ⋅ ⋅ ⋅ .

(3.37)

Considering only the phase transfer and change of temperature, pressure, and amount, eq. (3.22) transforms into G = G (T, p, n i ) = H (T, p, n i ) − TS = U + pV − TS

(3.38)

and dG(T, p, n) =

∂G (T, p, n i ) ∂G(T, p, n) ∂G(T, p, n) dT + dp + ∑ dn i . ∂T ∂p ∂n i

(3.39)

It follows at a constant pressure and temperature that dG p,T = ∑ μ i dn i .

(3.40)

Again, the system is in equilibrium when dG = 0. Without further discussion, it is clear that such a condition is hardly achievable in natural environments. 3.1.2.4 Chemical potential in real mixtures: Activity We stated that under environmental conditions, air can be regarded always as an ideal gas (otherwise the pressure p must be exchanged by the fugacity ψ). However, in real aqueous solutions at very high concentrations, for example scrubbing solutions in

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flue gas treatments, nucleation of CCNs (droplet formation), and saturated deep or salty waters, the chemical potential can be expressed by the same equations as for ideal solutions if concentration c (eq. (3.36)) is exchanged by activity a: μ i = μ⊖i + RT ln a i .

(3.41)

In real solutions the intermolecular (or interionic) distance is smaller and hence attractive forces (Coulomb interaction) occur, making the apparent concentration (which determines all thermodynamic relationships) smaller than the true one, expressed by the activity coefficient γ i : (3.42) ai = γi ci . The standard condition μ i = μ⊖i is given when RT ln a i = 0, i.e., a i = 1 (dimensionless fraction) or a i = 1 mol/L and a i = 1 mol/kg (molar concentration). The real solution approaches the ideal case when γ i → 1: μ real = μ ideal + RT ln γ i .

(3.43)

An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behavior in a mixture of chemical substances; it depends on temperature, chemical composition (i.e., on all electrolytes in solution), and ionic strength. In mixtures, the charge (valence) z of different ions is important for the value of a. The electrolytic dissociation (Chapter 4.4.1.3) of a binary salt is described by the general expression z− z+ z− Az+ , (3.44) ν+ B ν− 󴀘󴀯 ν+ A + ν − B for example,

NaCl 󴀘󴀯 Na+ + Cl− , (NH4 )2 SO4 󴀘󴀯 2 NH+4 + SO2− 4 .

It is convenient to define a mean ionic activity a± : μ± ≡

ν+ μ Aν+ + ν− μ Bν− = μ ⊖± + RT ln a± , ν

(3.45)

with ν = ν+ + ν− . It is not possible to estimate the activity coefficient of single ions, only the mean activity coefficient¹⁰ γ± (Debye–Hückel equation)¹¹: γ± =

∑z

√∏ γ zi .

(3.46)

This general equation simplifies for one-one-valence ions (NaCl for example): γ± = √γ+ γ− .

(3.47)

10 The term “mean” is here not used in its common sense of an average. 11 Peter Joseph William Debye (1884–1966) and Erich Armand Arthur Joseph Hückel (1896–1980) developed a theory by which we can calculate activity coefficients of electrolyte solutions (Debye and Hückel 1923).

114 | 3 Fundamentals of physicochemistry in the climate system

Tab. 3.1: Mean activity coefficients of electrolytes in aqueous solution at 298.15 K. Molality (in mol/kg)

0.001

0.005

0.01

0.05

0.1

0.5

1.0

KCl NaCl H2 SO4 HCl Na2 SO4 Na2 CO3 NH4 Cl NH4 NO3

0.966 0.966 0.737 0.966 0.887 0.891 0.961 0.959

0.927 0.930 0.646 0.929 0.778 0.791 0.911 0.912

0.902 0.906 0.543 0.904 0.714 0.729 0.880 0.882

0.818 0.779 – 0.730 0.536 0.565 0.790 0.783

0.771 0.736 0.379 0.796 0.453 0.488 0.792 0.726

0.655 0.689 0.221 0.757 – 0.288 0.620 0.558

0.611 0.664 0.186 0.809 – – 0.579 0.471

The theory of activity coefficients in solution is very complex (the interested reader should refer to the specialized literature, for example, Wright 2007); mean binary activity coefficients can be measured (Table 3.1) but also calculated according to the Pitzer theory (Pitzer 1973, 1979).

3.2 Equilibrium The term equilibrium means generally the condition of a system in which all competing influences are balanced. It is used differently in biology, physics, chemistry, and economics (and other disciplines too). Here we consider the chemical equilibrium (the state in which the concentrations of reactants and products have stopped changing over time), the gas-aqueous equilibrium (where the rates of condensation and vaporization of a material are equal), and the solubility equilibrium (any chemical equilibrium between solid and dissolved states of a compound at saturation). In environmental chemistry, the dynamic equilibrium (the states in which two reverse¹² processes occur at the same rate) is often considered. However, in nature, as an open system, equilibrium exists only on a microscale or is approximated – the general tendency of all chemical processes is irreversibility. In the previous chapters, we dealt with the conditions for equilibrium and summarize them here: Isolated system: dS = 0 Open system (isothermal-isochoric process): dF = 0 Open system (isothermal-isobaric process): dG = 0 Mixtures: dμ = 0

12 Note that reversible is not meant (often misused in literature) but opposed processes such as influx and outflow.

3.2 Equilibrium |

115

3.2.1 Chemical equilibrium: The mass action law We stated previously that a reversible process between two states characterizes equilibrium A 󴀘󴀯 B, whereas no limiting conditions are expressed for states A and B. Thus, it can be a chemical (reversible) reaction or any phase transfer (gas–liquid, solid–liquid, solid–gas). It is stated that all chemical reactions tend to reach equilibrium; however, the kinetics of the transfer process A → B can be so slow that under environmental conditions equilibrium will never be approached because other (faster) processes, such as mixing and transport, continuously interrupt the process A → B. Hence, only a few types of (fast) chemical reactions represent measurable equilibrium: acid–base reactions, adduct formation, complexation, and addition–dissociation. Phase equilibrium is often observed in nature: dissolution– precipitation, evaporation–condensation, and absorption–desorption. All nonchemical processes in multiphase systems can be subdivided into partial steps, with each chemical species separately being transported to the interface. In equilibrium, each substance has the same chemical potential in all phases. When the state variable changes (pressure, temperature, molar fraction) but equilibrium remains, the chemical potentials change. However, it holds that the changes are the same in all phases: dμ i = dμ󸀠i . Any chemical reaction or phase transfer including the chemical species Ai and Bj is described by (ν stoichiometric constant) k+

󳨀→ ν1 A1 + ν2 A2 + ν3 A3 + ⋅ ⋅ ⋅ ν m Am 󳨀 ← 󳨀󳨀 ν m+1 B1 + ν m+2 B2 + ν m+3 B3 + ⋅ ⋅ ⋅ .

(3.48)

k−

The law of mass action establishes the relationship between states A and B via the equilibrium constant K; the brackets denote the concentration (or for nonideal systems the activity and fugacity, respectively). By convention, the products form the numerator: K=

[B1 ]ν m+1 [B2 ]ν m+2 [B3 ]ν m+3 . . . . [A1 ]ν1 [A2 ]ν2 [A3 ]ν3 . . .

(3.49)

In eq. (3.48), k + and k − represent the rate constants of the partial processes, i.e., the forward (k + ) and back (k − ) reaction or transfer. Equilibrium also means that the fluxes of the forward and backward processes are equal: F+ = F− because of dμ i = dμ󸀠i and, therefore, dW T,V = 0 and ∆G T,p = 0. Hence, it holds that F+ = (

dn dn ) = k + [A1 ]ν1 [B2 ]ν2 ⋅ ⋅ ⋅ = F− = ( ) = k − [B1 ]ν m+1 [B2 ]ν m+2 . . . dt + dt −

It follows that K=

k+ . k−

(3.50)

(3.51)

In 1886, Jacob van’t Hoff (1852–1911) derived thermodynamically the law of mass action based on work from initial substances Ai and final substances (products) Bj as

116 | 3 Fundamentals of physicochemistry in the climate system

well as the following relationship between free energy and enthalpy and the equilibrium constant either for constant pressure or constant volume but always at constant temperature: (∆R F ⊖ ) V,T = (∆R G⊖ )p,T = −RT ln K . (3.52) From the general definition of chemical equilibrium (dμ i = dμ 󸀠i ), it follows when arriving at the equilibrium (depending on the rate constants, time is needed to achieve the equilibrium)¹³ the conditions (lowercase letters denote mass-related and not molar quantities, as denoted by uppercase letters) that (dg)p,T = 0

(isobar) and (df)V,T = 0 (isochoric–isothermal).

(3.53)

Another general condition for equilibrium follows: (g)p,T = (f)V,T = ∑ μ i dn i = 0 .

(3.54)

Because of ∑ dn i = ν i , it also follows that ∆R G = ∑ ν i μ i = 0. Now, the thermodynamic derivation of K becomes coherent: 0 = ∆R G = ∑ ν i μ i = ∑ (ν i μ ⊖i + RT ln c i i ) = ∆R G⊖ + RT ln K . ν

(3.55)

Using the Gibbs–Helmholtz eq. (3.28) and ∆R G⊖ = ∆R H ⊖ − T∆R S⊖ , we derive the universal van’t Hoff ’ reaction isobar: dln K ∆R H ⊖ . = dT RT 2

(3.56)

Transforming this equation, a practicable expression for the temperature-dependent (of every type) equilibrium constant then follows: K(T) = K298 exp [

1 1 ∆R H ⊖ ( − )] . R 298 T

(3.57)

3.2.2 Phase equilibrium In the climate system, the following phase equilibria occur: – gas–liquid (pure substance): almost water – water vapor relates to plane surfaces (rivers, lakes, ocean) and droplets (sea spray, cloud, fog, rain) but under special conditions other liquids such as crude oil/vapor (evaporation and condensation); – solid–liquid (pure substance): ice – water (melting and freezing); – solid–gas (pure substance): ice – water vapor (sublimation and deposition);

13 Modelers, treating fast equilibrium according to computer integration time, sometimes forget this. However, when the time to achieve equilibrium is greater than the numeric time step, nonsense is calculated.

3.2 Equilibrium

– – – –

| 117

solid–gas (binary system): adsorption of gases on solids and desorption; solid–liquid (binary system): adsorption of liquids or dissolved substances on solids and desorption; gas–liquid (binary system): gas dissolution in water (dissolution and evaporation). solid–liquid (binary system): solid dissolution in water (dissolution and precipitation).

The last two-phase transfer processes are also called dissolution equilibrium, and they play a crucial role in the environment: dissolution of gases from air in water and dissolution of solids in natural waters. The first three phase-transfer processes determine climate on Earth, the distribution of water among its liquid, vapor, and icy states. Adsorption on aerosol particles (and desorption) are important processes in soils and in atmosphere. 3.2.2.1 Gas-liquid equilibrium: Evaporation and condensation We can treat all liquids as condensed gases. Above every liquid, a vapor forms until it reaches equilibrium between both phases. At each temperature a part of the molecules in the liquid transfer to the surrounding air, consuming energy (enthalpy of evaporation). The vapor contains more energy than the liquid. The liquid is in equilibrium with gas when the flux of condensation is equal to the flux of evaporation. The equivalent vapor pressure p (in a closed volume or close to the liquid surface) is the vapor pressure equilibrium. In a closed system, it corresponds to the saturation vapor pressure. The vapor pressure equilibrium depends neither on the amount of liquid nor the vapor but only on temperature (and droplet size if not bulk water, see next chapter). However, in nature, gas-liquid equilibrium occurs only under very limited conditions: close to the water surface and within clouds. Evaporating water from the surface of a river, lake, or sea is advected by wind, thereby shifting the equilibrium to more evaporation. Theoretically, the ocean would slowly evaporate until it reaches atmospheric water vapor saturation. Fortunately, water vapor condenses in air and precipitates back to the sea (and land) by rain and snow, resulting in a global dynamic equilibrium (Chapter 6.1.1). Condensation and evaporation occur at any vapor pressure. When the vapor pressure becomes smaller than the equilibrium value, water evaporates. The change in the chemical potential (we set μ = G) is given by (cf. eq. (3.26)) dG = Vvap dp − Svap dT .

(3.58)

In equilibrium dG = 0 and defining the entropy of evaporation as Svap = ∆vap H/T (∆vap H enthalpy of evaporation) it follows that dp ∆vap H = , dT Vvap T

(3.59)

118 | 3 Fundamentals of physicochemistry in the climate system

which is called Clapeyron’s equation. Replacing the molar volume of evaporated water (Vvap ) through RT/p we obtain the Clausius–Clapeyron equation, describing the change in vapor pressure with temperature: dln p ∆vap H = dT RT 2

or

p2 = p1 exp [

∆vap H 1 1 − )] . ( R T1 T2

(3.60)

In laboratory praxis, from the Clausius–Clapeyron plot of ln p against 1/T, the enthalpy can be derived. The phase equilibrium in mixtures (recall that water in nature is always a solution) is more exactly described by Raoult’s law (Chapter 3.5.2). 3.2.2.2 Gas-liquid equilibrium: Special case of droplets (Kelvin equation) In air,¹⁴ we must consider droplets and not a bulk solution such as in rivers, lakes, or oceans. Experience shows that dispersed small droplets combine to form larger drops. That is because the enthalpy also depends on the surface: the aqueous amount in the form of a droplet possesses a higher chemical potential than the same amount of liquid after coalescence (bulk solution). Another consequence consists in the higher partial pressure droplets have (p∞ + ∆p = p) compared with a bulk volume having a flat surface (p∞ ). Assuming spherical particles, the change in vapor pressure ∆p can be simply derived. The change in free enthalpy dG T,n = dW V + dW A is expressed (T, n = constant) by the changing pressure-volume work dW V = −∆p dV, where dV = 4πr2 dr and the surface energy change dW A (r particle radius, γ surface tension, A surface) dW A = γ dA (eq. (3.99)), where dA = 8πr d r. Equilibrium occurs when dW A dW V =∂ =0. ∂ ∂r ∂r It follows finally that ∆p = 2γ/r. Now we get, taking into account that Vm = RT/p∞ , S=

p∞ + ∆p ∆p 2γ 2γVm p 2γMw = = 1+ =1+ = 1+ = 1+ , p∞ p∞ p∞ rp∞ rRT rρ w RT

(3.61)

where Vm is the molar volume of water (= Vw /nw ), and the volume of water (droplet) Vw = mw /ρ w and mw = Mw /nw (molar mass), p is the actual pressure, and p∞ is the equilibrium pressure of water. It is also possible to derive the equation, describing the pressure change through a change in the chemical potential μ = RT ln p (eq. (3.30)): p

p

∫ dμ = ∫ RT dln p = RT ln p∞

p∞

p = ∆μ . p∞

(3.62a)

On the other hand, d μ = Vm dp (cf. eq. (3.27), and we set d G = dμ and, finally, dμ = ∆μ obtaining p ∆μ=RT ln ∞ = Vm ∆p . (3.62b) p 14 Also in many technical processes (for example exhaust gas cleaning via wet scrubbing) droplets occur.

3.2 Equilibrium |

119

Now again replacing the expression for ∆p, we obtain the Kelvin equation; the equation is named after William Thomson (1824–1907), commonly known as Lord Kelvin: ln S = ln

2γVm p∞ + ∆p p = ≈ p∞ rRT p∞

or

S=

p 2γVm =1+ , ∞ p rRT

(3.63)

where ∆p ≪ p, and S is the saturation ratio (note that exp x ≈ 1 + x). This effect of surface tension on the equilibrium radius of an aqueous drop is also called the Kelvin effect. This equation¹⁵ is valid only for pure water, but in air, we always encounter diluted aqueous solutions. In combination with Raoult’s law, we can consider the role of dissolved matter in lowering the vapor pressure (not shown here). Equation (3.63) says that the formation of droplets is possible only for immense supersaturation; a droplet with r = 10 nm is stable only if supersaturation is 120% (p/p∞ = 1.12). The small water droplets are thermodynamically unstable because of their high vapor pressure. This agrees with the observation that droplets in air are formed only through condensation on nuclei. By contrast, when droplets exist in air, the Kelvin equation says that larger droplets grow via vapor condensation at the expense of smaller droplets, which evaporate. 3.2.2.3 Absorption of gases in water: Henry’s law Any gas in contact with a liquid arrives at equilibrium with the dissolved component, as found first by William Henry (1772–1836) in 1803 (Henry 1803): A(g) 󴀘󴀯 A(aq) .

(3.64)

The equilibrium constant is called Henry’s law constant H (also, reciprocal ratios are used); the dimensions of [A] in mol L−1 and of p in Pa are Hc =

[A(aq)] [A(g)]

or, expressed by the partial pressure of A,

Hp =

[A(aq)] . pA

(3.65)

The temperature dependency of equilibrium constants is described by the van’t Hoff equation (eq. (3.56)) where the reaction enthalpy must be replaced by the enthalpy of dissolution ∆sol H (do not confuse here Henry’s law constant H with enthalpy H): ∆sol G⊖ = −RT ln H = ∆sol H ⊖ − T∆sol S⊖ , dln H ∆sol H ⊖ = dT RT 2

or in other form

dln H ∆sol H ⊖ =− . d(1/T) R

(3.66)

15 This equation is also called the Gibbs–Thompson equation and the effect (surface curvature, vapor pressure, and chemical potential) is also called the Gibbs–Kelvin effect or Kelvin effect.

120 | 3 Fundamentals of physicochemistry in the climate system

This equation is valid only within a limited temperature range; for larger T changes, the standard dissolution enthalpy must by expressed by Kirchhoff ’s law (see textbooks on physical chemistry), taking into account the T dependency of molar heat, given by empirical interpolation formulas (A and I are constants): ln H = −

∆sol H ⊖ 1 A2 A3 2 − (A1 ln T + T+ T + ⋅⋅⋅) + I . RT R 2 6

(3.67)

In close relation to the Henry’s law constant are – Bunsen’s absorption coefficient α (the volume of gas absorbed by one volume of water at a pressure of 1 atmosphere) and – Ostwald’s solubility β (the quantity of solvent needed to dissolve a quantity of gas at a given temperature and pressure): α ⋅ RT = β = Hp RT .

(3.68)

However, these solubility coefficients were only used in older literature. Hence, Bunsen’s absorption coefficient α is identical to the partial pressure-related Henry’s law constant Hp (dimension in mol L−1 Pa−1 ). Another quantity used is the gas solubility S, the mass of a gas dissolved in 100 g of pure water under standard conditions, which is the partial pressure of the gas and the water saturation pressure is equal to 1 atm or 101.325 Pa. Approximately (without considering the density of the solution), it follows (M molar mass of the gas, Hp in mol L−1 Pa−1 ) that S = M ⋅ Hp ⋅ 10.1325

(exactly in grams of solute per 100 g water).

(3.69)

It is important to note that few simplifications were considered in application of Henry’s law (sometimes also called Henry–Dalton’s law): the validity of the ideal gas equation, ideal diluted solution, and the partial molar volume of the dissolved gas is negligible compared with that in the gas phase. However, the range of its validity under environmental conditions is appreciable. Only under very specific conditions (saturation level) of, for example, heterogeneous nucleation, evaporating droplets and dew, and salty waters is Henry’s law not valid. Absolute values of solubility cannot be found from thermodynamic considerations. Nevertheless, general rules are valid for all gases: – decreasing solubility with increasing temperature, – decreasing solubility with increasing salinity of waters (same ratio for all gases), and – increasing volume of aqueous solution with gas dissolution. The equilibrium eq. (3.64) only describes the physical dissolved gas species for gases without subsequent chemical hydrolysis, such as O2 , O3 , N2 , NO, and NO2 . However, immediately after aqueous dissolution many environmentally important gases (CO2 ,

3.2 Equilibrium |

121

SO2 , HCl, NH3 , HNO2 , HNO3 , organic acids) undergo hydrolysis with subsequent electrolytic dissociation, shown here for CO2 (an anhydride): CO2 (g) 󴀘󴀯 CO2 (aq) , CO2 (aq) + H2 O 󴀘󴀯 H2 CO3 , H2 CO3 󴀘󴀯 HCO−3 + H+ , + HCO−3 󴀘󴀯 CO2− 3 +H .

For acids, it is simpler: HNO2 (g) 󴀘󴀯 HNO2 (aq) , HNO2 (aq) 󴀘󴀯 NO−2 + H+ . Of interest, however, is the total solubility of the gas including the hydrolysis products. Hence an apparent Henry’s law constant was introduced, where the dissolved matter comprises the anhydride (e.g., CO2 or SO2 ) and the acid (H2 CO3 , H2 SO3 ). The acid can dissociate and thereby increases the total solubility of gas A, as described by the effective Henry’s law constant Heff (Table 3.2): 󳨀󳨀󳨀 󳨀→ 󳨀󳨀󳨀 󳨀→ HAO− ← AO2− , A + H2 O 󴀘󴀯 H2 AO ← 󳨀󳨀 󳨀󳨀 + + −H

Heff =

−H + [HAO− ] + [AO2− ]

[A(aq)] + [H2 AO] [A(g)]

(3.70) .

(3.71)

Excluded from the total solubility or effective Henry’s law are subsequent reactions, for example, the oxidation of dissolved SO2 into sulfuric acid (sulfate). The oxidation increases the flux into water and thereby the phase partitioning, but it cannot be described by equilibrium conditions (Chapter 3.6.5.4). For easily soluble gases such as HCl and HNO3 , the “physical” dissolved molecule does not exist (or is in immeasurably small concentrations, i.e., c(aq) → 0) because of full dissociation: HCl(g) 󴀘󴀯 HCl(aq) → Cl− (aq) + H+ (aq) . Therefore, Henry’s law constant for these gases represents the equilibrium between gas and the first hydrolysis states: H ≡ Heff =

[HAO− ] . [A(g)]

(3.72)

More limitations must be considered in the application of Henry’s law under atmospheric conditions. In droplet dispersions (clouds, fog, rain, wet scrubber), because of the different chemical composition of the CCNs and, thus, the initial droplets after their formation through heterogeneous nucleation, different equilibria occur on a microscale. It is important to note that then Henry’s law is valid only for each droplet with its gaseous surrounding, i.e., taking into account the gas concentration close to the

122 | 3 Fundamentals of physicochemistry in the climate system Tab. 3.2: Henry’s law constants (mol L−1 at m−1 ) and temperature dependency for selected gases: ∆ sol H ⊖ 1 1 H(T) = H 298 [ − )] (cf. eq. (3.57). Data from Sander (2015), who compiled 17,350 ( R T298 T values of Henry’s law constants for 4632 species collected from 689 references (http//www.henryslaw.org). −1

H298 (in mol m−3 Pa )

Species O2 O3 H2 O2 HO2 OH H2 N2 N2 O NO NO2 NO3 N2 O3 N2 O4 N2 O5 HNO2 HNO3 NH3 NH2 OH SO2 SO3 H2 S Cl2 Cl HCl ClO ClO2 Cl2 O HOCl NOCl ClNO2 ClNO3 CH4 Hg

Oxygen Ozone Hydrogen peroxide Hydroperoxyl radical Hydroxyl radical Hydrogen Nitrogen Dinitrogen monoxide Nitrogen monoxide Nitrogen dioxide Nitrate radical Dinitrogen trioxide Dinitrogen tetroxide Dinitrogen pentoxide Nitrous acid Nitric acid Ammonia Hydroxylamine Sulfur dioxide Sulfur trioxide Hydrogen sulfide Chlorine Chlorine atom Hydrogen chloride Monochlorine monoxide Chlorine dioxide Dichlorine monoxide Hypochlorous acid Nitrosyl chloride Nitryl chloride Chlorine nitrate Methane Mercury

⋅ 10−5

1.2 1.0 ⋅ 10−4 9.1 ⋅ 10−2 6.8 3.8 ⋅ 101 7.8 ⋅ 10−6 6.4 ⋅ 10−6 2.4 ⋅ 10−4 1.9 ⋅ 10−5 1.2 ⋅ 10−2 3.8 ⋅ 10−1 5.9 ⋅ 10−3 1.4 ⋅ 10−2 ∞ 4.8 ⋅ 10−1 2.1 ⋅ 103 5.9 ⋅ 10−1 1.4 ⋅ 103 1.3 ⋅ 10−2 ∞ 1.0 ⋅ 10−3 9.1 ⋅ 10−4 2.3 ⋅ 10−2 1.5 ⋅ 10−1 7.0 ⋅ 10−3 1.0 ⋅ 10−2 1.7 ⋅ 10−1 6.6 ⋅ 102 > 4.9 ⋅ 10−4 4.5 ⋅ 10−4 ∞ 1.4 ⋅ 10−5 1.3 ⋅ 10−3

−∆ sol H⊖ /R (in K) 1700 2800 6600 (5000) (4000) 530 1600 2700 1600 (2000) (2000) (2000) 4800 8700 4200 2900 2100 2000

3500 1800 5900

1900 2700

droplet’s surface and the aqueous-phase concentration (neglecting here further limitations through mass transport). This likely is the main reason (besides others such as surface-active components influencing the gas-liquid equilibrium) why in bulk experimental approaches (integral droplet collection and chemical analysis of water) deviations from Henry’s law have always been found. In modeling, the spectral resolution of particles and droplets (concerning in connection with size and chemical composition) is the only way to approach the reality.

3.2 Equilibrium

| 123

3.2.2.4 Solubility equilibrium: Solid–aqueous equilibrium If a solid substance (the solute) is in contact with a liquid (the solvent; however, we only consider water in the environment) without a chemical reaction with water molecules, dissolution proceeds only to a certain extent, called a saturated solution. This is in connection with the solid deposit of a heterogeneous system where the equilibrium is described by the concentration (or mixing ratio) of the solid substance in aqueous solution: A(s) 󴀘󴀯 A(aq) . (3.73) According to IUPAC terminology (IUPAC 2014), different terms such as dissolution, solution, and solvation must be distinguished. Solubility is a thermodynamic property referring to the ability of a given substance, the solute, to dissolve in a solvent. The solution is a homogeneous mixture of the solvent (which is the majority) and the solute. Dissolution is a kinetic process, the transfer of the (soluble) solid substance to the liquid solvent (water), and is quantified by its rate. Dissolution occurs because the solvent (water) is dipolar, attracts, and associates with molecules or ions of a solute. Dissolution is always accompanied by solvation, i.e., the dissolved molecule becomes surrounded by solvent molecules: A(aq) 󴀘󴀯 A (H2 O) n .

(3.74)

The index (aq) also often includes that the species is hydrated (solvated by H2 O). Additionally, solubility can be augmented by complexation (Chapter 4.4.1.5). Solubility quantifies the dynamic equilibrium state (eq. (3.73)) achieved when the rate of dissolution equals the rate of precipitation. Solubility depends on temperature. An equation similar to that for evaporation (eq. (3.60)) can be derived, where ∆sol H ∞ is the enthalpy of a solution¹⁶ for indefinite dilution: dln c ∆sol H ∞ . = dT RT 2

(3.75)

If the saturation concentration exceeds (e.g., by changing T and pH), the solute precipitates and forms a solid precipitate (or sediment). Salts dissociate (the charge is here not important for describing the solubility and is therefore ignored; cf. eq. (3.44)): Aα Bβ (s) 󴀘󴀯 αA(aq) + βB(aq) .

(3.76)

The equilibrium is described by (Chapter 3.2.1) Ksol =

[A]α [B]β . [Aα Bβ ]s

(3.77)

16 Also called solution enthalpy and enthalpy of dissolution (it includes the processes of dissolution and solvation).

124 | 3 Fundamentals of physicochemistry in the climate system Tab. 3.3: Solubility product constants in (mol/L)2 for 25 °C. Electrolyte CaSO4 Ksp a

4.9

⋅ 10−5

Ca(OH)2 5.0

MgCO3

⋅ 10−6

6.8

CaCO3

⋅ 10−6

3.4

a

⋅ 10−9

FeCO3 3.1

⋅ 10−11

FeS 8

⋅ 10−19

AlPO4 9

⋅ 10−21

Fe(OH)2 2.8 ⋅ 10−39

Calcite.

The term [AB]s denotes the concentration of AB in the pure substance AB and is therefore constant (e.g., dimension in mol/L or kg). We define a solubility product constant Ksp and can write (Table 3.3) Ksp = [A]α [B]β = Ksol [Aα Bβ ]s .

(3.78)

The T dependency in the case of electrolytes is now given by (cf. eq. (3.56)) dln Ksol ∆sol H ∞ = . dT RT 2

(3.79)

Note that in eqs. (3.77) and (3.78) instead of concentration c, activity a (Chapter 3.1.2.4) must be used more exactly. However, in the case of diluted solutions and difficult-todissolve substances (e.g., SiO2 , CaCO3 , AgCl), hence very small aqueous-phase concentrations, the activity coefficients are practically equal to 1, and we can use concentrations instead of activities. 3.2.2.5 Adsorption and desorption A measure for the adsorption of a substance on a surface is the coverage degree θ: θ=

number of occupied adsorption sites . number of available adsorption sites

(3.80)

In the case of multilayer formation, it is useful to express the coverage degree by θ = V/Vads , where Vads denotes the volume of the adsorbed substance in a monolayer. Adsorption and desorption can be described as well as the kinetic and equilibrium process. Equilibrium is described by the general condition f(n, p, T) = 0 in the gas phase and f(n, c, T) in the aqueous phase. The process is described at either constant pressure (adsorption isobar) or constant temperature (adsorption isotherm). There is no difference in the kinetic description of adsorption for the gas (g) or aqueous (aq) phase. The simplest adsorption isotherm after Freundlich and Langmuir is based on equilibrium: kads

󳨀󳨀󳨀 󳨀→ A(g, aq) + Psurface ← 󳨀󳨀 [A(ads) − Psurface ]

(3.81)

kdes

or, simplified, A(g, aq) 󴀘󴀯 A(ads). It is assumed that the change in coverage degree over time is proportional to the partial pressure of A and the number N of free adsorption sites: dθ ( ) = k ads pA N(1 − θ) ; (3.82) dt ads

3.2 Equilibrium

| 125

similarly we set eq. (3.83) for the desorption kinetic: (

dθ ) = k des Nθ . dt des

(3.83)

In equilibrium (K = kads /k des ) we have dθ/ dt = 0, and we obtain for gases (change p to c for dissolved substances in the aqueous phase) θ=

KpA . 1 + KpA

(3.84)

When KpA ≫ 1, then θ → 0. Normally, however, it is the condition KpA = 1 (low gas concentration) that leads to θ = KpA and θ ≪ 1. Consequently, eq. (3.82) simplifies to Rads = k 󸀠ads pA ; the adsorption site number N is included in the adsorption coefficient. Because θ = n/nmax (n – amount of adsorbed substance), and setting 1/K = β (in the sense of an adsorption coefficient, see eq. (3.68)), we finally obtain pA pA β + . = n nmax nmax

(3.85)

Another adsorption isotherm according to Brunauer, Emmet, and Teller (the so-called BET isotherm) is useful for the formation of multilayer adsorption, i.e., there is no principal limitation of saturation or coverage degree: (p∞ A

1 (E − 1)pA pA = + ∞ , EV EV − pA ) V mon mon pA

(3.86)

where p∞ denotes the saturation pressure of the pure liquid phase of the adsorbed gas A, V is the total volume of the adsorbed substance A (Vmon that of the monolayer), and E is an empirical constant. A special phenomenon is the adsorption of gases in porous media, such as water adsorption in soils, termed adsorption and capillary condensation. Conventional models of liquid distribution, flow, and solute transport in partially saturated porous media are limited by the representation of media pore space as a bundle of cylindrical capillaries (BCC); they ignore the dominant contribution of adsorptive surface forces and liquid films at low potentials. For small capillaries (radius 2–30 nm) the adsorbed water layers can be unified, i.e., the cylinder is filled with water, and a meniscus immediately forms at the liquid–vapor interface, which allows for equilibrium below the saturation vapor pressure p∞ . Meniscus formation is dependent on the surface tension of the liquid (Chapter 3.5.1) and the shape of the capillary. The Kelvin equation (eq. (3.63)) describes the lowering of the vapor pressure.

126 | 3 Fundamentals of physicochemistry in the climate system

3.3 Steady state As noted earlier, one of the general conditions for equilibrium and steady state¹⁷ is that the forward and backward fluxes of a process are equal (F+ = F− ). The specific condition to fulfill a chemical equilibrium is μ+ = μ − (eq. (3.54)). Although chemical equilibrium occurs when two or more reversible processes occur at the same rate, and such a system can be said to be in steady state, a system that is in steady state might not necessarily be in a state of equilibrium, because some of the processes involved are not reversible. A system in steady state has numerous properties that do not change over time. The concept of steady state has relevance in many fields, in particular thermodynamics. Hence, steady state is a more general situation than dynamic equilibrium. If a system is in steady state, then the recently observed behavior of the system will continue into the future. In stochastic systems, the probabilities that various different states will be repeated will remain constant. We will set up a generalized equation as follows (see also eq. (3.50)): (

dn dn dn ) = ( ) − ( ) = 0 or dt dt + dt −

F = F+ − F− = 0 ,

(3.87)

in connection with F+ the source term (emission Q) and F− the total removal term R (deposition and chemical conversion). In many systems, steady state is not achieved until some time has elapsed after the system is started or initiated. This initial situation is often identified as a transient state, the start-up or warm-up period. The term steady state is also used to describe a situation where some, but not all, of the state variables of a system are constant. For such a steady state to develop, the system does not have to be a flow system. Therefore, such a steady state can develop in a closed system where a series of chemical reactions takes place. The literature on chemical kinetics usually refers to this case, calling it steady-state approximation. Steady-state approximation, occasionally termed stationary-state approximation, involves setting the rate of change of a reaction intermediate in a reaction mechanism equal to zero. Steady-state approximation does not assume the reaction intermediate concentration is constant (and therefore its time derivative is zero). Instead, it assumes that the variation in the concentration of the intermediate is almost zero. The concentration of the intermediate is very low, so even a large relative variation in its concentration is small, if considered quantitatively. These approximations are frequently used because of the substantial mathematical simplifications this concept offers. Whether or not this concept can be used depends on the error the underlying assumptions introduce. Therefore, even though a steady state, from a theoretical point of view, requires constant drivers (e.g., constant inflow rate and constant concentrations in the inflow), the error introduced by assum-

17 Sometimes also called stationary state and Bodenstein approximation (IUPAC 2014).

3.3 Steady state | 127

ing steady state for a system with nonconstant drivers might be negligible if the steady state is approached fast enough (relatively speaking). This is often the case for very reactive chemical species, especially radicals such as hydroxyl (OH). Steady-state OH concentration is then expressed by the condition d[OH]/ dt = 0 from which follows ∑ k i [Ai ] [Bi ] = [OH] ∑ k j [Cj ] , i

(3.88)

j

where the terms on the left-hand side represent all reactions producing OH and those on the right-hand side all reactions consuming OH. However, in truth this is valid only for a short time, depending on the error being taken into account (a few minutes, but this time is long compared with the atmospheric OH lifetime on the order of seconds). The approximation of OH steady state is also useful for adopting a mean “constant” OH concentration (independent of diurnal cycles) (Chapter 4.4.9, Volume 2) to reduce second-order reactions to pseudo-first-order reactions (Chapter 4.2.3). The principle of stationarity (or instationarity) is also applied to the atmospheric budget of trace species. With the definition of the residence time (see Chapter 2.7 for more details) it follows from eq. (3.87) that ln

n(0) ∆t = , n(∆t) τ

(3.89)

where n(0) is the (initial) amount of a substance in air at t = 0. To fit the steady-state condition Q = R over a given unit of time (e.g., 1 year), there is no condition concerning the quantity of the residence time. Normally, it is believed that a short residence time (say, τ ≪ 1 yr) corresponds to a large removal capacity; if τ = 1 day (e.g., formic acid), after 7 days, 99.9% of the initial amount n(0) is removed from the atmosphere independently of the absolute amount. Consequently, the yearly removal capacity is some 50 times higher. As another consequence, the mean atmospheric concentration of this substance remains very low (but depends on the influx or emission). Regarding the example of a large residence time, τ = 10 years (e.g., methane), after 1 year only about 10% of n(0) is removed from the air, as follows from eq. (3.89). Yet we must consider that n(0) represents the total amount of the substance at an arbitrary time (here set t = 0); this consists of the actual emission flux and past cumulative emission versus the removal rate. Let us say an experiment with an emission process starts (year 1) with continuous emission over time (100 units per year); after 1 year, 90% remains in air due to the slow removal capacity (τ = 10 years). In year 2, the fresh emission (100 units) will be added to the remaining emission from year 1, but the absolute removal (10% relatively) is larger: (100 + 90) ⋅ 0.1 = 19 units. Hence, the atmospheric amount (and concentration) increases from year to year, but the absolute removal amount also rises until reaching equilibrium, when the yearly removal becomes equal to the emission (100 units) – that is, for the example of CH4 , in 10 years. In all subsequent years, the stationarity Q = R remains and a stationary concentration is achieved. The higher the

128 | 3 Fundamentals of physicochemistry in the climate system

residence time (and emission), the larger the atmospheric amount of the substance. Because of dn/ dt = F− = R = n/τ (eq. (3.87)) and the condition Q = R, it follows that natm = τ ⋅ Q .

(3.90)

However, this experiment simply implies that a steady state is achieved some time after the system is started and that Q is constant, which is the normal case for natural processes on a climatological timescale. With yearly rising emissions, as is typically the case for anthropogenic processes such as fossil fuel combustion, the system remains out of stationarity, and the time to achieve steady state is endless while the emissions continue to increase. Hence, the atmospheric concentration increases (as seen for GHGs). This increase is simply calculated from concentration increase (in %) = 100 ⋅

Qi − Ri , ni + Qi

(3.91)

where the subscript i denotes the year under consideration, n is the total amount in the air, and Q and R are the yearly amounts of emission and removal, respectively. For the example of CO2 , it follows using the values for 2010 (from Figure 3.16 and Table 5.1 in Volume 2) that 8.9 − 4.8 100 = 0.6% . 800 + 8.9 This is in full agreement with the measurements (shown in Figure 4.53, Volume 2), which shows that the increase for the period 2000–2005 is about 2.2 ppm year−1 and that this results in a 0.6% increase based on a total of 370 ppm. Despite the complexity of atmospheric processes, this approximation shows that nature follows simple generic principles. Let us return to the CO2 residence time. Equation (3.90) cannot be applied because the system is still far from steady state (F+ > F− ). Hence, the condition Q = R is invalid. It is stated that from a total of 8.9 Gt emitted carbon (year 2010), about 50% is removed by absorption through oceans and the continental biosphere. Hence, the anthropogenic CO2 uptake is biogenic – as discussed in Chapter 5.2.2, Volume 2 – and cannot be described by a first-order law eq. (3.89). The key question remains as to what controls the biogenic uptake of anthropogenic CO2 . Figure 5.1 in Volume 2 suggests that it is (so far) a linear process with 50% yearly uptake of emitted CO2 . Again, this discussion emphasizes that budget and time-dependent properties of trace species cannot be understood as purely physical or chemical. We conclude that 50% of emitted anthropogenic CO2 remains in the air in the absence of any considerable removal process and thus has an indefinite residence time.

3.4 Water: Physical and chemical properties Water is unusual in all its physical and chemical properties (Table 3.4). Its boiling point (abnormally high), its density changes (maximum density at 4 °C, not at the freezing

3.4 Water: Physical and chemical properties | 129

Tab. 3.4: Physical and chemical properties of water; data from Höll (2002), Franks (2000), and Lide (2005). Property

value

dimension

Molar mass Freezing point at 1 bar Boiling point at 1 bar Vapor pressure at 25 °C Latent heat of melting at 1 bar Latent heat of evaporation at 1 bar Specific heat capacity of water Specific heat capacity of ice Specific heat capacity of water vapor Critical temperature at 1 bar Critical pressure Critical density Maximum density (at 3.98 °C) Density of water at 25 °C Density of ice at melting point (0 °C) Density of gas at boiling point (100 °C) Viscosity, dynamic at 25 °C Viscosity, kinematic at 25 °C Surface tension of water at 25 °C Dielectric constant at 25 °C Prandtl number at 25 °C Cryoscopic constant O–H bond dissociation energy Bond energy, average at 0 K (H–O–H → O + 2 H) Conductivity, electrolytic, at 25 °C Conductivity, thermal, for water at 25 °C Conductivity, thermal, for ice at −20 °C Conductivity, thermal, for vapor at 100 °C Electron affinity at 25 °C Energy, internal (U) for water at 25 °C Enthalpy of formation, ∆H, at 25 °C Enthalpy (H = U + pv), at 25 °C Enthalpy of vaporization (liquid), at 0 °C Enthalpy of sublimation (ice Ih), at 0 °C Gibbs energy of formation, c ∆G, at 25 °C Surface enthalpy (surface energy) at 25 °C Surface entropy (= − dγ/ dt) at 25 °C Ionic dissociation constant, [H+ ][OH− ]/[H2 O], 25 °C O–H bond length (liquid, ab initio) H–O–H bond angle (liquid, ab initio) Redox potential E 0 : water oxidation d Redox potential E 0 : water reduction e

18.015268 1.00 100.0 3.165 332.5 2257 4187 2108 1996 647.096 220.64 322 1.0000 0.99701 0.91672 0.0005976 0.8903 0.008935 72 78.39 6.1 1.8597 492.2148 458.9 0.05501 0.610 2.4 0.025 −16 1.8883 −285.85 1.8909 45.051 51.059 −237.18 0.1179 0.0001542 1.821 ⋅ 10−16 0.991 105.5 1.229 −0.8277

g mol−1 °C °C kPa J g−1 J g−1 J g−1 K−1 J g K−1 J g K−1 K bar g L−1 g cm−3 g cm−3 g cm−3 g cm−3 cP a stokes b dyn cm−1 – – K kg mol−1 kJ mol−1 kJ mol−1 μS cm−1 W m−1 K−1 W m−1 K−1 W m−1 K−1 kJ mol−1 kJ mol−1 kJ mol−1 kJ mol−1 kJ mol−1 kJ mol−1 kJ mol−1 J m−2 J m−2 K−1 mol L−1 Å ° V V

Centipoises (= 0.008903 g cm−1 s−1 ). (= 0.8935 ⋅ 10−6 m2 s−1 ). c = chemical potential (μ). a

d

b

e

2 H2 O → O2 (g) + 4 H+ + 4 e− . 2 H2 O + 2 e− → H2 (g) + 2 OH− .

130 | 3 Fundamentals of physicochemistry in the climate system

point), its heat capacity (highest of any liquid except ammonia), and the high dielectric constant, as well as the measurable ionic dissociation equilibrium, for example, are not what one would expect from a comparison of water with other similar substances (hydrides). All the physical and chemical properties of water make our climate system unique and have shaped the course of chemical evolution. Water is the medium in which the first cell arose and the solvent in which most biochemical transformations take place. Thales of Miletus, who proposed the idea of the primacy of water (Chapter 2.1, Volume 2), suggested that at the beginning there was only water, somehow everything was made of it and is now composed of water, though perhaps not in the typical form of water (for example, air is a gaseous form of water, and rocks are a solid form of water, according to the ancient views). In the changes that occur, water is not created or destroyed – it just changes its properties (Lloyd 1970).

3.4.1 Water structure: Hydrogen bond Under certain conditions, an atom of hydrogen is attracted by rather strong forces to two atoms of another element instead of only one, so that it may be considered to be acting as a bond between them. This is termed the hydrogen bond. This statement is from Linus Pauling (1901–1994) in his book The Nature of the Chemical Bond (1939). At that time, the hydrogen bond was recognized as being mainly ionic in nature. The energy associated with the hydrogen bond is about 20 kJ mol−1 . Due to hydrogen bond-

H

H

O H

H H

O H

O H

H

O

H

O H Fig. 3.1: Water structure and hydrogen bonds (dotted lines) in a tetrahedral grid; note that the structure is not in a plane.

3.4 Water: Physical and chemical properties | 131

ing, water molecules form dimers, trimers, polymers, and clusters. Hydrogen bonds are not necessarily linear (Figure 3.1). The ion mobility of H3 O+ and OH− are anomalously high: 350 ⋅ 10−4 and 192 ⋅ 10−4 cm2 V−1 s−1 (25 °C) in comparison with (50– 75)⋅10−4 cm2 V−1 s−1 for most other ions. Chapters 4.4.1.1 and 4.4.3 deal with the chemistry of the proton (H3 O+ ) and aquated electron (H2 O− ), both fundamental species in nature (see also Chapter 6.1.2). Mobility is a result of the special structure of liquid water where the H2 O molecules are linked in chains, stabilized by hydrogen bonding, which also give liquid water great internal cohesion (Figure 3.1). Figure 3.2 (in the scheme, the tetrahedral structure shown in Figure 3.1 remains but is not clearly seen) illustrates that the proton (H+ ) is not really transported but only the charge – similarly to the OH− transport – thereby explaining the high ionic mobility. The water grid (quasi-crystalline) is restructured. Therefore, the high evaporation heat and entropy, the high surface tension, and relatively high viscosity are a result of the hydrogen bonding structure (Figure 3.1). Bernal and Fowler (1933) first proposed a water structure model in the sense of a “quasi-crystalline structure.” Many models of the structure of liquid water have been proposed (e.g., Rick 2004), but there is no consensus even on the number of H2 O molecules forming species (“polymers”). H3O+ H+ transfer H H

O H3O+

H

OH-

H

O

H

H H

O

H

O H

O H+ transfer to another H2O H Fig. 3.2: Formation and transport of hydronium (H3 O+ ) and hydroxide ions (OH− ) in the water grid (Figure 3.1) by charge transfer, i.e., changing hydrogen bonding (dotted line) from strong covalent to weak interaction.

132 | 3 Fundamentals of physicochemistry in the climate system

When water freezes, its crystalline structure is maintained (Figure 3.1) and determined by the prevailing conditions; at least nine separable ice structures exist. Normally, ice has a hexagonal structure when cooling down as liquid water; each O atom is surrounded by a regular tetrahedron of an additional four O atoms. The positioning of H is very complex. The four hydrogen bonds around an oxygen atom form a tetrahedron in a fashion found in the two types of diamonds. Thus, ice, diamond, and close packing of spheres are somewhat topologically related. Water ice is unusual because its density is less than that of the liquid water with which it is in equilibrium. This is an important property for the survival of life in water. When ice melts, a few hydrogen bridges (probably every fourth one) begin to break, the H2 O molecules close ranks, and the density consequently increases. Many salts crystallized from aqueous solutions are not water-free but take the form of well-defined hydrates. Other solid phases contain water present in changing amounts. A classic case is water coordinated onto oxoanions, for example, CaSO4 ⋅ 2 H2 O. The most frequent are cation complexes with water, for example, alums like [Al(OH2 )6 ]3+ ; this is an explanation for the high water content in rocks. Framework silicates (e.g., zeolites) hold huge amounts of water in air cavities; faujasite is the mineral with the highest water content: Na2 Ca[Al2 Si4 O12 ]2 ⋅ 16 H2 O (Strunz 1955). Like zeolitic grids, water (H2 O)n can build up cagelike inclusion structures (clathrate hydrates) where, in a skeleton of 46 H2 O, there exist six cavities of the same size and two additional, smaller, ones. The guest molecules in high-pressure clathrates are Ar, Kr, CH4 , and H2 S. Polywater (also termed anomalous water), which was first described in the 1960s in the Soviet Union and controversially discussed in the 1970s, does not exist, however, and was probably a mixture of colloidal silicic acid.

3.4.2 Water as solvent The polarity of water gives it important properties that the biosphere needs to function: It is a universal solvent, and it adheres and is cohesive. Thus, water facilitates chemical reactions and serves as a transport medium. Even in a covalent bond, atoms may not share electrons equally. In H2 O, the unequal electron sharing creates two electric dipoles along each of the O–H bonds. The H–O–H bond angle is 104.5°, 5° less than the bond angle of a perfect tetrahedron, which is 109.5°. They are in continuous motion in the liquid state; hence, hydrogen bonds are constantly and swiftly being broken and formed (Figure 3.2). Protolytic equilibrium is described in more detail in Chapter 4.4.1.1. Hydrogen bonding is unique for water. Bonds readily form between an electronegative atom (usually oxygen, nitrogen or sulfur) and a hydrogen atom covalently bonded to another electronegative atom in the same or another molecule: H⊕ –O⊖ –H⊕ ⋅ ⋅ ⋅O⊖ – and H⊕ –O⊖ –H⊕ ⋅ ⋅ ⋅N–. However, hydrogen atoms covalently bonded to carbon atoms (which are not electronegative) do not participate in hydrogen bond-

3.4 Water: Physical and chemical properties |

133

ing; hence, hydrocarbons are insoluble in water. However, organic compounds with oxygen (and nitrogen) containing functional groups (e.g., alcohols, aldehydes, acids, ketones) are water-soluble. The more oxygen groups and the fewer carbon atoms in a compound, the more soluble it is in water. It is the polarity and the hydrogen bond affinity that make water a solvent for many chemically different substances such as the following – oxygenated or nitrogen-containing organic compounds (most biomolecules, which are generally charged or polar compounds), – salts (electrostatic interacting solid grids) but also – nonpolar gases (biologically important CO2 , O2 , and N2 ); and all – polar gases (e.g., SO2 , NH3 , HCl, HNO3 , which are important to the atmosphere). It needs no further explanation that the solubility of nonpolar molecules is much less than that of polar substances. The property of interacting with water is also termed hydrophilicity (affinity to water: attraction) and, conversely hydrophobia (nonaffinity to water: repulsion).

3.4.3 Water vapor John Tyndall (1829–1892) wrote the following very clear phrase (Strachan 1866, p. 123): Aqueous water is always diffused through the atmosphere. The clearest day is not exempt from it; indeed, in the Alps, the purest skies are often the most treacherous, the blue deepening with the amount of aqueous vapor in the air. Aqueous vapor is not visible; it is not fog; it is not cloud, it is not mist of any kind. These are formed of vapor that was condensed to water; but the true vapor is an impalpable transparent gas. It is diffused everywhere throughout the atmosphere, though in very different proportion.

The content of water vapor in air varies from nearly zero up to about 4 Vol-%, depending on the temperature and saturation (Figure 3.3). Normally the chemical composition of air is based on dry air (cf. Table 1.2). Under normal conditions (20 °C and 60% RH), air contains around 1% water vapor (absolute humidity). The density of water vapor is less than that of other gaseous air constituents (N2 + O2 ); hence, wet air at the same temperature and pressure has a lower density than dry air. Consequently, at the same pressure dry air has a somewhat higher temperature (termed virtual temperature) than wet air to obtain the same density. This follows from the ideal gas equation p=ρ

RT , M

(2.65)

where p is air pressure, R the universal gas constant, T air temperature, and ρ air density (m/V), all of which are mean values of air. There are intensive quantities (p, T, and ρ) and extensive quantities (n, m, V, energy). Extensive quantities depend on the

134 | 3 Fundamentals of physicochemistry in the climate system

600

saturation value (in g m-3)

60

500

50 40

400

30 20

300 10 0

200

0

5

10

15

20

25

30

35

40

100 0 -20

0

20

40

60

80

100

temperature (in °C) Fig. 3.3: Saturation value of absolute humidity (g m−3 ) over water depending on temperature. Data from Sonntag and Heinze (1981).

system size or the amount of material in the system; intensive quantities do not. If one cubic meter of air is divided, then the intensive quantities will not change but the extensive properties will. Many ratios derived from two extensive quantities (e.g., density, chemical potential, specific fluxes) are intensive quantities. At this stage, we will ignore the fact that air is a mixture with PM in the form of droplets and solids and will only consider the gases (see also Chapter 4.1.2). It is important to note that air is not a mixture of different gases but a solution, because all gases can form solutions with each other in all ratios. The specific properties of individual gases will not change; therefore, the properties of air can be calculated from those of the constituents according to the dilution rule. The property E of a solution (e.g., pressure, mass) can be calculated from the part x i of the specific gases i, termed the mixing ratio (based on mass or volume, respectively) contributing to air: E = ∑ xi Ei .

(3.92)

We may consider p, V, and n as sums of the so-called partial quantities: n = ∑ ni ,

V = ∑ Vi ,

and

p = ∑ pi .

(3.93)

The partial volume V i is that volume that is occupied from the amount (expressed as mass or mole) of gas i under the same pressure as the air. The partial pressure is that pressure that would have the amount of gas i in the same volume of air. The number of moles is given by n i = m i /M i (m i is the mass and M i the molar mass of substance i) and the density by ρ i = m i /V. Without significant error, we calculated the mean molar

3.4 Water: Physical and chemical properties |

135

mass of dry air only from the main constituents N2 , O2 , and Ar as Mdryair = 0.78MN2 + 0.21MO2 + 0.01MAr = 28.96

(more precisely 28.9644). (3.94)

The mean molar mass of wet air (x is the mixing ratio of water vapor) is given by Mwetair = (1 − x) ⋅ 28.96 + x ⋅ 18.0 .

(3.95)

Under the same conditions (pressure and density) it follows from eq. (2.65) that p Tv = . Rρ (1 − x) ⋅ 28.96 + x ⋅ 18

(3.96)

Thus, with increasing humidity x the virtual temperature Tv increases under conditions of constant density and pressure (no changing quotient). In other words, at same T and p the density becomes smaller or at the same T and ρ the pressure increases. It follows that T/Tv = 1 − 0.378x. The water vapor in air is a result of the vaporization of water from the Earth’s surface. We can consider liquid water to be condensed vapor. At any given time, a certain number of molecules can escape the liquid from the surface to the surrounding air (known as evaporation). Because of air motion (turbulent mixing and advection), there is no equilibrium, i.e., the transfer of water molecules from the air back to the surface (known as condensation) in the same flux as evaporation. Such a state of equilibrium can only be reached in a closed, undisturbed chamber. Hence, the vapor pressure dependency shown in Figure 3.3 is theoretical and cannot be directly applied to the atmosphere. If the equilibrium between condensed and vaporous water is reached, the pressure is termed saturation pressure p∞ . These conditions are important for cloud formation but are also frequently observed in the tropics. The RH is the ratio of the vapor pressure p at temperature T to the saturation vapor pressure p∞ at the same temperature expressed as a percentage: RH =

100 ⋅ pH2 O . p∞ (T)

(3.97)

The water vapor pressure pH2 O is numerically identical to the mixing ratio xH2 O . The absolute humidity (or water vapor concentration or density) is the mass of water vapor in volume of air at a given temperature: mH2 O /V. From eq. (2.65) it follows that ρ H2 O = pH2 O

18 RH = p∞ (T) 0.18 . RT RT

(3.98)

Note that in all these equations the saturation vapor pressure is measured above a plane that is an “endless” water surface. Another important quantity is the dew point, the temperature at which, at a given absolute humidity, the saturation vapor pressure is reached, i.e., the RH becomes 100%. Under these conditions, water vapor starts to condense – when surfaces (in air, CCNs) are available.

136 | 3 Fundamentals of physicochemistry in the climate system

3.4.4 Water properties in relation to the climate system We would normally expect water – when comparing H2 O with H2 S, for example – to boil at −80 °C instead of 100 °C. This large difference is due to the relatively strong hydrogen bond (weak van der Waals interaction is on the order of only 4 kJ mol−1 ), which must be broken before separating H2 O molecules from the bulk liquid. This is expressed by the heat of vaporization (Table 3.4), which is one of the highest of all liquids (only that of H2 O2 is higher). This effect produces a liquid over most of the Earth’s surface (between 0 °C and 100 °C). Another property following from the structure of water is the high heat capacity. Water can absorb a lot of heat from a slight change in temperature. The temperatures of large natural water bodies are relatively constant and they act as thermal buffers in the climate system. Without the large heat of vaporization, soils (as seen in dry areas) would be overheated, but solar heat is taken for water evaporation, cooling the surface. The same amount of heat is released when the vapor condenses in the atmosphere to form cloud droplets. This causes the transport of heat from one site of the Earth to another. Without appreciable changes to the surface temperature, around 25% of solar radiation (and 50% of solar transmission) dissipates in the atmosphere. No detailed explanation is needed of the fact that this process of water evaporation and condensation forces the water cycle and creates our weather (and, ultimately, our climate). The high surface tension of water plays a major role in the formation of drops in clouds and fog. Surface tension is related to the cohesive properties of water; in other words, water is attracted to other water. This property results in the growth of cloud droplets into bigger drops after collision. Water can also be attracted to other materials. This is termed adhesion, a property of water that leads to capillary action, an important transport process for plants (besides transpiration). Liquid water is transparent to visible light, which allows photosynthesis to a considerable depth in large water bodies (up to more than 100 m in clear water). Water vapor (H2 O molecules) in the atmosphere absorbs strongly in the IR region, which is important for Earth’s heat budget (Chapter 2.3.3). The resulting greenhouse effect of atmospheric water is, by far, the strongest determinant of Earth’s surface climate. Naturally occurring GHGs have a mean warming effect of about 33 °C, and water causes about 36–70% of it. The global mean surface temperature (based on long-term near-surface measurements) is 14 °C (for land surfaces it is 8.5 °C and for sea surfaces 16.1 °C). Without water in the atmosphere, the global mean temperature would be far below the freezing point of water on land, which would be ice-covered and would not provide conditions for life. Large parts, at least, of the ocean (and likely globally) would also be frozen. Furthermore, atmospheric humidity is highly variable and responds to changes in atmospheric temperature (Figure 3.3), thus providing the most important feedback mechanism tending to amplify global climate changes induced by other factors (Figure 3.4). Furthermore, clouds contribute about 50% of planetary albedo (Figure 2.15),

3.5 Properties of solutions and droplets | 137

sources

aerosols and gases

CCN

vapor

land-use

clouds

precipitation

air temperature

radiation

evaporation

soil temperature

Fig. 3.4: Interaction between water cycle and changes in climate system.

and absorption of terrestrial radiation by clouds is equivalent to that of all GHGs other than water vapor. Water vapor in the upper troposphere and lower stratosphere is very critical in determining the rate at which radiative energy emitted by the atmosphere escapes to space. Being able to measure and forecast the evolution of the spatial and temporal patterns in water vapor and clouds is key to understanding the climate system, specifically water resources and ecosystem problems.

3.5 Properties of solutions and droplets Here, the physicochemical properties of solutions and droplets that are important for an understanding of cloud physics and chemistry will be briefly described. Atmospheric droplets are always solutions of gases and salts and partly suspended particles. Key properties, such as the size and salinity of droplets, are dominantly determined by CCNs (Chapter 3.6.4). Although droplets can normally be treated as diluted solutions, during the nucleation and evaporation processes highly concentrated solutions occur, and instead of concentrations in thermodynamic equations (if they are still valid), activities must be used (see Chapter 3.1.2.4).

138 | 3 Fundamentals of physicochemistry in the climate system

3.5.1 Surface tension and surface-active substances An important property of the surfaces of droplets is the surface tension that expresses the cohesion of water molecules (Chapter 3.4.1). On molecules existing close to a droplet surface, forces are directed to the inner part of the droplet. Therefore, all liquids tend to form spherical particles (if there are no counteracting forces such as gravitation and other outer forces). The reason is simple: a sphere of a given volume has the smallest surface of all bodies. Thus, a growing droplet needs to overcome molecular cohesion. There are two equivalent definitions of surface tension: (a) the surface tension γ of a liquid is the force f per unit length l (the dimension of surface tension is N m−1 or kg s−2 ) and (b) the surface tension γ of a liquid is the ratio of the change in the (surface) energy dW A of the liquid and the change in the surface area dA of the liquid (dimension: energy/surface but reduced in metric units to kg s−2 ): γ=

f dl dW A f = = . l l dl dA

(3.99)

Gibbs derived (so-called Gibbs’s isotherm) dγ = − ∑ Γ i μ i ,

(3.100)

i

where Γ i is the surface concentration, and the so-called surface excess is n i /A, i.e., the amount of matter per square unit. Insofar, eq. (3.100) is equivalent to eq. (3.40): (dG)p,T /A = (∑ n i μ i ) /A ≡ (dγ)p,T . i

Using eq. (3.36) in its derivative form dμ i = RT dln c it follows that dγ = −RT ∑ Γ i dln c i

(3.101)

1 dγ ) . ( RT dln c i

(3.102)

and Γi = −

Some organic substances dissolved in droplets or transported from the gaseous surroundings to the surface can accumulate at the surface (Figure 3.5) when hydrophilic and hydrophobic properties exist in one molecule (e.g., aliphatic alcohols, aldehydes, and acids). The importance of these films becomes clear when considering that all processes linked with the free enthalpy G of droplets (evaporation, adsorption, desorption, surface reactions) generally result in a change in G through a change in T, p, A, or n (derived from eqs. (3.37) and (3.38)): dG = −S dT + V dp + γ dA + ∑ μ i dn i .

(3.103)

In cloud and rainwater, polycarboxylic acids, having a molecular structure analogous to that of humic-like substances (HULIS), are the most effective surface-active species

3.5 Properties of solutions and droplets | 139

Fig. 3.5: Surface-active substances in a droplet.

in droplets. In addition, monocarboxylic acids and polyaromatic hydrocarbons can play an important role in the atmospheric aquatic system because of their surface-active potential (Facchini et al. 2000, Ćosović et al. 2007). Seidl and Hänel (1983) found in rainwater that soluble surface-active materials had concentrations on the order of 2 μmol L−1 and that this was too small to have a significant influence on a cloud’s physical processes. However, OA constituents can influence the surface tension of nucleating cloud droplets and thereby modify the critical supersaturation necessary to activate aerosol particles (APs). Kiss et al. (2005) found HULIS that accounted for 60% of the water-soluble organic carbon present in rural aerosols. The isolated OM present in a concentration of about 1 g L−1 decreased the surface tension of the aqueous solutions by 25–42% compared with pure water.

3.5.2 Vapor pressure lowering: Raoult’s law Solutions have two fundamental property changes compared with pure water: lowering the vapor pressure and freezing point depression. In cloud microphysics, these changes are crucial for droplet growth and precipitation formation. In about 1886, François Marie Raoult (1830–1901) discovered that substances had lower vapor pressures in solution than in pure form and that the freezing point of an aqueous solution decreased in proportion to the amount of a dissolved nonelectrolytic substance. The vapor pressure of a solution is equal to the sum of partial pressure, p = ∑ p i . The ratio of the partial vapor pressure of substance i in solution to the vapor pressure of the pure substance (subscript 0 denotes the pure substance) is equal to the molar fraction x of i: pi = xi . (3.104) p0i

140 | 3 Fundamentals of physicochemistry in the climate system

This law is strictly valid only under the assumption that the chemical interaction between the two liquids is equal to the bonding in liquids: the conditions of an ideal solution. In nature, we do not consider a solution between two liquids: water is the solvent and dissolved matter is predominantly nonvolatile, p i ≪ p∞ , where p∞ denotes the vapor pressure of pure bulk water, i.e., having a flat surface (cf. ClausiusClapeyron eq. (3.61)). Raoult also found that the relative lowering of vapor pressure of the solution (∆p/p) was proportional to the molar fraction x of the dissolved substance i: Mw p∞ − psol ni ni = xi = ≈ = ni , (3.105) p∞ n i + nw nw Vw ρ w where psol is the vapor pressure of the solution (in what follows, index w denotes pure water), n i denotes the mol number of the dissolved substance, and nw is that of water, where n i ≪ nw . We also have taken into account that nw = mw /Mw = Vw ρ w /Mw with mass mw , molar mass Mw (18 g mol−1 ), density ρ w (≈ 1 g cm−3 ), and volume of water Vw . In the case of a droplet, Vw = 4πr3 /3, and it follows from eq. (3.105) for the vapor pressure lowering of droplets that 3Mw psol B = 1 − ni =1− 3 3 p∞ 4πr ρ w r

(3.106)

and

B . (3.107) r3 The Kelvin eq. (3.63) that describes the vapor pressure change due to the curvature of the water surface (droplet) can now be written in slightly different form (note that exp x ≈ 1 + x): 2γVm A pr ≈1+ =1+ . (3.108) p∞ rRT r Köhler¹⁸ combined (Köhler 1936) two effects to describe the total change in vapor pressure: that of lowering of the vapor pressure in solutions (Raoult term eq. (3.107)) with that of the higher vapor pressure of droplets (Kelvin term eq. (3.108)), termed the (simplified) Köhler equation, ∆p = psol − p∞ = −p∞

∆p = psol + p r − p∞ = p∞ (1 +

A B − ) − p∞ , r r3

(3.109)

where A = 2γVm /RT and B = 3n i Vm /4π (n i denotes the number of moles of the dissolved substance). The Köhler equation also follows in rearranged form, where p(r, sol) = psol + pr : p(r, sol) A B S= =1+ − 3 , (3.110) p∞ r r where p(r, sol) is the droplet vapor pressure, depending on the radius and the solute concentration. 18 Hilding Köhler (1888–1982), meteorologist at Uppsala University.

3.5 Properties of solutions and droplets |

p p

A r

(pure water)

saturation ratio

ln

141

ln p ln p

A B  r r3

0.5

p p

0 (p

p )

(solution)

1

10

droplet radius (in μm) Fig. 3.6: Köhler curve.

Curves resulting from eq. (3.110) are called Köhler curves (Figure 3.6). From eq. (3.110) follows the droplet radius for supersaturation S = p/pw = 1: rsaturation = √

B . A

(3.111)

The maximum in a Köhler curve is given at dS/ dr = 0, which denotes the critical radius after activation: 3B rcritical = √ . (3.112) A Finally, it follows for the critical supersaturation that Scritical = 1 + √

4A3 . 27B

(3.113)

We see that the solution effect (Raoult term) is dominant when S = p/p∞ ≤ 1 + (4A3 /27B)1/2 , whereas S strongly decreases by further reducing the radius. By contrast, for S > 1 + (4A3 /27B)1/2 the Köhler curve approaches the curve for pure water (Figure 3.6). Each point on the Köhler curve represents the equilibrium vapor ratio of water, i.e., the RH at which a droplet with a given radius and amount of dissolved matter exists. For r < rcritical the equilibrium is stable; for constant S the droplet would evaporate water (because of the momentum of the greater pressure) if there is slight growth through the adsorption of water molecules and return to equilibrium. For r > rcritical the supersaturation S becomes smaller for larger droplets; therefore, water

142 | 3 Fundamentals of physicochemistry in the climate system

molecules would continuously absorb and enlarge the droplets. Conversely, smaller droplets are quickly undersaturated when losing water and tend to evaporate. This principle explains why cloud droplet growth comes at the expense of smaller droplets.

3.5.3 Freezing point depression The freezing point depression follows from the lowering of the vapor pressure. From the Clausius-Clapeyron equation and Raoult’s law it follows (∆sm H is the enthalpy of smelting) that RT 2 ) xi . (3.114) ∆T = ( ∆sm H Taking the molality m (defined as the ratio of the amount of dissolved matter and the mass of water, expressed in mol kg−1 and in contrast to molarity, which does not depend on T; in dissolved solution molarity is proportional to molality) we obtain ∆T = Kf m i ,

(3.115)

where Kf is the cryoscopic constant, which is empirical and can be determined experimentally; for water Kf = 1.86 K kg mol−1 . In clouds, the important effect is the existence of supercooled droplets, i.e., despite a certain freezing point, depression droplets remain at lower temperatures in liquid form because of the kinetic inhibition of crystallization. The homogeneous process is that spontaneous freezing occurs only for ≤ 232 K or −41 °C (TH ) and saturation near that of liquid water (Koop et al. 2003). However, the temperature when water ultimately becomes a solid (Ts ) may be lower; computer studies based on classical nucleation theory using experimental data suggest that the crystallization rate of water reaches a maximum around 225 K (−48 °C), below which ice nuclei form faster than liquid water can equilibrate (Moore and Molerino 2011). The heterogeneous process requires the presence of ice nuclei (INs) with a hexagonal crystal structure similar to that of water ice, which allows freezing at temperatures as high as −5 °C (Vali 2008). Heterogeneous ice nucleation in clouds with supercooled water results in the subsequent efficient growth of ice crystals because of the Bergeron–Findeisen process. It is assumed that this is the main initiation process of precipitation in the middle latitudes (Pruppacher and Klett 1997). It is remarkable that biological particles such as bacteria or pollen might be as active as both CCNs and heterogeneous INs. These biological particles are much larger than the inorganically or organically derived CCNs (but probably smaller in number density) and are important in the development of precipitation through giant CCNs and INs. However, there is as of yet no direct evidence that bacterial INs participate in cloud processes to any significant degree (Möhler et al. 2007). Although recognized for hundreds of years, artificial weather modification was not applied before the turn of the twentieth century. It started simply by introduc-

3.6 Heterogeneous processes: Multiphase chemistry in the climate system

| 143

ing artificial CCNs to cloud layers by guns, and later rockets and aircraft. By the late 1940s the introduction of “crystallization nuclei” (e.g., AgI, dry ice, and many others) affected the ice phase processes in supercooled clouds and larger hygroscopic particles (artificial precipitation embryos about 30 μm in diameter) to stimulate collision-coalescence processes in warm clouds. About ten countries applied different techniques, with varying degrees of success.¹⁹

3.5.4 Diffusion in solution Similar to the diffusion of molecules in air (or gases) (Chapter 2.5.4), the spontaneous transfer of a dissolved substance in solution from a site of higher concentration to the site of lower concentration is termed diffusion and described by Fick’s first law, eq. (2.86). As for gases, the driving force of diffusion is the concentration gradient (or, for real systems, the chemical potential). The aqueous diffusion coefficient can be described by RT kT Daq = = , (3.116) 6πNA ηr 6πηr where r is the radius of a diffusing particle and η the viscosity of the solution; Daq is on the order of 10−5 cm2 s−1 for many dissolved substances. Equation (3.116) is valid only in the case where the diffusing particles are spherical and much larger than the particles (molecules) of the solvent, i.e., water molecules.

3.6 Heterogeneous processes: Multiphase chemistry in the climate system The climate system is simplified as the water–soil–air system, representing the physical states of liquid, solid, and gaseous matter. We have already discussed the air (or atmosphere) as a multiphase system and, despite the volume-based dominance of gases, solid matter (aerosol particles) and liquid matter (cloud droplets) play a crucial role in weather formation and, hence, climate phenomena. Similarly, the hydrosphere (oceans) is considered a multiphase system where solid carbonates play a key role in the biogeochemical conditions. It is remarkable that in each reservoir, the minor phases are obviously the driving forces (water in air, solids in water, air/gas and water in soils). Therefore, studying the interfacial processes (solid–gas, solid–liquid,

19 We have proposed and successfully tested a modified technology of dry-ice blasting for cold fog dissipation, working on a process we call collision impaction (Möller 1999c, Möller et al. 2001, 2003). Möller (2001) proposed blasting of water ice pellets for cloud seeding; however, it is difficult to produce in situ small (low millimeter size) water ice pellets and blast them. The process corresponds to a seederfeeder mechanism and is expected to be very efficient.

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and gas–liquid interfaces in connection with the mass transfer and chemical reaction) is of high importance for understanding the climate system. There is no consistent use of the term heterogeneous chemistry (see Chapter 3.6.5.3 for a definition) – we restrict its application to surface chemistry (at present called interfacial chemistry) involving two phases, in atmospheric air–droplets and air– particles. Chemisty in droplets is aqueous (or solution) chemistry (see Chapter 5.2.5 for oxygen chemistry, Chapter 5.3.5.2 for nitrogen chemistry, Chapters 5.6.3.2 and 5.6.6.2 for carbon chemistry, and Chapter 5.7.4 for halogen chemistry). Chemistry in aerosol particles is of less importance, with the exception of sea salt particles (Chapter 5.7.2). By multiphase chemistry we understand the total chemistry in and between all phases (see Chapter 5.2.6 for oxygen multiphase chemistry and Chapter 5.4.4 for sulfur multiphase chemistry). Therefore, aerosol chemistry and cloud chemistry is multiphase chemistry, for example investigating ozone chemistry (formation and destruction) in interaction between interstitial gas-phase, cloud and aerosol particles (Chapter 5.2.6.2). However, chemistry also involves studying the chemical composition of airs, waters and solids (analytical chemistry); see Figure 3.10.

Fig. 3.7: Processes during phase transfer. Indices: ∞ – far from interface, 0 – beginning of diffusion layer, ads – outer surface, aq – inner surface and aqueous phase, diss – dissolved, prot – protolyzed form, k – reaction rate coefficients in gas phase (g), at surface (ads), and in aqueous phase (aq), Dg – diffusion coefficient, gas phase, Kads – sorption equilibrium coefficient, Daq – diffusion coefficient, aqueous phase, Kaq – equilibrium coefficient of protolysis, H – Henry’s law constant, H eff – effective Henry’s law constant, α – accommodation coefficient, γ – uptake coefficient.

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Characterization of the size-dependent chemical composition of particles and droplets is an important issue in atmospheric chemistry. In-cloud scavenging (in the past often called rain-out) comprises processes 3, 4, and 5, all of which accumulate material in cloud droplets, either transfered back into air (processes 7 and 8) or removed via precipitation (process 9). Together with this subcloud scavenging (or below-cloud scavenging – often previously referred to as washout), the chemical composition of wet deposition (precipitation) is determined. Precipitation chemistry in a more narrow sense deals with the chemical composition of rain and snow in a climatological sense, i.e., studying space and time dependency (location, season) and meteorological influences (air masses, rainfall characteristics). This short chapter can only present a brief overview; for more details, the reader is referred to the specialized literature: aerosols, clouds, and chemistry (Schryer 1982, Jaeschke 1986, Fuzzi and Wagenbach 1997, Pruppacher and Klett 1997, Guderian 2000, Hobbs 2000, McFiggans et al. 2005a, Barnes and Kharytonov 2008, Lohmann et al. 2016) and multiphase transport and chemistry (Helmig and Schulz 1997, Faghri and Zhang 2006). Whereas Figure 3.7 shows the processes on a microscale, Figures 3.8 and 3.9 represent the whole system on a macroscale, to which we turn first to discuss the limits of our understanding of a multiphase system. In air, permanent solid particles (atmospheric aerosols) exist, originating either from primary sources in the atmosphere or from gas-to-particle conversion in the atmo-

aerosols (particulate matter) gas-toparticleconversion (homogeneous nucleation)

heterogeneous nucleation

clouds (aqueous-phase chemistry)

evaporation in-cloud scavenging

secondary gaseous trace species gas phase chemistry

precipitation sub-cloud scavenging

rain (aqueous-phase chemistry)

primary gaseous trace species

emission

dry deposition

Fig. 3.8: Atmospheric multiphase system.

emission

wet deposition

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air gas

cloud

precipitation

aerosol

Fig. 3.9: Evolution from gas to aerosol, cloud, and precipitation; → nonreversible pathway, ↔ pathways in both directions, but not mandatory equilibrium.

sphere. All trace matter shows a high variability in concentration²⁰ because of chemical and microphysical processes. Liquid particles (cloud, fog, and rain droplets), however, are not permanent in the air and form and exist only under specific physicochemical conditions (the presence of condensation nuclei and water vapor saturation). The transition from molecules to droplets comprises many steps: 1. homogeneous nucleation of molecules: formation of nuclei and growth (“new particle formation”), 2. activation of potential condensation nuclei through water vapor adsorption, 3. heterogeneous nucleation: formation of droplets through water vapor condensation onto activated condensation nuclei, 4. adsorption of molecules onto particles and surface chemical reactions (heterogeneous chemistry), 5. absorption of molecules by droplets and droplet-phase chemistry (aqueous-phase chemistry, 6. cloud droplet growth and formation of precipitation elements (microphysical and dynamic processes), 7. desorption of molecules from particles and droplets, 8. evaporation of droplets: formation of solid residual particles and back transfer of dissolved gases and 9. precipitation and scavenging of gases and particles in subcloud layer (wet deposition).

3.6.1 Aerosols, clouds, and precipitation: The climate multiphase system Interactions among aerosols, clouds, and precipitation are critical in shaping the climate system. Aerosols, clouds, and precipitation are intrinsically linked (Figures 3.8 20 Excluding trace species with a very long residence time such as some halogenated hydrocarbons.

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and 3.9). APs are the condensation and freezing nuclei on which cloud particles form (heterogeneous nucleation process). APs are either directly emitted or produced from gaseous precursors via homogeneous nucleation (gas-to-particle conversion). Clouds occasionally produce precipitation, which removes trace species via in-cloud and subcloud scavenging back to the Earth’s surface (wet deposition). In most cases, however, clouds evaporate and transfer chemical species back to the air in the form of aged APs and secondary gaseous matter. This cloud processing (nucleation-evaporation cycle) is important for the transport, redistribution, and conversion of pollutants. Cloud processing ultimately leads to particle growth and generally to an increase in particle water solubility. Aqueous-phase droplet chemistry, however, can also produce organic polymers, which are an important part of SOAs. Cloud processing has long been identified as the main source of climate active sulfate aerosols. We have described the crucial role played by cloud and precipitation in the Earth’s energy budget and water cycle (Figure 3.10). Despite many important achievements, clouds and aerosols remain the largest source of uncertainty in the two most important climate change quantities: radiative forcing and climate sensitivity (Penner et al.

anthroposphere

emission

gases and particulates direct climate forcing

concentration fields

absorption, reflexion, albedo etc.

indirect climate forcing

LWC, cover, droplet size clouds and fog

radiation and temperature

intensity, frequency, duration precipitation

biosphere

Fig. 3.10: Climate impact system. → direct impacts, dotted line: feedbacks and indirect impacts.

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2001, IPCC 2007, 2013, AQCPC 2009, Lohmann et al. 2016). Whereas the role of GHGs in the absorption of terrestrial radiation is well understood and the interaction between APs and radiation has been well described (direct climate forcing), the dominant uncertainty among radiative forcing of climate change is the impact of aerosols on clouds (indirect climate forcing). Figure 3.10 illustrates the direct cause-impact relationships and feedbacks. Changing radiation, temperature, and precipitation are essential parameters for plant growth and, therefore, the biosphere’s emission capacity and biogeochemical cycling. The climate system is anthropogenically influenced through atmospheric emissions and land-use changes. The concentration fields of gases and PM are a result of emission patterns, atmospheric chemistry, and transport processes. All these processes depend on the climate. Qualitatively, the feedbacks are well known and for small-scale relationships have also been quantitatively described, such as temperature influence on biogenic emissions, parameters determining wind-blown mineral dust, and condensation nuclei activation. Nevertheless, on a large scale, when atmospheric (and oceanic) circulation and the completely multiphase (and multicomponent) chemistry must be considered as interlinked system, cloud formation and precipitation as essential climate variables are only poorly quantified. Moreover, the feedbacks of aerosols, clouds, precipitation, and climate as an interlinked system, and its sensitivity to perturbations, are not well understood (Pueschel 1995, Andreae et al. 2009a, Heintzenberg and Charlson 2009). There are simple and complex feedbacks or relationships, for example: – increasing humidity → increasing OH concentration; – increasing T → increasing stability → decreasing wind speed → decreasing PBL → increasing concentrations; – decreasing SO2 (and sulfate, resp.) → decreasing negative forcing → increasing T; – decreasing dust pollution (PM10 ) → increasing nanoparticulates → decreasing precipitation. A main reason for the difficulties in understanding the aerosol–cloud–precipitation system is the large range of spatial and temporal scales on which the involved processes act (Figure 3.11). Important microphysical processes, such as the formation of particles through homogeneous nucleation, are in the range of nanometers and nanoseconds, and the process of cloud droplet formation is in the range of micrometers and seconds. Cloud droplets have lifetimes of minutes to hours and the cloud system of hours to days. Precipitation is in ranges of millimeters (drops interaction) and a few hundred meters (subcloud scavenging) and minutes (falling raindrops). The organization of cloud systems, however, is a large-scale dynamic process taking place on spatial scales on the order of hundreds to thousands of kilometers and temporal scales between days and weeks. At the end of the upper scale are long-lived pollutants in the stratosphere and global climate feedbacks that exist from tens to hundreds of years.

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distance (km) 1E-10 10-10 1E-08 10-8

1E-06 10-6

0,0001 10-4

-2 0,01 10

11

2 100 10

10000 104

1000000000 109

decay of halocarbon

10000000 107

methane oxidation Interhemispheric transport SO2 oxidation cloud processing

100000 105

time (s)

1000 103 101 10

global

turbulence and microphysics dissipation eddies

10 0,1-1 10-3 0,001

10-5 0,00001

local

10-7 0,0000001 10-9 0,000000001

chemical elementary reactions

Fig. 3.11: Various processes having characteristic time and, hence, spatial characteristics (from local to global).

Disciplinary research on many individual aspects of the climate system has advanced substantially. However, do we need to study the system as a whole with attention to all the pertinent scales? Another enduring question is the extent to which we are able to understand the whole system. It seems to be more realistic to assume that a full understanding of natural processes remains an unattainable goal in science. Our present limited understanding of the climate and aerosol–cloud–precipitation system, however, is sufficient to establish an urgent challenge for climate control measures as suggested in Chapter 5.3.1 of Volume 2.

3.6.2 Gas-to-particle formation: Homogeneous formation of CCNs 3.6.2.1 Classical nucleation theory According to the Köhler eq. (3.110), the formation of droplets only from water vapor is impossible in air. However, some products of gas-phase reactions, such as SO3 /H2 SO4 (sulfuric acid), CH3 HSO3 (methanesulfonic acid), and many oxygenated organic compounds have low vapor pressures but a somewhat high affinity to H2 O. These molecules can accommodate each other (single-component nucleation) and among different species (multicomponent nucleation) and form a cluster of molecules as a metastable phase. After reaching a critical radius, they become stable. It is believed that in the atmosphere, gas-to-particle conversion occurs not by condensation of single species but rather by involving at least two, probably more, different species. Students know well from laboratory praxis that condensed fine matter forms when opened near bottles of aqueous ammonia solution and sulfuric acid, nitric acid, or hy-

150 | 3 Fundamentals of physicochemistry in the climate system

drochloric acid. Clearly single and combined reactions occur with different numbers of species, depending on the gaseous concentration and the stability of the embryo formed (g – gaseous, p – particulate): NH3 (g) + HCl(g) 󴀘󴀯 NH4 Cl(p) ,

(3.117)

NH3 (g) + HNO3 (g) 󴀘󴀯 NH4 NO3 (p) ,

(3.118)

NH3 (g) + H2 SO4 (g) 󴀘󴀯 NH4 HSO4 (p) ,

(3.119)

2 NH3 (g) + SO3 (g) + H2 O 󴀘󴀯 (NH4 )2 SO4 (p) , SO3 (g) + H2 O(g) 󴀘󴀯 H2 SO4 (p) , NH3 + HNO3 + SO3 + H2 O → (NH4 )2 NO3 HSO4 .

(3.120) (3.121) (3.122)

Interestingly, it was found that the formation of SOAs accelerates in the presence of SO2 and sulfuric acid (Jang et al. 2002, Edney et al. 2005, Surrat et al. 2007). The first step in atmospheric SO2 oxidation is OH addition (Chapter 5.4.3.1), and this radical can react with alkoxyl radicals (RO) to form sulfonic acid and further with organic peroxy radicals to form dialkyl sulfates: OH

RCH3 O

RCH3 O2

SO2 󳨀󳨀→ HSO3 󳨀󳨀󳨀󳨀󳨀→ ROHSO3 󳨀󳨀󳨀󳨀󳨀󳨀→ ROS(O2 )OR . (−HO2 )

(3.123)

These results strongly suggest the importance of particle phase reactions that lower the volatility of organic species, via accrecation (oligomerization) processes (Molina et al. 2004, Carlton et al. 2009). Organosulfates, including nitrated derivatives (e.g., nitroxy organosulfates), were detected in ambient aerosols (Surrat et al. 2007, 2008, Gómez-González et al. 2008). Jacobson et al. (2000) and Carlton et al. (2009) have also presented reviews on organic atmospheric aerosols. For reviews on atmospheric aerosol chemistry see Bouchier (2015), Zieman and Atkinson (2012), and George and Abatt (2010). Recently it was found that amines are far more efficient than ammonia in forming particles with sulfuric acid (Almeida et al. 2013) and that classical nucleation theory may not be directly applied to all atmospheric nucleation processes (KupiainenMaatta et al. 2014). Furthermore, organic species likely play a key role in nucleation and growth (Bianchi et al. 2016). The main concern of classical homogeneous nucleation theory²¹ was a thermodynamic description of the initial stage of nucleation from embryo to nucleus with a slightly larger size over the critical one (Seinfeld 1986, Pruppacher and Klett 1997, Seinfeld and Pandis 1998, Kulmala et al. 2000, Zhang et al. 2011). The rate of cluster formation (homogeneous nucleation) is described by R = k exp (−

∆G ) . kT

(3.124)

21 Charles Thomson Rees Wilson (1868–1959) made the first expansion cloud chamber experiments (Wilson 1897, 1899).

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The formation rate of 3 nm particles is often in the range 0.01–10 cm−3 s−1 in the boundary layer. However, in urban areas, formation rates are often higher (up to 100 cm−3 s−1 ), and rates as high as 104 –105 cm−3 s−1 have been observed in coastal areas and industrial plumes. Typical particle growth rates are in the range 1–20 nm h−1 in the midlatitudes depending on the temperature and availability of condensable vapors (Kulmala et al. 2004). The change in free enthalpy required to form a critical cluster of the new phase from the supersaturated nucleating phase is at first positive because the decrease in entropy is initially larger (regular structure formation) than the decrease in enthalpy (this follows from eq. (3.103) at p, T = constant): (∆G)p,T = Gcluster − Gvapor = n∆μ + γA ,

(3.125)

where ∆μ = μ cluster −μ vapor = −RT ln(p/p∞ ) ≡ −Vm ∆p, p is the actual vapor pressure of the cluster (p = p∞ + ∆p), and p∞ is the equilibrium vapor pressure of the nucleating substance; cf. eq. (3.62b). On the other hand, applying eq. (3.103) as a special case for T, n = constant, it follows (see also eq. (3.26) concerning volume-pressure change) that (∆G)T,n = ∆Vp + γA . (3.126) Here, ∆V = Vcluster − Vvapor and because Vcluster ≪ Vvapor under all conditions, ∆V = −Vvapor . The vapor phase is assumed to be ideal, so Vvapor = nRT/p∞ . The number of moles n corresponds to the number of molecules transferred from the vapor into the cluster, so n = Vcluster /Vm (Vm is the molar volume of the cluster phase) and with Vcluster = 4πr3 /3; it follows that (the same expression derived from eq. (3.125)) (∆G)T,n = −

4πr3 p RT ∞ + γA . 3Vm p

(3.127)

Finally, using the standard expression for the surface (of the cluster), replacing dA, and setting p/p∞ = S, we get (∆G)T,n = −

4πr3 RT S + 4πr2 γ . 3Vm

(3.128)

As a result, the nucleation curve (free energy change versus nucleus size) passes through a well-known single maximum point corresponding to the critical size of the nucleus (Figure 3.12). The process is at first reversible (as expressed in eqs. (3.117)– (3.121)). The radius of the critical cluster can be derived from eq. (3.126) under the condition ∂(∆G/∂r) = 0 (compared with the radius derived directly from the Kelvin equation) as 2γVm 2γM rcritical = = . (3.129) RT ln S RTρ ln S

152 | 3 Fundamentals of physicochemistry in the climate system

free enthalpy of cluster

'G

S 1

U 4S r 3  RT ln S  4S r 2J 3M

Gc

S !1

rc

radius Fig. 3.12: Change in free enthalpy during the formation of clusters from a vapor (homogeneous nucleation). Tab. 3.5: Critical size and number of H2 O clusters depending on supersaturation. Supersaturation

Radius (nm)

N H2 O

1.02 1.1 2 10

54 11 1.5 0.5

2.2 ⋅ 1010 2.0 ⋅ 105 500 18

Table 3.5 shows the critical radius of the pure water cluster independent of supersaturation. We can clearly see that under normal atmospheric conditions, the formation of water droplets is impossible. In atmospheric modeling the nucleation rate and number of clusters produced with a critical radius per volume is simple to approach from kinetic theory but is still highly controversial after almost a century of research (Spracklen et al. 2008, Merikanto et al. 2009). The fact that after about 120 years of effort we still cannot confidently predict the nucleation rates associated with this phase transition highlights the fact that even homogeneous vapor-phase nucleation is not an easy problem (Wyslouzil and Wölk 2016). The weakness of classical homogeneous nucleation theory lies in the importance of energy transfer (as opposed to mass transfer) along the chain of a growing molecular cluster (Bakhtar et al. 2005, Wasai et al. 2007). Altman et al. (2008) suggested that, to bring theory in line with experiments, certain fundamental propositions of nucleation theory should be revised. The inclusion of an additional contribution to the Gibbs energy of a cluster caused by the size dependence of the

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specific heat capacity of the cluster decreases the critical cluster size compared with the value calculated by the Kelvin equation. In what follows, we will consider the example of ammonium chloride formation in air. More precisely, we split reaction (3.117) into gaseous (monomolecular) and particulate (multimolecular) ammonium chloride: NH3 (g) + HCl(g) 󴀘󴀯 NH4 Cl(g) 󴀘󴀯 NH4 Cl(p) .

(3.130)

Pure NH4 Cl aerosols can grow in size to up to 1 μm (Gmelin 1936b). The particles are less hygroscopic than NaCl but easily soluble in water. The equilibrium constant is given by pNH3 pHCl cNH3 cHCl Kp = ≈ pNH3 pHCl and Kc = , (3.131) 2 cNH4 Cl p0 where p0 is the atmospheric pressure (assumed to be 1 bar). Gibbs’s eq. (3.132) and the Kelvin eq. (3.133) describe the temperature dependency of the equilibrium as well as the cluster-critical radius independent of the partial pressures of NH3 and HCl: RT ln Kp = μNH4 Cl(p) (T) − μNH3 (T) − μ HCl (T) , − ln

pNH3 pHCl p20

=

2γNH4 Cl MNH4 Cl = ln S . RTρ NH4 Cl r

(3.132) (3.133)

Hence, pNH3 pHCl must exceed Kp to obtain a critical cluster size. Seinfeld and Pandis (1998) used the expression ln Kp = 34.266 −

21.196 , T

which shows that Kp is relatively independent of T (K298 = 7.08 ⋅ 1014 ). Although Kp = pNH3 pHCl and in equilibrium pNH3 = pHCl , we now estimate the condition for NH4 Cl formation to be 1/ ∑ Kp = 0.37 ⋅ 10−7 atm (= 37 ppb), an impossible condition under free tropospheric conditions. Therefore, particulate NH4 Cl belongs to the minor constituents in air. However, to follow this example given by Seinfeld and Pandis (1998), we calculate the critical radius using eq. (3.129) and the data given M = 52.49 g mol−1 , γ = 150 ⋅ 10−5 N cm−1 , and ρ = 1.527 g cm−3 (Countess and Heicklen 1973). It follows that rcritical ≈ 1 nm for this numerical example (37 ppb gas concentration). Baek and Aneja (2005) estimated the reaction rate constant of NH3 + HCl → NH4 Cl to be k = 3.44 ⋅ 10−4 m3 μmol−1 s−1 and (recalculated for 298 K) k = 1.4 ⋅ 104 at m−1 s−1 . The most likely particle formation will go first through sulfate production (3.121) and subsequent NH3 absorption onto the sulfate clusters. Harrison and Kitto (1992) found pseudo-first-order reaction rate constants for absorbing gaseous ammonia of between 4 ⋅ 10−6 s−1 and 4.1 ⋅ 10−4 s−1 , corresponding to residence times between less than 1 h and a few hours.

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3.6.2.2 Formation of secondary organic aerosols OAs can originate as either primary organic aerosols (POAs) or SOAs. SOAs are defined as products of gas-phase oxidation from volatile organic compounds (VOCs) emitted from biogenic or anthropogenic sources, such as vegetation and combustion emissions (e.g., aldehydes such as nonanal²² and polycyclic aromatic hydrocarbons such as pyrene and naphthalene), which have partitioned from the gas to the aerosol phase (Kroll and Seinfeld 2008, Hallquist et al. 2009). POAs are emitted into the atmosphere from biomass burning, fossil fuel and biofuel use, and sea spray. An increase in SOA concentrations by up to 200% from preindustrial to present levels has been found over tropical oceans. OAs have a large impact on air quality, biogeochemistry, and the climate through interactions with reactive trace gases, water vapor, clouds, precipitation, and radiation (IPCC 2013, Herrmann et al. 2015). They can affect biogeochemistry through either their deposition of nutrients on land or ocean or by changing climate (Mahowald et al. 2011). They can influence climate by changing the Earth’s energy budget by scattering and absorbing the radiation or acting as CCNs. However, they represent one of the largest uncertainties in climate science, being for the most part a climate cooling species (IPCC 2013, Bouchier 2015). The formation of SOAs, leading to the formation of nanoparticles of blue haze over forested areas, is highly complex and not fully understood. Organic compounds (gases and particles) comprise a mixture of an extremely large number of different molecules (Goldstein and Galbally 2007, Ziemann and Atkinson 2012), with each compound further undergoing atmospheric chemical reactions to produce a range of oxidized products and, hence, myriads of secondary products (Hallquist et al. 2009). These products are likely involved in the earliest stages of particle nucleation and growth (Bianchi et al. 2016). Based on the mass balance of volatile organic carbon or on scaling of the sulfate budget, the global sources of SOAs are estimated to between 120 and 1820 Tg yr−1 (Goldstein and Galbally 2007, Hallquist et al. 2009). Recently, Tsigaridis et al. (2014) estimated SOA annual production rates ranging from 13 to 119 Tg yr−1 using 31 global chemistry transport and general circulation models. Recent laboratory studies suggest that SOA formation rates are higher than assumed in current models (Hodzic et al. 2016); best estimates are between 130 and 140 Tg yr−1 (Spracklen et al. 2011, Hodzic et al. 2016) with about 75% dominant biogenic fraction. There is also evidence that SOA removal by dry and wet deposition occurs more efficiently than some current models suggest and that photolysis and heterogeneous oxidation may be important (but currently ignored) SOA sinks. The predicted global SOA burden in the updated model is 0.88 Tg, and the corresponding direct radiative effect in the upper part of the atmosphere is 0.33 W m−2 . The newer estimates are almost one order of magnitude larger than previous ones (e.g., 15.3 Tg yr−1 by Lack 2003) but there remain large uncertainties, specifically in connection with removal processes.

22 Also called nonanaldehyde, pelargonaldehyde, or aldehyde C-9 (C9 H18 O).

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A number of studies suggest important pathways of SOA production from volatile organic precursors such as isoprene and monoterpenes, heterogeneous uptake of glyoxal and methylglyoxal, and oxidation of low-vapor-pressure intermediate-volatility and semivolatile organic compounds. The underestimation of model SOA compared with measured SOA suggests missing SOA precursors or underestimated atmospheric processing of organic compounds in the model. Previous studies showed that the oxidation of biogenic VOCs makes a major contribution to global SOA formation. Although isoprene and monoterpenes are generally emitted more abundantly, sesquiterpenes have attracted increasing interest in recent years owing to the exceptionally high reactivity of some species, particularly with ozone, and their generally high propensity to form SOAs upon oxidation (see Khan et al. 2017 for relevant literature). Thus, the representation in global chemistry transport models of the myriad of chemical processes involved in SOA formation has proven to be a challenging task. Zhang et al. (2009a) showed that the interaction between biogenic organic acids and sulfuric acid enhances nucleation and the initial growth of those nanoparticles. The fate of nuclei is particle coagulation, a process in which small particles (assumed spherical) collide with each other and coalesce completely to form larger spherical particles. Small particles are indeed spheroidal, and the assumption of spherical particles seems to be reasonable (Mitchell and Frenklach 2003, Balthasar et al. 2005). After a certain size, however, the particles cannot coalesce completely and start to form long chains, which eventually grow into three-dimensional fractal-like structures. Figure 3.13 shows the new particle formation and growth pathways. The surface coating particle growth

< 1 nm

10-50 nm

≤100 nm

nuclei coagulation nucleation

gas

adsorption

soot

emissions from combustion, plants, soils, seaspray

Fig. 3.13: Particle growth and formation of CCNs.

~200 nm

≥ 2000

CCN

cloud

156 | 3 Fundamentals of physicochemistry in the climate system

of primary hydrophilic soot particles plays an important role, likely via SO2 absorption and sulfuric acid formation and via NMVOC absorption, with its oxygenation possibly providing a matrix for the stabilization of very fine SOA particles.

3.6.3 Atmospheric aerosols and the properties of aerosol particles In physics, an aerosol is defined as the dispersion of solids or liquids (the dispersed phase) in a gas (the dispersant). More generally, dispersion is a heterogeneous mixture of at least two substances that are not soluble within each other (in contrast to molecular dispersion). However, the classical scientific terms are colloid and colloidal system. Colloids exist between all gas, solid, and liquid combinations, with the exception of gas-gas (all gases are mutually miscible), L – liquid, S – solid, G – gas: S+S

L+S

G+S

S+L

L+L

G+L

S+G

L+G

In addition to the terms sol and gel, Thomas Graham (1809–1869) introduced (Graham 1861) the terms colloid and colloidal condition of matter. The confusion in using different terms for classifying atmospheric disperse systems was already discussed by Grimm (1931). The WMO classification (manual of codes) of horizontal obscuration into categories of fog, ice fog, steam fog, mist, haze, smoke, volcanic ash, dust, sand, and snow shows that there is little scientific understanding of the atmospheric colloidal system behind the classification. Atmospheric aerosol always comprises the whole system, i.e., suspended particles in air, and so is in the air itself. The particles may be referred to as atmospheric (or aerosol) particles (APs); thus, only APs can be collected but not the aerosol (particles are separated from air). At present, the terms bioaerosol and biological aerosol have been introduced, but they are scientifically unsound.²³ Clearly, the role of biogenically derived APs (to call them biological particles is correct) has been reconsidered (prompted by insights from Pasteur 150 years ago²⁴) in a new light, i.e., not as a transmitter of diseases but playing a likely role as CCNs and INs (Möhler et al. 2007, Sun and Ariya 2006). Despite the term aerosol implying solids in air, the scientific community remains divided into those who treat hydrometeors (cloud and fog droplets) as belonging to atmospheric aerosols and those who do not. There is no question that atmospheric APs contain water and that the transfer from potential CCNs (CNs) via activated CCNs

23 The phrase “Bioaerosol is defined as airborne particles, large molecules that are living. . . ” (Gelencsér 2004, p. 70) contains two more errors: Aerosol is more than a particle and even the largest existing molecule is not living. 24 Louis Pasteur (1822–1895), see Pasteur (1862).

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157

size range of AP PM2.5

1

10

0.1

1

100

1000

PM10

1

mm

10

100

1000

μm

nm

coarse particles

fine particles ? Aitken nuclei, cluster

0.1

accumulation mode

nucleation mode

molecules

0.01

giant particles

soil and industrial dust fog and cloud droplets

condensation nuclei

pollen virus

rain drops hail grains

spore bacteria

Fig. 3.14: Size ranges and types of particles in air.

to haze particles (some scientists divide them into dry and wet haze) is more or less fluent. However, when forming mist,²⁵ the particles suddenly (heterogeneous nucleation) grow by several orders of magnitude in volume and become almost water droplets, containing some dissolved matter from the CCNs. The physical and chemical properties of hydrometeors, whether solid (icy particles) or liquid (water droplets), are very different from nonaqueous particles in the atmosphere. Therefore, by atmospheric aerosols we understand the entity of nonhydrometeor particles in the air from a few nanometers to a few micrometers in size (Figure 3.14). The limits are not fixed; the smallest particles might be a few molecules (embryo) or a macromolecule and the largest particles might be biological species such as pollen. The transfer to giant particles (which might have radii of hundreds of micrometers) also takes place.²⁶ These 25 If we can see less than 1 km through the cloud of water droplets, it is known as fog. If we can see between 1 and 2 km, we call it mist. A fog is a cloud that has come into contact with the Earth’s surface. Mist is very thin (concerning number density) fog (see Chapter 2.1.3.2). 26 It was suggested to set a threshold for particles with significant sedimentation velocity according to Stoke’s law.

158 | 3 Fundamentals of physicochemistry in the climate system

Tab. 3.6: Origin and types of atmospheric aerosol particles (further classification possible by biogenic, geogenic, and anthropogenic origin). Source characteristics Direct

indirect

a

Particle characteristics

Wind blown

Inorganic Organic Biological

Soil dust and sea salt Plant debris, degradation products Bacteria, viruses, pollen (POA)

Combustion

Inorganic Organic

Ash Smoke, soot (black carbon)

Industrial

Inorganic

Dust

Volcanic

Inorganic

Ash

Extraterrestrial

Inorganic a

Meteoric dust

gas emissions

Inorganic Organic

Salts (sulfate, nitrate, ammonium, chloride) SOA

Organic compounds have been detected in meteors (Volume 2).

large particles²⁷ no longer fit the scientific understanding of an aerosol (or colloidal system) because of their very small number concentration. In contrast to hydrometeors, APs are always in the air, but not all types of APs can be observed at any given time because of different sources and formation conditions (Table 3.6). APs are referred to as PM or simply dust. In 1879, Carl Wilhelm von Nägeli (1817–1891) divided suspended matter in air into three classes: (a) coarse (visible through human eyes), (b) sun dust²⁸ (visible through light scattering), and (c) nonvisible, detectable only through water vapor condensation (after Rubner et al. 1907). There is another fundamental difference between hydrometeors and APs: the sizedependent chemistry. The size distribution of hydrometeors (cloud droplets) ranges from about 1 to 40 μm, where a maximum is observed around 5–10 μm. They are well approximated as being spherical in form. Typical differences in cloud droplet chemical composition were found, but all hydrometeors consist of more than 99.999% H2 O. The size range of APs is three orders of magnitude greater, having several maxima (modes) and showing extreme differences in chemical composition and particle form from spheres to fibers and crystalloids. APs are ubiquitous in Earth’s atmosphere and can grow by several processes and age, and thereby change size and chemical composition. Whereas individual hydrometeors exist only in a range between minutes and

27 It is remarkable that hail particles can be produced in the upper atmosphere with diameters of many centimetres. It was reported that icy chunks (apart from its extraterrestrial origin) are likely to be produced in upper atmosphere too. 28 Called Sonnenstäubchen in German.

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hours in the air, APs can exist for minutes or months and, hence, be transported over long distances. Although we do not consider cloud droplets as APs, they play a crucial role in AP aging: after heterogeneous nucleation, the CCNs dissolve²⁹ in the aqueous phase and further gas uptake and aqueous-phase reactions provide mass for a residual after droplet evaporation (Figure 3.9). We will see later that typical AP substances (such as sulfate, organic acids, and macromolecular substances) are produced through cloud processing. Let us state that each AP is unique and singular despite the existence of several classes of particles. As a logical consequence, (full) scientific understanding would need single-particle sampling and analysis, an infeasible approach. By contrast, each PM sample contains more different molecules than we normally consider for the external gaseous phase. To understand the timely and spatial behavior of PM, we would need far more measurements than has been available until now. Without a doubt, PM climatology is only in its early stages. The role of APs in the climate system was outlined at the beginning of Chapter 3.6 and is summarized again here (Ramanathan et al. 2001, Carslaw et al. 2010): 1. optical function: changing visibility (by reducing it), 2. radiation function: changing atmospheric heat budget (cooling tendency), 3. water cycle function: cloud and thereby precipitation formation (increasing and decreasing) and 4. chemical function: providing a surface for heterogeneous chemistry. Without a detailed explanation, it is self-evident that a quantified description of atmospheric aerosols is extremely important for understanding the climate system. However, it is so complex that no complete picture will be seen in the near future. Much is known about the chemical composition and sources of APs, but modeling their impact on climate remains a highly uncertain task. This seems like a dilemma, but there are two simple answers. First, understanding complex systems normally takes time. Second, our current understanding of aerosols, clouds, and climate is sufficient to pass on the available scientific results and conclusions as management tools into the hands of engineers and politicians. It is simple: end the era of fossil fuel combustion. It is outside the scope of this book to describe AP mechanics, i.e., microphysics and dynamics (Friedlander 1977, Twomey 1977, Hinds 1982, Kouimtzis and Samara 1995, Harrison and van Grieken 1998, Mészáros 1999, Spurny 1999, 2000, Baron and Willeke 2001, Vincent 2007, Kondratyev et al. 2006, Boucher 2015, Tomasi et al. 2017).

29 This is valid only for the water-soluble part of CCNs; water-insoluble particles or parts will form a suspension in drops, whereas the water-soluble surface-layer coat is dissolved (as observed for soot and SOA particles).

160 | 3 Fundamentals of physicochemistry in the climate system

Here, we only summarize the important topic of atmospheric aerosol size distribution (Jaenicke 1999). Figure 3.14 shows that the size range covers several orders of magnitude. Therefore, the common logarithm of the radius³⁰ is useful to describe the different distribution functions: dN(r)/ dlg r = f(lg r) or dN(r)/ d r = f(lg r)/2.302 ⋅ r. N(r) is the cumulative number size distribution (or integral of radii) with dimension cm−3 , and r the particle radius: ∞

N(r) = ∫ n(r) d r ,

(3.134)

0

where n(r) is the differential number size distribution, which denotes a number density (not number concentration) having dimension cm−3 cm−1 : n(r) =

dN(r) . dr

(3.135)

Their sizes range from a few nanometers to a few micrometers (Figure 3.14), often with pronounced concentration modes around a few tens of nanometers (Aitken mode), in the range ∼ 100–500 nm (accumulation mode) and at a few micrometers (coarse mode; Figure 3.15). Coarse-mode particles typically originate from the dispersion of solid and liquid matter such as soil, dust, and sea spray. Submicron particles are usually mixtures of primary particles (almost combustion products from biomass smoke and diesel soot) and secondarily produced particles via the gas-to-particle conversion (the most important is sulfuric acid from SO2 oxidation and organic compounds from the oxidation of VOCs). APs must also satisfy the fundamental thermodynamic principles (which are important in chemical analysis and for studying particle origins); x is the mixing ratio of component i: – ∏ i x i ≤ Ks (solubility equilibrium); – ∑i x+i = ∑j x−j (electroneutrality); – ∑i x i + xH2 O = 1 (closure). APs generally comprise the following three types of matter or fractions (Table 3.7): – highly water soluble inorganic salts, – insoluble mineral dust and – carbonaceous material. A water-soluble fraction (mostly a mixture of ammonium, sulfate, nitrate, and chloride compounds) was studied extensively, and several models of the geographical dis30 The logarithm of a physical quantity instead of the quantity itself is mathematically incorrect because the logarithm must always be a value. The origin of the logarithm of a physical quantity is based on the integral ∫ dx x = ∫ dln x = ln x + c; finally, the definition ln x ≡ ln(x/x 0 ) is valid where the reference value x0 = 1 (e.g., pressure, mol fraction).

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Tab. 3.7: Principal chemical composition of PM. Origin

≳ 95%

1–5%

< 1%

Soil dust Sea salt Industrial dust Secondary inorganic Secondary organic

O, Si, Al Na, Cl Ca, O, C − + SO2− 4 , NO3 , NH4 C, O

Fe, Ca, K SO2− 4 , Mg Fe, elements Cl H

All elements All elements All other elements – S, N

140000

200

number 120000 160

mass

120

80000 60000

80

40000 40

dm/dlogDp (in μg m-3)

dN/dlogDp (in cm-3)

surface 100000

20000 0 0.00

0.01

0.10

1.00

0 10.00

particle diameter (in μm)

Fig. 3.15: Particle size distributions from an inner street site in Stockholm; data from Mohnen (1995).

tribution and climatic effects of this group of compounds in the aerosol have appeared. This group includes sea salt (sodium, magnesium, and chloride) and secondary inorganic aerosols (ammonium, sulfate, and nitrate), as well as a small fraction of watersoluble soil dust (potassium, calcium) and organic aerosols (organic acids and SOAs). Because in cloud and rainwater we also find many dissolved metal ions (mainly Fe, Cu, and Mn; but no metal can be excluded in extremely small concentrations), their origin is crustal matter and sea salt. Insoluble inorganic matter is predominantly soil dust but also occasionally volcanic ash and industrial dust. Oxygen and silicon (silicates) are the dominant elements. Whereas soil dust is only inconvenient, volcanic particles emitted into the upper troposphere can influence the climate for 1–2 years and be dangerous for aviation. Industrial dust, predominantly flue ash from coal combustion, initially provides a certain acid neutralization potential in the air (in plumes); however, in the emissions of heavy metals only mercury plays a global role because of its volatility and various chemical species. Transition metal ions (TMIs) (Fe, Mn, and Cu) play a huge role in aqueous-phase redox processes (Chapter 5.2.5).

162 | 3 Fundamentals of physicochemistry in the climate system Whereas secondarily produced APs are < 1 μm, soil dust is > 1 μm. Sea salt particles can have the same range of sizes as CCNs (approximately 0.2 μm) but are largely in the lower micrometer range. Industrial dust can range from nanometersized particles (soot from combustion) to coarse particles. Biological particles also range from submicron size (bacteria) to 10–30 μm (pollen) (Matthias-Maser 1998). The three fractions (insoluble minerals, carbonaceous material, and soluble salts) contribute roughly one-third each to total PM; however, this can vary according to the source characteristics and – for secondary matter – depend on the reaction conditions. Hence, the plural term aerosols is associated with special source and chemical regimes characterizing the aerosol type: marine aerosol, rainforest or tropical aerosol, arctic aerosol, desert dust aerosol, and so on. Carbonaceous material includes organic compounds (OAs) ranging from easily soluble to insoluble, plus unsoluble elemental carbon (EC) and black carbon (BC) and biological species.³¹ Organic compounds cover a very wide range of molecular forms, solubilities, reactivities, and physical properties, which makes complete characterization extremely difficult, if not impossible. The reader is encouraged to review the following papers: Jacobson et al. (2000), Decesari et al. (2000), Penner et al. (1993), Penner (1995), Gelencsér (2004, 2007), McFiggans et al. (2005b), Kanakidou et al. (2005), Sun and Ariya (2006), Facchini and O’Dowd (2007) Timonen et al. (2008), and Hallquist (2009). A large fraction of PM is soot, the historic symbol of air pollution. There was a long dispute in the literature on the definition of soot, which is also called EC, BC, and graphitic carbon (Cachier 1998, Gelencsér 2004). Surely, soot is the best generic term to refer to impure carbon particles resulting from the incomplete combustion of a hydrocarbon (EM – elemental matter is also found in the literature and might “integrate” EC and BC). The formation of soot depends strongly on the fuel composition. It spans carbon from graphitic (EC) through BC to organic carbon (OC) fragments. Each of the available methods (optical, thermal, and thermo-optical) refers to a different value; it remains a simple question of definition. Hence, comparison of the various soot measurement methods is senseless. The atmospheric implications of soot particles are that they – provide the largest surface-to-volume ratio for heterogeneous processes, – form the most complex structural nanoparticles, – carry (toxic) organic substances, and – warm the atmosphere through light absorption.

31 Speciation of carbon sources is possible via isotopic studies. The carbon isotope 14C is produced in the upper atmosphere and enters the biological carbon cycle at a relatively constant initial ratio to 12C. On the other hand, 14C is completely depleted in fossil fuels due to radioactive decay. Thus, the combination of ratios of 12C,13C, and 14C enables the quantification of different carbon source contributions to carbonaceous samples.

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OM was observed in marine aerosol particles for many decades and was linked to the enrichment of sea spray by biogenic matter transferred from the sea surface to the tropospheric boundary layer through bubble-mediated production processes (O’Dowd et al. 2002b). Ceburnis et al. (2011) have demonstrated a predominant (80%) marine biogenic source for fine carbonaceous particles in clean marine air over the Northeast Atlantic. This biogenic carbon component resides in particle sizes predominantly contributing to cloud nuclei, pointing to a direct link between plankton and marine cloud-climate interactions. In addition, the anthropogenic contribution to marine organic carbon aerosol is still significant, illustrating the role of hemispheric and longrange transport having notable impacts in nominally pristine marine environments. Marine sources can contribute around 30% to the amount of total carbon (TC) in polluted air masses sampled at Mace Head, Ireland, which has not been quantified so far. New research has found that the sooty brown clouds, caused primarily by the burning of coal and other organic materials in India, China, and other parts of South Asia, might be responsible for some of the atmospheric warming that had been attributed to GHGs (Ramanathan and Crutzen 2003, Ramanathan et al. 2007). Atmospheric brown clouds (ABCs) are layers of air pollution consisting of aerosols such as BC, organic carbon, and dust that absorb and scatter solar radiation. ABCs also contain other anthropogenic aerosols such as sulfates, nitrates, and fly ash, which primarily scatter solar radiation. In Europe, carbonaceous matter ranges from 0.17 μg m−3 (Birkenes, Norway) to 1.83 μg m−3 (Ispra, Italy) for EM and for OC from 1.20 μg m−3 (Mace Head, Ireland) to 7.79 μg m−3 (Ispra, Italy). The percentage of TC to PM10 in rural backgrounds amounts to 30%: 27% OM and 3.4% EM, respectively (Yttri et al. 2007). Within this range are values measured in Berlin and surrounding areas: 1.3–2.2 μg m−3 EM and 2.8–3.4 μg m−3 OC, whereas TC contributes 20% to PM10 (Tables 3.8 and 3.9).

3.6.4 Formation of cloud droplets: Heterogeneous nucleation As seen from the Köhler eq. (3.110), the condensation of water vapor onto preexisting droplets is only possible when the saturation ratio is larger than one. However, the mass transfer of water molecules is possible for S < 1 (aqueous particles do not exist) when the solid particle surface provides a large enough affinity to H2 O. This property is termed hygroscopicity. Each crystalline water-soluble surface dissolves or deliquesces at a certain RH (Table 3.10). Petters and Kreidenweis (2008) present a method to describe the relationship between particle dry diameter and CCN activity using a single hygroscopicity parameter κ, now often called the effective hygroscopicity parameter. Values of the hygroscopicity parameter are between 0.5 and 1.4 for highly-CCN-active salts such as sodium chloride, between 0.01 and 0.5 for slightly to very hygroscopic

164 | 3 Fundamentals of physicochemistry in the climate system Tab. 3.8: Composition of particulate matter PM10 in Berlin and environs (μg m−3 ) (daily samples over 1 year: 2001/2002); data from Beekmann et al. (2007) and Möller (2009b). Species

Street side

Urban

Rural

Total PM10 Residual a OC BC Sulfate Nitrate Ammonium Chloride Sodium Calcium Potassium Magnesium Iron

34.5 15.3 4.3 4.3 4.1 3.4 2.0 0.50 0.34 0.42 0.20 0.05 0.7

24.4 9.4 3.4 2.2 3.6 3.0 1.8 0.19 0.29 0.19 0.14 0.04 0.2

20.1 6.8 2.8 1.3 3.6 3.0 1.8 0.21 0.34 0.16 0.09 0.05 0.1

a

Insoluble minerals.

Tab. 3.9: Classified composition (%) of particulate matter PM10 in Berlin and environs. Species Insoluble minerals a OC + BC Sulfate + nitrate + ammonium Other soluble minerals Total a

Street side

Urban

Rural

44 25 27 4

38 23 34 5

34 20 42 4

100

100

100

Residual (Table 3.8).

organic species, and 0 for nonhygroscopic components. Observations indicate that atmospheric PM is typically characterized by 0.1 < κ < 0.9. Surfactants apparently decrease the deliquescence point (Chen and Lee 2001) by up to 8% RH. Figure 3.16 shows the behavior of ammonium sulfate with increasing humidity; a dry particle with a diameter of 100 nm does not grow over a wide range of humidity changes (range a) but suddenly, shortly before reaching the deliquescence point, (range c) it changes by about 240% of the particle volume by water absorption. With decreasing humidity, however, the particle will not lose all its water again but only according to Köhler theory (hysteresis curve), i.e., it exists in a metastable state (range b). Particles that reach the deliquescence point are called activated CCNs. Beyond this deliquescence point, the particle takes up water continuously with increasing RH according to the following equilibrium equation: RH =

pH2 O = aH2 O , p∞ H2 O

(3.136)

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Tab. 3.10: Deliquescence point (RH in %) for pure salts. Substance

Deliquescence point

MgCl2 ⋅ 2 H2 O NH4 HSO4 K2 CO3 ⋅ 2 H2 O NH4 NO3 NaCl (NH4 )2 SO4 NaNO3 KHSO4

33 40 43 62 76 80 80 86

mobility diameter (in nm)

160

Increasing humidity decreasing humidity Köhler theory

b

140

120

c

100 a 80 40

50

60

70

80

90

relative humidity (in %) Fig. 3.16: Experimental estimated particle growth with increasing and decreasing humidity (humidogram) for synthetic (NH4 )2 SO4 with r = 50 nm at 20 °C, after Weingartner et al. (2002).

where a is the activity of water in the salt solution, p the water partial pressure, and p∞ the saturation pressure (T depending). Optically, these water-coated particles (we call them haze particles) show light scattering similar to cloud droplets (the key difference is that the number of haze particles is larger but the size is much smaller than that of cloud droplets); therefore, the sky becomes milky and visibility decreases. When pH2 O > p∞ H2 O , water condenses onto the activated CCNs and the particle volume roughly increases by at least two orders of magnitude to form mist, fog, or cloud droplets. This process is termed heterogeneous nucleation. Supersaturation is always a result of the adiabatic cooling of the air parcel. Because of the release of the condensation heat and the entrainment of dryer air from surrounding, droplet formation (or cloud extensions) is limited. From a mass transfer point of view, the heterogeneous nucleation is also a nucleation scavenging of PM, the first process of in-cloud scavenging, followed by gas uptake. Junge (1963) described it by the simple equation caq = ε

cp , LWC

(3.137)

166 | 3 Fundamentals of physicochemistry in the climate system

where caq is the concentration of dissolved particles in the droplet phase and ε is the fraction (0. . . 1) of the scavenged (washout) PM in air (cp gas-phase PM concentration). Under normal boundary layer conditions, ε = 0.9 . . . 1.0 is estimated (Mészáros 1981). Despite the fact that only a small percentage of the total number of particles serve as CCNs (and are thus scavenged), these few particles contribute more than 90% of PM mass, whereas smaller non-CCN particles contribute less than 10% of PM mass but more than 99% of the number concentration (Figure 3.16).

3.6.5 Scavenging: Acommodation, adsorption, and reaction (mass transfer) 3.6.5.1 Mass transfer: General remarks Let us now consider mass transfer from the gas phase to a droplet or onto an atmospheric particle (AP) according to the scheme presented in Figure 3.7. This process includes the following steps (seen here from the gas phase point of view in direction to the particle, but the transfer can be reversed): – turbulent transport of molecules in the particle (to the diffusion layer interface), – molecular diffusion to the particle surface (interface), – adsorption onto the surface (specifically solid particles but for droplet surfactants, for example) or absorption (uptake) into the particle (mainly droplets, but this does not exclude solids), – chemical surface reactions (if possible), – desorption into the gas phase, – diffusion and mixing in particle and – simultaneous chemical reactions (if possible) in condensed phase (e.g., aqueousphase chemistry or solid-phase chemistry). From gas kinetic theory one can derive the number of collisions of a gas molecule with a particle. In Chapters 2.5.1 and 2.5.2, we derived different expressions for the number of collisions (z) between molecules and a wall (cN Av dt/6) and among molecules (√2cN v dt), where cN is the molecule density (N/V)³², the area A has different definitions (see subsequent discussion), and v is the mean molecular speed. In what follows, the subscript 0 refers to the surface (interfacial layer), the subscript g close to the surface layer (about one mean free path), and the subscript ∞ denotes the gas phase concentration far from the surface, i.e., x∞ ≫ l. According to Figure 3.18, the number of striking molecules is z = (cN )g Avx dt, with A = πr2 (r is the particle radius). We must now consider that only a fraction of molecules has the speed vx expressed by vx f(vx ) dv (eq. (2.74)). From gas kinetic theory (Gombosi 1994) it can be derived that vx = v/4. Finally, the gross (maximum) flux Fcoll onto the particle surface (= number 32 Note that normally in the scientific literature the molecular density is denoted by n, which is identical to the Loschmidt number n0 in an ideal gas under standard conditions.

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| 167

of collisions in terms of number per unit of time and unit area) is given by Fcoll =

1 z 1 (cN )g v ≡ 2 = 2 Rcoll , 4 πr dt πr

(3.138)

where R is the rate (number of collisions per time)³³ and (cN )g is the number concentration of gas molecules close to the particle. We define a net flux (not each collision leads to an uptake), introducing the uptake coefficient γ, which refers to the net (sometimes also termed effective) uptake of gas molecules by droplets. Because the near-surface concentration is unknown, we replace it by the gas-phase concentration (cN )∞ and introduce a further effective uptake coefficient γeff : Fnet = γFcoll =

1 1 γ(cN )g v = γeff (cN )∞ v . 4 4

(3.139)

Distinguishing between γ and γeff (introduced by Pöschl et al. (2005) but not used by other authors, to my knowledge) is meaningful because it reflects the transport from the bulk gas phase close to the particle surface (∞ → g), which might have limitations, expressed by the actual surface collision flux Fcoll and the average gas kinetic flux Fcoll (cf. eq. (3.138)): 1 Fcoll = (cN )∞ v . (3.140) 4 From eqs. (3.138) and (3.139) it follows that (cN )g Fcoll γeff = = γ (cN )∞ Fcoll

and

Fnet = γFcoll = γeff Fcoll .

(3.141)

If there is no concentration gradient in the particle surrounding ((cN )g ≈ (cN )∞ ) it follows that γ = γeff . The ratio γeff /γ represents a gas diffusion correction factor. The mean molecular speed v is given by eq. (2.77), the “weighted arithmetic mean of all velocities.” Care must be taken in the terminology of different “averaged” velocities (recall the discussion on different uses of the terms velocity and speed in Chapter 2.5.2). This maximum flux (eq. (3.139)) occurs only in the absence of gas-phase diffusion and solubility limitations and in the absence of chemical reactions. When chemical reactions occur in the interfacial region (Figure 3.7), reactive loss at the surface competes with mass accommodation and subsequent reaction in the liquid phase (see subsequent discussion). The gas uptake by liquid droplets is widely described by the so-called resistance model (cf. Chapter 2.6.1 on dry deposition), where substance A must overwhelm layers with a specific resistance (Figure 3.17). The idea of this model is to describe the single processes (transport, adsorption, dissolution, and reaction) as decoupled processes. The dimensionless parameter γ (0 ≤ γ ≤ 1) is termed the net uptake coefficient, which describes the total process including all physical or chemical partial processes, here

33 Recall the difference between flux F and rate R: F =

1 AR

=

1 dc A ( d t ).

168 | 3 Fundamentals of physicochemistry in the climate system

Fig. 3.17: Resistance model of mass accommodation.

given by the gas-phase diffusion (“resistance” 1/Γg or “conductance” Γg ) and net uptake (resistance 1/γ): 1 1 1 = + . (3.142) γeff Γg γ Again, when gas-phase diffusion has a low resistance, it becomes γ = γeff , or, in other words, if the rate of diffusion of gas to the surface is large, then 1/Γg can be neglected. The net uptake coefficient γeff represents the major observable parameter in laboratory studies; it is also sometimes called the measurable and apparent uptake coefficient. Table 3.11 lists some γ values for common gas species. Tab. 3.11: Measured net uptake coefficient γ on water surface at 273 K; data from Davidovits et al. (2006). Gas-phase species

γ

SO2 H2 O2 H2 O HCl NH3 HNO3 HBr DMS HI CH3 OH C2 H5 OH CH3 OOH

0.34 0.24 0.22 0.18...0.23 0.12...0.20 0.15 0.079...0.26 0.13 0.091 0.056 0.049 0.012

3.6 Heterogeneous processes: Multiphase chemistry in the climate system |

169

The most common formula used to calculate the gas transport coefficient is (Pöschl et al. 2005) 4Dg 4 l 4 = Γg ≈ = Kn . (3.143) 3r 3 vr From eq. (3.143) exactly the same expression for Dg is derived as given already with eq. (2.89). The ratio between the mean free path l and droplet radius r is defined as the Knudsen number. Another empirical formulation is known (Davidovits et al. 2006): Γg ≈

0.75 + 0.238Kn . Kn(1 + Kn)

(3.144)

With regard to mass transfer to a particle surface, we must distinguish between three so-called transport regimes: – Kinetic regime: The radius of the particle is small compared with the mean free path of the molecule (this is valid for particles in the nucleation mode); r ≫ l or Kn ≫ 1. – Continuum regime: The radius of the particle is large compared with the mean free path of the molecule (this is valid for particles in the accommodation mode and, thus, for all hydrometeors);); r ≫ l or Kn ≪ 1. – Transition regime: The radius of the particle is on the order of the mean free path of the molecule (this is valid for the CCNs); r ≈ l or Kn ≈ 1. In the transfer regime, which is important for CCN formation and activation, several approaches are known to solve the Boltzmann equation (Fuchs theory, Fuchs and Sutugin approach, Dahneke approach, Sitarski and Nowakowski approach; see Seinfeld and Pandis (1998) and Pruppacher and Klett (1997)). In what follows, we will consider only uptake by cloud droplets, i.e., the continuums regime. For more details, see Pöschl et al. (2005), Davidovits et al. (2006), and Morita and Garrett (2008). It should be noted that termination and symbols are different from those used in the scientific literature (Pöschl et al. 2005). The mean free path is about 60 nm for most atmospheric gases under standard conditions (Pöschl et al. 2005). Figure 3.18 shows schematically accommodation along the x-axis. Mass accommodation occurs when a gas molecule strikes a particle surface; for solid particles adsorption and surface chemistry almost occur, and for hydrometeors absorption (dissolution) and aqueous-phase chemistry must be considered (Figure 3.17). The uptake of molecules by droplets lowers the gas-phase concentration near the surface ((cN )0 < (cN )g < (cN )∞ ) and results in a subsequent gas-phase diffusion to the surface because of the concentration gradient. The mass accommodation coefficient³⁴ α is the probability that a molecule that strikes a particle surface will be adsorbed or enter the

34 In the scientific literature, similarly defined parameters are called condensation coefficient, sticking coefficient, sticking probability, trapping probability, adsorptive mass accommodation coefficient, accommodation coefficient, and thermal accommodation coefficient (Pöschl et al. 2005). The term

170 | 3 Fundamentals of physicochemistry in the climate system

Fig. 3.18: Mass transfer into droplets.

liquid. In a further application of the resistance model, we split the net uptake into two processes in series: adsorption and dissolution (with possibly an aqueous-phase chemical reaction; see subsequent discussion). Pöschl et al. (2005) proposed the term “surface accommodation coefficient” for α. In eq. (3.145), surface chemistry is excluded because it would be a parallel process to adsorption (α must be replaced in the case of heterogeneous chemistry by another adequate parameter because this would increase the incoming flux): 1 1 1 = + . γ α Γaq

(3.145)

The mass accommodation process can also be defined as the fraction of the collision flux to the surface, which is adsorbed; no adsorption means a collision where the gas molecule is “reflected” back to the gas phase. Therefore, it holds that: Fads = αFcoll =

1 α(cN )g v ≡ k ads (cN )g , 4

(3.146)

“sticking” is often used for the case of “chemisorption,” i.e., the binding energy between the gas molecule and the (solid) surface is large, and “trapping” is used for “physisorption” when the binding energy (more precisely adsorption energy) is small (< 50 kJ mol−1 ); in the case of liquid droplets, “sticking” means absorption/dissolution.

3.6 Heterogeneous processes: Multiphase chemistry in the climate system

| 171

where k ads is the rate constant of adsorption (Chapter 3.6.5.2). Similarly, we can also define the desorption flux Fdes = k des (cN )0 . The mass accommodation coefficient is also defined through α=

Number of molecules absorbed by particle . Number of molecules that collide with particle surface

From eq. (3.146) it follows that 1 αv . (3.147) 4 After the molecule enters the liquid, it diffuses away from the surface into the inner droplet; this net flux into the liquid is given by Fsol = k sol (cN )0 . We just complete the transfer chain of a molecule A: k ads =

A(∞) → A(g) → A(0) → A(aq) . The net flux (gas molecule uptake by droplets) is given by the difference between adsorption and desorption: Fnet = Fads − Fdes

or

1 1 γ(cN )g v = α(cN )g v − k des (cN )0 . 4 4

(3.148)

Setting the net incoming flux from the gas phase equal to the net flux into the liquids Fsol gives 1 Fnet = Fsol or (3.149) γ(cN )g v = k sol (cN )0 . 4 Combining both eqs. (3.148) and (3.149) leads to α = γ (1 +

k des ) k sol

or

1 1 1 k des 1 = + . = + γ α αk sol α Γsol

(3.150)

If k sol ≫ k des , it follows that γ = α; Γsol denotes the process of the solvation or dissolution of an adsorbed gas molecule. Comparing eq. (3.150) with eq. (3.145) we see that Γaq ≡ Γsol in the absence of chemical reactions (eq. (3.168)). In general, the aqueousphase conductance Γaq can include dissolution (limited by slow diffusion into the droplet and by saturation), an aqueous-phase chemical reaction, and heterogeneous surface reactions. The coefficient Γsol is also a pure number, but its value (in contrast to α and γ) is not restricted to numbers less than one. The solubility-limited uptake coefficient Γsol varies with time t. The gas is exposed to the droplet and is given by the following relationship (Daq – aqueous-phase diffusion coefficient of dissolved substance) (Fogg 2003): v t 1 1 √ = , (3.151) Γsol 4 Hp ⋅ RT Daq where Hp is Henry’s law constant (Hp RT = caq /cg , see eq. (3.68)). If the solubility is low or the exposure time was so long that the droplet is saturated, Γsol can then be

172 | 3 Fundamentals of physicochemistry in the climate system

neglected. According to the resistance model, more processes that are parallel and in series can be added or split (e.g., surface or heterogeneous chemical reactions and bulk phase chemical reactions). For solid particles without phase dissolution, the last term in eq. (3.150) is omitted (γ = α). 3.6.5.2 Adsorption In Chapter 3.2.2.5 we described adsorption and desorption. No type of adsorption isotherm can describe the adsorption of soluble gases on the water surface because the net flux is given by the dissolution flux: Fnet = Fads − Fdes + Fsol ≈ Fsol .

(3.152)

Henry’s law (Chapter 3.2.2.3) gives the gas-liquid equilibrium. In the case of surface or bulk chemical reactions, the flux equation (mass budget) is expressed by Fnet = Fads − Fdes + Fhet + Fchem ≈ Fhet + Fchem .

(3.153)

The next two sectionss deal briefly with mass transfer, including surface chemistry and bulk chemistry. 3.6.5.3 Surface chemistry: Kinetics of heterogeneous chemical reactions Heterogeneous chemistry is defined as the chemistry involving two phases, where the reaction occurs on the condensed phase substrate, either liquid or solid, i.e., at the interface: solid–gas, solid–aqueous, or aqueous–gas. In the proper sense, it is surface or interfacial chemistry. Surface chemistry can be roughly defined as the study of chemical reactions at interfaces. Surface chemistry is of particular importance to the fields of heterogeneous catalysis, electrochemistry, biochemistry, and geochemistry. In contrast to this, multiphase chemistry deals with the chemical reactions occurring simultaneously in all phases. In the atmosphere, the condensed phase consists of droplets (clouds and fog), particles (ice, inorganic salts, organic particles such as biomaterial, SOA, and carbonaceous material), and anything on Earth’s surface (vegetation, soils, waters, materials) (Pöschl and Shiraiwa 2015). Many smog chamber studies have been carried out under dry conditions. However, humidity can lead to wetted surfaces, such as films or droplets, which accelerate surface chemical conversions. Photochemistry plays a huge role in interfacial processes (George et al. 2015) (Chapter 4.5.3). However, nonradical processes that do not occur at sufficient speed in a homogenous phase can be important at interfaces (e.g., NOx chemistry in Chapter 5.3.5.2). Owing to the fact that the effective surface reaction is rather fast, transport to the interface determines the overall rate of the process (Kolb et al. 2010). Substance A can undergo chemical conversion at a droplet (or particle) surface after adsorption: A(ads) → B(ads), see Figure 3.18. This chemical flux is given by Fhet =

3.6 Heterogeneous processes: Multiphase chemistry in the climate system

| 173

k het (cN )0 . Using the adsorption equilibrium condition K = (cN )0 /(cN )g it follows that Fhet = k het K(cN )g = k 󸀠het (cN )g .

(3.154)

If a gas molecule which strikes a surface and goes into surface chemical conversion subsequently – this is the steady state with Fhet = Fads – we get (eq. (3.146)) Fhet = k 󸀠het (cN )g = Fads =

1 α(cN )g v . 4

(3.155)

This also represents the maximum heterogeneous chemical conversion rate, i.e., it is limited by the adsorption flux. Now replacing (cN )g by (cN )∞ using eq. (3.141), and the mean molecule velocity by eq. (2.77), we obtain max Fads ≡ Fhet =α

RT γeff (cN )∞ √ = k 󸀠󸀠 het (c N )∞ . γ 2πM

(3.156)

Note that this flux is normalized per unit of area, and to convert it to the “more chemical” heterogeneous chemical rate Rhet (dimension concentration per unit of time), we must first include the total particle surface A per volume of air (∑ i A i , where A i is the single-particle surface) and then convert the molecule density (cN )∞ into the gasmNA NA A phase concentration cg of species A using cN = NV = nN V = MV = c M : Rhet = − (

NA 󸀠󸀠 dc∞ k c∞ = k∞ ) =A het A ⋅ c ∞ . dt het M het

(3.157)

For the gas bulk phase, the specific heterogeneous rate constant (mm – mass of molecule) is given by k∞ het = α

γeff 1 √ kT . γ m3/2 π m

(3.158)

The important conclusion is that heterogeneous chemical transformations depend on the available particle surface A. Table 3.12 summarizes the different expressions for fluxes and mass transfer parameters. Let us finally consider the change of surface density (cN )0 over time assuming a steady state: d(cN )0 = k ads (cN )g − k des (cN )0 − k het (cN )0 − k sol (cN )0 = 0 . dt

(3.159)

It follows, assuming that k ads ≫ k des , that (cN )0 = (cN )g

1 1 Kads

+

khet +ksol kads

= (cN )g

k ads . k het + k sol

(3.160)

174 | 3 Fundamentals of physicochemistry in the climate system

Tab. 3.12: Expressions for gas-particle mass transfer (note the difference between flux F and rate R); (c N )∞ , (c N )g , (c N )0 , (c N )aq molecule density of the same substance far from the particle (∞), close to the particle (g), at the particle surface (0), and in the particle and droplet; p – gas partial pressure far from droplet, c ∞ – gas-phase concentration far from particle, c g – gas-phase concentration near particle, c aq – aqueous-phase concentration; k – mass transfer coefficient (recalculable into specific rate constant); g – gas phase, aq – aqueous phase, het – interfacial layer (chemistry), in – interfacial layer (transport), coll – collision, ads – adsorption (surface striking), sol – dissolution, diff – diffusion in gas phase, des – desorption, net – net flux (eqs. (3.148), (3.152), and (3.153).) Flux or rate

Parameter

1 (c N )g v 4 1 Fcoll = (c N )∞ v 4 1 Fads = αFcoll = α(c N )g v = kads (c N )g 4 Fcoll =

v=√

α=

8RT πM

Fads Fcoll

kads =

1 αv 4

Fnet

γeff = γ

(c N )g (c N )∞

Fdes = kdes (c N )0 = kdes Kdes (c N )g Fnet =

γ 1 1 γ(c N )g v = γeff (c N )∞ v ≡ kads (c N )g 4 4 α

γ=

Fcoll

Fsol = ksol (c N )0 k∞ het = α

Fhet = khet (c N )0

kT γeff 1 √ γ m 3/2 π m

Fchem = kaq (c N )aq aq

Fdiff = kdiff (c ∞ − c g ) =

c aq kdiff ) (p − RT H eff

g

R air = aq

R air =

3 Dg r

kaq p 1 = − RT c aq H eff kg

aq

Fchem = −kaq c aq F aq =

kdiff =

1 r2 4r = + kg 3Dg 3αv

c aq kg ) (p − RT H eff c aq dp = ∑ k i p − LWC ⋅ kg (p − ) dt H eff i dc aq c aq kg = ∑(kaq )i c aq − ) (p − dt RT H eff i

3.6.5.4 Mass transfer into droplets with chemical reaction After gas-phase diffusion onto a droplet surface, in addition to dissolution limitation, enhancement of the mass-transferred substance by chemical removal is also possible. The resistance model equation, combining eqs. (3.143) and (3.146), is then enlarged to (ΓR denotes chemical processes) 1 1 1 1 = + + . γeff Γg α Γsol + ΓR

(3.161)

3.6 Heterogeneous processes: Multiphase chemistry in the climate system

| 175

The reactive uptake coefficient ΓR for the nonreversible reaction is given by the relationship (cf. eq. (3.151)) (Fogg 2003) 1 v 1 1 = , ΓR 4 Hp ⋅ RT √D k aq aq

(3.162)

where k aq is the aqueous-phase reaction rate constant, and Hp is Henry’s law constant (Hp RT = caq /cg , see eq. (3.68)). In the case of simultaneous surface chemistry (heterogeneous chemistry) and bulk chemistry, the resistance model leads to 1 1 1 = + + γeff Γg α

1 1 Γsol

1 +Γ

1 chem

+

1 Γ het

,

(3.163)

where Γchem and Γhet refer to in-droplet and droplet surface chemistry, respectively. Sometimes only one of the four stages shown in eq. (3.162) is the significant rate-determing step (RDS), so it is then possible to assume that γeff ≈ Γg (fast absorption or chemical reaction: gas diffusion limited) γeff ≈ α (fast gas-phase diffusion and reaction: sticking limited) γeff ≈ Γsol (low solution or saturated droplet, no reaction: dissolution limited) γeff ≈ ΓR (fast gas diffusion and effective accommodation but slow reaction and saturation) From the measurements of the effective uptake coefficient, the aqueous-phase reaction rate constant can be calculated, as long as the gas-phase and liquid-phase diffusion coefficients and Henry’s law constant are known. As mentioned previously, a gas transfer into droplets is characterized by a continuums regime. The unsteady-state diffusion flux (this means that Fdiff depends on t as well as on x) of species A along the x-axis to a stationary droplet (Figure 3.18) was described by Seinfeld and Pandis (1998), where c(x, t) is the concentration, depending on time and location: 1 ∂ ∂c =− 2 (x2 Fdiff ) . ∂t x ∂x

(3.164)

Recall that Fdiff = −Dg (dc/ dx) is given by Fick’s first law. This molar flux is given in moles per unit of area and time at any radial position. Now, after derivation and assuming that Dg is constant, it follows that ∂c ∂2 c 2 ∂c = Dg ( 2 + ) . ∂t x ∂x ∂x

(3.165)

After some time steady state is reached (∂c/∂t = 0). Seinfeld and Pandis (1998) have shown that under atmospheric conditions for almost all chemical species of interest this relaxation time is about 10−3 s or less. The integration of d2 c 2 dc =0 + dx2 x dx

176 | 3 Fundamentals of physicochemistry in the climate system

with the boundary conditions (r is the droplet radius) c(x, t) = c∞

(x > r)

c(∞, t) = c∞ c(r, t) = cg leads to the simple solution c(x) = c∞ −

r (c∞ − cg ) x

or

c(x) − c∞ r = . c∞ − cg x

(3.166)

Note that we use cg as the gas-phase concentration close to the surface (where l ≪ r), in contrast to c0 , which denotes the surface concentration of the adsorbed species. The total flow (or rate) RS onto the droplet surface (4πr2 ) is given by RSdiff = 4πr2 (Fdiff )x=r = −4πr2 Dg

dc = 4πrDg (c∞ − cg ) dx

(3.167)

because the derivation of eq. (3.167) leads to (dc/ dx) = −(r/x2 )(c∞ − cg ) and x = r (at the droplet surface). The total flux onto the droplet surface is described by eq. (3.168): S = Fdiff

Dg (c∞ − cg ) . r

(3.168)

The flux to the droplet per volume is obtained by dividing the molar flow RS by the droplet volume (4πr3 /3); note that we now consider a volume-based flux instead of surface-based flux, which is equivalent to the change in concentration per unit of time: (

3Dg dc aq ) = Fdiff = 2 (c∞ − cg ) = k diff (c∞ − cg ) . dt aq r

(3.169)

Now, substituting the molar concentration c (p = cRT) by the gas-phase partial pressure p far from the droplet and the near-surface concentration by the aqueous-phase concentration according to Henry’s law, we obtain aq

Fdiff =

caq 3Dg (p − ) . 2 Heff r RT

(3.170)

We see that the diffusion flux into the droplet depends strongly on the droplet radius: smaller droplets under otherwise constant conditions will have a larger gas uptake than larger droplets. Equation (3.170) represents the flux into a single droplet, with the dimension mass per droplet volume and time, for example, mol L−1 s−1 . To obtain the mean flux into a cloud droplet we must integrate the single-droplet flux over all droplets (N(r) is the droplet size distribution): ∞

aq

Fdiff =

4 aq π ∫ N(r)Fdiff (r)r3 dr . 3 0

(3.171)

3.6 Heterogeneous processes: Multiphase chemistry in the climate system

aq

| 177

aq

In the case of a monodisperse cloud, Fdiff = Fdiff holds. Of interest is the total flux into all cloud droplets, i.e., in the liquid-water volume. From the volume of air we obtain for the air-volume-related flow, expressed as a change in the gas-phase partial pressure per unit of time (e.g., ppb s−1 ), the equation aq

(Fdiff )

aq

air

= RT ⋅ LWC ⋅ Fdiff .

(3.172)

To consider the flux into a droplet, a so-called two-layer model is used, which consists of the diffusion layer (x → r) and an interfacial layer at the droplet surface (between c0 and caq ) (Figure 3.18). The interfacial flux corresponds to the adsorption flux (eq. (3.146)) but now based on the droplet volume, so (A is the surface and V the volume of the droplet) aq

Fin =

A 3v 3 1 √ 8RT 3α p. Fads = α (cN )g = α p= V 4r 4r RT πM √ 4r 2πMRT

(3.173)

The interfacial mass transfer coefficient is k in = 3αv/4r. Schwartz and Freiberg (1981), Schwartz (1986), and Seinfeld (1986) all introduced a mass transfer coefficient k g and set the overall mass transfer equation to F aq = k g (c∞ − cg ) = where

caq kg (p − ) , RT Heff

1 1 1 = + . k g k diff k in

(3.174)

(3.175)

It follows for the overall mass transfer coefficient, now split into two partial steps, diffusion to the surface and transfer through the surface, that 1 r2 4r . = + k g 3Dg 3αv

(3.176)

This conception is similar to that for dry deposition (Chapter 2.6.1) to explain “partial conductance”; the first term on the right-hand side in eq. (3.176) denotes the resistance of diffusion and the second the interfacial transfer. The steps that follow after interfacial transfer are the (fast) salvation or protolysis reactions until equilibrium is reached, diffusion in a droplet (until reaching steady-state concentrations or, in other words, a well-mixed droplet), and, finally, aqueous-phase chemical reactions. Let us first consider a pseudo-first-order reaction: aq

Fchem = −k aq caq .

(3.177)

Because there are no other sources of the substance transferred to the droplet than the mass transfer from the gas phase into the droplet (i.e., excluding chemical production in the aqueous phase), we obtain under steady-state conditions F aq =

kg caq caq k diff aq aq ) = Fdiff = ) = Fchem = −k aq caq . (p − (p − RT Heff RT Heff

(3.178)

178 | 3 Fundamentals of physicochemistry in the climate system It follows that k g = k diff , and a “modified” Henry’s law including aqueous-phase reactions results: k aq p 1 = − RT . (3.179) caq Heff kg The following equations now describe the mass budget of a soluble and chemically active species in a cloud (considering eqs. (3.170), (3.178), and (3.178) and assuming that LWC is constant), where k i is the reaction rate coefficient in the gas phase: caq dp = ∑ k i p − LWC ⋅ k g (p − ) , dt H eff i

(3.180)

kg caq dcaq ) . = ∑(k aq )i caq − (p − dt RT H eff i

(3.181)

4 Fundamentals of chemistry in the climate system As a short definition, chemistry is the scientific study of matter, its properties, and interactions with other matter and with energy. It follows that inorganic and organic chemistry is the science of matter, physical and theoretical chemistry the science of properties and interactions, and analytical chemistry the science to study the composition and structure of bodies. Studying the chemistry of a natural system occurs by chemical quantitative analysis of the different kinds of matter. To obtain a three-dimensional distribution of the concentration of specific substances or, in other words, the chemical composition of the environment, we need innumerable analyses. This is the static approach to obtaining an average chemical composition over a given time period, depending on the lifetime of the substances of interest. However, concentration changes occur over time because of transportation (motion), transformation (chemical reactions), emission, and deposition (seasonal and diurnal variation). Hence, we also need a dynamic approach (chemical monitoring and modeling). We can study chemical reactions – which means establishing their kinetics and mechanisms – only in the laboratory under controlled (and hence replicable) conditions in a large variety of reaction chambers. Based on our definition of the global environment, it appears to be a multireservoir system (air, water, soil) and a multiphase system (gaseous, aqueous, and solid). The fundamental law of nature is the law of the conservation of matter. Matter occurs in two states: flowing energy and cycling material. The environment, however, is an open system and is in permanent exchange with its surrounding Earth system and, thus, space. Therefore, we generally expect changes and variations in internal energy and mass over time. From a chemical point of view, the interest lies in the quantification of the amount – in terms of the number of particles and, thus, mass – of different chemical species in a given volume.

4.1 State of matter In physics, a state of matter or phase is one of the distinct forms that matter takes on. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Matter in the solid state maintains a fixed volume and shape, with component particles (atoms, molecules, or ions) close together and fixed in place. Matter in the liquid state maintains a fixed volume but has a variable shape that adapts to fit its reservoir (bulk water such as rivers, lakes, oceans, and droplet water). Its particles are still close together but move freely. Matter in the gaseous state has both variable volume and shape, adapting both to fit its reservoir (atmosphere, soil pores). Its particles are neither close together nor fixed in place. Matter in the plasma state has variable vol-

https://doi.org/10.1515/9783110561265-004

180 | 4 Fundamentals of chemistry in the climate system

ume and shape, but, in addition to neutral atoms, it contains a significant number of ions and electrons, both of which can move around freely. Plasma is the most common form of visible matter in the universe. Many compounds (matter) that are important in the climate system exist at the same time in different states or, in other words, in phase equilibrium, such as solid–liquid, liquid–gas, and solid–gas. The only compound that exists in our climate system in three states (solid, liquid, gas) simultaneously is water (H2 O).

4.1.1 Atoms, elements, molecules, compounds, and substances The atom is the smallest unit that defines the chemical elements and their isotopes; the nucleus consists of protons and neutrons. The number of protons in an atom’s nucleus is known as the atomic number and is equal to the number of electrons in the neutral (nonionized) atom. Recall that it is the number of protons in the nucleus that defines an element, not the number of protons plus neutrons (which determines its weight). Elements with different numbers of neutrons are called isotopes, and different elements with the same number of neutrons plus protons (nucleons) are called isobars. A chemical element is a pure chemical substance consisting of a single type of atom distinguished by its atomic number. Elements are divided into metals, metalloids, and nonmetals. Whereas metals and nonmetals are well defined, metalloids (which have properties in between metals and nonmetals) are not. Of the six metalloids (B, Si, Ge, As, Sb, Te), only silicon and boron are important in environmental chemistry, and arsenic is an important anthropogenic pollutant. Nonmetals (H, C, N, O, P, S, Se, halogens, novel gases) mainly compose our atmospheric and biospheric environment and constitute evaporable molecules (from selenium no gaseous compounds in the air are known and from phosphorus such molecules were discovered only recently). A molecule is an electrically neutral group of two or more atoms held together by chemical bonds. Only a few molecules are homonuclear, that is, they consist of atoms of a single chemical element, such as oxygen (O2 ), nitrogen (N2 ), hydrogen (H2 ), chlorine (Cl2 ), and others. Mostly they form a chemical compound composed of more than one element, like water (H2 O). Chemical compounds can be molecular compounds held together by covalent bonds, salts held together by ionic bonds, intermetallic compounds held together by metallic bonds, or complexes held together by coordinate covalent bonds. Molecules, as components of matter, are common in organic substances (and therefore living organisms). Molecules in inorganic substances make up most of the oceans and atmosphere.

4.1 State of matter

| 181

An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving the species¹ a net positive (anion) or negative (cation) electrical charge. Ions in their gaslike state are highly reactive and do not occur in large amounts on Earth, except in flames, lightning, electrical sparks, and other plasmas. In an aqueous environment (bulk waters and atmospheric droplets), ions, which are produced by chemical reactions (electrolytic dissociation and redox processes), play a huge role. However, the majority of familiar solid substances on Earth, including most of the minerals that make up the crust, mantle, and core of the Earth, contain many chemical bonds but are not made of identifiable molecules, termed substances. Atoms and complexes connected by noncovalent bonds such as hydrogen bonds or ionic bonds are generally not considered single molecules. In addition, no typical molecule can be defined for ionic crystals (salts) and covalent crystals (network solids), although these are often composed of repeating unit cells that extend either in a plane (such as in graphene) or three-dimensionally (such as in diamond, quartz, or sodium chloride). Glass is an amorphous solid (noncrystalline) material that exhibits a glass transition, which is a reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle state to a molten or plastic state. In glasses, atoms may also be held together by chemical bonds without the presence of any definable molecule, but also without any of the regularity of repeating units that characterizes crystals. However, natural glasses are rare.

4.1.2 Pure substances and mixtures With the exception of magma, the only liquid in the natural Earth’s environment is water.² Pure water, however, exists only in a gaseous state, as water vapor. Natural water is an aqueous solution of gases, ions, and molecules, but it also contains undissolved, suspended, or colloidal inorganic particles of different sizes and chemical compositions and biogenic living or dead matter, for example cells or plants, sometimes called hydrosol. A solution is a homogeneous mixture composed of two or more substances but only one phase, such as aqueous or gaseous, of air. In such mixtures, a solute is a substance dissolved in another substance, known as a solvent. A mixture is a composite made up of two or more different materials, which remain chemically distinct from each other, such as solutions, suspensions, and colloids. It is important to note that air is a solution (a homogeneous mixture of different gases, because all gases can form solutions with each other in all ratios; nitrogen is a solvent) containing undis-

1 The term species is normally only used in biology as a basic unit of biological classification. In recent years, the term chemical species has come into use as a common name for atoms, molecules, molecular fragments, and ions, for example. 2 And natural oil, which remains outside of our description of the climate system.

182 | 4 Fundamentals of chemistry in the climate system

solved substances such as aqueous particles³ (droplets of clouds, fog, and rain) and solids (dust particles). Hence, air (or the atmosphere) is a heterogeneous mixture. For the definition of an aerosol, see Chapter 3.6.3. Consequently, natural waters and soils are always heterogeneous mixtures. In chemistry, a pure substance is often referred to as a “chemical substance”; thus, no pure substances exist in nature, only in solutions or mixtures.

4.1.3 Radicals, groups, and nomenclature We saw in Chapter 3.1 that T (and, to a lesser extent, p) is the key parameter in determining the inner energy of a system and, hence, a chemical conversion’s ability to move forward. Thermal reactions are therefore limited in the atmosphere (in industrial chemical reactors, temperature increase is the most important trigger initiating and accelerating conversions). In nature, where the modification of reaction conditions is limited and not under the control of the chemical system itself, reactive radicals play a crucial role (often referred to as free radicals, but there is no difference in the use of the terms) (Tables 4.1 and 4.2). Justus von Liebig (1803–1873) and Friedrich Wöhler (1800–1882) founded the theory of radicals in 1832. At that time, radicals were regarded as “elements” of organic chemistry. Now we call them characteristic groups such as methyl (–CH3 ), hydroxy (–OH), phenyl (–C6 H5 ), carboxyl (–CO), cyano (–CN), and so forth. At present we also talk only about free radicals, a molecular entity such as ∙ CH3 , ∙ OH, ∙ CN, or Cl∙ possessing an unpaired electron. Radicals are atoms, molecules, or ions with unpaired electrons in an open shell configuration. The unpaired electrons cause them to be highly chemically reactive. Although radicals are generally short-lived because of their reactivity, long-lived radicals exist. The prime example of a stable radical is molecular dioxygen O2 in the triplet state. Oxygen is also the most common molecule in a diradical state. Multiple radical centers can exist in a molecule. Other common atmospheric Tab. 4.1: Important reactive radicals (cf. Table 4.2). Source element

Radicals

Oxygen Hydrogen Nitrogen Sulfur Carbon Halogens

O (O1 D, O3 P), OH, HO2 , O−2 , O−3 , RCH2 O, RCH2 O2 H NO3 HSO3 (SO−3 ), HSO5 (SO−5 ), SO−4 CH3 , HCO, RCO Cl, ClO, Br, BrO

3 Under specific conditions in the stratosphere at very low T (≤ −82 °C) there are liquid droplets of nitrous and sulfuric acid.

4.1 State of matter

| 183

Tab. 4.2: Most important free radicals in environmental chemical processes. Formula

Systematic name

Trivial name

H∙ O∙ O−∙ O2 −∙ O3 −∙ HO∙ HO∙2 HO−∙ 2 HO∙3 R∙ RO∙ RO∙2 (ROO∙ ) RC∙ (=O) RC(=O)O∙ RC(=O)OO∙ ∙ CH 3 HC∙ (=O) HC(=O)O∙ CH3 C∙ (=O) CH3 C(=O)O∙ ∙ CN ∙ SCN ∙ CS HS∙ CO−2 CO−3 HNO HN∙∙ ∙ NH 2 PO∙ NO∙ NO∙2 NO∙3 Cl∙ Cl−∙ 2 ClO∙ ClO∙2

Monohydrogen, hydrogen Oxygen, monooxygen Oxide(1−) Dioxide(1−) Trioxide(1−) Hydroxyl Hydrogen dioxide Hydrogendioxide(1−) Hydridotrioxygen Alkyl Alkoxyl Alkyldioxyl Alkanoyl Acyloxy Acyl peroxy Methyl Hydridooxidocarbon Formoxy Acethyl Acethoxy Nitridocarbon, cyanogen Nitridosulfidocarbon Thiocarbonyl Hydridosulfur Dioxidocarbonate Trioxidocarbonate Oxidanimine, azanone Hydridonitrogen, nitrene Dihydridonitrogen Oxidophosphorus Oxidonitrogen Dioxidonitrogen Trioxidonitrogen, nitrogen trioxide Chlorine atom Dichloride Oxidochlorine Dioxidochlorine

Atomic hydrogen Atomic oxygen a – Superoxide anion Ozonide anion Hydroxyl radical Hydroperoxyl radical Hydrogen peroxide anion Trioxydanyl – – (Not alkoxy) f Alkyl peroxy radical Acyl Carboxyl – Methyl radical Oxomethyl, formyl (Carboxyl from formic acid) Methylcarbonyl (Carboxyl from acethic acid) Cyanyl Thiocyanate radical CS radical d Sylfanyl Carbon dioxide anion radical e Carbonate radical e Nitroxyl Azanediyl, Azanylene, Azanylidene Azanyl Phosporyl Nitrosyl b Nitryl c Nitrate radical – Chlorine radical Chlorosyl, chlorine monoxide Chlorine dioxide

a

The systematic name of molecular oxygen (O2 ) is dioxygen and that of ozone (O3 ) is trioxygen. Nitrogen monoxide, nitric oxide. c Nitrogen dioxide. d This is an example of there being no name and the radical is named by its formula. e This is an example of how the name is derived from the standard trivial name of the nonradical entity. f Alkoxy group: R–O–. b

184 | 4 Fundamentals of chemistry in the climate system

substances of low-reactive radicals are nitrogen monoxide NO and nitrogen dioxide NO2 (Table 4.2). Let us consider the following reactions between the OH radical and a simple organic compound (k in cm3 molecule−1 s−1 ): OH + CH4 → H2 O + CH3 OH + HCHO → H2 O + HCO

k CH4 = 6.9 ⋅ 10−15 , −11

k HCHO = 1 ⋅ 10

.

(4.1) (4.2)

Three radicals are involved in reactions (4.1) and (4.2): hydroxyl OH as the primary reactant as well as the very reactive radicals methyl CH3 and formyl HCO.⁴ According to IUPAC recommendations, the formulas should be given as ∙OH, ∙CH3 , and HC∙ O, where the dot symbolizes an unpaired electron and should be placed to indicate the atom of highest spin density, if possible. In this book, we cancel out the dots for clarity and so as not to make the symbols more complicated (e.g., as in ∙ O−2 or O2 −∙ ). Table 4.1 lists the most important atmospheric radicals. A radical may have positive, negative, or zero charge. Metals and their ions or complexes often possess unpaired electrons, but by convention they are not considered radicals. Depending on the core atom that possesses the unpaired electron, the radicals can be described as carbon-, oxygen-, nitrogen-, or metal-centered radicals. If the unpaired electron occupies an orbital with a considerable s or more or less pure p character, the respective radicals are termed σ- or π-radicals. Radicals exist in gas and liquid (aqueous) phases. They play an important role in many chemical transformations. In natural waters, radical ions, or radicals that carry an electric charge, exist. Those positively charged are called radical cations and those negatively charged are called radical anions, but the most important is the superoxide anion O−2 . Radicals are produced by (a) electron transfer, (b) thermolysis, and (c) photolysis or radiolysis (A and B represent atoms and molecular entities as well): e−

A 󳨀󳨀→ A−∙ heat, radiation

AB 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ A∙ + B∙ Presently there are two fields where a more detailed knowledge of the thermodynamic properties of radicals would be extremely useful. The first is biomedicine. The discovery of superoxide dismutase and nitrogen monoxide as messengers has led to an explosive growth in articles in which one-electron oxidations and reductions are explored. Organic radicals play an important role in the treatment of cancers. The other is atmospheric chemistry, where the modeling of reactions requires accurate reduction potentials.

4 Note that the symbol for formyl is also used differently here than in the literature: HOC and CHO (the aldehyde group H–C=O).

4.1 State of matter

| 185

Radicals play a key role in chain reactions, in which one or more reactive reaction intermediates (frequently radicals) are continuously regenerated, usually through a repetitive cycle of elementary steps (the “propagation step”). The propagating reaction is an elementary step in a chain reaction in which one chain carrier is converted into another. The chain carriers are almost radicals. Termination occurs when a radical carrier reacts otherwise. An example of possible ozone destruction is shown below (R–Cl – chloro-organic compound): radiation

R–Cl 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ R + Cl O3 + Cl → O2 + ClO O3 + ClO → 2 O2 + Cl Cl + H → HCl ClO + NO2 → ClNO3

initiating propagating (chain) termination

Without termination, the gross propagating step results in 2 O3 → 3 O2 and can very often be cycled depending on parallel reactions. In the preceding example, the products of termination (HCl, ClNO3 ) can act as source molecules and provide Cl radicals through photodissociation. Many molecular entities (groups) exist as radicals, groups in organic compounds, and ions, for example HS∙ (sylfanyl), –SH (mercapto), and HS− (hydrogen sulfide). In addition, in practice, trivial names are often used; the IUPAC developed systematic names to derive formulas. However, trivial names are used widely. Atoms or groups of atoms other than the central atom are called anionic ligands (Table 4.3).

4.1.4 Units for chemical abundance: Concentrations and mixing ratios Air is a multiphase and multicomponent system, in other words, a solution of gases and a mixture of particles. The latter we divide into liquid droplets and solids. Solid particles are also often mixtures and always contain water to different extents, i.e., they are humid. In troposphere, droplets are exclusively aqueous solutions (hydrometeors), but in the stratosphere, droplets can be formed from sulfuric and nitric acids. Despite the proposal by scientific organizations (IUPAC and IUPAP) to use only SI units (Appendix B), for practical purposes different units to describe the abundance of air constituents are in use. In chemistry, concentration is the measure of how much of a given substance is mixed with another substance. This can apply to any sort of chemical mixture, but most frequently, the concept is limited to homogeneous solutions, where it refers to the amount of solute in a substance. Air always provides a heterogeneous mixture. We can define a unit of air volume (in the sense of a space), let us say 1 m3 , that is filled with an amount (how much there is or how many there are of something that you can quantify) of a substance (gas and condensed matter). Amount (mass, volume, number) denotes an extensive quantity, i.e., the value of an extensive quantity increases or decreases when the reference volume changes. The amount of a

186 | 4 Fundamentals of chemistry in the climate system

Tab. 4.3: Names of some groups as ligands, as prefix for substituents in organic compounds, and as ions. Note: oxo and oxy are often used synonymously, but oxo more often in inorganic and oxy in organic chemistry (here we follow that use). Formula

As ligand

As prefix

As ion Formula

Name Hydrogen Hydride

–H

Hydrido

–

H+ H−

–OH –OOH

Hydroxo Hydridodioxido

Hydroxy Hydridodioxido

OH− –

Hydroxide

–O– –O− =O

– – Oxo

Oxy Oxido Oxo

O2−

Oxide

–O−2 (–O–O− ) –O–O– –O–O–O–

Dioxygen Peroxo, peroxy –

– Dioxy Trioxy

O−2 O2− 2 O−3

Superoxide Peroxide Ozonide

–S– –S− =S

Thio, sulfido – –

Thio Sulfido Thioxo

S2−

Sulfide

–SH S2 (S–S–)

Mercapto f Disulfido

Mercapto Dithio, sulfinyl

HS− S2− 2

Hydrogensulfide Disulfide

=NH –NH2 –NO –NO2

Imido d Amido e Nitrosyl Nitro

Imido Amino Nitroso Nitro

NH2− NH−2 – NO−2

Imide Amide

=CO =CS –COOH CH3 S– CH3 O– –CN –OCN (–O–C≡N) –CNO (–C≡N–O) –NCO (–N=C=O) –SCN (–S–C≡N) –CH3

Carbonyl a Thiocarbonyl b Carboxyl Methylthio – Cyano c Cyanato Fulminato – Thiocyanato Methanido

Carbonyl Thiocarbonyl Carboxo Methylthio Methoxy Cyano Cyanate – Isocyanate Thiocyanato Methyl

– – – CH3 S− – CN− – CNO− – SCN− –

–F –Cl –Br –I

– – – –

Fluoro Chloro Bromo Iodo

F− Cl− Br− I−

a

e

b

f

New systematic name: oxidocarbonato. New systematic name: sulfidocarbonato. c New systematic name: nitridocarbonato. d New systematic name: hydridonitrodo.

Nitrite

Methanethiolate Cyanide Fulminate Thiocyanate g Fluoride Chloride Bromide Iodide

New systematic name: dihydridonitrido. New systematic name: hydridosulfido. g Old: rhodanide.

4.1 State of matter

| 187

substance in a given gas volume is strongly determined by the gas laws. By contrast, an intensive quantity (pressure, temperature) does not change with volume. We can quantify the amount of a substance in different terms: – mass m (related to a prototype made from iridium and stored in Paris), measured in kilograms (kg), – volume V (how much three-dimensional space is occupied by a substance), measured in cubic meters (m3 ), – number N (the sum of individuals such as molecules, particles, droplets), dimensionless, and – mole n (1 mole corresponds to the molecular weight or to a fixed number of molecules expressed by the Loschmidt constant n0 ), dimensionless (abbreviated mol). Mass, volume, mole, and pressure (note that pressure is an intensive quantity) are linked in the general gas equation (which, however, is only valid for diluted mixtures, which is true when we consider traces in air), as seen in eq. (2.56). We can also apply the gas law based on the partial quantities m = ∑ m i , V = ∑ V i , p = ∑ p i , and n = ∑ n i in two forms: p i V = n i RT

and

pV i = n i RT .

(4.3)

Hence, for any mixing ratio x i , by taking into account the gas equation for a given substance i, it follows that xi =

ni Vi mi pi = = = . n V m p

(2.66)

These ratios are termed (dimensionless) mixing ratios (or fractions) by the amount of moles, volume, mass, and pressure, respectively. The large advantage in its use compared with concentrations⁵ (moles or mass per volume) lies in its independence from p and T. Depending on the magnitude of the mixing ratio, the most convenient units can be – percent: %, where 1% = 10−2 – parts per million: ppm, where 1 ppm = 10−6 – parts per billion: ppb, where 1 ppb = 10−9 – parts per trillion: ppt, where 1 ppt = 10−12 Normally, a decision must be made regarding which quantity the mixing ratio will be based on (volume or mass) and then written ppmm or ppmV (also written ppm(m) or ppm(V)), respectively (Table 4.4).

5 However, when measuring an atmospheric substance, p and T must be co-measured to allow for standard recalculations for exact averaging and intercomparisons.

188 | 4 Fundamentals of chemistry in the climate system Tab. 4.4: Recalculation between mass concentration c i (μg m−3 ) and mixing ratio x i (ppb) under standard conditions (25 °C and 1 bar). Compound Ozone Hydrogen peroxide Sulfur dioxide Nitrogen monoxide Nitrogen dioxide Nitrous acid Nitric acid Ammonia Hydrogen chloride Benzene

O3 H2 O2 SO2 NO NO2 HNO2 HNO3 NH3 HCl C6 H6

x(V)i , ppb

c(m)i , μg m−3

1 1 1 1 1 1 1 1 1 1

1.96 1.39 2.63 1.22 1.89 1.92 2.56 0.69 1.63 3.23

A standard volume of air (e.g., 1 m3 ) is well defined but hard to measure when taking into account the volume of condensed matter (hydrometeors and PM). Normally, we can neglect the volume (fraction) of the condensed matter occupying a volume of air because of the small values on the order of 10−6 (Table 1.2), which is orders of magnitude smaller than the best gas volume measurement facility. The volume of condensed matter, however, can be well measured using optical methods. One must also consider when soluble gases are distributed among the gas and the droplet phases in air. Easily soluble gases (such as HCl and HNO3 ) will be transferred quantitatively in a cloud from the gas to the liquid phase (scavenging efficiency equal to one). Partially soluble gases (such as SO2 and CO2 ) are distributed among the phase according to Henry’s law. Hence, the partial pressure is calculated according to p i = p i (g) + p i (aq) ,

(4.4)

where p(g) = n(g)RT/V(g) and p(aq) = n(aq)RT/V(aq) = p(g)Heff RT ⋅ V(aq)/V(g) because of n(aq) = p(g)V(aq)Heff . The reservoir distribution δ (ratio of molar mass in the aqueous phase to the molar mass in the gas phase) is given by δ=

naq Vaq = Heff RT ≈ LWC ⋅ Heff ⋅ RT , ng Vg

(4.5)

where Heff is the effective Henry’s law constant (Chapter 3.2.2.3). The volume ratio between the phases is given by V = V(aq)/V(g) ≈ V(aq)/air volume = LWC, whereas air volume = V(aq) + V(g) ≈ V(g). The total partial pressure is now described by p i = p i (g) ⋅ (1 + LWC ⋅ Heff ⋅ RT) = p(g) ⋅ (1 + δ) .

(4.6)

In all cases, when δ ≪ 1 (i.e., p(g) < p), the partial pressure of a substance must be corrected in equations by the factor 1/(1 + δ). The concentration can be defined based on mass (e.g., g L−1 or g m−3 ), number (e.g., cm−3 ), and mole (molarity, for example,

4.1 State of matter

| 189

mol L−1 or molar or M): c(m)i = m i /V ,

(4.7a)

c(N)i = N i /V ,

(4.7b)

c(n)i = n i /V .

(4.7c)

Using the gas law (eq. (2.56)), and taking into account eqs. (2.66) and (4.3), a recalculation between mass concentration and the mixing ratio is based on x i = c(m)i

RT Mi , p

(4.8)

where M i is the molar mass of substance i. Gaseous trace species are often measured in mass concentration (e.g., μg m−3 ). It is obligatory also to measure pressure and temperature because otherwise there is no way to perform a recalculation between the mass concentration and mixing ratio. For standard conditions (1 atm = 1.01325 ⋅ 105 Pa and 25 °C = 298.15 K) mass concentrations of some compounds are listed for 1 ppb in Table 4.4. Only molecules in very small concentrations (especially reactive radicals such as OH and HO2 ) are quantified in number concentrations, for example, the number of radicals in a volume (cm−3 ). This concentration measure is also used for the particle number of condensed matter (droplets and solid particles). Based on heterogeneous reactions and optical properties, another quantity – the surface-to-volume (of air) ratio – is useful for describing the condensed phase. For droplets, it is simple to define the volume of an individual droplet based on its diameter assuming a spherical form. The mass, number, and surface quantities of particles show a very different (but characteristic) behavior when related to the size distribution (Figure 3.14). Concerning the chemical composition of condensed matter, there are two ways to describe its abundance. First, chemically analyzing the matter (either single-particle or a collected mass of particles) provides the concentrations (or mixing ratios) related to the volume (or mass) of the condensed phase, for example, moles (or mass) of a substance per liter of cloud water and mass of a substance per total mass of PM. When sampling the condensed phase, normally for hydrometeors, all droplets are collected in a bulk solution (however, multistage cloud water impactors are also available). For solid PM, different particle size fractions can be collected. A subscript denotes the cut-off during sampling (e.g., PM10 , PM2.5 , and PM1 ), i.e., the value denotes the aerodynamic diameter in micrometers of (not sharp) separation between particles smaller than the given value. TSP stands for total suspended matter (i.e., it is sampled over all particles sizes). Second, the specific concentration of a substance in condensed matter can be related to the volume of air. To do so, the volume (or mass) concentration of the total condensed matter in air must be known. This is given by the LWC for hydrometeors

190 | 4 Fundamentals of chemistry in the climate system

and the total mass concentration of PM. The resulting value of the mass of dissolved or PM in a volume of air is the atmospheric abundance (eq. (4.9)), and this air quality value can be compared between different sites. The concentration of a substance in cloud water, however, also depends on the cloud’s physical properties. This is also true of fog and precipitation. Hence, with hydrometeor sampling the simultaneous registration of the LWC and rainfall amount is obligatory (eq. (4.10)): c i (air) = x i (PM) ⋅ m(PM) ,

(4.9)

where x i (PM) denotes the mixing ratio of component i in PM (∑ x i = 1) and m(PM) denotes the total mass of PM in an air volume. In analogy to species dissolved in cloud water, the aqueous-phase concentration must be multiplied by the LWC: c i (air) = m i (aq) ⋅ LWC .

(4.10)

When using averaged concentration values it is strongly recommended to calculate them from so-called weighted values, specifically LWC for cloud and fog water and precipitation amount for rain and snow. Only these weighted values represent the correct total abundance of trace substances in air. The averaged precipitation composition, for example, as annual mean results from ∑ni R i c i (aq) , (4.11) R where R i denotes the precipitation amount for sample i, and R denotes the annual (or any other timescale) precipitation amount (rainfall rate). In analogy to cloud water chemical composition it follows that c i (aq) =

c i (aq) =

∑ni c i (aq)LWCi n LWC

=

∑ni c i (aq)LWCi , ∑i LWCi

(4.12)

where LWC is the arithmetic mean of samples LWC i and n is the number of samples. Another concentration measure is important for ions in hydrometeors and soluble substances in PM: the normality and the equivalent. Because of the condition of electroneutrality, the sum of the equivalent concentration of all cations must be equal to the sum of the equivalent concentration of all anions in droplets and solid particles. Normal (N) is one gram equivalent of a solute per liter of solution. The definition of a gram equivalent varies depending on the type of chemical reaction being discussed – it can refer to acids, bases, redox species, and ions that will precipitate. More formally, a gram equivalent of a substance taking part in a given reaction is the number of grams of the substance associated with the transfer of NA electrons or protons or with the neutralization of NA negative or positive charges, where NA is Avogadro’s number. The expression of concentration in equivalents per liter (or more commonly, microequivalents per liter, μeq L−1 ) is based on the same principle as normality. A normal solution is one equivalent per liter of solution (eq L−1 ), where c i (n) denotes the molar concentration or molarity (e.g., in mol L−1 ≡ M) and e symbolizes the ionic charge: c i (eq) = ci (n) ⋅ e .

(4.13)

4.2 Theory of chemical reactions

|

191

4.2 Theory of chemical reactions One of the key concepts in classical chemistry is that all chemical compounds can be described as groups of atoms bonded together and that chemical reactions can be described as the making and breaking of those bonds. Hence, we introduce this chapter with a short excursus on chemical bonding. To understand chemical bonds deeper, it is necessary to hold a good size chemical textbook. Chapter 4.2.1 presents knowledge reduced to a minimum only to illustrate the principles. On the other hand, it is my experience (even as a chemist) that this is sufficient (for nonchemists). For an understanding of chemical conversions occurring in the climate system, specifically in air and water, it is important to know the different types of reactions (Chapter 4.2.2). For the quantitative description of chemical conversions, specifically chemical modeling, it is important to know the kinetic equations (Chapter 4.2.3).

4.2.1 Chemical bonding Chemical reactions involve (with the exception of nuclear reactions) only changes in the electronic structure of atoms. Chemists are interested only in three elementary particles, electrons, protons, and neutrons. The last two particles we have introduced as parts of the atomic nucleus, characterizing the given element (Chapter 4.1.1). The structure of the atomic electronic shell (recall that the number of electrons is equal to the number of protons in an uncharged atom) is characterized by so-called orbitals, synonymous with the term wave function but has no illustrative meaning (as shown by pictures in many textbooks, as also here in Figure 4.2). The electron cannot be particulate described in space and time – it is a probability function of energy density, characterized by so-called quantum numbers. For the purposes of this book, to apply chemistry to environmental processes, it is not necessary to go into details of the atomic structure. Chemical bonding occurs when one or more electrons are simultaneously attracted to two nuclei. This is the most important fact about chemical bonding that you should know. In its most fundamental sense, the structure of a molecule is specified by the identity of its constituent atoms and the sequence in which they are joined together, that is, by the bonding connectivity. This, in turn, defines the bonding geometry – the spatial relationship between the bonded atoms (Figure 4.1). The energy of a system of two atoms depends on the distance between them. At large distances, the energy is zero, meaning “no interaction.” At distances of several atomic diameters attractive forces dominate, whereas at very close approaches the force is repulsive, causing the energy to rise. The attractive and repulsive effects are balanced at the minimum point in the curve (Figure 4.1). The internuclear distance at which the potential energy minimum occurs defines the bond length. This is more correctly known as the equilibrium bond

192 | 4 Fundamentals of chemistry in the climate system

energy

repulsion

attraction

bond energy

internuclear distance equilibrium bond length Fig. 4.1: Potential energy between two atoms (chemical bond).

length because thermal motion causes the two atoms to vibrate about this distance. In general, the stronger the bond, the smaller will be the bond length. The bond energy is the amount of work that must be done to pull two atoms completely apart; in other words, it is the same as the depth of the “well” in the potential energy curve shown in Figure 4.1. This is almost, but not quite, the same as the bond dissociation energy actually required to break a chemical bond (we will encounter this later in our discussion of photodissociation); the difference is the very small zero-point energy. In general, bonds may be ionic or covalent. The transfer of electrons from one atom to the other forms an ionic bond. If electrons are lost, the atom becomes a positively charged ion (Na+ for example), and if electrons are gained, the atom becomes a negatively charged ion (Cl− for example). The ion pair that results is held together loosely by electrostatic attraction. Both ions form a crystal, sodium chloride, or common salt (NaCl)n . Metals release electrons, forming a microcrystalline structure (metallic bond), where the electrons move freely in the conduction band, explaining electric and thermal conductivity. In other cases, electrons are not transferred but shared between atoms (covalent bond). In elementary molecules with identical atoms, such as N2 , O2 , and Cl2 , electrons are shared equally. On the other hand, in heteronuclear molecules, which consist of unlike atoms (such as H2 O), the electrons forming a bond are shared unequally; this kind of bonding is called polar covalent. The number of (so-called valence) electrons in the outer shell determines the group in the periodic table of elements based on the octet rule. Only novel gases (in group VIII or zero, hence right- or leftmost in the periodic table of elements) hold complete shells with eight electrons (He in s-orbital two electrons) and are extremely stabile and exist as atoms only (gaseous) (Table 4.5). All other elements, having between one and seven electrons in their outer shell, form molecules (covalent or metallic bonds). Elements with few outer electrons (1–3) tend to be electropositive, i.e., to release the outer electrons to become stable with the lower octet shell. Ele-

4.2 Theory of chemical reactions

| 193

Tab. 4.5: Electronic configuration of first 20 atoms of the periodic table of the elements at the ground level; z ordinal number. z

Element

1s

2s

2p

3s

3p

4s

1 2

H He

Hydrogen Helium

1s2

↑ ↑↓

3 4

Li Be

Lithium Beryllium

2s1 2s2

↑↓ ↑↓

↑ ↑↓

5 6 7 8 9 19

B C N O F Ne

Boron Carbon Nitrogen Oxygen Fluorine Neon

2s2 2p1 2s2 2p2 2s2 2p3 2s2 2p4 2s2 2p5 2s2 2p6

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑ ↑ ↑ ↑↓ ↑↓ ↑↓

↑ ↑ ↑ ↑↓ ↑↓

↑ ↑ ↑ ↑↓

11 12

Na Mg

Sodium Magnesium

3s1 3s2

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑ ↑↓

13 14 15 16 17 18

Al Si P S Cl Ar

Aluminum Silica Phosphorus Sulfur Chlorine Argon

3s2 3p1 3s2 3p2 3s2 3p3 3s2 3p4 3s2 3p5 3s2 3p6

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑ ↑ ↑ ↑↓ ↑↓ ↑↓

↑ ↑ ↑ ↑↓ ↑↓

↑ ↑ ↑ ↑↓

19 20

K Ca

Potassium Calcium

4s1 4s2

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

↑↓ ↑↓

1s1

↑ ↑↓

ments with more electrons (five to seven) tend to be electronegative, i.e., to take up electrons to become stable with the full octet shell. Only elements from group 4 (C and Si) hold balanced electron affinity, i.e., they provide four electrons but also take up four electrons. This property makes the chemistry of carbon (organic world) and silica (mineral world) so unique in terms of the diversity of molecules and structures. The number of electrons that an element can take on, give up, or share with other atoms (Table 4.6) determines the valence or oxidation number of an atom. A chemical bond is described by two different theories, which, however, show for simple structure very similar results, the valence bond theory (VB) and the molecule orbital theory (MO). It is again useful to emphasize that there exist no different electrons (in some books named σ or π electron), they are all equal but occupy different electron configurations according to the energetic level, whereas the position of an electron is unknown at a given time (Heisenberg uncertainty principle). Figure 4.2 shows different orbitals. – σ orbitals result from overlapping of s–s, s–pz , and pz –pz atomic states; they have a cylindrical, i.e., rotation, symmetry along the bond axis z (vertically arranged in a diagram).

194 | 4 Fundamentals of chemistry in the climate system

Tab. 4.6: Oxidation numbers (valences) of some important elements in climate system (Note: the number 0 – zero – is the neutral elemental state). Element

Most common oxidation numbers

Rare oxidation numbers

O H Ca, Mg K, Na C N S Cl Br I F Mn Fe Cu Cr

−2, 0 0, +1 +2 +1 −4, +2, +4 −3, 0, +1, +2, +4, +5 −2, +4, +6 −1 −1 −1 −1 +1, +2 +2, +3 +1, +2 +3, +6

−1

z

z

+

+

−3, −2, −1, 0, +1, +3 −1, +3 0, +2, +3 0, +1, +3, +4, +5 0, +1, +3, +4, +5 0, +1, +3, +4, +5 +3, +4, +6, +7 0 0

z

-

+

y

-

y

x

x

s

x

px

z

+

-

-

+ d xy

y

pz

z

-

+ -

+ d x 2 -y2

Fig. 4.2: Symmetry of electron configurations for s, p, and d levels.

–

π orbitals result from lateral overlapping of px –px and pz –pz atomic states; they form two lobes above and below the two nuclei. Along the bond axis z, the electron residence probability is zero.

As seen in Table 4.5, carbon with its valence structure 2s2 2p2 should have only two bonds, but we know that it provides almost four bonds (such as in CH4 ). This is ex-

4.2 Theory of chemical reactions

| 195

plained by the concept of valence hybridization: the mixing of atomic orbitals into new hybrid orbitals (with different energies, shapes, and so forth, than the component atomic orbitals). In methane, one s orbital is mixed with three p orbitals, resulting in four equivalent sp3 hybrids, giving the characteristic tetrahedrally coordinated carbon (Figure 4.3).

H H

C H H

Fig. 4.3: Tetrahedrally coordinated carbon in methane, explained by sp3 hybridization (angle between two H atoms 109°).

For another example, ethene (C2 H4 ) has a double bond between the carbon atoms. For this molecule, carbon will sp2 -hybridize, because one π bond is required for the double bond between the carbon atoms, and only three σ bonds are formed per carbon atom. In ethene, the two carbon atoms form an σ bond by overlapping two sp2 orbitals and each carbon atom forms two covalent bonds with hydrogen by s–sp2 overlap all at 120° angles (trigonal-planar). The π bond between the carbon atoms perpendicular to the molecular plane is formed by 2p–2p overlap. The hydrogen–carbon bonds are all of equal strength and length, which agrees with experimental data. The free rotation as it is found in alkanes (single bond) is lost; hence, isomers are formed. H

H C=C

H

H

Friedrich August Kekulé (1829–1896) proposed in 1865 the formula for benzene (C6 H6 ), shown in Figure 4.4 with alternating single and double bonds, often simplified as follows:

The isomers proposed by Kekulé are conjugated double bonds; Figure 4.4 shows two different formula schemes. Conjugated double bonds in a molecule mean that the single and double bonds alternate. This enables the electrons to be delocalized over the

196 | 4 Fundamentals of chemistry in the climate system

H

H

H

H

H

H

H

H

H

H

H

H

Kekulé scheme

H

H H

H

C C

C

C

C C

H

H

H

H

H

H

H

H

Fig. 4.4: Formula of benzene, C6 H6 .

Tab. 4.7: Valence hybrids. Coordination Hybrid number

Geometric assembly

Examples

2 3 4 5

sp sp2 sp3 sp3 d

Ethine C2 H2 Ethene C2 H4 Methane CH4 Phosphorus pentachloride PCl5

6

sp2 d2

Linear, < 180° Trigonal planar, < 120° Tetrahedral, < 109°28󸀠 Trigonal bipyramidal, < 120° inside the mean plane and < 90° to the head Octahedral, < 90°

Sulfur hexafluoride SF6

whole system and so be shared by many atoms. In other terms, the delocalized electrons may move around the whole system. Benzene, a natural constituent of crude oil, is the best-known example. Finally, in ethine (C2 H2 ) a triple bond is realized by sp hybridization, giving a linear structure: H–C≡C–H; Table 4.7 shows different hybrid types with an important geometric assembly. In any stable structure, the potential energy of its atoms is lower than that of the individual isolated atoms. Thus the formation of methane from its gaseous atoms (a reaction that cannot be observed under ordinary conditions but for which the enthalpy is known from indirect evidence), 4 H + C → CH4 , is accompanied by the release of heat and is thus an exothermic process. The quantity of heat released is related to the stability of the molecule. The smaller the amount of energy released, the more easily can the molecule absorb thermal energy from the environment, driving the foregoing reaction in reverse and leading to the molecule’s

4.2 Theory of chemical reactions

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197

decomposition. A highly stable molecule such as methane must be subjected to temperatures exceeding 1000 °C for significant decomposition to occur. Many molecules are energetically stable enough to meet the above criterion, but are so reactive that their lifetimes are too brief to make their observation possible. The molecule CH3 , methyl, is a good example (it is a radical): it can be formed in air by the reaction CH4 + OH, but it is so reactive that it combines with almost any molecule it strikes within a few collisions.

4.2.2 Types of chemical reactions A chemical reaction is a process that results in the interconversion of chemical species; Table 4.8 summarizes the basic reaction types. Chemical reactions might be elementary reactions or stepwise reactions. A stepwise reaction consists of at least one reaction intermediate and involves at least two consecutive elementary reactions. Parallel reactions are several simultaneous reactions that form different respective products from a single set of reactants (Svehla 1993, Muller 1994). Thermodynamics is important for describing chemical reactions (Chapter 3.1). As seen earlier, it explains whether a reaction is “voluntary” and in which direction and in what state equilibrium is. Hence, thermodynamics also describes mechanisms but without providing information on the explicit pathway. Many reactions can be parallel and, hence, competitive. In quantifying the overall chemical processes (production or decay of substances), because of the substantial mathematical simplifications, it is important to delete reactions of minor importance (i.e., those with reaction rates about two orders of magnitude less than the fastest reaction). The task of chemical kinetics is to describe the speed at which chemical reactions occur. The reaction rate is the change in the number of chemical particles per unit of time through a chemical Tab. 4.8: Types of chemical reactions; A, B, and C any atomic, ionic or molecular entity, H hydrogen, e− electron. Term

Reaction scheme

Addition Insertion Abstraction Hydrogen atom transfer (HAT) Dissociation a Protolytic dissociation Proton transfer Electron transfer Radioactive decay b

A + B → A–B A + B–C → B–A–C A–B + C → A + B–C A–H + B → A + B–H A–B → A + B A–B → A+ + B− A + H+ → A–H+ A + e− → A− or A + B− → A− + B A→D+E

a b

Thermal or irradiative. A, D, and E are atoms only.

198 | 4 Fundamentals of chemistry in the climate system

reaction. This is the term RN =

dN [number/time] . dt

Because n = N/NA (NA is the Avogadro constant), the rate (or speed) can also be expressed in mole per unit of time: Rn =

dn [mole/time] . dt

Finally, because c = N ⋅ M/V (M is the molar mass), Rc is the change of concentration per unit of time: dc Rc = [mass/volume ⋅ time] . dt In chemistry, the last concentration-related term is normally used, and eq. (4.14) shows the recalculation: R=

dn V dc dN = NA = . dt dt M dt

(4.14)

In nature, especially the climate system, the investigation of chemical reactions can be limited. All early attempts to estimate reaction rates were unsuccessful because too many variables existed. The concentration measurements of different trace species – together with meteorological parameters that describe transport, mixing, and phasestate conditions (in so-called complex field experiments) – are extremely helpful in several directions. These directions include: (a) establishing empirical relationships between substances and other atmospheric parameters to gain insights into mechanisms, (b) recognizing still unidentified or not yet considered substances under specific measurement conditions, and (c) providing data sets for model evaluations. Kinetics, that is, the study of rate laws and measurement of rate constants, can only be done under laboratory conditions, whereas reaction conditions should be simulated in special reactors (“smog chambers”) closely resembling the atmospheric one. Once established, the k-value of an elementary reaction is universally applicable; in other words, “pure chemistry” is independent of meteorological and geographical specifics but the conditions for reactions (pressure, temperature, radiation, humidity) and the concentration field depend on location. This is the difference with “air chemistry.” For more detailed information on chemical kinetics, see Zumdahl (2009), Atkins (2008), and Houston (2006).

4.2.3 Chemical kinetics: Reaction rate constant Even complex chemical reaction mechanisms can be divided into several definite elementary reactions, i.e., the direct electronic interaction process between molecules or atoms when colliding. To understand the total process A → B (e.g., the oxidation

4.2 Theory of chemical reactions

| 199

of sulfur dioxide to sulfate in CTM and climate models), it is often adequate to describe only the overall reaction, sometimes termed the gross reaction, independently of whether the process A → B proceeds via a reaction chain A → C → D → E → . . . → Z → B. The complexity of mechanisms (and thereby the rate law) significantly increases when parallel reactions occur: A → X apart from A → C, E → Y apart from E → F. Many air chemical processes are complex. If only one reactant (sometimes termed an educt) is involved in a reaction, we call it a unimolecular reaction, that is, the reaction rate is proportional to the concentration of only one substance (firstorder reaction). Examples are all radioactive decays, rare thermal decays (almost autocatalytic) such as PAN decomposition, and all photolysis reactions, which are very important in air. The most frequent are bimolecular reactions (A + B); for example, simple molecular reactions (NO + O3 → NO2 + O2 ) are frequently radical reactions (NO + OH → HNO2 ), but these are second-order reactions. However, trimolecular reactions are common in the atmosphere (O+O2 +N2 → O3 +N2 ) because the primary collision complex A ⋅ ⋅ ⋅ B is energetically unstable and must transfer excess energy onto a third collision partner (third-order reaction). Collision partners are almost the main constituents of air (N2 and O2 ) and because of their dominant concentration it results in a probability of collision that is orders of magnitude larger than a collision between trace molecules. Beside N2 and O2 , also H2 O is a frequent collision partner (for example HO2 + HO2 + H2 O → H2 O2 + O2 + H2 O), probably because of its specific role in the transfer complex (charge transfer, hydrogen bonding, or steric reasons). The number of reactants from which the concentration of the reaction rate depends determines the reaction order. Third-order reactions might be considered elementary (despite the fact that the collision partner certainly does not collide at the same time with A and B). All reactions with higher or noninteger numbers principally reflect the kinetics of complex mechanisms. A bimolecular reaction can be written in three different schemes: B

A + B → C + D or A 󳨀󳨀󳨀→ C or (−D)

A

B 󳨀󳨀󳨀→ D . (−C)

(4.15)

The following rate law holds (recall that the brackets denote the concentration of substance A, and so forth, and k is the reaction rate constant⁶: −

d[B] d[C] d[D] d[A] =− = = = k[A][B] = R dt dt dt dt

(4.16)

6 Rate contants for gas-phase reactions of organic compounds with OH, O3 , NOy , and Cl and their dependence on temperature and pressure were measured for many reactions (Baulch et al. 1980, IUPAC 2015, Sander et. 2011); the mechanistic understanding of these reactions has also been substantially improved (Calvert et al. 2015). For the reaction of inorganic species with oxidants see IUPAC Subcommittee on Gas Kinetic Data Evaluation (http://www.iupac-kinetic.ch.cam.ac.uk/; Atkinson et al. 2004, 2006, 2007, 2008, IUPAC 2015). A good compilation of aqueous-phase chemical reactions and equilibria can be found in Williams et al. (2002) and Herrmann et al. (2005, 2015).

200 | 4 Fundamentals of chemistry in the climate system

An important quantity to describe the state of chemical reaction (4.15) is the reaction quotient Q: [C][D] . (4.17) Q= [A][B] In contrast to eq. (3.49), the concentrations are not expressed as equilibrium (when the reaction reaches equilibrium, the condition Q = K is fulfilled). To solve the differential eq. (4.16) analytically, we substitute time-dependent concentrations by ([A]0 −x) and ([B]0 − x), where the subscript 0 denotes the initial concentration for t = 0 and x expresses the concentration of any of the products (assuming that neither C nor D is included in other reactions): x

t

0

0

dx ∫ = k ∫ dt . ([A]0 − x) ([B]0 − x)

(4.18)

By partial fraction decomposition, we get k=

[A]0 ([B]0 − x) 1 ln , t ([A]0 − [B]0 ) [B]0 ([A]0 − x)

(4.19)

or, for the simple case where A = B (2A → products), we obtain k=

1 1 1 1 1 )= . ( − t [A]0 − x [A]0 t [A]0 ([A]0 − x)

(4.20)

Often in nature there are situations where the concentration of a second reactant B can be considered constant in the given period or its relative timely change ∆[B]/[B] can be neglected. This we assume most often when the concentration of B is much greater than that of A, and so the numerical error remains small; this is the case in many reactions where O2 is the partner. Another case is the steady state of B (d[B]/ dt = 0). Then the concentration of B can be included in the rate constant and the reaction type is reduced to a pseudo-first-order reaction with mathematical simplifications in subsequent treatment: d[A] (4.21) − = k[A][B] = k 󸀠 [A] . dt Similar trimolecular reactions (recall that the third collision partner is often in high excess) can be simplified to pseudo-second-order and eventually even to pseudo-firstorder. The solution of a first-order rate law is simply [A]

[A]

t

[A]0

[A]0

0

d[A] = ∫ dln[A] = k ∫ dt . ∫ [A]

(4.22)

The exponential time dependency of concentration of A follows: [A] = [A]0 exp(−kt) .

(4.23)

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| 201

From eq. (4.23) useful characteristic times such as the half-life τ1/2 and residence or lifetime τ can be derived. The half-life is defined as the time when the initial concentration is reduced by half: [A] = 0.5 [A]0 : τ1/2 =

1 ln 2 . k

(4.24)

More important for the climate system is the residence time, which is simply the reciprocal of k, but only in the case of a first-order process (Chapter 2.7): τ = 1/k. The residence time τ corresponds to the condition A/A0 = e (this follows from eq. (4.23)), where e is a mathematical constant, sometimes termed the Euler number (e ≈ 2.7183). In other words, the initial concentration of A is decreased to about 37%. The rate-determining step (RDS), sometimes also called the limiting step, is a chemistry term for the slowest step in a chemical reaction chain. In a multistep reaction, the steps nearly always follow each other, so that the product(s) of one step is/are the starting material(s) for the next. Therefore, the rate of the slowest step governs the rate of the whole process. In a chemical process, any step that occurs after the RDS will not affect the rate (see the discussion on net ozone formation in Chapter 5.2.6.2) and, therefore, does not appear in the rate law. Svante August Arrhenius (1859–1927) found empirically that between the logarithm of the reaction rate k and the reciprocal temperature a linear relation exists, which is similar to van’t Hoff’s reaction isobar (eq. (3.56)) dln k EA = dT RT 2

(4.25)

and now called the Arrhenius equation, where EA is the activation energy: k = k m exp (−

EA ) . RT

(4.26)

The term exp(−EA /RT) simply expresses the fraction of chemical species with a permole higher energy than EA . The Boltzmann distribution follows from eq. (2.73), which shows the probability of molecules having (or exceeding) a certain speed or energy, when taking into account that 3RT/2 is equivalent (eq. (2.60)) to the mean molar kinetic energy of the molecules (recall that the mean molecular kinetic energy is 3kT/2). Thus, EA is the (molar) kinetic energy required for the transfer from A+B to the transition state AB‡ . The factor k m expresses the maximum reaction rate constant (EA → 0 or T → 0), also called the Arrhenius constant. The interpretation of k m originates possibly both from collision theory and from the theory of the transition state; in reality, k m depends on T (often β = 12 ): (4.27) k m = BT β . Exceptions to the validity of eq. (4.27) are trimolecular reactions where k is decreasing with increasing T. This becomes clear when we consider that the transition complex

202 | 4 Fundamentals of chemistry in the climate system AB‡ can thermally decompose back to A + B instead of transforming to C + D (4.28a): +M(kd )

ka

‡ 󳨀→ A+B 󳨀 ← 󳨀󳨀 [AB ] 󳨀󳨀󳨀󳨀󳨀→ C + D + M .

(4.28a)

kb

According to the kinetic theory of gases, the reaction rate (here expressed as the number concentration cN of molecular changes per unit of time) is equal to the number of collisions zAB of all molecules between A and B in volume V, where the factor 2 means that at each collision two molecules disappear: RN =

dcN 2zAB = k m (cN )A (cN )B = . dt V dt

(4.29)

Now, expressing zAB by eq. (2.83) and taking into account the mean molecular diameter dA and dB as well as a molar mass MA and MB according to eq. (2.81), it follows for k m that πRT 1 1 + ). (4.30) k m = (dA + dB )2 √ ( 2 MA MB Thus, in k m = f(T 1/2 ), k m clearly represents the maximum reaction rate constant. Not all collisions result in a successful reaction, i.e., turnover according to eq. (4.28a), because the transition state AB is formally in equilibrium with the reactants, described by a pseudo equilibrium constant K ‡ = [AB‡ ]/[A][B]. This circumstance is taken into account by the introduction of a probability factor γ (also called a steric factor, but not to be confused with the accommodation coefficient, despite some similarities) in the Arrhenius equation: k = γ ⋅ k m exp (−

EA EA ) = k 0 exp (− ) . RT RT

(4.31)

Equation (4.15) for bimolecular reactions can also be written in the following forms (note k c = k d [M]): ka

kc

‡ 󳨀→ A+B 󳨀 󳨀→ C + D , ← 󳨀󳨀 [AB ] 󳨀

(4.28b)

kb

k

→C+D, A+B 󳨀 k+

󳨀󳨀→ A+B ← 󳨀󳨀 C + D .

(4.28c) (4.28d)

k−

The rate law of this process is given by −

d[B] d[A] =− = k[A][B] ≡ k a [A][B] − k b [AB‡ ] , dt dt d[C] d[D] = = k[A][B] ≡ k c [AB‡ ] − k b [AB‡ ] . dt dt

(4.32a) (4.32b)

potential energy

4.2 Theory of chemical reactions



ƒ

203

H‡

H‡

AB

|

R

AB ‡

H

C+D reaction coordinate

Fig. 4.5: Energetic scheme of a bimolecular reaction; instead of enthalpies (∆H), also free enthalpies can be used (∆G) in this scheme.

The rate law related to the transition state is d[AB‡ ] dt

= k a [A][B] − k b [AB‡ ] − k c [AB‡ ] .

(4.33)

In what follows, we will represent the reaction rate constants of process eq. (4.28) in different approaches. First we assume a steady state for the short-lived intermediate d[AB‡ ]/ dt = 0 (Bodenstein principle) and further assuming that AB‡ once formed will preferably react to C+D because of the much larger free reaction enthalpy ∆− H ‡ compared with ∆+ H ‡ (Figure 4.5), and therefore k c ≫ k b , and it follows that K‡ =

[AB‡ ] [A][B]

=

ka ka ≈ . kb + kc kc

(4.34a)

On the other hand, it follows from the rate laws (4.32a) and (4.32b) that K‡ = hence k = k a (1 −

[AB‡ ] [A][B]

=

ka − k , kb

kb kb ) ≈ k a (1 − ) . kb + kc kc

(4.34b)

(4.35)

In the case of a fast transfer of the transition complex to the products (successful reaction) k c ≫ k b , it follows that k ≈ k a . Now, as a second approach, we assume the transition complex AB‡ is in equilibirium with the initial reactants, where we use the general relationships eqs. (3.49)

204 | 4 Fundamentals of chemistry in the climate system and (3.52), and the state variables are related to the transition state AB‡ (recall ∆G = −RT ln K): K‡ =

[AB‡ ] [A][B]

=

∆+ G‡ ka ∆+ H ‡ ∆+ S ‡ = exp (− ) = exp (− ) exp ( ) . kb RT RT R

(4.34c)

Finally, from eqs. (4.32a) and (4.32b) follows the approach −

d[educts] d[products] = = k a [A][B] − k b [AB‡ ] = k c [AB‡ ] − k b [AB‡ ] , dt dt

(4.36)

hence (cf. eq. (4.34a) but without assuming the steady state for AB‡ ) K‡ =

[AB‡ ] [A][B]

=

ka . kc

(4.34d)

Combining eqs. (4.34b) and (4.34d), eq. (4.35) follows consistently for k, i.e., the first step is rate determing, a most likely assumption (k = k a ). The rate of product formation (“successful” reaction) is equal to the rate of the AB‡ right-hand transformation in eq. (4.28) but also to the disappearance (turnover) of A (or B). It follows finally from eq. (4.34d) that k ≈ ka = kc

[AB‡ ] [A][B]

= k c K ‡ = k c exp (−

∆+ H ‡ ∆+ S ‡ ) exp ( ) . RT R

(4.37)

On the other hand, comparing eq. (4.37) with eq. (4.32) we obtain k = k 0 exp (−

EA ∆+ H ‡ ∆+ G‡ ) = k 󸀠 (− ) = k c (− ) , RT RT RT

(4.38a)

where k c exp(∆+ S‡ /R) = k 󸀠 , and it follows that EA = ∆+ G‡ − RT ln

k0 . kc

(4.39a)

Hence, the activation energy is not (completely) identical to the activation enthalpy ∆+ H ‡ , as is often reported in the literature. Figure 4.5 shows schematically the chemical reaction of type (4.28). It follows that for the reaction enthalpy of the total process (A + B = C + D), ∆R H = ∆− H ‡ − ∆+ H ‡ is the difference in the transition state enthalpies of the backward and forward reactions (Figure 4.5). ∆+ H ‡ is the difference between the enthalpy of the transition state and the sum of the enthalpies of the reactants in the ground state. This is termed activation enthalpy (Figure 4.5). The transition state AB‡ is formed at a maximum energy. Principially we can describe each chemical reaction as an equilibrium, as shown by eq. (4.28d), even assuming that k + ≫ k − and, hence, k ≈ k + . Now, describing the overall process or, in other words, the formation of (C+D) in equilibrium, where ∆R G is the free reaction enthalpy, we get also k ≈ k + = k − exp (−

∆R G ) . RT

(4.38b)

4.2 Theory of chemical reactions

| 205

Combining eq. (4.38a) with eq. (4.38b) we obtain k = k 0 exp (−

EA ∆R G ) = k − exp (− ) RT RT

and EA = ∆R G − RT ln

(4.38c)

k0 . k−

(4.39b)

Then the difference between ∆R G and ∆+ G‡ describes eq. (4.40): ∆R G = ∆+ G‡ − RT ln

kc . k−

(4.40)

According to kinetic theory, the rate constant k c represents the ratio of the mean translation velocity of AB‡ to the displacement vdt the transition state passes, with 1/k c = τ = h/kT, where h is Planck’s constant and k Boltzman’s constant. The Eyring equation follows from eq. (4.37): k=

∆+ H ‡ ∆+ S ‡ kT exp (− ) exp ( ) h RT R

or

ln

k ∆+ H ‡ k ∆+ S ‡ =− + ln + . T RT h R

(4.41)

The Eyring plot ln(k/T) = f(1/T) gives a straight line with slope −∆+ H ‡ /R, from which the enthalpy of activation can be derived, and with intercept (ln(k/h) + ∆+ S‡ /R), from which the entropy of activation is derived. Reaction scheme (4.28) is valid but with the most likely belief that k c ≫ k b there is no flux from transition state AB‡ back and, hence, no equilibrium. The Arrhenius factor γ simply explains that the formation of AB‡ is inhibited, i.e., only a fraction of collisions A + B turn to AB‡ despite the fact that the reacting molecules provide the needed activation energy EA . Let us now compare reactions (4.42a) and (4.42b) between the OH radical and a simple organic compound (k in cm3 molecule−1 s−1 ); see eqs. (4.1) and (4.2): OH + CH4 → H2 O + CH3 OH + HCHO → H2 O + HCO

k CH4 = 6.9 ⋅ 10−15 , −11

k HCHO = 1 ⋅ 10

.

(4.42a) (4.42b)

The two reaction rate constants are very different (ratio more than 104 ), resulting in a residence time of methane of about 10 years and that of formaldehyde of only a few days. Both transition states represent a hydrogen bonding and H abstraction (H3 CH ⋅ ⋅ ⋅ OH and HO ⋅ ⋅ ⋅ HCHOH), and it is not likely that in the case of methane the transition state turns with a probability of more than a factor of 104 back to the initial substances compared with formaldehyde. The reason of rate differences lies in the activation energy, which is much higher for methane than for the formaldehyde reaction. The Arrhenius plot ln k versus 1/T gives a straight line with a slope –EA /R, from which the activation energy can be derived, and with intercept ln k 0 . Normally, in

206 | 4 Fundamentals of chemistry in the climate system

standard chemical reference books or tables, rate constants are given for 25 °C (about 298 K), and the following equation can be used for recalculations: ln

1 1 k(T) EA = ( − ) k 298 R 298 T

or

k(T) = k 298 exp (

EA 1 1 ( − )) . R 298 T

(4.43)

The activation energy of chemical reactions lies in the range 20–150 kJ mol−1 . The time to process A + B → C + D is on the order of only 10−12 s. This corresponds to k = k m and, thus, γ = 1 (sometimes in the literature the steric or probability coefficient is denoted by A); this means that each collision will turn the state A + B into C + D. Controversially, when γ = 0, no collision results in a chemical conversion. The reality is somewhere in between. In the case of (pseudo-) first-order reactions, the dimension of the reaction rate constant k is a reciprocal time (e.g., 1/s). To obtain a better understanding of the rate of disappearance of a pollutant, it is often useful to take a rate r in % h−1 ; the recalculation is then made using the following expression: r = 100 [1 − exp(−k ⋅ 3600)]

and

k=

r − ln (1 − 100 ) . 3600

(4.44)

For illustration, a reaction with k = 10−5 s−1 has a specific conversion of r = 3.5% h−1 and a residence time of about 1 day (exactly 27.7 h). Therefore, after 1 day of air mass travel, which is equivalent to (typical wind speed 5 m s−1 ) a distance of about 500 km, the initial concentration has decreased to about 37%. It is important not to confuse the reaction rate constant (sometimes referred to as the specific reaction rate) with the absolute reaction rate R (= dc/ dt = kc), which is often termed the simple turnover flux (mass per volume and time). In air chemistry, this reaction rate is often given in ppb ⋅ h−1 . Recalculation between concentration c and mixing ratio x is then given by eq. (4.8). Finally, there exist zero-order reactions where the reaction rate does not depend on the concentration of the reactant and remains constant until the substance has disappeared. Zero-order reactions are always heterogeneous.

4.3 Catalysis Almost all reactions in the environment, living organisms, and chemical reactors are catalytic, i.e., a substance called the catalyst increases the rate of a reaction without modifying the overall standard enthalpy change in the reaction. This process is termed catalysis according to IUPAC (2014). An example is the oxyhydrogen reaction that needs at 1 bar and 280 K about 1011 years to produce 1 mol H2 O. However, in the presence of finely divided platinum, the reaction starts to become explosive, as found by Johann Wolfgang Döbereiner (1780–1849) in 1823. Berzelius introduced the term catalysis in 1835.

4.4 Electrochemistry

| 207

The catalyst is both a reactant and product of the reaction. Catalysis can be divided into homogeneous catalysis, in which only one phase is involved (e.g., stratospheric ozone decay), and heterogeneous catalysis (e.g., exhaust gas cleaning), in which the reaction occurs at or near an interface between phases. Both types of catalysis proceed in gas and aqueous phase. In biological (aquatic) systems, the catalyst is called an enzyme (biocatalyst), which controls metabolism. Sometimes a process where the reaction rate is reduced is called negative catalysis. However, strictly speaking, it should be called inhibition and the substance the inhibitor.⁷ The term catalysis is also often used when the substance is consumed in the reaction (e.g., base-catalyzed hydrolysis of esters). Strictly speaking, this substance should be called an activator. A bimolecular reaction of the type A + B → C + D proceeds catalytically via (K catalyst) K

B

→ [K . . . A] 󳨀 → [K . . . A . . . B] 󳨀󳨀󳨀→ C + D . A󳨀 (−K)

(4.45)

From the reactant(s) and the catalyst are produced reactive intermediates, which react faster than only the reactants together. The status of thermodynamic equilibrium is not affected, just the reaction rate is increased by choosing other reaction mechanisms.

4.4 Electrochemistry We extensively discussed how chemical reactions are always connected with energy turnover; in most cases, the energy appears as heat. However, in electrolytes (see the next Chapter 4.4.1), the chemical species (ions) having a charge can spontaneously transport electrical energy and produce an electrical current, called a galvanic (or voltaic) cell, such as in a battery. This is the conversion of chemical into electrical energy. Conversely, when a chemical reaction is caused by an externally supplied current, as in electrolysis, electrical energy is converted into chemical energy. Both processes are called electrochemical reactions. Electrical energy is the energy carried by moving electrons in an electrical conductor, such as an electrolyte. It is beyond the scope of this book to discuss electrochemistry in galvanic cells because they only exist in technical systems and biological cells. Here we only consider chemical reactions where electrons are transferred directly between molecules or atoms, known as oxidation-reduction reactions, and a hydrated electron, an extra electron solvated in liquid water. 7 To stabilize some products (foods, cosmetics), radical scavengers are added. There was also an idea in geoengineering to add chemicals to the atmosphere to avoid stratospheric ozone depletion. However, to my mind, any attempt to “control” atmospheric chemistry will be unsuccessful due to the stochastic character of transport and mixing processes (control is impossible) and due to the large volume (and subsequent time) for chemical processing.

208 | 4 Fundamentals of chemistry in the climate system

In general, electrochemistry describes the overall reactions when individual redox reactions are separate but connected by an external electrical circuit and an intervening electrolyte.

4.4.1 Electrolytic dissociation Friedrich Wilhelm Ostwald (1856–1932) and Svante Arrhenius propounded the electrolytic dissociation theory in the 1880s (Arrhenius 1887). The principal feature of this theory is that certain compounds, termed electrolytes, dissociate in solution to give ions, as shown by eq. (3.44). Positively charged ions are called cations and negatively charged ions are known as anions. This results in the conductivity of the solution. The theory of electrolytes is not limited to aqueous solutions, but because of the aspect of environmental chemistry, we only consider electrolytes in water. In contrast to the thermal dissociation AB 󴀘󴀯 A + B, reaction time (kinetics) plays no role: electrolytic dissociation occurs immediately. The law of mass action for the reaction AB 󴀘󴀯 A+ + B− is given by [A+ ][B− ] K= . (4.46) [AB] Note that K in eq. (4.46) is an apparent dissociation constant, depending on the electrolyte concentration and only valid for weak electrolytes; to get the true dissociation constant, the concentrations must be replaced by the activities. With the degree of dissociation α = [A+ ]/[AB] ≡ [B− ]/[AB], it follows (compare with the degree of dissociation in eq. (4.54)) that (4.47) K = α 2 [AB] . A weak electrolyte is only partially dissociated, i.e., apart from the ions A+ and B− , a substantial amount of the undissociated compound AB is in solution; almost all organic acids and bases are weak electrolytes, as are a few salts such as HgCl2 , Hg(CN)2 , and [Fe(SCN)3 ]2 . Strong electrolytes are practically fully dissociated in aqueous solution, i.e., [AB] → 0; these are almost all salts and strong acids and bases. We will not consider here the influence of electric currents on electrolytes (termed electrolysis), a task of electrochemistry. This is a very important field of industrial chemistry and (water electrolysis based on solar energy) future green chemistry. In biochemistry, also, many electric phenomena occur; we will only briefly consider photosynthesis (Chapter 6.1.2). However, in aqueous systems in the environment, many electron transfer processes occur; they will be discussed subsequently in connection with redox processes (Chapter 4.4.2) and photocatalysis (Chapter 4.5.3). Ions in aqueous solution are always hydrated, i.e., surrounded by water molecules A+ (H2 O)n , according to the polar structure; the charge is not fixed in such a water complex.

4.4 Electrochemistry

|

209

4.4.1.1 Acids, bases, and the ionic product of water Acids (HA) are species that produce hydrogen ions (H+ ) during their aquatic dissolution, whereas bases (BOH) produce hydroxide ions (OH− ): HA 󴀘󴀯 H+ + A− , +

(4.48)

−

BOH 󴀘󴀯 B + OH .

(4.49)

This definition (Arrhenius–Ostwald theory) does not treat ions as acids. Johannes Nicolaus Brønsted (1879–1947) modified the Arrhenius definition (Brønsted 1934): Acids (A) are chemical species that separate H+ , whereas bases (B) take up H+ : A 󴀘󴀯 B + H+ ,

(4.50)

with Ka = [B][H+ ]/[A] the acidity constant. According to this definition, H+ is not an acid, whereas OH− is a base (chemically correct notation would be HO− ). Bivalent (or multivalent) acids (H2 CO3 , H2 SO4 , H3 PO4 ) and bases dissociate stepwise: H2 A 󴀘󴀯 H+ + HA− , −

+

2−

HA 󴀘󴀯 H + A

.

(4.51) (4.52)

The Brønsted theory includes the Arrhenius–Ostwald theory and is the most useful for the environmental application of diluted aqueous systems with a gas–liquid interaction. The advantage of the Brønsted theory is that the formation of acids and bases occurs via protolysis reactions including the corresponding acids and bases. In accordance with the Brønsted definition, Table 4.9 lists the most abundant acids and bases. Note that the listed species in PM (aerosols) do not occur in ionic form or free acids (e.g., H2 SO4 ) but only as salts (e.g., NH4 NO3 and NH4 HSO4 ); O2− denotes oxides (this “ion” does not exist in aqueous solution) and RCOOH organic acids. Hydroperoxides are weak acids because the following equilibria form radical ions: H2 O2 ↔ H+ + HO−2 , HO2 ↔ H+ + O−2 , and ROOH ↔ H+ + ROO− (Chapter 5.2.5). It is remarkable that in soils and waters strong acids are almost absent, with the exception of macromolecular humic acids in some soils. Many soils and natural waters tend to be even slightly alkaline. Air (however, acidity occurs only in atmospheric water; see discussion in Chapter 4.6.1) is almost acidic. This reservoir separation is a result of biogeochemical cycling; because of the chemical neutrality condition, the whole climate system is neutral. The degree of dissociation α describes the status of the equilibrium eq. (4.50) and therefore the acid strength: [B] . (4.53) α= [A] + [B] For α = 0.5 it follows that [A] = [B]. For binary solutions (acid + water), the degree of dissociation was originally defined as α󸀠 =

[H+ ] [B] = . [A] [A]

(4.54)

210 | 4 Fundamentals of chemistry in the climate system

Tab. 4.9: Acids and bases in the environment. Strong acids

Weak acids

Strong bases

Weak bases

Gases (in air)

H2 SO4 HCl HBr HNO3 HNO2 H3 PO4

RCOOH ROOH HO2 H2 O2

none

NH3 RNH2

Particulate matter, Soils, and aqueous solutions (waters)

(HSO4 − ) b

RCOOH c HCO−3 NH+4 HSO−3 H2 PO−4 HPO2− 4

CO2− 3 HCO−3 OH− [O2− ] a RCOO− PO3− 4

SO2− 4 HSO−4 SO2− 3 HSO−3 NO−3 NO−2 H2 PO−4 HPO2− 4

a

Metal oxides. Almost dissociates to sulfate. c Humic acids in soils are partly strong (pKa < 4.5). b

Therefore, it follows from eqs. (4.53) and (4.54) that α=

α󸀠 . 1 − α󸀠

(4.55)

The solvent H2 O itself is amphoteric, that is, it reacts both as an acid and as a base. We can specify eq. (4.50) as follows: H2 O 󴀘󴀯 OH− + H+ , +

+

H3 O 󴀘󴀯 H2 O + H .

(4.56) (4.57)

Liquid water dissociates in accordance with eq. (4.56) only to a small percentage (0.00000556% – 1 L water contains 55.6 mol H2 O and produces 10−7 mol L−1 H+ ). The acid constant, often called the acidity⁸ constant Ka , is defined as ([B][H+ ])/[A]. Including the corresponding base reaction H2 O + B ←→ A + OH−

(4.58)

a base constant is defined as Kb = [A][OH− ]/[B]. Note that formally hydroxide is an acid (the weakest acid) and dissociates (theoretically) further according to OH− 󴀘󴀯 O2− + H+ , where O2− is an oxide ion that does not exist in solution (it is formally the

8 It is recommended to use only the term acid constant to avoid mistakes with the term acidity (Chapter 4.6.1), which is different from the equilibrium constant Ka based on the mass effect law.

4.4 Electrochemistry

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211

strongest base) because this “equilibrium” is fully shifted toward the left side. An example for reaction eq. (4.58) is the dissociation of ammonia: NH3 + H2 O 󴀘󴀯 NH4 OH 󴀘󴀯 NH+4 + OH− .

(4.59)

What we see is that ammonium (NH+4 ) is an acid. Whereas gaseous ammonia NH3 is (apart from organic amines RNH2 ) the only important gaseous base in air, it will be removed by wet deposition to soils after dissolution as an acid (NH+4 ), making the soil more acidic. Equation (4.56) does not represent a chemical reaction since the hydrogen ion (or proton) H+ does not exist free in aqueous solutions. Instead, it “reacts” with H2 O in accordance with eq. (4.57) to the hydronium ion in a first step (Wicke et al. 1954), and then hydration occurs, for example, to H9 O+3 . Hence, more precisely we must write any acid dissociation in the form HA + H2 O 󴀘󴀯 H3 O+ + A− , +

−

H2 O + H2 O 󴀘󴀯 H3 O + OH .

(4.60) (4.61)

For simplification, we disregard that H+ + H2 O → H3 O+ (it is conventional to use the symbol H+ ).⁹ The high mobility of the proton in aqueous solutions (contribution to the conductivity) is provided by tunnel transfer belonging to hydrogen bridges in H2 O clusters (see also Chapters 3.4.1 and 5.1.3). The dissociation of neutral water is very low (α 󸀠 = 1.8 ⋅ 10−9 ), which is why water activity lg[H2 O] = 1.745 is constant and is included in all equilibrium constants. Using the equilibrium expressions of eqs. (4.50) and (4.56), the relationships Ka Kb = Kw

and

pKa + pKb = pKw

(4.62)

are valid, where the water ionic product Kw = [H+ ][OH− ] ≈ 10−14 or, written in logarithmic form, pKw = − lg Kw ≈ 14. In contrast to the hydrogen ion (H+ ), the oxonium ion H3 O+ (H+ ⋅ H2 O – also termed protonated water) is an acid (hydronium is an old but still frequently used term). With pKa (H3 O+ ) = −1.74 the ion H3 O+ is the strongest acid that exists in aqueous solution. That means that acids with Ka > Ka (H3 O+ ) ≈ 55 are totally protolyzed (α → 1) and do not exist as acids in aqueous solution. Ka values of these “very strong” acids are only imprecisely detectable because Ka → ∞ (Table 4.9). With pKa (H2 O) = ([H+ ][OH− ])/[H2 O] ≈ 15.74, the hydroxide¹⁰ ion OH− is the strongest base existing in aqueous solutions and a one-electron donor according to OH− + X → OH + X− ; note that [H2 O] ≈ 55 mol L−1 was used in the preceding equations.

9 According to recommendations given by IUPAC, only the symbol H+ should be used. 10 It should never be termed hydroxyl because that is the name of the OH radical.

212 | 4 Fundamentals of chemistry in the climate system

Tab. 4.10: pKa values (mol-L units) of different acids (298 K). Acid

H+ + base

pK a

HCl HO2 NO2 HNO3 H2 O+2 HOCH2 SO3 H HSO−4 SO2 (+H2 O) Fe(H2 O)3+ 6 HNO2 Fe(H2 O)5 OH2+ CO2 (+H2 O) HCOOH CH3 COOH HO2 HSO−3 H2 S NH+4 HCO−3 H2 O2 HOCH2 SO−3 HS−

H+

−6.23 −5 −1.34 −1 < 0.1 1.92 1.76 2.2 3.3 3.5 3.55 3.74 4.75 4.7 7.2 7.2 9.23 10.3 11.7 11.7 12.9

󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯 󴀘󴀯

+ Cl−

H+ +− O2 NO2 H+ + NO−3 H+ + HO2 H+ + HOCH2 SO−3 H+ + SO2− 4 H+ + HSO−3 H+ + Fe(H2 O)5 OH2+ H+ + NO−2 H+ + Fe(H2 O)4 (OH)+ H+ + HCO−3 H+ + HCOO− H+ + CH3 COO− H+ + O−2 H+ + SO2− 3 H+ + HS− H+ + NH3 H+ + CO2− 3 H+ + HO−2 H+ + − OCH2 SO−3 H+ + S2−

We now formulate the general reaction equation for corresponding acids and bases: (4.63) A1 + B2 ←→ B1 + A2 . The definition of acids can extend according to the solvent theory as follows (this definition is symmetric concerning the acid–base relationship, in contrast to the Brønsted theory): Acids/bases increase/decrease H+ or increase/decrease OH− : A ←→ H+ + B− −

A + OH ←→ B

−

(donor acid),

(acceptor acid).

(4.64) (4.65)

According to the pKa value rank, acids could be subdivided (this is not an objective ranking) into strong and weak acids (Table 4.10); recall that pK = − lg K: Very strong Strong Weak Very weak

pKa ≤ pKa (H3 O+ ) = −1.74 −1.74 < pKa ≤ 4.5 4.5 ≤ pKa ≤ 9.0 pKa ≥ 9.0

4.4 Electrochemistry

| 213

1.0

mol fraction x

0.8 0.6

H2CO3

CO32-

HCO32-

0.4 0.2 0.0 2

4

6

pH

8

10

12

14

Fig. 4.6: Dissociation diagram for carbonic acid; pK1 = 3.76 and pK2 = 10.38.

Figure 4.6 shows for carbonic acid the two-step dissociation depending on the pH; between pH 4.8 and 9.3 only bicarbonate (HCO−3 ) exists in solution, below pH 2.8 only undissociated H2 CO3 , and above pH 11.6 only carbonate (CO2− 3 ). 4.4.1.2 pH value As we have seen, [H+ ] is an important chemical quantity in the diluted aqueous phase. In 1909, Søren Peder Lauritz Sørensen (1868–1939) defined pH (derived from Latin pondus hydrogenii) as pH = − lg[H+ ] . (4.66) Today, the pH as an acidity measure is defined based on activity as pH (≡ paH) = − lg aH+ . As stated in Chapter 3.1.2.4, single activities, however, are not measurable. Therefore, using mean activities a± , a conventional pH scale is defined based on fixed buffer solutions with known pH values. Another acidity measure is the Hammett acidity function H0 , H0 = pKa + lg[B] − lg[A] , (4.67) where H0 = − lg[H+ ]. In what follows, no distinction is made between various pH definitions based on the assumption that in most cases in the environment aH+ = a± = [H+ ] and γ = 1 (activity coefficient). A generalized acid–base equation follows from eqs. (4.48), (4.56), and eq. (4.57): A + H2 O ←→ H3 O+ + B .

(4.68)

Therefore, it follows that pKa = pH − lg ([B]/[A])

or

pH = pKa − lg ([A]/[B]) ,

(4.69)

which is also called the Henderson–Hasselbalch equation and describes the derivation of pH as a measure of acidity (using pKa ) in biological and chemical systems. The

214 | 4 Fundamentals of chemistry in the climate system

(mean) hydrogen ion activity in terms of pH can be estimated directly using the hydrogen electrode (against a reference electrode) and measuring the electrical potential E. The hydrogen electrode is still the basic reference system for all pH measurement techniques, based on the redox process H2 󴀘󴀯 2 H+ + 2 e described by (see also eq. (4.102) and eq. (4.103)) EH = E0 +

RT RT ln aH+ − ln pH2 , F 2F

where E0 is the standard potential (= 0 per definitionem) for aH+ = 1 and pH2 = 1 atm, F is the Faraday constant), hence E = (RT/F) ln aH+ . However, because of a discomfort some researchers feel when working with hydrogen electrodes, other reference electrodes are used (having the electric potential EB ), which again are in reference to a hydrogen electrode: E = EB − EH ; it follows that pH =

F (E − EB ) . 2.303RT

(4.70)

Equation (4.70) does not reflect the diffusion potentials that make pH measurements more complicated. The accuracy of pH estimations in natural water samples (pH range 3–8) is no better than ±0.1 pH units despite the quality assurance of the pH measurement against standards to be ±0.02 in this range of pH (Schwabe 1976). 4.4.1.3 Hydrolysis of salts and oxides It is known that aqueous solutions of certain salts are not neutral but acid or alkaline, depending on how the salt contains the cation of a weak base or the anion of a weak acid. This effect results because the ions of the weak base or acid, which are in aqueous solution apart from hydrogen and hydroxide ions, respectively, must be in equilibrium with the corresponding undissociated molecule. We consider a salt formed by neutralization of a weak acid with a strong base, for example, calcium carbonate CaCO3 . Dissolved CaCO3 (note it dissolves with great difficulty) is fully dissociated into calcium and carbonate ions, but carbonate is in equilibrium with bicarbonate HCO−3 : CaCO3 → Ca2+ + CO2− 3 , + − CO2− 3 + H 󴀘󴀯 HCO3 .

As a result, new water molecules dissociate according to H2 O 󴀘󴀯 H+ + OH− and the concentration of the produced bicarbonate is practically equal to the concentration of hydroxide ions; hence, we can write the overall equilibrium in terms of − − CO2− 3 + H2 O 󴀘󴀯 HCO3 + OH .

4.4 Electrochemistry

| 215

In the presence of gaseous nitric acid (HNO3 ), which then is simultaneously dissolved (and dissociated into H+ + NO−3 ), the following reaction takes place: + − 2+ + HCO−3 + NO−3 . Ca2+ + CO2− 3 + H + NO3 → Ca

This is the acid neutralization property of natural limestone (soil-derived dust) but also flue ash from coal-fired power stations. Other salts with similar properties (such as alkali salt of organic acids) do not occur under natural environmental conditions. An example of a salt formed from a weak base and a strong acid and naturally found in the environment is ammonium nitrate, NH4 NO3 , which is fully dissociated into ammonium and nitrate ions, but ammonium is in equilibrium with ammonia, making the aqueous solution slightly acidic: NH+4 󴀘󴀯 NH3 + H+ . Soluble oxides do not occur under natural environmental conditions but are constituents of industrial dust (flue ash, cement), specifically calcium oxide (CaO), which will be fully transformed into the hydroxide CaO(s) + H2 O → Ca2+ + 2 OH− . The elementary steps behind the gross reaction are as follows (right after the dissociation of CaO into Ca2+ + O2− ): O2− + H+ → OH− , H2 O → H+ + OH− . 4.4.1.4 Buffer solutions When adding an acid or base to an aqueous solution, normally pH changes drastically. Many biological processes (in soils and organisms), however, proceed only within certain and limited pH ranges. To obtain this insensitivity, the system needs buffer solutions. A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. The pH value of these solutions remains relatively constant against added acids or bases and dilution. The effectiveness of soil buffering systems depends on numerous physical, chemical, and biological properties of soils and waters. Equation (4.69) is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid–base reactions. The ratio [A]/[B] or [acid]/[conjugate base] is termed the buffer ratio. The hydrogen activity (assuming f = 1) is calculated in a buffer for acid and bases, respectively: [A] [B] and aOH− = K . aH+ = K [B] [A] The buffer capacity is a measure to express the amount of acid or base to effect a change in pH; it is defined by β = dc/ dpH. For the case of a weak acid and its salt

216 | 4 Fundamentals of chemistry in the climate system

the buffer capacity is obtained by differentiation of the Henderson–Hasselbalch equation (eq. (4.69)) in its form pH = pK + 0.4343 ln

c , cA − c

where cA is the concentration of the acid and c the concentration of its salt; it follows that dc c β= ) . (4.71) = 2.303c (1 − dpH cA Weak acids such as almost all organic acids can play the role of buffering strong acids in nature. Solutions containing an acid and its salt (e.g., acetic acid and acetate) convert H+ from strong acids (nitric and sulfuric acid) and from CH3 COO− into undissociated CH3 COOH without changing the pH (in certain limits). A buffer solution for bases contains ammonia (NH3 ) and ammonium (NH+4 ). In nature, phosphates such as KH2 PO4 and Na2 HPO4 are buffer solutions for pH range 5.4–8.0, and borax, a natural mineral (sodium tetraborate Na2 B4 O7 ) together with hydrogen chloride (HCl) is a buffer for pH range 7.6–9.2. Organic acids (e.g., citric acid) with Na2 HPO4 provide a buffer solution in the pH range 2.2–8. Blood is protected against pH changes by a buffer from NaHCO3 and Na2 HPO4 . Buffer solutions of a defined composition also have an exact known pH (and are therefore references for pH electrodes). 4.4.1.5 Complex ions We already stated that electrolytic dissociation in water is always combined with hydration, i.e., the formation of water complexes X(H2 O)n , where H2 O is termed the ligand (n is the number of ligands). A complex ion has a metal ion at its center with a number of other molecules or ions surrounding it. These can be considered as being attached to central ions by coordinate (dative covalent) bonds.¹¹ Cations can add atoms, ions, and molecules, which already have eight electrons in the valence shell (octet). The ligand donates electron pairs to the cation, which are then jointly used, for example: Ni2+ + 4 CN− → [Ni(CN)4 ]2− Fe2+ + 6 CN− → [Fe(CN)6 ]4− Pb4+ + 8 CN− → [Pb(CN)8 ]4− The coordination number is given by the number of monovalent ligands, above four, six, or eight. Complex ions can be mixed, i.e., contain different ligands (Table 4.11). The name of the cation (metal) is derived from Latin, for example cuprate (Cu), ferrate (Fe), or plumbate (Pb). In the case where the complex contains different ligands, first the anionic and then the neutral species are written in alphabetical order. The valence of

11 In some cases, the bonding is actually more complicated than that.

4.4 Electrochemistry

| 217

Tab. 4.11: Common ligands in complex ions (cf. Table 4.3). F− Cl− O2− O2− 2 OH−

Fluoro Chloro Oxo Peroxo Hydroxo

SO2− 3 SO2− 4 S2 O2− 3 S2− C2 O2− 4

Sulfito Sulfato Thiosulfate Thio Oxalato

NH−2 NO−2 ONO− NO−3 CN−

Amino Nitro Nitrito Nitrato Cyano

SCN− NO CO NH3 H2 O

Thiocyano Nitrosyl Carbonyl Amino Aqua

the metal is given in parentheses, for example: [CuCl4 ]2− = tetrachlorocuprate(II) ion, Na2 [CuCl4 ] = disodium tetrachlorocuprate. An excess of ligands can dissolve many metals; AgCN dissolves with great difficulty and precipitates when cyanide is added to a solution of Ag+ . However, when adding more cyanide, AgCN is again dissolved: Ag+ + CN− 󴀘󴀯 AgCN AgCN + CN− 󴀘󴀯 [Ag(CN)2 ]− Transition metals, such as Fe, Mn, and Cu, are soil components and play an important role in redox reactions. Its solubility depends on pH (hydroxo complexes) and the concentration of available ligands. The equilibrium constants for complex ions must be known to describe the chemical status because different ferrato complexes also have different specific reaction rates in redox processes. 4.4.1.6 The CO2 –carbonate system In water, the following chemical carbon-IV species exist in equilibrium: carbon dioxide (CO2 ), carbonic acid (H2 CO3 ), bicarbonate (HCO−3 ), and carbonate (CO2− 3 ). Additionally, the phase equilibria with gaseous CO2 and a possible solid body such as CaCO3 and MgCO3 must be considered. Free carbonic acid has not been isolated, but the structure O=C(OH)2 in aqueous solution is confirmed. Often the expression CO2 ⋅ H2 O is also used for carbonic acid. The sum of the dissolved carbonate species is denoted as total dissolved inorganic carbon (DIC) and is equivalent to other terms used in the literature: DIC ≡ ΣCO2 ≡ TCO2 ≡ CT = [CO2 ] + [H2 CO3 ] + [HCO−3 ] + [CO2− 3 ]. The carbon dioxide (physically) dissolved in water – denoted here by CO2 (aq) – is in equilibrium with gaseous atmospheric carbon dioxide CO2 (g). There is no way to separate nonionic dissolved CO2 (aq) and H2 CO3 ; therefore, it is often lumped into CO2 ∗ (aq). Analytically, DIC can be measured by acidifying the water sample, extracting the CO2 gas produced, and measuring it. The marine carbonate system represents the largest carbon pool in the climate system, meaning it is of primary importance for partitioning atmospheric excess carbon dioxide generated by human activities. The ocean is saturated with CaCO3 , which represents the largest carbon reservoir in sediments in the forms of calcite and aragonite (Zeebe and Gattuso 2006). The

218 | 4 Fundamentals of chemistry in the climate system

higher carbonate (in terms of DIC) solubility is because of dissolved CO2 , which con− verts carbonate (CO2− 3 ) into higher soluble bicarbonate (HCO3 ). It follows that the capacity of the ocean for CO2 uptake is still very large – the system is far from saturation in DIC (or total carbonate, respectively) but rather in equilibrium. With increasing atmospheric CO2 , the seawater CO2 /carbonate concentration increases, and vice versa, i.e., in the case of decreasing atmospheric CO2 concentrations the ocean will degas CO2 , thereby leading to a new equilibrium. This means that, even in the case of carbon capture from the atmosphere (Chapter 5.2.3, Volume 2), the reduction of atmospheric CO2 is not equivalent to (or less than) the captured CO2 . The history of anthropogenically released CO2 is the story of the coupled ocean-atmosphere reservoir. Seawater is slightly alkaline (pH ≈ 8.2) because of the equilibrium between CaCO3 bottom and dissolved carbonate; the subscript s denotes solid phase, aq dissolved phase, and g gaseous phase (note that ions are generally dissolved chemical species): H2 O

2+ 2− 󳨀󳨀 󳨀→ CaCO3 (s) 󳨀 ← 󳨀󳨀 Ca + CO3

CO2− 3

+ H2 O 󴀘󴀯

HCO−3

−

+ OH

solubility product L (or Ks ) ,

(4.72)

hydrolysis constant 1 .

(4.73)

Carbonate acts as a base. The solubility of CaCO3 at 20 °C in water is only about 0.007 g L−1 as carbon. CaCO3 water solubility (mg L−1 ) decreases linearly with increasing temperature – [CaCO3 ] = 80.3 − T (r2 = 0.997), T in °C – and increases slightly with increasing CO2 partial pressure – [CaCO3 ] = 56.5 + 0.0219 ⋅ [CO2 (g)] (r2 = 0.986; 20 °C), valid in the range 20–1000 ppm CO2 (data from D’Ans and Lax 1943). Processes (4.72) and (4.73) describe the solid–liquid equilibrium at the oceanic bottom (sediment–seawater interface) and with suspended matter in seawater (calcareous organisms). Moreover, similarly, the processes of heterogeneous nucleation and droplet formation from CCNs as well as generally the solid–water interfacial process are described (Figure 4.7). Hence, seawater is an excellent solvent for acidic gases such as SO2 (used for flue-gas desulfurization at some coastal site power stations) and atmospheric CO2 . The ratio between atmospheric and oceanic (water-dissolved) CO2 is described by the Henry equilibrium (eq. (4.74); see also Chapter 3.2.2.3): CO2 (g) 󴀘󴀯 CO2 (aq) true Henry’s law constant HCO2 .

(4.74)

This “physical” equilibrium depends only on temperature. As mentioned earlier, it is not possible to measure CO2 (aq) but only the sum CO2 (aq) + H2 CO3 ; hence, all listed equilibrium constants are related to an apparent Henry’s law constant: Hap =

[CO2 (g)] [CO2 (g)] ≈ =H. [CO2 (aq)] + [H2 CO3 ] [CO2 (aq)]

(4.75)

As seen later, taking into account the hydrolysis constant of H2 CO3 , the percentage of carbonic acid is very small (∼ 0.3%), so that Hap ≈ H is valid in measurement errors. Figure 4.8 shows the temperature dependency of the Bunsen absorption coefficient α

4.4 Electrochemistry

gaseous carbon dioxide

particulate matter (PM)

carbonate aerosol

gas phase

CO2(g) desorption

| 219

absorption

scavenging

evaporation

aqueous phase

CO2(aq) decomposition

scavenged / deposited carbonate

dissolved carbon dioxide

hydrolysis

CO2-aq (H2CO3)

precipitation

protolysis

HCO3-

sedimentation

carbonate suspended

dissolution

protolysis

CO32-

dissolution

solid (sediment) phase

precipitation

CaCO3

Fig. 4.7: Multiphase CO2 – carbonate system.

(data from D’Ans and Lax 1943). This coefficient is directly related to the Henry’s law constant via α = H ⋅ RT, where H has the dimension mol L−1 atm−1 . An empirical fit, which is slightly different for two ranges of temperature, results in (r2 = 0.999) α = 0.0008 ⋅ T 2 − 0.0585 ⋅ T + 1.6992 2

α = 0.0002 ⋅ T − 0.0256 ⋅ T + 1.283

(0 − 25 °C) , (25 − 60 °C) .

Carroll and Mather (1992) have shown that between 0 °C and 100 °C the dependency of H from T is nearly linear. From the empirical data can be derived H=

1 , 11.39 + 0.81 ⋅ T

T in °C .

A “true” equilibrium is given through subsequent chemical reactions, leading to the higher solubility of CO2 in water. Dissolved CO2 forms bicarbonate via different steps: CO2 (aq) + H2 O 󴀘󴀯 HCO−3 + H+ k4.77

󳨀󳨀󳨀 󳨀󳨀 󳨀→ CO2 (aq) + H2 O ← 󳨀󳨀 H2 CO3 k−4.77

apparent first dissociation constant Kap ,

(4.76)

hydration constant Kh ,

(4.77)

220 | 4 Fundamentals of chemistry in the climate system 1.8

Bunsen absorption coefficient

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

35

40

45

50

55

60

temperature (in °C) Fig. 4.8: Solubility of CO2 in water (at 1 atm CO2 ) in terms of the dimensionless Bunsen absorption coefficient α depending on temperature (in volume dissolved CO2 /volume of solution); data from Gmelin (1943).

H2 CO3 󴀘󴀯 H+ + HCO−3 HCO−3

+

󴀘󴀯 H +

CO2− 3

true first dissociation constant K1 ,

(4.78)

second dissociation constant K2 .

(4.79)

CO2 hydration (4.77) is relatively slow, and in comparison with total dissolved CO2 the concentration of H2 CO3 is very low (negligible). Reaction (4.77) occurs for pH < 8; for pH > 10 reaction (4.80) is dominant, in the pH region 8–10 both reactions are parallel, and it is complicated to study the kinetics. Hence, reliable kinetic data are valid only for pH < 8 and pH > 10, respectively: k4.80

− 󳨀󳨀󳨀 󳨀󳨀 󳨀→ CO2 (aq) + OH− ← 󳨀󳨀 HCO3

hydrolysis constant 2 .

(4.80)

k−4.80

However, reaction (4.80) plays no role in natural waters with the exception of the initial state of cloud/fog droplet formation from alkaline CCN (e.g., flue ash and soil dust particles). The “best” estimates of the reaction rate constants (the minus sign prefix means the inverse reaction) were k 4.77 = 0.03 s−1 (25 °C) and k−4.77 = 20 s−1 (25 °C) as pseudo-first-order rates and k 4.80 = 8400 L mol−1 s−1 and k −4.80 = 2 ⋅ 10−4 s−1 . All K and k data given here are taken from Gmelin (1973); Sigg and Stumm (1996) Stumm and Morgan (1995) also adapt these data. The equilibrium constant of the apparent first dissociation (4.76) is given by Kap =

[HCO−3 ][H+ ] = K1 Kh . [CO2 (aq)]

(4.81)

4.4 Electrochemistry

| 221

Tab. 4.12: Equilibrium constants in aqueous CO2 – carbonate system (data from Gmelin (1973) unless otherwise noted). T (in °C) 10−2 atm−1

mol L−1 )

H (in Kap (in 10−7 mol L−1 ) a K1 (in 10−4 mol L−1 ) Kh ⋅ 103 ( b ) K2 (in 10−11 mol L−1 ) Kap = Ks ⋅ Kh (in 10−7 mol L−1 ) a b

0

5

7.70 2.64 – – 2.36 –

– 3.04 1.56 1.96 2.77 3.06

10 5.36 3.44 – – 3.24 –

15

20

– 3.81 1.76 2.16 3.71 3.80

25

3.93 4.16 1.75 2.52 4.20 4.41

3.45 4.45 1.72 2.59 4.29 4.45

Lide (2005). Kh = [H2 CO3 ]/[CO2 (aq)].

Kap can be relatively easily estimated from equilibrium concentration measurements, and the hydration constant Kh is calculated according to eq. (4.80) (Table 4.12). The adjustment of equilibria (4.78) and (4.79) is fast; the direct estimation of the dissociation constants K1 and K2 is not possible from concentration measurements (only indirectly through potentiometric or conductometric measurements). The true first dissociation constant K1 (pK = 3.8) is three orders of magnitude larger than the apparent dissociation constant Kap . Hence, carbonic acid is ten times stronger than acetic acid but acetic acid can degas CO2 from carbonic solutions because H2 CO3 is decomposed by about 99% into CO2 (which escapes from the water) and H2 O, as follows from Kh . This makes the aqueous carbonic system unique: carbonic acid exists as well (but in very low concentrations) as H2 CO3 (in kinetically inhibited equilibria) and largely as CO2 ⋅ H2 O, where CO2 degassing is also inhibited. The second dissociation constant characterizes bicarbonate as a very weak acid (pK2 = 10.4). The aqueousphase concentrations of different C(IV) species can be calculated from the following equilibrium expressions: [CO2 (aq)] = H ⋅ [CO2 (g)] ,

(4.82)

[H2 CO3 ] = H ⋅ Kh [CO2 (g)] , [HCO−3 ] [CO2− 3 ]

(4.83) + −1

= H ⋅ K1 Kh [CO2 (g)][H ]

,

+ −2

= H ⋅ K1 K2 Kh [CO2 (g)][H ]

(4.84) .

(4.85)

At a typical surface seawater pH of 8.2, the speciation between [CO2 ], [HCO−3 ], and [CO2− 3 ] is 0.5%, 89%, and 10.5%, showing that most of the dissolved CO2 is in the form of HCO−3 and not CO2 . For the description of the overall gas–aqueous equilibrium the so-called effective Henry’s law constant is used: Heff =

[CO2 (g)] [CO2 (g)] = . DIC [CO2 (aq)] + [H2 CO3 ] + [HCO−3 ] + [CO2− 3 ]

(4.86)

222 | 4 Fundamentals of chemistry in the climate system

Using expressions (4.82)–(4.85), it follows for the total DIC DIC = H [CO2 (g)] (1 + Kh (1 + K1 [H+ ]−1 + K1 K2 [H+ ]−2 ))

or

DIC ≈ H [CO2 (g)] (1 + Kap [H+ ]−1 + Kap K2 [H+ ]−2 ) .

(4.87a) (4.87b)

The true Henry’s law constant strongly depends on temperature. From data listed in Gmelin (including more up to 50 °C, not listed in Table 4.12) can be derived (r2 = 0.99) H = 0.061 ⋅ exp(−0.023 ⋅ T)

T in °C .

Expressions for K1 and K2 independent of temperature T (in K) and salinity S (‰) are given by Lueker et al. (2000); k 0 = 1 mol kg−1 seawater: −3633.86 + 61.2172 − 9.6777 ⋅ ln T + 0.011555 ⋅ S − 0.0001152 ⋅ S2 , T −471.78 + 25.929 + 3.16967 ⋅ ln T + 0.01781 ⋅ S − 0.0001122 ⋅ S2 . log(K2 /k 0 ) = T

log(K1∗ /k 0 ) =

In Lueker et al. (2000) and Dickson et al. (2007), the equilibrium constant K1∗ is expressed as [H+ ][HCO−3 ] K1∗ = , [CO2 (aq)] + [H2 CO3 ] which corresponds to 1 [CO2 (aq)] 1 1 1 [H2 CO3 ] + + = + ≈ . ∗ = − − + K1 [H ][HCO3 ] [H ][HCO3 ] Kap K1 Kap Hence, care is taken to adopt constants from different studies to avoid confusing similar symbols that are based on different equilibria. Moreover, using the same name for different definitions presents another source of confusion. It follows that pK1∗ (≈ pKap ) = 5.8472 and pK2 = 8.966 (pK = − log(K/k 0 ), whereby S = 35‰ and 25 °C. From the values listed in Table 4.12 it would follow that pKap (≈ pK1∗ ) = 6.3 and pK2 = 11.63, considerably different from the values for seawater. This certainly explains the different calculated concentrations based on given atmospheric CO2 partial pressures (see subsequent discussion). At 25 °C and water having pH = 8.1, the equilibrium concentration of total DIC can be calculated from eq. (4.87b) as (in mol L−1 and CO2 (g) in 10−6 ppm) DICseawater = 8.2 ⋅ [CO2 (g)] ,

(4.87c)

using K values given for pure water (Table 4.12) and seawater, respectively. This is followed by 380 ppm atmospheric CO2 for DIC in water 11 mg C L−1 and in seawater 37 mg C L−1 . The measured DIC in surface seawater (Dickson et al. 2007) amounts to 27.6 mg L−1 as carbon or 0.0023 mol L−1 and is in the range of the foregoing estimates. This suggests that the K values are either known only with significant uncertainties or

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(more likely) that the seawater DIC is not always in equilibrium. Calculations and laboratory experiments for equilibrium estimates exclude interactions with solid CaCO3 . Assuming that the relationship is valid, it can be tuned by taking the measured values (28 mg L−1 carbon in surface seawater and 384 ppm atmospheric CO2 ) to get DICseawater = 6.1 ⋅ [CO2 (g)]DICseawater = a(T, pH) ⋅ [CO2 (g)]

(4.87d)

or generally DICseawater = a(T, pH) ⋅ [CO2 (g)] .

(4.87e)

It is important to note that the “factor” a depends on the seawater pH and (to a lesser extent) T; in eq. (4.87d) a = 6.1 is valid only for pH = 8.1, but at pH = 7.9 and pH = 8.2 the factor varies twofold, 3.8 and 7.7, respectively. This means that with decreasing seawater pH the uptake capacity for atmospheric CO2 decreases significantly. Increasing sea surface temperature (SST) also leads to decreasing DIC; from eq. (4.87b), taking into account the temperature dependency of H and Kap , a linear fit follows in the range 0–30 °C (r2 = 0.99) with a slope of −0.13 mg L−1 C. However, the relationship between atmospheric CO2 is more complicated because of the buffer capacity of seawater (besides carbonate in a more exact treatment all buffering chemical species – for example borate – must be considered). The buffer capacity of carbonized water (here seawater) is given to complete the acid-based reaction − CO2 (aq) + CO2− 3 + H2 O 󴀘󴀯 2 HCO3

primarily buffering.

(4.88)

Anthropogenic CO2 dissolves in seawater, produces hydrogen ions, and neutralizes carbonate ions. Hence, H+ concentration (and pH) will not change in small ranges depending on the CO2 partial pressure increase and the available carbonate in seawater. Nevertheless, when seawater pH declines as a result of rising CO2 concentrations, the concentration of CO2− 3 will also fall (reaction (4.89)), reducing the calcium carbonate saturation state. Marine carbonates also react with dissolved CO2 through the reaction CO2 (aq) + CaCO3 (s) + H2 O 󴀘󴀯 2 HCO−3 + Ca2+

secondary buffering.

(4.89)

This reaction depends on the calcium carbonate saturation state Ω; the latter is expressed by [Ca2+ ] [CO2− 3 ] , (4.90) Ω= LCaCO3 where LCaCO3 is the solubility product. Unless sufficient carbonate is present, CaCO3 will dissolve back into the surrounding seawater. Because the ocean is in contact with carbonate sediments, both on shelves and in the deep sea, the ocean as a first approximation is roughly saturated with respect to calcite. If we assume that the concentration of Ca2+ has remained nearly constant, this is equivalent to a roughly constant carbonate-ion concentration. In regions where Ω > 1.0, the formation of shells and skeletons is favored. Below a value of 1.0, the water is corrosive and the dissolution of

224 | 4 Fundamentals of chemistry in the climate system

pure aragonite and unprotected aragonite shells will begin to occur. Equation (4.91) is a bit curious because from reaction (4.73) it follows that Ks =

[Ca2+ ] [CO2− 3 ] [CaCO3 ]

and

Ks [CaCO3 ] = [Ca2+ ] [CO2− 3 ] = L CaCO3 ,

(4.91)

where the CaCO3 activity of the solid body is set by convention at one. Therefore, Ks ≡ L and, hence, Ω = 1. Supersaturation and undersaturation remain, therefore, in small limits. However, water bodies with insufficient solid CaCO3 are generally undersaturated. Oceanic uptake of anthropogenic CO2 leads to a shift between carbonate and bicarbonate, in other words, to a larger solubility of mineral CaCO3 . It was argued that, as a consequence of higher CO2 partial pressures, the surface layers of the ocean will become undersaturated with calcium carbonate, according to eq. (4.90), with possible catastrophic biological consequences for a variety of marine organisms (e.g., coral reefs, shells, and skeletons of other marine-calcifying species). However, from general aspects, it seems unlikely that CaCO3 supersaturation is a precondition for carbonate biomineralization for the following three reasons: (a) life processes are sharply out of equilibrium; (b) biomineralization depends on the active transport of ions through biomembranes driven by metabolic energy and so do not depend on the free energy of any carbonate reaction; and (c) calcium carbonate structures of living organisms can be covered by organic tissue, representing a barrier against fast exchange processes (Wagener 1979). The ecological consequences of a possible change in the calcium carbonate supersaturation, with respect to calcareous organisms, can only be examined experimentally. Furthermore, CO2 uptake leads to so-called oceanic acidification. With a very good approximation (i.e., neglecting the carbonate concentration compared with that of bicarbonate), eq. (4.87) can be reduced to [CO2 (g)] =

[H+ ][DIC] HKap

(4.92)

and further transformed into pH = logDIC − logHKap − log [CO2 (g)] .

(4.93)

Unfortunately, DIC is a function of pH, and therefore no simple relationship between atmospheric CO2 concentration and seawater pH can be found. Pearson and Palmer (1999) held DIC constant to estimate the relationship between changing atmospheric CO2 and pH, assuming a preindustrial pH of 8.25 at the preindustrial CO2 value of 280 ppm. However, there is no serious argument for holding DIC constant over time; by contrast, Sabine et al. (2004) have shown that oceanic DIC reflects the accumulated atmospheric CO2 . Caldeira and Berner (1999) held carbonate constant and used the formula (simply derived from eq. (4.85)) [CO2 (g)] =

[H+ ]2 [CO2− 3 ] HKap K2

,

(4.94)

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225

atmospheric CO2 mixing ratio (in ppm)

1200

1000

800

600

400

200

0 7.95

8.00

8.05

8.10

8.15

8.0

8.25

pH Fig. 4.9: Relationship between atmospheric CO2 mixing ratio and seawater pH assuming a pH of 8.25 at a CO2 mixing ratio of 280 ppm and constant seawater carbonate concentration.

from which pH = 0.5 log [CO2− 3 ] − 0.5 log HKap K 2 − 0.5 log [CO2 (g)] ≡ const − 0.5 log [CO2 (g)] (4.95) follows and const = 6.474, assuming a preindustrial pH of 8.25 at the preindustrial CO2 value of 280 ppm; Figure 4.9 shows this relationship. It follows that by the year 2100, using the scenario without carbon capture and storage (CCS) technology (Chapter 5.3.1, Volume 2) for about 1000 ppm CO2 , the seawater pH would decrease to 7.96. From reactions (4.88) and (4.89) it follows that increasing CO2 would lead to increasing bicarbonate, whereas carbonate is transformed into bicarbonate and the carbonate concentration is adjusted through bicarbonate dissociation (4.79) and CaCO3 dissolution (4.72), but the relation is strongly nonlinear. From reaction (4.79) it follows that increasing [H+ ] leads to a decrease in the carbonate ion concentration. Hence, it is more likely that oceanic acidification will be faster than predicted from eq. (4.95) and Figure 4.9, which can be concluded from the measurements of surface water pH (Marsh 2009, Caldeira and Rau 2000). According to Ocean Station ALOHA, current pH (2008) is about 8.08, but from eq. (4.95) it follows that pH = 8.18. Finally, it makes no sense to adopt relationships such as (4.94) or (4.95) to calculate historical and future seawater pH. There is no scientific justification to set the preindustrial seawater pH at 8.25. When using the reference 384 ppm CO2 and pH = 8.08 as measured values for 2008, it follows from eq. (4.95) that pH = 8.15 is “preindustrial,” i.e., related to 280 ppm CO2 . Exact measurements of pH in natural waters are completely uncertain to the second decimal place.

226 | 4 Fundamentals of chemistry in the climate system

Tab. 4.13: Mean data sets from deep-water Station ALOHA (A Long-Term Oligotrophic Habitat Assessment; 22°45󸀠 N, 158°00󸀠 W) located 100 km north of Oahu, Hawaii. Data from John E. Dore (2009) Hawaii Ocean Time-series surface CO2 system data product, 1988–2008, http://hahana. soest.hawaii.edu/hot/products/products.html, SOEST, University of Hawaii, Honolulu, HI. Parameter

1988–2008

1992–1998

2003–2008

pH (measured) T , in °C n (sample number) TA a in μeq kg−1 DIC b in μmol kg−1 [CO2 (aq)] c , in μmol kg−1 d −1 [CO2− 3 ] , in μmol kg − e [HCO3 ] , in μmol kg−1 pCO2 , in ppm f [CO2 (g)], in ppm g

–h 24.9 ± 1.1 203 2306 ± 13 1975 ± 15 9.8 ± 0.4 234 ± 6 1731 345 ± 16 366 ± 10

8.10 ± 0.01 24.8 ± 1.3 52 2300 ± 14 1966 ± 12 9.6 ± 0.2 235 ± 5 1721 337 ± 13 360 ± 3

8.09 ± 0.01 24.9 ± 1.1 57 2308 ± 11 1980 ± 11 10.0 ± 0.3 231 ± 5 1737 356 ± 14 380 ± 3

Total alkalinity, measured by open cell titration; TA = [HCO−3 ] + 2[CO2− 3 ] + others. Measured by coulometry. c Free seawater CO concentration. 2 d Seawater carbonate ion concentration. e Calculated as difference between DIC and CO (aq) + CO2− 2 3 f Mean seawater partial pressure, calculated from DIC and TA. g Mean atmospheric CO mixing ratio (from Mauna Loa). 2 h Measured pH values only from the selected periods available for the density of seawater (S = 35‰, 25 °C): 1.023343 kg L−1 (Dickson et al. 2007). a

b

Dore et al. (2003, 2009) found that over two decades of observation (Station ALOHA, see Table 4.13) the surface ocean grew more acidic at exactly the rate expected from the chemical equilibration with the atmosphere. However, that rate of change varied considerably in terms of seasonal and interannual timescales and even reversed for a period of nearly 5 years (Figure 4.10). The concentrating/diluting effect of salinity changes on DIC can be removed from the measured data through the normalization to a constant S (= 35‰ where nDIC = 35 DIC/S)¹². Whereas S has no seasonal pattern, DIC (and nDIC) have distinct annual cycles, largely driven by the input of DIC from below (via winter mixing) and biological drawdown of CO2 (via photosynthesis). Year-to-year changes seem to be driven by climate-induced changes in ocean mixing and attendant biological responses to mixing events. Evidence was found for the upwelling of corrosive “acidified” water onto the continental shelf (Feely et al. 2008). It is not possible to fit the measured data in Table 4.13 with the equilibrium equations derived earlier, suggesting that either (a) different equilibrium constants are valid in 12 Figure 4.10 is an interesting example of how to make misinterpretations when not considering collateral factors.

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227

2010 2000 1990 1980 1970 1960 1950

DIC in μmol kg-1

measured DIC 1940 1930 2000

0 3

11 1

18 22 26 30 33 3 41 4 48 2 6 60 63 6 nDIC normalized to S = 35‰

1

1990 1990

1980 1980

1970 1970

1960 1960

1950 1950 0

375 750 112 150 187 225 262 300 337 375 412 450 487 525 562 600 637 675 712 750 1990 1992 1994 2000 2002 2006 2008 5 0 5 0 1996 5 0 1998 5 0 5 0 5 0 2004 5 0 5 0 5 0

year Fig. 4.10: Trend of dissolved inorganic matter (DIC) at Station ALOHA (see Table 4.13 for details); data from John E. Dore (2009), Hawaii Ocean Time-series surface CO2 system data product, 1988– 2008, SOEST, University of Hawaii, Honolulu, HI, http://hahana.soest.hawaii.edu/hot/products/ products.html (see also Dore et al. 2003, 2009).

seawater compared with pure water or (b) the seawater DIC concentration is not fully described by equilibrium conditions. The latter is possible because of the fact of the mixing and varying biological activity with respect to assimilation and respiration. Over the period 1990–2008, Table 4.13 allows us to derive an increase of DIC of about 15 μmol C L−l or (taking into account the atmospheric CO2 increase from 354 to 386 ppm) about 6 μg C per ppm CO2 . In other words, oceanic DIC increased yearly by about 10 mg C m−3 seawater or about 4 Tg C in 1-m surface layer of the oceans, corresponding to only 0.3 Gt in a 75-m layer. The yearly ocean uptake, however, is assumed to be about 2 Gt C yr−1 (Volume 2). Hence, the subtropical station ALOHA cannot re-

228 | 4 Fundamentals of chemistry in the climate system

flect the global seawater chemistry. On the other hand, using eq. (4.87d), for the mentioned period a DIC increase corresponding to 3.5 Gt in 75-m layer would follow. This result is much closer to the estimates, but, as discussed in connection with eq. (4.87e), changing T and pH must be taken into account. Moreover, this calculated inorganic carbon concentration does not incorporate the fact that carbon is continuously released to the atmosphere and oceans by degassing from metamorphism and magmatism and by the weathering of carbonate minerals and organic carbon and is continuously consumed by the production of carbonate and organic carbon sediments. Hence, the total DIC load of the ocean can be expected to vary over time. Finally, the uptake of atmospheric CO2 by the sea surface is a dynamic process that depends on an interlinking of oceanic and wind circulation. Observations suggest that the Southern Ocean sink of CO2 weakened between 1981 and 2004 by 0.08 ⋅ 10−15 g decade−1 relative to the trend expected from the large increase in atmospheric CO2 , and this trend is attributed to the observed increase in wind (Le Quéré et al. 2007).

4.4.2 Oxidation–reduction reaction (redox process) Oxidation and reduction are key processes in chemical evolution and, thus, in the environment. Oxidation and reduction are always linked processes (hence, redox as shorthand for reduction–oxidation reaction): Ared + Box → Aox + Bred .

(4.96)

Reaction eq. (4.96) describes all chemical reactions in which atoms have their oxidation number (oxidation state) changed. Oxidation state is defined as the charge an atom might be imagined to have when electrons are counted according to the following agreed-upon set of rules (cf. Table 4.6): 1. The oxidation state of a free element (uncombined element) is zero. 2. For a simple (monoatomic) ion, the oxidation state is equal to the net charge of the ion. 3. Hydrogen has an oxidation state of +1 and oxygen has an oxidation state of −2 when they are present in most compounds.¹³ 4. The algebraic sum of the oxidation states of all atoms in a neutral molecule must be zero, whereas in ions the algebraic sum of the oxidation states of the constituent atoms must be equal to the charge of the ions.

13 Exceptions to this are that hydrogen has an oxidation state of −1 in hydrides of active metals, e.g., LiH, and oxygen has a (formal) oxidation state of −1 in peroxides.

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Hence, oxidation and reduction can be defined by the following three criteria, where all oxidations meet criteria 1 and 2 and many meet criterion 3, but this is not always easy to demonstrate: 1. the complete, net removal of one or more electrons from a molecular entity (also known as de-electronation), 2. an increase in the oxidation number of any atom within any substrate, and 3. the gain of oxygen or loss of hydrogen of an organic substrate. The redox process eq. (4.96) can be formally divided into oxidation and reduction: Ared → Aox + e− and −

Aox + e → Ared ;

(4.97a) (4.97b)

−

Box + e → Bred

and −

Bred → Box + e .

(4.97c) (4.97d)

The reducing agent (also called a reductant or reducer) is thereby an electron donor and the oxidizing agent (also called an oxidant or oxidizer) is an electron acceptor. With the extension of criterion 3, oxygen is an oxidizing agent and hydrogen a reducing agent according to O2 + e− → O−2 +

and

(4.98)

−

(4.99)

H→H +e .

Because of the general principle of electroneutrality and mass conservation, oxidation and reduction must be balanced in a completely natural environment.¹⁴ The gross “reaction” of sequences eqs. (4.98) and (4.99) is H2 O 󴀘󴀯 H2 O (via a complex chain H2 O → 2 H + O → H2 O). Water is the source substance of oxidizing agents (oxygen and related substances) and reducing agents (hydrogen and related substances),¹⁵ whereas in the biosphere hydrogen is enriched and oxygen depleted and vice versa in the atmosphere. This simple difference (gradients in “reservoir” chemical potential) creates biogeochemical driving forces. As biology is relatively ubiquitous in the hydro- and pedosphere, the most ubiquitous elements that readily undergo redox transformations – iron in a ferrous/ferric (Fe2+ /Fe3+ ) system and oxygen – are commonly encountered. Many microbial species when starved of oxygen (anoxic conditions) turn to metals to shuttle their electron transport chains along and store energy via organophosphates for later use in living processes, such as reproduction or building protective coatings.

14 Analog, we stated earlier (Chapter 4.4.1.1) that acidity and alkalinity must be balanced in the whole climate system (being neutral). Later we will see that oxidation tends to produce acidity (in the atmosphere) and reduction tends to produce alkalinity (in the biosphere). 15 Analogously, water is the source substance of acidity (H+ ) and alkalinity (OH− ).

230 | 4 Fundamentals of chemistry in the climate system

In atmospheric chemistry, the term oxidant is frequently used. This is a qualitative term that includes all trace gases with a greater oxidation potential than oxygen (e.g., ozone, peroxyacetyl nitrate, hydrogen peroxide, organic peroxides, NO3 ). Hence, oxygen is excluded (which is why the term reactive oxygen species (ROS) was introduced). This “definition” of an oxidant is incorrect and should not be used in this narrow sense. As reaction eq. (4.96) suggests, the determination of whether a chemical species is a reducing or oxidizing species is relative and depends on the specific redox potential of the pairs of half-reaction eqs. (4.97) and (4.98). If a half-reaction is written as reduction eqs. (4.97b) and (4.97c), the driving force is the reduction potential. If a half-reaction is written as oxidation eqs. (4.97a) and (4.97d), the driving force is the oxidation potential related to the reduction potential by a sign change. So the redox potential is the reduction–oxidation potential of a compound measured under standard conditions against a standard reference half-cell. In biological systems, the standard redox potential is defined at pH = 7.0 versus the hydrogen electrode and partial pressure of pH2 = 1 bar. However, the concept of current flow is only applicable to aqueous systems.¹⁶ In the gaseous phase of air, electron exchange occurs in the transition state of two molecular entities, in a wider sense of charge transfer complexes. Any substance in a specified phase has an electrochemical potential (μ i )el consisting of the chemical potential μ i (partial molar free enthalpy) and a specified electric potential E, (4.100) (μ i )el = μ i + zFE , where z is the number of elementary charges (e) exchanged in the oxidation–reduction process and F is the Faraday constant (molar electric charge F = e ⋅ NA ). The electromotive force E (the equivalent of the term redox potential) is the energy supplied by a source divided by the electric charge transported through the source: −zFE = ∆R G. By contrast, the electric potential is the work required to bring a charge from infinity to that point in the electric field divided by the charge (for a galvanic cell it is equal to the electric potential difference for zero current through the cell). The molar charge zF ⋅ n (n is the number of moles) is defined as the electric charge Q (base unit coulomb) and the electric current I (base unit ampere) is defined as the rate of charge flow; recall that electric work is expressed by E dQ (eq. (3.37)) I=

dQ dn = zF . dt dt

(4.101)

The electric charge can be set in relation to amount.¹⁷ This equality is important for understanding the equivalence between mass conversion (dn/ dt) and current flow

16 In the natural environment, only aqueous systems occur, but under laboratory conditions any other solution can be considered (e.g., organic solvents), thereby providing carriers for electrons. 17 For electric charge it follows that Q = zFn = zenNA = ze ⋅ m/m m , where z is dimensionless, m m the mass of an elementary (charged) entity, m the mass of all transferred charged entities, and e the elementary charge. The elementary charge is a fundamental physical constant; it is the electric charge

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| 231

(dQ/ dt). Using eqs. (3.49) and (3.52), we can describe the free enthalpy of the redox process eq. (4.96) by ∆R G = −RT ln K + RT ln

[Aox ] [Bred ] = −zFE , [Ared ] [Box ]

(4.102)

whereas −RT ln K = ∆R G⊖ is the standard free enthalpy (in equilibrium). The important Nernst equation then follows: E = E⊖ +

RT [Aox ] [Bred ] ln zF [Ared ] [Box ]

or (25 °C)

E = E⊖ +

0.05916 [Aox ] [Bred ] . (4.103) log z [Ared ] [Box ]

Standard redox potentials are listed in Table 4.14. From eq. (4.103), when only considering the half-reaction oxidation or reduction, an adequate reduction potential Ered and oxidation potential Eox can be derived: RT [Aox ] , ln zF [Ared ] RT [Bred ] . = E⊖red + ln zF [Box ]

Eox = E⊖ox +

(4.104)

Ered

(4.105)

It follows for the coupled process that E = Ered + Eox .

(4.106)

Equation (4.104) describes the (oxidation) reaction eq. (4.97a); therefore, the reverse (reduction) process eq. (4.97b) is expressed by eq. (4.105) when substance B is replaced by A. Because Eox (A) = Ered (A), it also follows then that E⊖red = E⊖ox . This explains why “only” reduction standard potentials are listed in the literature, almost always termed the electrode potentials of half-reactions (Table 4.14). For solutions in protic solvents (water is the most important one), the universal reference electrode for which the standard electrode potential is zero by definition under standard conditions (25 °C, 1 bar H2 ) and at all temperatures is the hydrogen electrode (H+ /H2 ). In Table 4.14, the absolute electrode potentials for hydrogen are given,

e carried by a single proton or, equivalently, the magnitude of the electric charge carried by a single electron, which has charge −e, where e = 1.602⋅10−19 C (≡ 4,803⋅10−10 g1/2 cm3/2 s−1 ). Because of the fixed mass of protons and electrons, the charge is equivalent to a mass. In what follows, we give some definitions and dimensions, including an expression in the centimeter-gram-second system of units. Electromotive force (EMF) = electric potential (work done ≡ energy)/electric charge; (electric) energy [mass ⋅ length2 ⋅ time−2 ] = charge ⋅ potential (or voltage). Energy: 1 erg = 1 g ⋅ cm2 ⋅ s−2 = 10−7 J. Force: 1 dyn = 1 g ⋅ cm ⋅ s−2 = 10−5 N (note that electromotive “force” is not equivalent to mechanic “force”: force = energy/length). Charge is defined via the force it exerts on other charges, and current is then defined as charge per unit of time. Charge is measured in coulombs (1 C = 1 F ⋅ V ≡ 1 A ⋅ s). The current (charge/time; dimension in amperes, A) is the flow of charge across a surface at the rate of 1 C s−1 . The voltage between two points (electric potential difference) is equal to the work done per unit of charge against a static electric field to move the test charge between two points. This is measured in units of volts (1 V = 1 J C−1 ≡ 1 W A−1 ). Dimension of voltage: 1 V = 1 kg ⋅ m2 s−3 A−1 .

232 | 4 Fundamentals of chemistry in the climate system

Tab. 4.14: Standard electrode potential (in volt) of selected half-reactions in aqueous solution. Date from Milazzo and Caroli (1978), Bard et al. (1985), Wardman (1989), Holze (2007), Armstrong et al. (2013). e− electron transferred from electrode or donor, e−aq hydrated electron. Note the standard state is the ideal 1 molar concentration for aqueous species; thus if H+ occurs, in the half-reaction, the standard state is pH = 0 (1 mol L−1 ). For species that are gaseous at 25 °C, the standard state is a partial pressure of 105 Pa. The potential of the standard hydrogen electrode (SHE) is defined to be zero (0). In reactions where no H+ is involved, the electrode potential depends not from pH. The electrode potential for other pH can be calculated using the Nernst equation. Reactants −

e H+ + e− 2 H+ + 2 e− 2 H+ + 2 e− 2 H2 O + 2 e− O + 2 H+ + 2 e− O2 (g) + e− O2 (aq) + e− O2 + 4 H+ + 4 e− O2 + 4 H+ + 4 e− O2 + 2 H+ + 2 e− O2 + 2 H2 O + 4 e− O2 + H2 O + 2 e− O2 + H+ + e− O + e− O− + H2 O + e− O−2 + 2 H+ + e− O−2 + 2 H2 O + e− O3 + 2 H+ + 2 e− O3 + e− O3 + e− O3 + H+ + e− O3 + H2 O + 2 e− OH + e− OH + e− OH + H+ + e− OH + H+ + e− HO2 + H+ + e− HO2 + H+ + e− HO−2 + H2 O + 2 e− H2 O2 H2 O2 + H+ + e− H2 O2 + H+ + e− H2 O2 + 2 H+ + 2 e− NO + e− NO2 + e− NO3 + e− CO2 + e− CO−2 + H+ + e− CO−3 + e− Cl + e− Cl2 (aq) + e− Cl2 + e− Cl−2 + e−

Products → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → →

E (in V)

Comment

e (aq) H H2 H2 H2 + 2 OH− H2 O O−2 O−2 2 H2 O 2 H2 O H2 O2 4 OH− HO−2 + OH− HO2 O− 2 OH− H2 O2 H2 O2 + 2 OH− O2 + H2 O O−3 O−3 O2 + OH O2 + 2 OH− OH− OH− H2 O H2 O H2 O2 H2 O2 3 OH−

−2.89 −2.32 0.0000 −0.41 −0.8277 +2.421 −0.35 −0.18 +1.229 +0.816 +0.695 +0.401 +0.076 +0.10 +1.61 +1.59 +0.91 +0.695 +0.32 +1.03 +0.91 +1.77 +1.246 +2.02 +1.4 +2.730 +2.31 +1.46 +1.05 +0.878

Alternative: H2 O + e− → H2 O−

OH + H2 O OH + H2 O 2 H2 O NO− NO−2 NO−3 CO−2 HCO−2 CO2− 3 Cl− 2 Cl− Cl−2 2 Cl−

+0.80 +0.39 +1.763 −0.11 +1.04 +2.466 −1.90 +1.52 +1.57 +2.432 +1.36 +0.666 +2.126

−

Absolute: 4.281 V pH = 7

pH = 7

(0.32 . . . 0.57) pH = 7 and p(O3 ) = 100 Pa

pH = 14 pH = 7 pH = 7

pH = 7 Alternative: NO + H+ + e− → HNO

4.4 Electrochemistry

| 233

which can be interpreted in the following way. A redox couple more negative than 0.414 V should liberate hydrogen from water and a couple more negative than 0.828 V should liberate H2 from 1 mol L−1 OH− solution.

4.4.3 Hydrated electron: A fundamental species Besides the hydrogen ion (H+ ) and hydroxide ion (OH− ), another fundamental species exists in aqueous solutions, the hydrated electron e−aq . The hydrated electron e−aq , also written H2 O− or e− (aq) and first postulated by the radiation chemist Gabriel Stein (1920–1976)¹⁸ in 1952 and characterized in 1962 by recording its absorption spectrum (Stein 1968, Hart and Anbar 1970, Hughes and Lobb 1976). However, in a natural environment there is no liquid water where radiation smaller than 195 nm exists to provide the reactions (cf. reactions (5.74)–(5.76)) OH− + hν → OH + e− , +

−

H2 O + γ → H2 O + e +

λthreshold ≤ 195 nm , with a subsequent reaction ,

+

H2 O → H + OH . These reactions explain the biological impact of such radiation, i.e., gamma rays during nuclear catastrophes and shortwave (cosmic) radiation; the OH radicals react with all biomolecules as seen from Table 4.15 (OH is the strongest oxidizing agent, see Table 4.14). The solvated electron¹⁹ and especially the hydrated electron have since been found to be an extremely important reactive species. When the solvent medium is water, the hydrated electron becomes essential to myriad physical, chemical, and biological processes. In a simple picture of an electron in a cavity, the description of the hydrated electron state structure is analogous to that of a hydrogen atom, with a ground state of an s-type and an excited state of a p-type character. They absorb between 600 and 800 nm and appear blue. However, hydrated electrons are far more complex because of the ultrafast dynamics of structural change, solvation, and recombination (Paik et al. 2004). It is the simplest electron donor, and all of its reactions are in essence electron transfer reactions (Logan 1967). What is known is that their presence enhances the reactivity of water molecules with other molecules in a number 18 Stein, G. (1952) Disc. Faraday Soc. 12, 227 19 Many papers refer to the first observation of a solvated electron in 1864 by Weyl (Pogg. Ann. 123, 350), who studied the dissolution of some alkali and earth alkali metals in liquid ammonia and who observed the characteristic deep blue color of the solution (owing to the light absorption of solvated electrons) and formation of hydrogen, called hydrogen ammonia. However, Kraus (1908) first postulated the existence of “an electron, surrounded by an envelope of solvent molecules.” Liquid ammonia dissociates similarly to H2 O: 2 NH3 󴀗󴀰 NH−2 + NH+4 . The reaction of potassium with liquid ammonia is thereby very similar to that of sodium with water (see below in text): K+NH3 (l) → KNH3 → KNH2 +H. Amides (–NH2 ) are well-known compounds; today, we know that K reacts with NH+4 via electron transfer, forming the ammonium radical NH4 , which decomposes into NH3 + H.

234 | 4 Fundamentals of chemistry in the climate system

Tab. 4.15: Aqueous chemistry of hydrated electrons; X – halogen; R – organic residue (data from Hart and Anbar 1970, Hughes and Lobb 1976, Buxton 1982). k (L mol−1 s−1 )

Reaction e−aq + O2 e−aq + H3 O+ e−aq + e−aq e−aq + OH e−aq + H + H2 O e−aq + CO2

→ → → → → →

O−2 H + H2 O H2 + 2 OH− OH− H2 + OH− CO−2

e−aq + NO−3 e−aq + N2 O e−aq + RX e−aq + Mn2+ e−aq + Fe3+ e−aq + Cu2+ e−aq + HCOOH a e−aq + CH3 COOH

→ → → → → → → →

NO2− 󳨀󳨀→ (NO2 )aq + 2 OH− 3 󳨀 N2 + O− RX− → R + X− Mn+ Fe2+ Cu+ products products

a

1.9 ⋅ 1010 2.3 ⋅ 1010 0.54 ⋅ 1010 3.0 ⋅ 1010 2.5 ⋅ 1010 7.7 ⋅ 109

H2 O

1.0 ⋅ 1010 0.87 ⋅ 1010 3.8 ⋅ 107 3.5 ⋅ 108 3 ⋅ 1010 1.4 ⋅ 108 1.8 ⋅ 108

Alcohols are unreactive.

of important chemical, physical, and biological processes. Hydrated electrons form when an excess of electrons is injected into liquid water. In fact, hydrated electrons and hydrogen atoms constitute a conjugated acid–base pair (eq. (4.109)), the former being the basic and more strongly reducing species. Students of chemistry know the dangerous experiment in which one places elemental sodium (or potassium) into liquid water: 2 Na + 2 H2 O → H2 + 2 Na+ + 2 OH− . In detail, however, this reaction becomes heterogeneous when Na encounters H+ and H2 O. The elemental step of the preceding reaction is Na(s) + H+ → Na+ + H(g), an electron transfer from Na onto H+ ; however, more precisily, first an electron transfer on H2 O occurs²⁰: Na

H+

(−Na )

(−H2 O)

H

H2 O 󳨀󳨀󳨀󳨀󳨀+→ H2 O− 󳨀󳨀󳨀󳨀󳨀→ H 󳨀 → H2 . Elemental sodium acts as a strong reducing agent (such as a cathode); it corresponds to the electrochemical H2 O reduction H2 O + 2 e− → H2 + 2 OH− .

20 Note the style of writing chemical reactions A + B: This is in line with the fate of B (= H2 O), where above the arrow the other reactant is written (Na, H+ , and H, respectively), and below the arrow are the corresponding products (Na+ , H2 O). Compare with eq. (4.15).

4.4 Electrochemistry

| 235

In what follows, we will write hydrated electrons with the symbol e−aq or H2 O− unless it exists only in H2 O clusters where n = 6–50: e− + n H2 O → (H2 O)−n .

(4.107)

In the natural environment, there are only two ways to produce e−aq , either chemically or under solar light conditions via so-called photosensitizers (Chapter 4.5.3). The only known direct chemical production (Hughes and Lobb 1976) is aq

− − 󳨀󳨀→ H + OH− ← 󳨀󳨀 H2 O (= H2 O + eaq ) .

(4.108)

Therefore, in anoxic medium and (e.g., biogenic) in situ hydrogen production, this is an important pathway to initiate reduction chains by electron transfer processes. The hydrogen atom and hydrated electron are interconvertible. Reaction eq. (4.108) represents a conjugated acid–base pair, in other words, H is a (very weak) acid in an equilibrium where K = 2.3 ⋅ 10−10 mol L−1 (pKa = 9.6), k 4.108 = 2 ⋅ 107 L mol−1 s−1 , and k −4.108 = 16 L mol−1 s−1 . The back reaction eq. (4.108) is so slow that it can be neglected compared with other reactions of hydrated electrons. Reaction eq. (4.108) shows that the electron is the ultimate Lewis base²¹: H 󴀘󴀯 H+ + e−aq .

(4.109)

The most studied and likely formation of e−aq under normal environmental conditions happens via photosensitization by reversible electron transfer (Chapter 4.5.3). Photoinduced electron transfer was demonstrated in many molecules where the donor and acceptor were linked together intramolecularly (Kavarnos and Turro 1987). The efficiency of intramolecular electron transfer is strongly influenced by the separation distance between the donor and acceptor and the structure of the molecular link. The donor–acceptor groups can form collision complexes or exchange electrons at a large distance. In “electron hopping” mechanisms, an electron proceeds from donor to acceptor via a series of consecutive “hops” to various acceptor groups. This mechanism plays a crucial role in the primary stages of photosynthesis where consecutive electron transfer takes place. A hydrated electron reacts rapidly with many species with a reduction potential more positive than −2.9 V. Tunneling²² between solvent traps can also explain the mobility of e−aq since it is much higher than expected for a singly charged ion with a radius of 0.3 nm (Buxton 1982). Once e−aq is produced, the timescale for the formation of subsequent reactive species (H, HO2 , OH, H2 O2 ) is on the order of only 10−7 s. Table 4.15

21 Lewis acid–base theory uses electrons instead of proton transfer and specifically states that an acid is a species that accepts an electron pair while a base donates an electron pair: A+ (Lewis acid: electron acceptor) + B− (Lewis base: electorn donor) → A–B (coordinate covalent bond). 22 Tunneling or quantum tunneling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier (cf. Figure 4.5) that it classically could not surmount.

236 | 4 Fundamentals of chemistry in the climate system lists some reactions of e−aq ; many reactions are so fast that they occur at the diffusion controlled limit (∼ 1010 L mol−1 s−1 ). The lifetime of e−aq is on the order of 1 ms, but e−aq does not react with OH− and H2 . The back reaction of eq. (4.109) leads to atomic hydrogen: k 4.110 = 2.26 ⋅ 1010 L mol−1 s−1 (Tojima et al. 1999): e−aq + H3 O+ → H + H2 O .

(4.110)

This reaction only proceeds in acid solution, whereas in neutral and alkaline solutions e−aq reacts with O2 (for the fate of superoxide O−2 see Chapter 5.2.5.2): O2 + e−aq → O−2 .

(4.111)

Interestingly, the previously discussed reaction of elemental sodium with water is now considered a source of hydrated electrons (Hughes and Lobb 1976): Na + H2 O → Na+ + e−aq .

(4.112)

Again, considering our principle of main pathways according to the overall rate, the fate of e−aq in natural waters and hydrometeors is the formation of superoxide/ hydroperoxyl radicals (Figure 4.11), but whether the electron transfer goes directly onto O2 or via H+ plays no role because all reactions proceed very fast. The gross water splitting process is given by e−aq

H2 O 󳨀󳨀→ H + OH− ,

(4.113)

where hydrated electrons are produced by reaction eq. (4.125a). We see that this primary process of photosynthesis occurs in plant cells as well as in abiotic environments. Only the oxygen content determines the further fate of hydrogen, either excess hydrogen for a reducing environment or the formation of Ox Hy in an oxic environment. In natural waters, electron scavengers (specifically N2 O) reduce the lifetime of e−aq . Other electron scavengers are O2 (eq. (5.79)), O3 (eq. (5.119)), and H2 O2 (eq. (5.99)); see eqs. (5.114)–(5.117) for the fate of O− : H2 0

󳨀󳨀→ NO2 + 2 OH− , e−aq + NO−3 → [NO2− 3 ]󳨀 e−aq

e−aq + N2 O 󳨀󳨀→ N2 + O− . H+

(4.114) (4.115)

H O2

eaq

HO2 H+

O2

O -2

Fig. 4.11: Simplified scheme of hydrated electron fate in natural water (possible scavenging by ozone not shown; see also Figure 5.10).

4.5 Photochemistry

| 237

4.5 Photochemistry Photochemistry is the branch of chemistry concerned with chemical reactions caused by the absorption of light (far UV to IR). Solar-driven photochemistry is the only way in the environment to create reactive species such as radicals, which then initiate thermal chemical conversions. Without photochemistry (i.e., no radiation), our planet would be almost chemically inactive. There are many excited states of a molecule that do not result in chemical conversions such as photodissociation (Figure 4.12). Photodissociation (often also called photolysis) is the cleavage of one or more covalent bonds in a molecular entity, resulting from the absorption of light (Figure 4.13). Photochemical paths offer the advantage over thermal methods of forming thermodynamically disfavored products, overcoming large activation barriers in a short time, and allowing reactivity otherwise inaccessible by the thermal method. In atmosphere and surface water, photolysis is of high importance, especially for producing radicals. - hQ emission)

AB

+ hQ (absorption)

AB*

A+B

+ M (quenching)

photophysical

photochemical

Fig. 4.12: Electronic excitation of a diatomic molecule, also called potential energy curve (inharmonic oscillator). A ground state, B first excited state, 1 direct dissociation from exited ground state, 2 direct dissociation from ground state, 3 radiation transfer from excited state, 4 excitation from ground state.

energy

B

1

2

3 4 A

interatomic distance

Fig. 4.13: Photophysical and photochemical process.

238 | 4 Fundamentals of chemistry in the climate system

4.5.1 Photoexcitation: Electronic states In Chapter 4.2.1, we introduced the orbitals, synonymous with the term wave function, as the spatial residence of electrons in the shells of atoms and molecules that form chemical bonds. Between the ground state, which is the level of the lowest potential energy of a species, and the photodissociation, which is the broken chemical bond, i.e., from one molecule two chemical species form, are many well-defined excited states of the molecule (but also the atom) according to quantum theory. Whereas in atoms only changes in the energy by different electronic transfers are possible, in molecules different rotational and vibrational states (Figure 4.13), visible in spectra as bands, also occur. Excitation of rotation and vibration takes place in the IR range (absorbtion and emission). A description of the equivalent orbitals is done by so-called quantum numbers. The principal quantum number n determines the energy of the electron (shell). The principal quantum number determines the shell, often named K, L, M, N,. . . (from inner to outer shells), equivalent to n = 1, 2, 3, 4, . . . The magnetic quantum number ml (= 0, ±1, ±2, ±3, . . . ) follows from the magnetic moment of the electrons rotating around the nucleus. The orbital angular momentum of an electron is determined together with the orbital quantum number²³ l (= 0, 1, 2, . . . , n − 1). The orbital quantum number characterizes the different types of orbitals: s, p, d, f, . . . for l = 0, 1, 2, 3, . . . Hence, it follows 1s, 2p,. . . and so forth electrons (Table 4.5). Finally, the spin quantum number (also called the spin projection quantum number) ms, which has only one value (±1/2, i.e., spin down or up), is associated with the self-rotation of electrons (spin) (Table 4.16). The important Pauli principle says that no orbital ever contains more than two electrons, and if there are two electrons in the same orbital, they have a paired spin (symbol ↑↓). Before electrons occupy an orbital twice, first different orbitals in subshells are occupied. The ground state is a configuration with the maximum unpaired electrons or spins (Hund’s rule). Paired spins (↑↓) compensate for single spins and result in zero total spin, a configuration known as a singlet. The angular momentums of two parallel spins (↑↑) add up to a total spin different from zero, a configuration termed a triplet. Generally, the energetic level of a triplet configuration is lower than that of a singlet. This is caused by the Coulomb rejection, which decreases between electrons with spin correlation. In atoms and molecules, total quantum numbers result from individual electron quantum numbers. Here we only consider the total orbital quantum number L, which results from the single orbital quantum number l according to L = l1 + l2 , l1 + l2 − 1, . . . , | l1 − l2 | as integer numbers (0, 1, 2, 3, . . . ) and is denoted by capital letters S, P, D, F,. . . The total spin S is for two electrons, S = 1, 0. For three electrons (because each electron has the spin s = 1/2) it appears for all electronic states (also called terms)

23 Also called azimuthal and secondary quantum number.

4.5 Photochemistry

|

239

Tab. 4.16: Relationship between quantum numbers. Orbital

s p d f g

Values

Number of values for m

l=

m=

0 1 2 3 4

0 −1, 0, +1 −2, −1, 0, +1, +2 −3, −2, −1, 0, +1, +2, +3 −4, −3, −2, −1, 0, +1, +2, +3, +4

1 3 5 7 9

3/2, 1/2, 1/2. The multiplicity M of a term is given by the value 2S + 1, i.e., the number of possible energetic levels with respect to total spin. For a closed shell S = 0 holds, and it follows that M = 1 (singlet). For a single electron S = s = 1/2 holds, and it follows that M = 2 (doublet). For two unpaired electrons S = 1 holds, and it follows that M = 3 (triplet). We will meet these terms for two different oxygen atoms (singlet and triplet in Chapter 5.2.2). In the symbols 3 P and 1 D the upper-left index denotes the multiplicity (here triplet or singlet) and the capital letter denotes the total orbital quantum number (P for L = 1 and D for L = 2). Similar molecules are described where instead of Latin letters (S, P, D, F), Greek letters (Σ, Π, ∆, Φ) are used. The general molecular term symbol of a molecule is 2S+1

+/−

Λ g/u ,

where the quantum number Λ takes the values 1, 2, 3, 4. . . or is characterized by the symbols Σ, Π, ∆, Φ The upper-left index denotes the total spin quantum number (from S = 1 a singlet follows and from S = 1 a triplet follows), the upper-right index has the symbol + or − and denotes the reflection symmetry in an arbitrary plane along the internuclear axis (− means change and + means retention) and the lower-right index (symbol g or u)²⁴ denotes parity. The symbol for dioxygen O2 in its ground state is 3 Σ−g . However, normally, two atomic molecules are situated as a singlet. Two homoatomic molecules (such as O2 ) show no vibration terms (i.e., they do not absorb or emit in the IR range); electromagnetic radiation can only interact with an oscillating dipole, but a homoatomic molecule does not change its dipole. Depending on the radiation wavelength, molecules show different excited states (vibrational-rotational) from which a lower energetic state and the ground state are gained either by light emission (phosphorescence and fluorescence) or collision with another molecule (quenching), where energy is transferred to the collision partner. Because oxygen is (apart from nitrogen) the most abundant collision partner in air, O2 can transfer from the (unusual) triplet ground state into the energetic higher singlet state O2 (1 Σ+g ) and O2 (1 ∆g ) (Chapter 5.2.2). 24 From German g = gerade (even) and u = ungerade (uneven).

240 | 4 Fundamentals of chemistry in the climate system

4.5.2 Photodissociation: Photolysis rate coefficient Figure 4.12 shows schematically a photochemical process. It is beyond the scope of this book to go into detail about photoexcitation. According to the quantum structure of the electronic molecular system, these photons are absorbed corresponding to existing bands of rotational and vibrational states (Figure 4.13). The excited molecule AB* can turn back to the ground state through light emission (fluorescence or phosphorescence) but also via collision with any molecule, termed quenching. Only when the absorbed light energy (corresponding to a photolysis threshold wavelength) is large enough to overcome the intermolecular distance can the excited state turn into breakdown products A + B. Photolysis is represented by hν

AB 󳨀󳨀→ A + B .

(4.116)

The term hν symbolizes the energy of a photon (h is Planck’s quantum and ν is frequency; recall that c = νλ, where λ is the wavelength and c the speed of light). A first-order law describes the rate of photolysis reaction: d[AB] = −jAB [AB] , dt

(4.117)

where j is the photolysis rate coefficient, often also called the photolysis rate constant (sometimes photolysis frequency – which physically is the most correct term), but in contrast to the reaction rate constant k (which only depends on T), j depends on many parameters and is not constant but changes continuously over time. The dimension of j is reciprocal time, termed photolytic residence time, τ = j−1 . For a daily mean estimate of the photochemical conversion rate according to eq. (4.117), it is useful to determine an average rate coefficient as j=

1 tsunset − tsunrise

t sunset

∫ j(∆t) d t ,

(4.118)

t sunrise

where ∆t is the time interval of the integration step. The photolysis rate coefficient j i of molecule i is calculated by integrating the product of the spectral actinic flux E(λ), spectral absorption cross section σ(λ), and photodissociation quantum yield Φ(λ) over all relevant wavelengths (Madronich 1987): λ max

j i (λ, T) = ∫ E(λ)σ i (λ, T)Φ i (λ, T) d λ .

(4.119)

λ min

Because of the quantum characteristics of light absorption in the consideration of photochemistry, we use here spectral quantities, i.e., per unit of wavelength intervals (given in nanometers despite the SI recommendation of meters). The actinic flux E λ in terms of photons per unit of time, in traditional terms called light intensity, photon flux, irradiance or radiant flux, and simply radiation, which

4.5 Photochemistry

| 241

has caused some confusion, is the quantity of light available to molecules at a particular point in the atmosphere that, after absorption, drives photochemical processes in the atmosphere. Actinic flux describes the number of photons (or radiation) incident on a spherical surface, such as the molecule of an atmospheric species, and is a suitable radiation quantity for photolysis rate coefficient determination. The actinic flux and the irradiance split into a diffuse and a direct part. Actinic flux measurements are not trivial (Ruggaber et al. 1993, Kazadzis et al. 2004). They require spectroradiometers with specially configured optics to enable measurements of radiation equally weighted from all directions. The actinic flux does not refer to any specific orientation because molecules are oriented randomly in the atmosphere. This distinction is of practical relevance: the actinic flux (and, thus, a j-value) near a brightly reflecting surface (e.g., over snow or above a thick cloud) can be a factor of three times higher than that near a nonreflecting surface. Hence, the presence of clouds can drastically change the actinic flux throughout the atmosphere. The absorption cross section σ(λ) is a measure of the area (dimension: cm2 molecule−1 ) of a molecule (given by the electron density function) through which a photon cannot pass without being absorbed, where its energy is equivalent to a molecular quantum term (otherwise it will be reflected), in contrast to the definition of a collisional cross section. Furthermore, the dimensionless quantum yield Φ(λ) is the ratio of the number of excited (or dissociated) molecules to the number of absorbed photons (dimensionless with values 0. . . 1). This quantity depends on wavelength and approaches one at the so-called threshold wavelength. The quantum yield is numerically dimensionless but is formally measured in molecules per photon. The spectral actinic flux is the integral of spectral radiance L(λ) over all solid angles of a sphere (cf. Figure 2.13 and Table 2.9): E(λ) = ∬ L (λ, θ, φ) cos θ dθ dφ .

(4.120)

Radiation usually propagates equally in all directions; thus, L(λ) is independent of direction and eq. (4.120) simplifies to E(λ) = L (λ, θ, φ) ∬ cos θ dθ dφ = 4πL (λ, θ, φ) .

(4.121)

Equation (4.119) for the j-value can be transformed (through integration) into a more applicable form using the mean values of σ and Φ for given wavelength intervals ∆λ (as tabulated in standard books and sources, for example, Finlayson–Pitts and Pitts 2000): j=

λi

∑

E(λ)σ(λ)Φ(λ) .

(4.122)

λ=290 nm

The values for σ(λ) and Φ(λ) were determined from laboratory investigations. For the actinic flux with respect to the solar zenith angle θ, height z, and wavelength λ, either measurements or calculations are needed. All radiative transfer modeling is ultimately based on the fundamental equation of radiative transfer, or the transfer of energy as

242 | 4 Fundamentals of chemistry in the climate system Tab. 4.17: Some important photolysis in air (after Hough 1988); residence time τ = 1/j. Number

Reactant

Products

Photolysis rate (s−1 )

τ (h) a

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

O3 NO2 HNO2 HNO3 NO3 HCHO HCHO CH3 CHO ClONO2 Cl2

O(1 D) O(3 P) + NO OH + NO OH + NO2 Different H + HCO CO + H2 H + CH3 CO ClO + NO2 2 Cl

2 ⋅ 10−4 exp(1.4 secθ) 1.45 ⋅ 10−2 exp(0.4 secθ) 0.205 ⋅ j 2 (3 ⋅ 10−3 exp(0.4 secθ)) 3 ⋅ 10−6 exp(1.25 secθ) 3.29 ⋅ j 2 6.65 ⋅ 10−5 exp(0.6 secθ) 1.35 ⋅ 10−5 exp(0.94 secθ) = j6 2.9 ⋅ 10−5 = j1

0.3 0.01 0.06 38.0 0.003 2.1 6.9 2.1 9.4 0.3

a

Calculated for θ = 30° (approximate maximum value in Central Europe).

photons (Chandrasekhar 1960). Analytic solutions to the radiative transfer equation (RTE) exist for simple cases; however, for more realistic media with complex multiple scattering effects, numerical methods are required. Hough (1988) gives another useful expression for j in parameterized form: j i = a i exp (b i ⋅ sec θ) ,

(4.123)

where a i and b i are substance-specific constants (Table 4.17). It is clear that eq. (4.123) reflects the Lambert–Beer law (eq. (2.16)) and is analogous to the Arrhenius equation (eq. (4.26)). Figure 4.14 shows two examples of photolysis frequency for 2 days with different degrees of cloudiness. As mentioned, clouds scatter solar radiation and can reduce as well as enhance photodissociation.

3

j(NO2) (in 10-3 s-1)

j(O1D) (in 10-5 s-1)

12 25.07.1995 17.05.1995

2

1

10 8 6 4 2 0

0 3

6

9

12

15

time (in CET)

18

21

3

6

9

12

15

18

time (in CET)

Fig. 4.14: Diurnal variation of j-O(1 D) and j-NO2 on two different days in summer 1995, measured at airport in Munich, Germany. July 25 was a cloud-free day with a few cumulus clouds at noon, whereas on May 17 cloudiness was between 4/8 and 7/8 (after Reuder 1999).

21

4.5 Photochemistry

| 243

4.5.3 Photocatalysis: Photosensitization and autoxidation Photocatalysis is the acceleration of a photoreaction in the presence of a catalyst, which absorbs light and produces reactive species that enter into subsequent reactions with reactants. It is incorrect to refer to direct photolysis (e.g., of ozone) with subsequent formation of identical reactive species as a photocatalytic process. The generic reaction scheme is given here, where W represents a chromophoric substance (the photocatalyst) and A an electron acceptor (Hoffmann 1990, Hoffmann et al. 1995): A

→ (W+ − A− ) → products . W + hν → W∗ 󳨀

(4.124)

There are several pathways to product formation: (radical separation), W+ + A− W+A (ground-state reversible reaction), WA (coupling reaction), W+ + A + e− (sensitization). It was experimentally verified that in all natural waters chromophoric substances exist (e.g., chlorophyll) that can produce hydrated electrons after illumination and, consequently, reduce dissolved O2 (Faust and Allen 1992, Anastasio et al. 1997): aq

hν

W 󳨀󳨀→ W+ + e− 󳨀󳨀→ e−aq

(4.125a)

∗ O2

(4.125b)

hν

W 󳨀󳨀→ W 󳨀󳨀→ (W+ − O−2 ) → W+ + O−2

Many oxides (and partly sulfides) of transition state metals (Wo, No, Ir, Ti, Mn, V, Ni, Co, Fe, Zn, and others) have been characterized as inorganic semiconductors for their ability to support photosensitization (Table 4.18). The generic reaction M + hν → M+ + e− has been known for over 100 years. Their oxides (e.g., TiO2 , ZnO, Fe2 O3 ) produce hole-electron pairs when absorbing photons with energy equal to or greater than the band gap energy Eb of the semiconductor (Figure 4.15) (Fujishima et al. 1999): hν

TiO2 󳨀󳨀→ e−cb + h+vb .

(4.126)

In the absence of suitable electrons and hole scavengers adsorbed to the surface of semiconductor particles, recombination occurs within 1 ns: W+ (h+vb ) + e− (e−cb ) → W .

(4.127a)

Many organic substances have been found to act as photosensitizers such as phenones, porhyrines, naphthalenes, pyrenes, benzophenones, and cyano compounds, as well as inorganic species such as transition metal complexes and many others (Kavarnos and Turro 1987). In the presence of sunlight they produce hydrated electrons e−aq or directly O−2 in accordance with eq. (4.125). This happens continuously in

244 | 4 Fundamentals of chemistry in the climate system

Tab. 4.18: Electrochemical series of metals (standard electrode potential in V). Metal

Potential

Reduced species

Mg Al Ti Mn Cr Zn Fe Cd Co Ni Pb

−2.372 −1.662 −1.63 −1.185 −0.913 −0.762 −0.447 −0.403 −0.280 −0.257 −0.126

Mg2+ Al3+ Ti2+ Mn2+ Cr2+ Zn2+ Fe2+ Cd2+ Co2+ Ni2+ Pb2+

energy adsorption econduction band

Eb

reduction e-

(ox + e- → red)

e-

oxidation (red → ox + e-)

recombination

valence band h+

adsorption

Fig. 4.15: Photosensitization of a semiconductor; E b is the energy of the band gap.

natural waters, mainly at the interface with air, under the formation of ROS, thereby allowing for oxidation processes, including corrosion and autoxidation. At first glance this seems confusing because e−aq works as a reducing species, but the key oxidizing species in solution is the OH radical (a strong electron acceptor similar to the atmospheric gas phase), which is produced in a chain of electron transfer processes (for more details see Chapter 5.2.5): e−

H+

e−

H+

e−

O2 󳨀󳨀→ O−2 󳨀󳨀→ HO2 󳨀󳨀→ HO−2 󳨀󳨀→ H2 O2 󳨀󳨀→ OH + OH− Dunstan, Jowett, and Goulding studied²⁵ the rusting of iron and published (Dunstan et al. 1905) the “hydrogen peroxide theory.” It was shown, however, that iron exposed to water and oxygen, with the exclusion of carbon dioxide, underwent rusting. The

25 Wyndham Rowland Dunstan (1861–1949), Hooper Albert Dickinson Jowett (1870–1936), Ernest Goulding (1870–1938).

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245

researchers concluded that Whitney (1903) was correct in assuming that pure oxygen and liquid water alone were essential to the corrosion of iron, the presence of an acid being unnecessary. The detection of hydrogen peroxide during the corrosion of many metals gave rise to the idea that it acted as an intermediary in corrosion processes. The H2 O2 formation in autoxidation processes had been proposed by Traube (1882) despite the fact that nothing was known about formation mechanisms. First, Schönbein (1861) showed that H2 O2 is formed during the slow oxidation of metals in atmospheric air. Dunstan et al. (1905) wrote the reaction according to Fe + H2 O → FeO + H2 , Fe + O2 + 2H2 O → Fe(OH)2 + H2 O2 ,

and

2 FeO + H2 O2 → Fe2 O2 (OH)2 (rust) . In modern terms we write this sequence as follows: O2

H2 O

Fe 󳨀󳨀→ [Fe+ –O–O− ] 󳨀󳨀󳨀󳨀󳨀−→ [Fe+ –O–O–H] → [Fe2+ ⋅ ⋅ ⋅ − O–O–H] (−OH )

H2 O

󳨀󳨀󳨀󳨀󳨀−→ Fe

2+

(−OH )

+ H2 O2 → Fe3+ + OH− + OH .

Once oxides of iron are formed (they are semiconductors), the process accelerates similarly to eq. (4.126) due to photosensitization. Autoxidation, defined as a very slow oxidation process where dioxygen undergoes addition to bodies, can be written (B – chemical body or substrate, A – other compounds reactive to oxygen, e.g., NO) O2

B(s) + O2 → B–O–O(s) 󳨀󳨀→ B–O(s) + O3 , B–O–O(s) + A → B–O(s) + AO . The formation of singlet dioxygen in biochemistry is well known (which can subsequently react with olefins): W∗ + 3 O2 → W + 1 O2 .

(4.128a)

As a transient step, this reaction can first proceed in the following reaction sequence: W∗ + 3 O2 → W+ + O−2 → W + 1 O2 .

(4.128b)

However, when appropriate scavengers are present, the valence band holes h+vb function as powerful oxidants, whereas the conduction band electrons e−cb function as moderately powerful reductants. In aqueous solution, e−cb can transfer to H2 O, gaining the hydrated electron H2 O− or e−aq , which moves along the water structure until it is scavenged by electron receptors. Much less is known about the nature and fate of W+ and h+vb . We speculate that they can recombine again with free electrons or react

246 | 4 Fundamentals of chemistry in the climate system

with main anions in solution, producing radicals, thereby amplifying the oxidation potential (Ollis et al. 1989, Turchi and Ollis 1990, Litter 1999): W+ (h+vb ) + OH− → W + OH , +

W

(h+vb )

−

+ Cl → W + Cl .

(4.127b) (4.127c)

Nonetheless, it is clear that the rate of the oxidative half-reaction involving h+vb is closely related to the effective removal of the partner species, i.e., e−cb , by suitable electron scavengers, which must be present in the solution and available at the semiconductor interface. By contrast, in processes aiming at the oxidative destruction of a target organic substrate, any hole scavengers present in the same environment are potential competitors for the consumption of h+vb . As far as electron scavenging is concerned, the most common electron scavenger, in aerated aqueous solutions, is O2 , and its role has already been emphasized (eq. (4.125a)) (Litter 1999).

4.6 Environmental relevance of acidity The term acid rain denotes one of the most serious environmental problems, i.e., the acidification of our environment. Acidity is a chemical quantity that is essential for biological life (Schwabe 1959). It is a result of the budget between acids and bases existing in the regarded reservoir, which ultimately is an equilibrium state because of the interaction of all biogeochemical cycles, including the water cycle. Consequently, the anthropogenic disruption of biogeochemical cycles leads to changing acidity (Stumm et al. 1983). Acidification is used to describe a process by which a given environment is made more acidic (Odén 1976). The term acidity is often used to characterize the ability of a compound to release hydrogen ions (H+ ) to water molecules as a measure, expressed by pH value, but sometimes denoted acid capacity or acid strength, not to be confused with the acid constant Ka , although Ka is a measure of acid strength. By contrast, the alkalinity (also called basicity or basic capacity) is used to characterize the ability of a compound to be a proton acceptor. This definition, limited to only free H+ , is not appropriate for the atmospheric multiphase system because of the gas–liquid equilibrium of acids and bases in the pH range of interest. Therefore, Waldman et al. (1982) defined atmospheric acidity as the “acidity” in the aqueous, gaseous, and aerosol phases, representing the sum of individual compounds being measured. They wrote, “The net acidity, however, is measured in solution, following eluation or extraction of the sample. Measurements of sample acidity are performed with a pH electrode.” Not all these definitions help clarify what we must understand about atmospheric acidity. The term acidifying capacity (Möller 1999b) is only of qualitative value and encounters the same basic problems as for defining the oxidizing capacity of the atmosphere (Becker et al. 1999). The problem lies in the different points of view between

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the analytical chemist and impact researcher. Svante Odén (1924–1986) wrote (Odén 1976), “The problem of air pollution or the impact of a specific pollutant can only be understood when reactions and interactions between all reservoirs are taken into account.” The impact (acidification) is caused by acid deposition, which is a result of atmospheric acidity or, in other words, the acidifying capacity of the atmosphere. The changing acidifying capacity of the atmosphere is only part of a larger problem – changes in the chemical climate caused by a variety of emissions into the atmosphere. The importance of atmospheric acidity, and especially acid fog, had already been identified by the late nineteenth century as a cause of forest damage (Wislicenus et al. 1916) as well as by Robert Angus Smith (1817–1884) while analyzing rainwater in the middle of the nineteenth century. Smith was, in fact, not the first to use the term acid rain (as recorded almost everywhere in literature). The term was coined by the Frenchman Hippolyte Ducros (1805–1879), a pharmacist in Nimes who studied the composition of hail in 1842 (see Chapter 2.4.5, Volume 2). However, it is worth briefly describing the formation and function of natural acidity. There are only three very strong acids (HCl, HNO3 , and H2 SO4 ) that are not directly emitted in nature (except a small amount of HCl from volcanoes). Gaseous HCl produced from sea salt particles is equivalent to the consumption of other strong acids (HNO3 and H2 SO4 ) because of heterogeneous reactions and HCl degassing (Chapter 5.7.2). Hence, from NO and reduced sulfur emissions globally strong acids will be produced via oxidation (Chapters 5.3.5 and 5.4.3). Assuming a 50% conversion of naturally emitted NO and reduced sulfur into acids (which surely represents a maximum), about 1.5 Teq yr−1 acidity is provided. Direct acid emissions are known for organic acids (HCOOH and CH3 COOH corresponding to about 0.15 Teq yr−1 ) (Kesselmeier et al. 1997) and indirectly via HCHO oxidation; assuming that only 10% of HCHO is converted into HCOOH via the cloud water phase (Chapter 5.6.5), an additional 3 Teq yr−1 is produced. The quantification of other organic acids (oxalic, propionic, butyric, and many others) is impossible due to missing source information but is likely negligible compared with the aforementioned estimate. The high concentrations (1–2 ppb) found in coniferous forests (Kesselmeier et al. 1997) of formic and acetic acids and their relationship to plant physiological parameters (photosynthesis, transpiration, and stomatal conductance) suggest an ecological controlling function. However, most of the acidity in ecosystem budgets is produced in soils from humic substances. In contrast, atmospheric acidity moves and so affects other ecosystems through weathering. From a budget point of view, carbon dioxide produces global precipitation (assuming pH = 5.6 and taking into account global rainfall) of about 2 Teq yr−1 in the form of HCO−3 . For global weathering, carbonic acid seems to be dominant, but other acids are not negligible. Moreover, only organic acids, sulfuric acid, and nitric acid can produce acid rain down to a pH of around 4 locally. By contrast, formic acid/formate and acetic acid/acetate are efficient buffers not only in the laboratory.

248 | 4 Fundamentals of chemistry in the climate system

4.6.1 Atmospheric acidity In atmospheric waters (cloud, fog, and rain droplets), the following ten main ions − − + − 2+ 2+ + + must be taken into account: SO2− 4 , NO3 , Cl , HCO3 , NH4 , Ca , Mg , Na , K , and + H (Granat 1972, Möller and Zierath 1986, Möller and Horváth 1989). Of minor impor− 2− − − tance are HSO−4 , HSO−3 , SO2− 3 , NO2 , CO3 , F , and OH . Because of the electroneutrality condition, the equation (4.129a) ∑ [cationi ] = ∑ [anionj ] i

j

must hold.²⁶ In this and the following equations, only the equivalent concentrations will be used; otherwise, the stoichiometric coefficients must be considered, for exam2− ple, 1 eq SO2− 4 ≡ 0.5 mol SO4 . Relationship (4.129a) must not be confused with the + definition of an acid [H ] = [A] − [B], where A denotes acids and B bases. It follows from (4.129a) that [H+ ] = ∑ [anioni ] − ∑ [(cation without H+ )j ] = [A] − [B] . i

(4.129b)

j

Werner Stumm (1924–1999) introduced (see, for example, Stumm et al. 1983, Stumm and Morgan 1981, 1995, Stumm 1987, Sigg and Stumm 1996, Zobrist 1987) acidity as a base neutralizing capacity (BNC), corresponding to the equivalent of all acids in solution, titrated to a given reference point, BNC ≡ [Acy] = [A] + [H+ ] − [OH− ] ,

(4.130)

and a corresponding alkalinity as an acid neutralizing capacity (ANC): ANC = [Alk] = [B] + [OH− ] − [H+ ] .

(4.131)

Equations (4.130) and (4.131) are, therefore, not based on the electroneutrality eq. (4.129a) because they also include weak acids and bases that are not protolyzed in solution at the given pH (meaning in nonionic form) but contribute to acid or base titration. The first attempt to determine airborne acidity was made by careful titration inserting microliter quantities of a NaOH solution (Brosset 1976) using Gran’s titration method (Gran 1950). The reference points, however, are not objective criteria.²⁷ Zobrist (1987) extended this definition to the general equations [Acy]total = [H+ ] + [A] − [B] ≈ [Acy]H+ = [H+ ] + [A]strong − [B]strong ,

(4.132)

where Acytotal denotes the total acidity (including weak acids) and AcyH+ the free acidity. 26 This equation can also be used as a quality control measure for analytical procedures in atmospheric water: if the deviation of the quotient Σ[anions]/Σ[cations] is ≥ 20% from unit (1), the analysis must be repeated, or the samples should be rejected. 27 The German DIN 38406 (1979) defined the acid capacity (in German Säurekapazität) as being equivalent to the hydrochloric acid consumption of pH = 4.3 and the sum of all carbonaceous bonded − + cations: [Acy]H+ = [HCO−3 ] + 2[CO2− 3 ] + [OH ] − [H ].

4.6 Environmental relevance of acidity

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249

These definitions might be useful for bulk water bodies such as rivers and lakes. Atmospheric water, however, as mentioned earlier, consists of single droplets that are mixed up during sampling (obtaining a bulk water sample). Moreover, individual samples collected in the field will furthermore mix, for example, when obtaining a timeaveraged sample. All this means that individual droplets or samples with different acidity/alkalinity are mixed, resulting in acid–base reactions and a shifting liquid– gas equilibrium with a new reference point having an averaged “final” acidity. Therefore, it is important to define acidity and alkalinity as conservative parameters, i.e., they are independent of pressure, temperature, and ionic strength as well as CO2 gas exchange. The acidity is then defined as (Liljestrand 1985, Sigg and Stumm 1996) − [Acy] = [H+ ] − [HCO−3 ] − [CO2− 3 ] − [OH ] = −[Alk]

(4.133)

and, using eq. (4.129b), [Acy] = [A∗ ] − [B] , where A∗

without HCO−3 , CO2− 3

(4.134)

and OH− . It follows, using the equilibrium ex-

= anions pressions for the ions (see Chapter 4.4.1.6 concerning carbonate protolysis chemistry, especially eqs. (4.76)–(4.79)), that [Acy] = [H+ ] − (Kap HCO2 [CO2 (g)] + Kw ) [H+ ]−1 − Kap K2 HCO2 [CO2 (g)] [H+ ]−2 . (4.135)

Adopting standard conditions (340 ppm CO2 , 298 K) it follows that [Acy] ≈ [H+ ] − 4.42 ⋅ 10−12 [H+ ]−1 − 2.2 ⋅ 10−22 [H+ ]−2 .

(4.136)

Equation (4.135) is only valid when the partial pressure (p0 ) is not changed, i.e., neglecting reservoir distribution between the gas and aqueous phases. The whole mass of the gas (expressed as p0 ), however, is distributed between the gas phase (expressed as equilibrium partial pressure, peq = p0 − p󸀠 = n(g)RT/V(g)) and the aqueous phase, expressed as n(aq) = V(aq)Heff RT, where p󸀠 = peq Heff RT and H(CO2 )eff =

[CO2 (aq)] + [H2 CO3 ] + [HCO−3 ] + [CO2− 3 ] [CO2 (g)]

.

(4.137)

The reservoir distribution ratio ς (mass in aqueous phase/mass in gas phase) is given by n(aq) (4.138) = Heff Vr RT , ς= n(g) where Vr denotes the volume ratio between the phases (volume aqueous phase/ volume gas phase): V(aq)/V(g)) ≈ V(aq)/air-volume = LWC. In cases where ς ≪ 1 does not hold, in eq. (4.135) the gas-phase concentration must be expressed by the equilibrium gas-phase concentration: [CO2 (g)] = (1 + ς) [CO2 (g)]eq .

(4.139)

250 | 4 Fundamentals of chemistry in the climate system

dissolved percentage (in %)

100

80

60

40

20

0

2

3

4

5

6

7

8

9

Fig. 4.16: Reservoir distribution of gases between gas and liquid phases.

Figure 4.16 shows that under “normal” atmospheric conditions with water pH between 4 and 5.7 almost all HNO2 and NH3 dissolve into droplets, whereas SO2 and CO2 remain in the gas phase. In pH range 6–8, SO2 is effectively scavenged but CO2 is measurably transferred from the gas to the aqueous phase only above a pH of about 8. In Figure 4.17, the “acidity” parameters [H+ ], [OH− ], [Acy], and [Alk] are calculated based on eqs. (4.133) and (4.135) and then expressed as a logarithm with a dependency on pH; Figure 4.17 presents some characteristic points: pH (340 ppm CO2 ) < 5.60 = 5.60 > 5.60 (but < 10.3)

[Acy] [H+ ]

≈ →0 5.7 (Figure 4.17). After mixing two samples, one with pH < 5.7 and another with pH > 5.7, the physically meaningful averaged [H+ ] does not follow from [H+ ]i based on precipitation-weighted means because H+ is not a conservative value. Let us first consider the procedure for the physically meaningful averaging of concentrations from conservative species (such as Ca2+ , SO2− 4 ). The averaged precipitation composition of annual (or any time period related) means results from crain =

∑i R i c i , R

(4.150)

where R i denotes the precipitation amount for sample i, and R denotes the annual precipitation amount (rainfall rate), i.e., R = ∑ R i . Similarly, we derive for cloud water an expression for LWCi , which is the mean LWC from collecting an individual cloud

28 CO2 is also an anhydride; however, because of its constant concentration, the acidity contribution only depends on solution pH.

4.7 Isotopes in atmospheric chemistry and geochemistry

water sample: ccloud =

∑i c i LWCi . ∑i LWCi

|

255

(4.151)

These equations can also be applied to [Acy] taking into account standard conditions (eq. (4.136)), where const = 4.42 ⋅ 10−12 mol2 L−2 : [Acy]i ≈ 10−pHi − const ⋅ 10pHi

(4.152)

Finally, we get an averaged pH for rainwater (for cloud water R i must be replaced by LWCi and R by ∑ LWCi ): pH = − lg (−0.5

∑ R i [Acy]i √ ∑ R i [Acy]i 2 + 0.25 ( ) + const) . R R

(4.153)

It is important to view this relatively complicated formula as an estimation of averaged pH or [H+ ]. This average represents the resulting acidity of “physically mixed” samples taking into account the neutralization of acids and bases. The following sequence summarizes the steps: – pH measurement of sample i, transformation into [H+ ]i according to eq. (4.66); – Calculation of [Acy]i according to eq. (4.152); – Calculation of [Acy] according to eq. (4.150) or (4.151); – Recalculation of [H+ ] based on eq. (4.141); and – Transformation into pH based on eq. (4.66).

4.7 Isotopes in atmospheric chemistry and geochemistry In Chapter 4.1.1 we defined isotopes as elements with different numbers of neutrons. Naturally occurring nuclides define a path in the chart of nuclides corresponding to the greatest stability of the neutron/proton (N/Z) ratio. For nuclides of low atomic mass, the greatest stability is achieved when the number of neutrons and protons is approximately equal (N = Z); these are the so-called stable isotopes. However, as the atomic mass increases, the stable neutron/proton ratio increases until N/Z = 1.5. Radioactive decay occurs when changes in N and Z of an unstable nuclide cause the transformation of an atom of one nuclide into that of another, more stable, nuclide; these radioactive nuclides are termed unstable nuclides (Kendall and Caldwell 1998). During disintegration, radioactive isotopes emit alpha or beta particles and sometimes also gamma rays. Stable isotopes are nuclides that do not appear to decay to other isotopes on geologic timescales but may themselves be produced by the decay of radioactive isotopes. The various isotopes of an element have slightly different chemical and physical properties because of their mass differences. Under the proper circumstances, these

256 | 4 Fundamentals of chemistry in the climate system

differences can manifest themselves as a mass-dependent isotope fractionation effect. Two main types of phenomena produce isotopic fractionations: isotope exchange reactions and kinetic processes. Isotope exchange reactions can be viewed as a subset of kinetic isotope reactions where the reactants and products remain in contact in a closed, well-mixed system such that back reactions can occur and chemical equilibrium can be established. Under these circumstances, isotopic equilibrium can also be established. Stable isotope ratio variations are regulated by physical and chemical laws. These rules depend on a relation with mass differences between isotopes. New classes of isotope variation effects that deviate from mass-dependent laws, termed mass-independent isotope effects, were discovered in 1983 and have a wide range of applications in basic chemistry and nature. The original isotopic compositions of planetary systems are a function of nuclear processes in stars. Over time, isotopic compositions in terrestrial environments change by the processes of radioactive decay, cosmic ray interactions, mass-dependent fractionations that accompany inorganic and biological reactions, and anthropogenic activities such as the processing of nuclear fuels, reactor accidents, and nuclear-weapons testing. Stable isotope compositions of low-mass (light) elements such as oxygen, hydrogen, carbon, nitrogen, and sulfur are normally reported as δ values (delta notation) given in units of parts per thousand (given as ‰ or per mil) relative to a standard of known composition. δ values are calculated by convention as follows: δ (in ‰) = (Rsample /Rstandard − 1) ⋅ 1000 , (4.154) where R denotes the ratio of the heavy to light isotope (e.g., 34 S/32 S) in the sample and standard, respectively, which for oxygen is δ18 O (in ‰) = (

(O18 /O16 )sample − 1) ⋅ 1000 . (O18 /O16 )standard

(4.155)

For oxygen, the standard is Standard Mean Ocean Water (SMOW). In general, isotope ratio alterations are attributable to conventional thermodynamic, kinetic, translational, and gravitational phenomena. For sulfur, carbon, nitrogen, and oxygen, the average terrestrial abundance ratio of the heavy to the light isotope ranges from 1:22 (sulfur) to 1:500 (oxygen); the ratio 2 H:1 H is much lower at 1:6410. A positive δ value means that the isotopic ratio of the sample is higher than that of the standard; a negative δ value means that the isotopic ratio of the sample is lower than that of the standard. For example, a δ15 N value of +30‰ means that the 15 N/14 N of the sample is 30 parts per thousand, or 3% higher than the 15 N/14 N of the standard. Many isotope chemists advocate always prefacing the δ value with a sign, even when the value is positive, to distinguish between a true positive δ value and a δ value that is merely missing its sign (a frequent occurrence with users unfamiliar with isotope terminology).

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Tab. 4.19: Abundance ratios and reference standards for some environmental isotopes. Isotope

Ratio measured

Abundance ratio of standard

2H

2 H/1 H

3 He

3 He/4 He

6 Li

6 Li/7 Li

11 B

11 B/10 B

13 C

13 C/12 C

15 N

15 N/14 N

18 O

18 O/16 O

34 S

34 S/32 S

37 Cl

37 Cl/35 Cl

87 Sr

87 Sr/86 Sr

1.5575 ⋅ 10−4 1.3 ⋅ 10−6 8.32 ⋅ 10−2 4.04362 1.1237 ⋅ 10−2 3.677 ⋅ 10−3 2.0052 ⋅ 10−3 4.5005 ⋅ 10−2 0.324 0.710

Various isotope standards are used for quoting light stable-isotopic compositions (Table 4.19). The δ values of each of the standards were defined as 0‰. δD and δ18 O values are normally reported relative to the SMOW standard (Craig 1961) or the equivalent Vienna-SMOW (VSMOW) standard. δ13 C values are reported relative to either the PDB (Pee Dee Belemnite) or the equivalent VPDB (Vienna-PDB) standard. δ18 O values of low-temperature carbonates are also commonly reported relative to PDB or VPDB. Biological processes are generally unidirectional and are excellent examples of kinetic isotope reactions (Kohen and Limbach 2005). Organisms preferentially use the lighter isotopic species because of the lower energy “costs” associated with breaking the bonds in these molecules, resulting in significant fractionations between the substrate (heavier) and the biologically mediated product (lighter). Kinetic isotopic fractionations of biologically mediated processes vary in magnitude, depending on reaction rates, concentrations of products and reactants, environmental conditions, and – in the case of metabolic transformations – species of the organism. The variability of the fractionations makes interpretation of isotopic data difficult, particularly for nitrogen and sulfur. The magnitude of the fractionation depends on the reaction pathway utilized (i.e., which is the rate-limiting step) and the relative energies of the bonds severed and formed by the reaction. In general, slower reaction steps show greater isotopic fractionation than faster steps because the organism has time to be more selective (i.e., the organism saves internal energy by preferentially breaking light-isotope bonds). Analysis of the distribution of stable isotopes in atmospheric trace gases is a way of gaining additional knowledge that might not otherwise be available. This approach requires knowledge of the isotopic signature of emissions sources and chemical reactions. The isotopic composition of these gases provides constraints on the relative distribution of the fluxes from sources, natural or anthropogenic, of different isotopic compositions. The relationship between the composition of the gas in the atmosphere and the average value of the sources is determined by the fractionation effect of the

258 | 4 Fundamentals of chemistry in the climate system

removal processes, in particular the reaction with OH. Thus, knowledge of the fractionation effect is essential in determining the relative distribution of the fluxes from isotopically different sources. Stable isotopes²⁹ are analyzed on either gas- or solid-source mass spectrometers, depending on both the masses of the isotopes and the existence of appropriate gaseous compounds stable at room temperature. Because stable isotope effects are small, their measurement (necessarily mostly) by stable isotope ratio mass spectrometry has always been tedious and elaborate. Progress in this field has been enormous. Measurements have become exceedingly precise, down to 0.005‰. Thus, for instance, variations in the ∼ 1.1% natural abundance of 13 C as small as 5 ppm are detectable (Brenninkmeijer 2009). Measurements are now mostly based on gas chromatography techniques, i.e., in a flow of carrier gas (helium), and not on transfer under vacuum in a dual viscous inlet system. This has meant smaller samples and more analyses at the same time. Analyzing delta values has brought new insights into physical chemistry, solar system origin models, terrestrial atmospheric and biogenic evolution, polar paleoclimatology, snowball Earth geology, and present-day atmospheric sciences (Katzman 2016, Johnson et al. 2002). For example, Archean sulfide and sulfate minerals commonly exhibit anomalous ratios among four stable sulfur isotopes, 32 S, 33 S, 34 S, and 36 S. These anomalous relationships, referred to as sulfur mass-independent fractionation (S-MIF), provide strong evidence for an early anoxic atmosphere. What were the temperatures 20,000 years ago? The 18 O/16 O ratio of oxygen in water molecules in polar ice or of oxygen in carbonates deposited on the ocean floor that long ago is the source of quantitative information. With lower polar temperatures less 18 O is accumulated in ice (Brenninkmeijer 2009). The isotopic composition of an atmospheric trace gas can be significantly different from the average composition of the source fluxes as a result of isotopic fractionation in removal mechanisms. This is described by the mass balance relations for two isotopic masses, A and B, where F is flux, λ specific removal rate (= 1/τ), and M mass of the isotope in air (steady-state content) (Stevens and Wagner 1989): F A = λA M A

and

FB = λB M A .

(4.156)

The ratio of the isotopic species in the atmosphere, RA = MA /MB , is then RA = Rsource (λB /λA ) ,

(4.157)

29 Radioisotopes can be analyzed by counting the number of disintegrations per unit of time on gamma-ray or beta-particle counters or analyzed on mass spectrometers. Radioactive isotopes can be measured using a number of methods, depending on the mass, abundance, type of decay involved, accuracy desired, and money available. Some, of course, can be analyzed on solid source mass spectrometers (e.g., uranium-series isotopes). Otherwise, radioisotopes are analyzed on liquid scintillation counters and gas proportional counters (both with enrichment) and on accelerator mass spectrometers.

4.7 Isotopes in atmospheric chemistry and geochemistry

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259

where Rsource = MA /MA is the isotope ratio of the source flux. For gases removed only by reaction with OH radicals, the relative rates of removal are equal to the relative rate constants of the reaction, k B /k A = α, the kinetic isotopic fractionation effect (KIE). The quantity (α − 1) ⋅ 103 expressed in per mil (‰) will be used frequently as the KIE. The preceding equation becomes δsource = δA + (α − 1) (1 + δA ⋅ 10−3 ) ⋅ 103 ,

(4.158)

where δ is defined in eq. (4.154). When a gas undergoes a series of reactions, the isotopic composition for an element at any intermediate state compared to that of the initial source is determined only by the KIE of the loss reaction involving that state; the KIE of the intermediate reactions leading to that state are cancelled out, provided there are no competing mechanisms. For example, in the case of atmospheric CH4 , which goes through several reactions leading to CO, the carbon isotopic composition of the CO product is δCO = δsource + (α CO − 1) ⋅ 103

and

δCO = δCH4 + (α CH4 − 1) ⋅ 10 − (α CO − 1) ⋅ 103 , 3

where α CH4 and α CO are the ratios of the reaction rates of 13 C and 12 C to OH for CH4 and CO, respectively. That is, carbon isotope investigation can result in new insights into budgets and sources of organic compounds (Goldstein and Shaw 2003).

5 Substances and chemical reactions in the climate system As mentioned at the beginning of this book, we will treat the chemistry for application to the climate system according to the elements and its compounds depending on the conditions of reactions and whether the substance exists in the gaseous or condensed (aqueous and solid) phase. Normally, in standard chemistry textbooks this chapter would outline elements and their compounds according to the groups of the periodic table of the elements. Here we do it according to their abundance and importance in the environment (Tables 5.1 and 5.2). There is no need (as in standard textbooks) to characterize the properties and use of the pure substances and their formation under laboratory/industrial conditions. Summary information is given on the occurrence in the environment (detailed information on sources, emission, trends, and concentration are provided in Volume 2; see also Chapter 6.2 in this volume); the main part describes chemical behavior under environmental conditions. At present,¹ the periodic table of the elements has 118 confirmed elements; a total of 98 elements occur naturally.

5.1 Hydrogen Hydrogen, the lightest element, is characterized as being onefold positive (such as the alkali metals) and onefold negative (such as the halogens), so it moves between the main Groups 1 and 7. Hydrogen forms with all elements the largest number of compounds. There is another particularity: If a hydrogen atom oxidizes, an elementary particle, the proton H+, results; its diameter is on the order of 105 smaller than “normal” cations. However, the ionization energy of H is so large that protons do not exist freely (naturally in the climate system).

5.1.1 Natural occurrence Hydrogen is the most abundant element in the universe and represents 76.5% of the total elemental mass. It is the only element that can escape the upper atmosphere into

1 Since 2014, four new elements have been added to the periodic table, elements with atomic numbers 113 (nihonium Nh), 115 (moscovium Mc), 117 (tennesine Ts), and 118 (oganesson Og). With the discoveries now confirmed, the 7th period of the periodic table of elements is complete, according to IUPAC. Before 2014, elements 114 (fleronium Fl) and 116 (livermorium Lv) were known as superheavy elements. https://doi.org/10.1515/9783110561265-005

262 | 5 Substances and chemical reactions in the climate system

Tab. 5.1: Chemical abundance of elements and oxides in mass %; by conventions, the oceans are included in Earth’s crust (for the chemical composition of air, see Table 1.2). Space H He O C Ne Fe N Si Mg S

a a

49.3 24.6 6.4 5.4 5.9 3.4 3.0 2.5

Sum 100

Meteorites

Earth

O Si Mg Fe S Al Ca Ni Na Cr K

Fe O Si Mg S Ni Ca Al

52.80 15.37 13.23 11.92 2.10 1.15 0.90 0.65 0.62 0.19 0.13

Sum 97.91

32.1 30.1 15.1 13.9 2.9 1.8 1.5 1.4

Sum 98.8

Earth’s core

Earth’s mantle Earth’s crust

Fe Ni S

O Mg Si Fe Ca Al Na

88.8 5.8 4.5

Sum 99.1

44.8 22.8 21.5 5.8 2.3 1.2 0.3

Sum 99.7

O Si Al Fe Ca Na Mg K

46.1 28.2 8.23 5.63 4.15 2.36 2.33 2.09

Sum 99.65

a

H and He represent 98% of total elemental mass (H 76.5% and He 23.5%); the other elements are set at 100% as the sum.

Tab. 5.2: Reservoir distribution (1019 g element ormolecule for water); after Schlesinger (1997), unless otherwise noted. Reservoir

C

Ch

Ck

O

H2 O

Sg

Atmosphere Ocean Land plants Soils, organic Fossil fuels Sediments Clathrates d Rocks m

0.075 3.8/0.07 a 0.06 0.15 0.7 ∼ 5000/1500 l 1.1 3200–9300 e

0.0766 3.8–4.0/ a 0.054–0.061 0.15–0.16 0.4 6600–10,000 j

– -/0.06 a 0.095 0.16

119 12,500 b negl. (negl.)? negl. 4745 c – 1200 f

1.7 14,000 negl. (negl.)? negl. 1500 – ∼ 2,000,000

negl. 128 negl. negl. 0.001 247 i – ?

a

6000/1500 l

Carbonate / dissolved organic carbon (DOC). In water molecules. c Held in Fe O and evaporitic CaSO . 2 3 4 d Methane hydrates, after Kvenvolden and Lorenson (2001). e Estimated by using mean element abundance (Clarke 1920) and assuming a crust mass of 4.9⋅1025 g (Table 3.2 in Volume 2), sediments likely are included (the chemical form is not specified). f Held in silicates. g After Möller (1983). h After Pidwirny (2008). i Held in CaSO4 . j Not specified into carbonate and organic C. k After Pédro (2007). l Carbonate/buried organic (kerogene). m In mantle: 5–1023 g (Pédro 2007). b

5.1 Hydrogen

| 263

outer space by diffusion thanks to its small mass. Because of the excess of hydrogen in the universe, hydrides (OH2 , CH4 , NH3 , and SH2 ) should have the highest molecular abundance among the compounds derived from these elements. On Earth, hydrogen occurs as an element (H2 ) in the atmosphere. Most hydrogen is bonded in water (H2 O). Most minerals of Earth’s upper mantle contains small amounts of hydrogen, structurally bound as hydroxy group (OH). Another – and possibly the most dominant – reservoir of hydrogen is through hydrocarbons (Cx Hy ), fossil fuels, but also organic compounds delivered to Earth after its formation and stored deep in the lithosphere. Under oxygen-free conditions, the product from thermal dissociation of hydrocarbons (note that T and p are extremely large at depths of 20 km and more) is C + CO2 + H2 . Hydrogen can transform deep carbon into CH4 and H2 O. In 1900 Armand Gautier (1837–1920) first detected hydrogen as being continuously present in air. As the second most abundant reactive gas in the troposphere after CH4 , hydrogen is present at about 500 ppb. The troposphere has an estimated 155 Tg of hydrogen gas (H2 ), with approximately a 2-year lifetime. The dissociation of water (into hydrogen and oxygen), however, is only possible under natural conditions in the upper stratosphere (Chapter 5.2.7). Ultimately, hydrogen comes from water via thermal dissociation deep in the Earth and via water splitting by photosynthesis (Chapter 6.1.2). The photochemical production from HCHO photolysis accounts for about 45% of the total source of H2 . It returns by combining with the OH radical in air back to water. Soil uptake (55 Tg yr−1 ) represents a major loss process for H2 and contributes 80% of the total destruction. H2 oxidation by OH in the troposphere contributes the remainder. Obviously, the atmospheric trend of H2 was continuous since the 1990s; these increases originate from anthropogenic sources: industry, transportation and other fossil fuel combustion processes, biomass burning, and nitrogen fixation in soils. Natural sources include volcanism and soil emanation. Higher levels of hydrogen will add more water vapor to the stratosphere, where it can affect stratospheric ozone. Ideas on a future so-called hydrogen technology could lead to a permanent hydrogen leakage; a small loss of the order of 1% from the hydrogen-based energy industry would increase hydrogen sources twofold.

5.1.2 Compounds of hydrogen Table 5.3 lists compounds of hydrogen found in natural environments. Hydrides with metals do not exist freely owing to their reactivity (they may have existed during Earth’s formation). The hydrides of carbon (CH4 ), nitrogen (NH3 ), sulfur (H2 S), and phosphorus (PH3 ) are the most important in the global cycling of elements essential for life; they represent the most reduced compound (produced in the biosphere)

264 | 5 Substances and chemical reactions in the climate system

Tab. 5.3: Principal compounds of hydrogen; ROS – reactive oxygen species. Hydrides Oxoacids Carboxylic acids Aqua complexes Hydroxo complexes Hydrocarbons ROS

CH4 NH3 PH3 H2 O Om X(OH)n (X = C, N, P, S, Si) R–(COOH)n [M(H2 O)n ]m+ [M(OH) n ](m−n)+ RH OH HO2 H2 O2

H2 S

HF

HCl

HBr

HI

compared to most oxidized compounds (produced in the atmosphere): CH4 ↔ CO2 /H2 CO3 NH3 ↔ NO/HNO3 PH3 ↔ P2 O5 /H3 PO4 H2 S ↔ SO2 /H2 SO4 Nearly all environmentally important chemical compounds contain hydrogen (Table 5.3); these compounds and their chemistry will be discussed in later sections on the other elements (O, N, S, C, P, halogens). The high importance of the H+ (hydronium ion) in terms of acidity was already shown in Chapter 4.4.1.1 (acids and bases) and the relationships between H2 O, H, H+ , and e−aq in Chapter 4.4.3. Hydrogen is the ultimate reducing species (and therefore the key in photosynthesis) and the species with the highest energy density² (liberated when oxidizing to H2 O). The most important compound of hydrogen is water (H2 O); its properties were presented in Chapters 3.4.1 and 3.4.2. Water is the source of hydrogen as well as oxygen (and, ultimately, ozone) and reactive Hx Oy species (OH, HO2 , and H2 O2 ) being among ROSs of crucial importance for all oxidation processes in the climate system.

5.1.3 Chemistry Many sources of hydrogen gas and a few major sinks account for its relatively short lifetime. The main pathway in the production of hydrogen atoms in air is via the conversion of methane (CH4 ) by OH radical and subsequent photolysis of formaldehyde (HCHO); see reactions (5.40)–(5.44). This process accounts for about 26 Tg H yr−1 (Novelli et al. 1999): OH (multistep)

hν

CH4 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HCHO 󳨀󳨀󳨀󳨀→ H . −HCO

2 Followed by CH4 and liberated when oxidizing to CO2 .

5.1 Hydrogen

| 265

Other important H formation proceeds through OH + CO → H + CO2 (eq. (5.33)) and H2 + OH → H + H2 O (eq. (5.3)). Once H is gained in the troposphere, it combines quickly with O2 to produce the important hydroperoxyl radical HO2 (Chapter 5.2.3): k 5.1 = 5.4⋅10−32 (T/300)−1.8 [N2 ]cm3 molecule−1 s−1 over the temperature range 200– 600 K: (5.1) H + O2 + M → HO2 + M . Hugh Stott Taylor (1890–1974) first proposed the formation of HO2 (in the photochemical reaction H2 + O2 ) in 1925³; it was detected by mass spectroscopy in 1953 by Foner and Hudson (1953). The relatively fast reaction with the HO2 radical, producing OH, can be of interest only in the stratosphere, k 5.2 = 7.2 ⋅ 10−11 cm3 molecule−1 s−1 (298 K): H + HO2 → 2 OH . (5.2a) This reaction splits into two further product pathways of minor importance: H + HO2 → H2 + O2 ,

(5.2b)

H + HO2 → H2 O + O .

(5.2c)

Pioneering work in studying the reactions between H2 and O2 was done by Hinshelwood and Williamson (1934). It is worth summarizing here the most important reactions. The gross reaction 2 H2 + O2 = 2 H2 O is highly exothermic but does not proceed at a measurable rate at ambient temperatures because of the high activation energy needed to break the O–O (493 kJ mol−1 ) and H–H (436 kJ mol−1 ) bonding (Table 5.4). Several reactions produce free atomic H (Table 5.5 and Figure 5.1); however, under aerobic conditions (always in air and surface waters), H combines quickly with oxygen into HO2 (reaction (5.1)). The main sink (apart from soil uptake) of molecular hydrogen is the relatively slow reaction with OH, k 5.3 = 6.7 ⋅ 10−15 cm3 molecule−1 s−1 at 298 K: H2 + OH → H + H2 O .

(5.3)

Hence, if there is more H2 in the stratosphere, it will react with hydroxyl radicals, increasing the water content in the stratosphere. Modeling studies show that this increase in H2 O cools the lower stratosphere. There are several excited species of molecular hydrogen, but there is no direct photodissociation of molecular hydrogen in the interstellar medium because atomic hydrogen depletes the spectrum above 13.6 eV, which corresponds to a wavelength smaller than 90 nm. At temperatures of 2000 K, only 0.081% of H2 dissociates, and this fraction increases to 7.85% at 3000 K (95.5% at 5000 K). In Chapter 4.4.1.1, we encountered the species H+ (proton) in the aqueous phase; however, it does not freely exist and is only present in combination with H2 O as the 3 Trans. Faraday Soc. 21, 560

266 | 5 Substances and chemical reactions in the climate system

Tab. 5.4: The oxyhydrogen reaction; M – collision partner. Starting phase

O2 + energy → O + O

Chain propagation

O + H2 → OH + H H + O2 → HO2 H + HO2 + M → H2 O + O + M H + HO2 + M → 2 OH + M OH + OH + M → H2 O2 + M OH + H2 → H2 O + H HO2 + HO2 → H2 O2 + O2 HO2 + H2 → H2 O2 + H H2 O2 + OH → H2 O + HO2 H2 O2 + hν → 2 OH H2 O2 + hν → H2 O + O H2 O2 + hν → H + HO2

Termination

H + HO2 + M → H2 + O2 + M H + H + M → H2 + M H + OH → H2 O OH + HO2 → H2 O + O2 O + O → O2

Tab. 5.5: Reactions producing H under environmental conditions. Educts H2 O + hν CH4 + hν HCHO + hν RCHO + hν HNO2 + hν CO + OH NH2 + NO2 H+ + e−aq

→ → → → → → → →

Products

Comment

H + OH H + CH3 H + HCO H + RCO H + NO2 H + CO2 H + OH + N2 H

λ < 242 nm } Only in upper atmosphere λ < 230 nm λ < 370 nm Very important λ < 310 nm Unimportant λ < 361 nm Unimportant Very important After NH3 + OH → NH2 + H2 O (unimportant) After photosensitization (important)

hydronium ion H3 O+ . In the gas phase, H+ (but not under atmospheric conditions because the ionization energy is very high: 1311 kJ mol−1 ) can be produced from atomic hydrogen. Atomic hydrogen has a large affinity to electrons (H− ), but this species exists only in hydrides. Most elements produce hydrides that range from very stable – the best known is water OH2 – to very unstable. It is likely that at an early state of chemical evolution, many unstable metal hydrides (such as NaH) were formed. In the accretion phase of the Earth, they then decomposed into hydrogen (H2 ) in contact with water: H2 O

NaH(s) 󳨀󳨀󳨀󳨀󳨀+→ H− 󳨀󳨀󳨀󳨀󳨀−→ H2 (g) . (−Na )

(−OH )

5.1 Hydrogen

OH

HO2

+/- e-

OH-

| 267

H2O2

O2

H2O

H+

e-

H

H2 hν

HX HNOn H2SOm H2CO3

CH4 NH3 H2 S RH

HCHO multistep

CO2

Fig. 5.1: Main chemical pathways of hydrogen and its compounds; X = Cl, Br, F, I; n = 2, 3; m = 3, 4. Note: The formation of CH4 , NH3 , H2 S, and RH is only possible under anaerobic conditions by microorganisms and plants (assimilation).

Hydrogen undergoes several reactions in the aqueous phase. Under conditions of photocatalytic formation of e−aq , elemental hydrogen is obtained, which has a timescale on the order of 10−7 s until the formation of subsequent reactive species (H, HO2 , OH, H2 O2 ) (Figure 5.1): H+ + e−aq → H or

H2 O + e−aq → H2 O− → H + OH− .

(4.109)

Atomic hydrogen is the major reducing radical in some reactions under anaerobic conditions.⁴ It effectively reacts as an oxidant forming hydride intermediates such as H+

H + I− → [H⋅ ⋅ ⋅I− ] 󳨀󳨀→ H2 + I , H+

H + Fe2+ → [Fe3+ ⋅ ⋅ ⋅ H− ] 󳨀󳨀→ H2 + Fe3+ .

(5.4) (5.5)

In its reactions with organic compounds the hydrogen atom generally abstracts H from saturated molecules or adds to the centers of unsaturated molecules; the fate of organic radicals is well known (Chapter 5.2.4): H + CH3 OH → H2 + CH2 OH , H + H2 C=CH2 → CH3 CH2 .

(5.6a) (5.6b)

Hydrogen atom transfer (HAT) reactions are ubiquitous and play a crucial role in chemical reactions occurring in the atmosphere, biology, and industry. This kind of reaction consists of a concerted movement of a proton and an electron in a single kinetic step from one group to another (see for example eq. (5.40)): A–H + B → A + B–H . In the atmosphere, the most common and traditional HAT reaction is that associated with the abstraction of a hydrogen atom from organic molecules through an OH radical 4 Fast radical–radical reactions (in parentheses k in 1010 L mol−1 s−1 ) such as H + H → H2 (1.3), OH + OH → H2 O2 (0.53) and OH + H → H2 O (3.2) play no role in natural waters because of other available reactants in concentrations orders of magnitude greater.

268 | 5 Substances and chemical reactions in the climate system via R–H + OH → R + H2 O (eq. (5.39)), but also in the reactions Hx Oy + OH → Hx−1 Oy + H2 O (eqs. (5.24)–(5.26). These reactions involve a single hydrogen transfer: O–H ⋅ ⋅ ⋅ O → O ⋅ ⋅ ⋅ H–O

(one transition) ,

O–H ⋅ ⋅ ⋅ O → O ⋅ ⋅ ⋅ H–O → O–H ⋅ ⋅ ⋅ O

(two transition, crossing–recrossing event) .

More recently (Kumar et al. 2016), a framework has emerged for a new class of HAT reactions that involves double hydrogen transfers (well described in organic chemistry, for example, Barker et al. 2017): A + H2 B → AH2 + B . These reactions are broadly classified into four categories: (a) addition, (b) elimination, (c) substitution, and (d) rearrangement. Hydration and dehydration are classic examples of addition and elimination reactions, respectively, whereas tautomerization and isomerization belong to a class of rearrangement reactions. Atmospheric acids (e.g., dimers of H2 SO4 ) and water typically mediate these reactions. Another type of hydrogen transfer is the proton transfer between O atoms (see also Chapter 3.4.1), which takes place without a barrier: H2 O ⋅ ⋅ ⋅ H+ ⋅ ⋅ ⋅ OH2 , HO− ⋅ ⋅ ⋅ H+ ⋅ ⋅ ⋅ OH− .

5.2 Oxygen Oxygen is the most abundant element in the climate system and on Earth (excluding the core, where iron is more abundant but only because of its molar mass) and in space (excluding hydrogen and novel gases) (Table 5.6). Hence, water (H2 O) is the most abundant compound in the universe. Although C and N are among the first four elements (again excluding hydrogen and novel gases) in the universe, they are much less abundant on Earth because of their high volatility. The enrichment of oxygen on Earth is due to its ability to form stable oxides with all other elements (only the core consists of elemental iron and nickel). It is widely accepted that free oxygen in an atmosphere is the result (and, hence, the indication) of biological life. Without photosynthesis by plants and other organisms, free oxygen would exist only in trace amounts in air due to the photodissociation of H2 O. However, without respiration, oxygen would rise above its present levels and cause oxidative stress. The cycling of oxygen is inextricably linked with that of carbon (CH4 also stands for any hydrocarbon): respiration, mineralisation, combustion

󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀→ CH4 + 2 O2 󳨀 ← 󳨀󳨀 CO2 + 2 H2 O . hν (photosynthesis), CO2 utilization

5.2 Oxygen

| 269

Tab. 5.6: Ranking list of elements, based on mass-%; excluding H2 (make up 98% of all elements) and novel gases. Reservoir

Element

Subsum %

Ranking

1

2

3

Space Earth’s crust Earth’s core Earth

O O Fe Fe

C Si Ni O

Fe Al S Si

84.7 82.5 99.1 77.3

Element

Total sum %

4

5

6

7

8

N Fe

Si Ca

Mg Na

S Mg

K

Mg

S

Ni

Ca

Al

99.9 99.6 99.1 98.8

In chemical bonds, oxygen is derived mostly from monooxygen (O), less from dioxygen (O2 ), and only as an unstable intermediate from trioxygen (O3 ): =O (oxo group) and –O– (alkoxy group), specifically: –OH (hydroxy group) –O–O– (dioxy group, peroxy/peroxo) –O–O–O– (trioxy group, ozonide) Atmospheric oxygen in its different forms (O, O2 , and O3 ) provides oxidizing agents for the decomposition of organic compounds (symbolized in Figure 5.2 as (CH2 O)n ), where it turns back into H2 O via several reactive (biologically and atmospherically important) Hy Ox species (Chapter 5.2.3). Oxygen is only known in electronegative bonding, with the exception of peroxides (−1), in the oxidation state −2. Only fluorine is more electronegative than oxygen, but elemental F does not exist in nature. Therefore, it forms oxides with all other elements.⁵ In the past few decades, the role of molecular oxygen in forming metal complexes, which play the role of oxygen carriers in biochemistry, has been studied. Molecular oxygen in its 3 ∑−g ground state has triplet multiplicity but not singlet multiplicity, unlike most natural compounds. Unpaired electrons in two different molecular orbitals account for the paramagnetism of molecular oxygen. The high O2 dissociation energy (493.4 kJ mol−1 ) does not allow, under tropospheric conditions, photolytic decay into oxygen atoms. Triplet multiplicity is the reason why most reactions of oxygen with organic substances, although exergonic, do not proceed at normal temperatures but upon heating or in the presence of catalysts. Thus, reactions of organic compounds with dioxygen are kinetically inhibited. The other main and very stable oxygen compound is water (H2 O) because the O–H bonding cannot be broken by photodissociation in natural environments. Therefore, oxygen comprises four chemical groups from O1 to O4 (Figure 5.3). Transfers between these groups provide very few special reactions. The variety of species within groups O1 and O2 is large, whereas group O3 plays the role of connecter between groups O1 and O2 . Group O4 only plays a (hypothetical) transient 5 Xenon (Xe) also forms oxides (and fluorides); from He, Ne, and Ar stable compounds are unknown.

270 | 5 Substances and chemical reactions in the climate system

CO2 (10)

O2 (119)

H2O (12500)

(CH2O)n (negl.) Fig. 5.2: Oxygen in chemical reservoirs and chemical cycling; numbers represent total mass of oxygen in 1019 g (almost all CO2 is dissolved in seawater as carbonate and molecular oxygen in air); (CH2 O)n represents organic compounds including biomass.

O3 chemistry O3-, O3 O2 + O1

O2 chemistry

O3 + O1

decay

O2 (3O2, 1O2), O2-, HO2, H2O2

O1 + O2

O1 chemistry O (3O, 1O), O-, OH, OH-, H2O

decay

O1 + O3

O4 chemistry O4(?), HO4-, H2O4 Fig. 5.3: Chemical species and schematic relationships between O1 and O4 chemistry.

state from O3 to O2 . Hydrogen radicals (H) and ions (H+ ) are closely connected with oxygen chemistry; in Chapter 4.4.2, we stated that H and O are the “symbols” for reduction and oxidation, respectively. The chemistry of oxygen species is very complex; all oxygen species are interlinked with all other chemical species found in the environment.

5.2 Oxygen

| 271

5.2.1 Natural occurrence Our present atmosphere contains 119 ⋅ 1019 g molecular oxygen (20.94% in dry air), which represents only 0.006% of total oxygen on Earth, which is almost completely fixed in oxides (cf. Table 5.2), very likely of primordial origin. Oxygen forms oxides with all elements (with the exception of novel gases), but naturally only those of quartz (SiO2 ), iron oxide (Fe2 O3 ), and alumina (Al2 O3 ) are dominant as different minerals in Earth’s crust. Soluble oxides (from alkali and alkaline earth metals) do not exist naturally. In air, gaseous oxides of sulfur, nitrogen, and carbon play an important role, whereas oxides of halogens are in trace amounts only but important in atmospheric ozone chemistry. As shown in Table 5.3, oxygen is bound in oxoacids from which the − stable and environmentally important anions sulfate (SO2− 4 ), nitrate (NO3 ), carbonate 3− 2− (CO3 ), and phosphate (PO4 ) are derived. Nitrates and phosphates are a result of microbiological activities. Carbonates and sulfates (as calcium) are sediments; however, almost all sulfate is found dissolved in seawater. Oxygen forms the environmentally important carboxylic acids (Table 5.3) and is within oxygenated hydrocarbons (alcohols, aldehydes, and ketones). In air, apart from molecular oxygen (O2 ), ozone (O3 ) and hydrogen peroxide (H2 O2 ), atomic oxygen (O) exists in very small traces only intermediary. Under natural conditions (i.e., preindustrial times), O3 is produced only in the stratosphere and transported down to Earth’s surface. Modeling has shown that about 2000 Mt O3 is yearly transported from the stratosphere into the troposphere, most of it destroyed in the free troposphere. Hence, O3 concentration increases with altitude and preindustrial surface O3 mixing ratios were around 10 ppb and less. At present, human activity results in the additional yearly formation of about 2000 Mt O3 in the troposphere and the near-surface O3 concentration has risen to 30–40 ppb. H2 O2 forms in air through radicals, which originate after O3 photolysis in subsequent reactions and photocatalytically from O2 at the interface.

5.2.2 Oxygen, dioxygen, and ozone: O, O2 , and O3 Molecular oxygen (O2 ) cannot be photochemically destroyed in the troposphere because of a lack of short wavelengths (see subsequent discussion and Chapter 5.2.7 on stratospheric chemistry). The main fate of O2 in the troposphere is to bond to radicals (X) to produce peroxo radicals (see reaction (5.1) and subsequent discussion), an important step in the oxidation of trace gases: X + O2 → XO2

(X = O, Cl, Br, R, and others) .

(5.7)

The role of singlet dioxygen (1 ∆g and 1 ∑+g ), where two electrons in the outer shell (2p4 ) are in the degenerated π-symmetric orbitals with antipodal spin (total zero spin), is well known in organic chemistry. Singlet dioxygen is a metastable species, and be-

272 | 5 Substances and chemical reactions in the climate system cause of its excitation energy of 94 kJ mol−1 it is chemically extraordinarily reactive. In the gas phase, photoexcitation, which leads to the formation of singlet molecules from triplets, are quantum chemically forbidden. There are several ways to form singlet dioxygen. In the gas phase, the photolysis of ozone produces excited O2 molecules (reaction (5.8c); however, it only occurs in the upper stratosphere): O3 + hν → O(3 P) + O2 (1 Σg )

λthreshold = 611 nm ,

(5.8a)

O3 + hν → O( D) + O2 ( ∆g )

λthreshold = 340 nm ,

(5.8b)

O3 + hν → O(1 D) + O2 (1 Σ+g )

λthreshold = 267 nm .

(5.8c)

1

1

As for many excited molecular states, quenching (collisional deactivation) is the most important fate, k 5.9 = 1.6 ⋅ 10−18 cm3 molecule−1 s−1 (M = O2 ) at 298 K: 1

O2 + M → O2 + M .

(5.9)

Singlet dioxygen is directly produced from triplet dioxygen by collision with so-called photosensitizers A∗ (electronically excited molecules), which transfer energy to O2 in the ground state; the third collision partner M stabilizes the transfer complex: O2 (3 Σ−g ) + A∗ (+M) → O2 (1 Σ+g ) + A(+M) .

(5.10a)

This reaction can occur in air (for example, with excited SO2 ) but is of great importance in condensed phases, especially cells. Once singlet dioxygen forms, it undergoes interconversion reactions: O2 (1 Σ+g ) + A∗ (+M) → O2 (1 ∆+g ) + A(+M) , O2 (1 ∆+g )

+ O2 (1 ∆+g )

→

O2 (1 Σ+g )

+ O2 (3 Σ−g )

(5.10b) .

(5.10c)

1O 2

is probably not important in initiating chemical changes in the lower atmosphere, at least in the gas phase; excited molecules dissolved in water droplets can promote chemical changes under special circumstances. In the stratosphere and mesosphere, each of the bound excited states gives rise to characteristic emission features of the airflow, both by day and at night (Schiff 1970, Wayne 1994). In the past, it was assumed that singlet dioxygen played a role in urban smog chemistry (Pitts 1970). In the troposphere, only the photodissociation of ozone and nitrogen dioxide produces atomic oxygen. The photodissociation of O3 produces several oxygen species including the triplet O (reaction (5.8a)) and the singlet O (reaction (5.8b)); the formation of O(3 P) and O2 in the ground state is already possible at very large wavelengths (Crutzen et al. 1999, Ehhalt 1999): O3 + hν → O(3 P) + O2 (3 Σg )

λthreshold = 1180 nm .

(5.10d)

The different absorption bands are termed Chappuis bands (440–850 nm), Huggins bands (300–360 nm), and Hartley bands (200–310 nm); the strongest absorption occurs at 250 nm. These different absorption bands play a key role in the atmosphere

5.2 Oxygen

| 273

(a) to prevent radiation in the lower atmosphere with wavelengths less than about 300 nm, which destroys life, and (b) to provide O(1 D) from O3 photolysis (reaction (5.8b)), which subsequently forms other ROSs (Chapter 5.2.4). Once O(3 P) is formed, it ultimately combines with oxygen to produce O3 , k 5.11 = 5.6 ⋅ 10−34 [N2 ]cm3 molecule−1 s−1 at 298 K: O(3 P) + O2 + M → O3 + M . (5.11) In all these reactions with molecular oxygen, we can assume a constant O2 concentration of 5.6 ⋅ 1018 molecules cm−3 under standard conditions. Furthermore, taking into account the constant N2 concentration (2.08 ⋅ 1019 molecules cm−3 ), a pseudofirst-order rate constant k 5.11 = 6.4 ⋅ 104 s−1 follows and a lifetime of only 1.5 ⋅ 10−5 s for O(3 P). About 90% of O(1 D) turns by quenching into the triplet oxygen, k 5.12 = 4.4 ⋅ 10−11 cm3 molecule−1 s−1 (M = N2 ) at 298 K: O(1 D) + M → O(3 P) + M .

(5.12)

The only other (and this is one of very few initial reactions producing ROSs) reaction of O(1 D) is with H2 O, which produces OH radicals (reaction (5.16)). There are known faster reactions of singlet oxygen (with N2 O and H2 ), but the water vapor concentration is orders of magnitude greater in the lower atmosphere. Thus, only in the upper atmosphere, where extremely low [H2 O] is found, do these reactions become important (Chapter 5.2.7). Finally, we consider the photodissociation of molecular oxygen: O2 + hν → O(3 P) + O(3 P)

λthreshold = 242 nm ,

(5.13a)

3

1

λthreshold = 175 nm ,

(5.13b)

1

1

λthreshold = 137 nm .

(5.13c)

O2 + hν → O( P) + O( D) O2 + hν → O( D) + O( D)

Reaction (5.13a) refers to the Herzberg continuum (230–280 nm), which consists of three bands. It is clear that O3 formation (reaction (5.11)), as well as O3 photolysis, occurs. Hence, at 30 km (above the peak in the ozone layer), we observe substantial reductions in the amount of radiation received between 225 and 275 nm. The O2 photodissociation in the Schumann–Runge continuum (125–175 nm) directly produces O(1 D) and initiates many radical reactions (but almost all molecules photodissociate under the influence of such hard radiation); this is at altitudes of 100–200 km. The solar H Lyman-α line (121.6 nm) is, through O2 photodissociation, an important source of O(1 D) production throughout the mesosphere and lower thermosphere. The Lyman-α line also dissociates H2 O at altitudes between 80 and 85 km, where the supply of water vapor is maintained by methane oxidation even for very dry conditions at the tropospheric–stratospheric exchange region. An increase in HOx follows and thereby a sharp drop in the ozone concentration near the mesopause (see Chapter 5.2.7 on stratospheric O3 cycles). The ozone concentration rapidly recovers above 85 km owing to the rapid increase in O produced by the photodissociation of

274 | 5 Substances and chemical reactions in the climate system

O2 through the absorption of UV solar radiation in the Schumann–Runge bands and continuum. Above 90 km, there is a decrease in ozone due to photolysis and because the production of ozone through the three-body recombination of O2 and O becomes slower with decreasing pressure. The O2 photodissociation and subsequent O3 formation in the lower stratosphere is the most important source of O3 in the troposphere via the stratosphere– troposphere exchange. The tropospheric net O3 formation is another important source, especially due to anthropogenic enhancement. Figure 5.4 shows all principal oxygen reactions; note that O2 photolysis can be excluded in the climate system in the more narrow sense close to the Earth’s surface. The exit pathways (sinks) to products (Figure 5.4) are only possible if there are additional elements and compounds (Chapter 5.2.3.2). In a pure oxygen gas system, we only consider four reactions, (5.8a), (5.8b), (5.10d), and (5.11), forming a steady state: M

hν

hν

3 󳨀→ O(3 P) ←󳨀 O(1 D) ←󳨀󳨀 O3 󳨀 ← 󳨀󳨀 O( P) . O2

Fig. 5.4: Ox Hy gas-phase chemistry; dotted lines denote photolysis only in the stratosphere; other sources and sinks occur in the presence of species other than Hy Ox .

5.2 Oxygen

| 275

It follows for steady-state concentrations of O(3 P) and O(1 D) that [O3 ] =

k 5.12 [O2 ][O(3 P)] . j5.8a + j5.8b

(5.14)

Besides O3 photolysis (reactions (5.8a) and (5.10d)), there is only one other important O(3 P) source to provide the only net source for O3 formation in the troposphere: NO2 + hν → O(3 P) + NO

λthreshold = 398 nm .

(5.15)

NO3 photodissociation (eq. (5.178b)) also produces O(3 P), but NO3 concentrations are very small compared with those of NO2 . Without discussing it here in detail, O3 has several chemical sinks, where reactions with NO and NO2 are the most important (Chapter 5.3.5.1), but alkenes also react with O3 (Chapter 5.6.7) and heterogeneous loss is important (Chapter 5.2.6.2).

5.2.3 Reactive oxygen species I: OH, HO2 , and H2 O2 (Hx O y species) The OH radical is the most important species in the atmosphere. This is often referred to as the “detergent” of the troposphere because it reacts with many pollutants (specifically VOCs), often acting as the first step in their removal. The effect of radical reactions in the chemistry of air pollution, specifically photochemical smog, was recognized by Leighton (1961). However, it was not recognized before 1970 that sufficient OH is in fact produced in the troposphere via reactions (5.8b) and (5.16). Levy (1971, 1972, 1973) demonstrated on the basis of plausible photochemical reaction mechanisms that radical reactions are important also in the troposphere. The role of OH and HO2 in tropospheric chemistry is highlighted by Warneck (1973), Heicklen (1976), Logan et al. (1981), and Ehhalt (1999); see Lelieveld et al. (2016) and Dusanter and Stevens (2017) for recent advances in chemistry and the distribution of OH and HO2 radicals in the atmosphere. 5.2.3.1 Atmosphere, free of trace species We now extend the chemical system from pure oxygen by adding first H2 O as the second abundant oxygen species in air and will observe the formation of reactive Ox Hy species (Table 5.7). Besides reaction (5.12), O(1 D) reacts in another channel (to about 10%) with H2 O to hydroxyl radicals (OH): O(1 D) + H2 O → 2 OH

k 5.16 = 2.2 ⋅ 10−10 cm3 molecule−1 s−1 at 298 K .

(5.16)

Since hydroxyl OH (this is the neutral form of the hydroxide ion OH− , see reaction (5.111) for example)⁶ is derived from H2 O, it returns to water by abstraction of H 6 To avoid confusing between radical OH and anion OH− , the anion should be referred to only as hydroxide and not hydroxyl (as often found in literature).

276 | 5 Substances and chemical reactions in the climate system Tab. 5.7: All important Hx , Oy , and Hx Oy species; x, y = 1, 2, 3, 4, and 5. Note that ions (which can be specified as anions and cations depending on whether they have a positive or negative charge, respectively) only exist freely in the aqueous phase and in ionic bonds in the solid phase (they also exist in the gas phase under strong radiation); H+ does not exist freely – only aquated. Some species are formed only under extreme conditions or are very short-lived. Systematic names are derived from hydrogen (H), oxygen (O), and oxide (O− ), where the subscripts 1, 2, 3, 4, and 5 denote mono-, di-, tri-, tetr-, and pent- (e.g., H2 O4 = dihydrogentetroxide). Oxidation state −3

Species H2

Formation/destruction

O−

H2 O

Name

+ e−

+ H/OH−

Hydrated electron + H+

−2

H2 O OH− O2− (=O or –O–)

OH H2 O 󴀘󴀯 OH− + H+ OH− 󴀘󴀯 O2− + H+

Water a Hydroxide ion Oxide (2–) i

−1

H− O− O2− 2 (–O–O–) OH H2 O+ HO−2 H2 O2

H − e− OH 󴀘󴀯 O− + H+ O2 + 2 e− H2 O − H H2 O − e− /OH + H+ HO2 + e− HO−2 + H+

Hydride i Oxide (1–) i Peroxide i Hydroxyl radical b Water radical ion Conjugated base of H2 O2 Hydrogen peroxide g

−1/ ± 0

O−2 HO2 O−3 HO3 HO−3 H2 O3 HO−4 H2 O4 H2 O5

O2 + e− O2 + H/O−2 + H+ O3 + e− O−3 + H+ /OH + O2 HO3 + e− HO−3 + H+ O3 + OH− HO2 + HO2 /2 OH + O2 H2 O2 + O3

Superoxide ion c Hydroperoxyl radical d ozonide ion e Hydrogen trioxide f Conjugated base of H2 O3 Trioxidane g Conjugated base of H2 O4 Tetraoxidane g Hydrogen pentoxide g

±0

H O O2 O3

H2 O + hν (H2 O − OH) O2 + hν (O2 − O) O+O O + O2

Hydrogen (atom) Oxygen (atom) Dioxygen Trioxygen (ozone)

+1/2

O+2

O2 − e−

+1 a

+

+

H (H3 O ) O3 H+

Dioxygenyl ion +

−

H2 O + H2 O 󴀘󴀯 H3 O + OH O3 + H+

Proton (hydrogenium) h Protonated ozone

Systematic name: dihydrogen monoxide. Systematic name: hydridooxygen; IUPAC name: oxidanyl. c IUPAC name: dioxide(1–), hyperoxide also termed but not recommended (with the exception in German). d IUPAC name: dioxidanyl, other name: hydroperoxo. e IUPAC name: trioxidane–1–id–3–yl. f Other names: hydrotrioxy radical, hydrogen ozonide. g Systematic names for hydrogen polyoxides can be found in the comment in the table heading; here: dihydrogentrioxide (other name: hydridotrioxygen). h Also oxonium. i Only in compounds or extremely short-lived form. j See Denis (2013); also termed ozone hydrogen peroxide. b

5.2 Oxygen

| 277

from nearly all hydrocarbons RH; this pathway is a definitive sink for OH. However, the organic radical R combines with O2 (reaction type (5.7)) and in many subsequent reactions produces organic oxygen radicals and recycles HO2 (see next Chapter 5.2.3.2): RH

OH 󳨀󳨀󳨀→ H2 O . (−R)

A second important pathway is the addition of OH to different species (SO2 , NO, NO2 ) producing oxoacids: X

→ XOH . OH 󳨀 A third pathway is OH transformation into the hydroperoxyl radical HO2 : O3

OH 󳨀󳨀󳨀󳨀→ HO2 . (−O2 )

HO2 can turn back into OH (with O3 , but later we will see that NO is most important), resulting in the scheme hν (multistep)

O3 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ OH 󴀘󴀯 HO2 → H2 O2 and thereby leading to overall ozone destruction in a clean atmosphere. Later we will see that the presence of other trace gases will enhance O3 destruction in NO x free air. The following two reactions provide recycling between OH and HO2 (they are in a relatively fixed ratio of about 1:100 as OH/HO2 but vary and show different diurnal patterns) and perform the most important ozone destruction in a remote atmosphere. In the presence of other trace gases, more dominant pathways exist, and in NO-containing air, a net formation of O3 rather than destruction occurs, k 5.17 = 7.3 ⋅ 10−14 cm3 molecule−1 s−1 and k 5.18 = 2.0 ⋅ 10−15 cm3 molecule−1 s−1 at 298 K: OH + O3 → HO2 + O2 ,

(5.17)

HO2 + O3 → OH + 2 O2 .

(5.18)

The net result of this reaction sequence is O3 destruction according to 2 O3 → 3 O2 , whereas the radicals cycle OH 󴀘󴀯 HO2 . HO2 produces hydrogen peroxide, H2 O2 : k 5.19a = 1.6⋅10−11 cm3 molecule−1 s−1 and k 5.19b = 5.2⋅10−32 [N2 ]cm3 molecule−1 s−1 (M = N2 ) at 298 K: HO2 + HO2 → H2 O2 + O2 , HO2 + HO2 + M → H2 O2 + M .

(5.19a) (5.19b)

The dimerisation of HO2 proceeds at around 298 K by two channels: one bimolecular and the other termolecular. A cyclic hydrogen bond intermediate ⋅ ⋅ ⋅ H–O–O ⋅ ⋅ ⋅ H–O–O ⋅ ⋅ ⋅ is very likely, which explains the “abnormal” negative dependence on T and the pressure dependence (Atkinson et al. 2004). Enhancement in the presence of H2 O (M = H2 O) was observed; k 5.19c = k 5.19b [1 + 1.4 ⋅ 10−21 [H2 O]

278 | 5 Substances and chemical reactions in the climate system exp(2200/T)]cm3 molecule−1 s−1 , for 1 Vol-% H2 O. It follows that k 5.19c = 1.6k 5.19b at 298 K (an increase of H2 O2 concentration has been observed above cloud layers). HO2 + HO2 + H2 O → H2 O2 + H2 O .

(5.19c)

Again assuming steady states, we can formulate different expressions for the radical concentrations and production rates (taking into account all reactions listed thus far): d[HO2 ] = k 5.17 [OH][O3 ] − k 5.18 [HO2 ][O3 ] − 2k 5.19a [HO2 ]2 . dt

(5.20)

However, an important source term of HO2 is still missing, the reaction between OH and CO (eq. (5.33)): d[OH] =( dt 1+

2

j k5.12 [M] 5.8b k5.16 [H2 O]

+ k 5.18 [HO2 ] − k 5.17 [OH]) [O3 ] ≈

2j5.8b 1+

k5.12 [M] k5.16 [H2 O]

[O3 ] , (5.21)

[OH] ≈

j5.8b ( k 5.17 1 +

2 k5.12 [M] k5.16 [H2 O]

)−

k 5.18 [HO2 ] . k 5.17

(5.22)

Note that [M]/[H2 O] ≥ 100. Hence, OH production is proportional to O3 photolysis with singlet oxygen formation (see also Chapter 4.4.9 in Volume 2). The first term in eq. (5.21) contributes a maximum value of about 107 molecules cm−3 to [OH], whereas the second term suggests that [OH] is about 0.03 ⋅ [HO2 ]. This is remarkably consistent with measurements of OH and HO2 despite the simple expressions and neglecting many other important source and sink terms in the complex OH chemistry, for example, in connection with CO, NO y , and VOCs (see following discussion and Figure 5.4); the ratio [OH]/[HO2 ] does not differ significantly from measured values, where [OH] ≈ (0.005 . . . 0.03) ⋅ [HO2 ] ≈ (3 . . . 8) ⋅ 106 molecules cm−3 as a noon maximum. In the free troposphere (FT), H2 O2 photolysis is regarded as an important radical feedback (Crutzen 1999). The photodissociation of H2 O2 into two OH radicals was first shown by Urey et al. (1929). To complete the Ox Hy chemistry, further reactions should be noted, which are unimportant near the Earth’s surface but become of interest in the FT and upper atmosphere. The photolysis of H2 O2 is very slow and heterogeneous sinks (scavenging by clouds, precipitation, and dry deposition) can be neglected in the upper atmosphere. H2 O2 + hν → 2 OH

λthreshold = 360 nm ,

(5.23a)

H2 O2 + hν → H2 O + O( D)

λthreshold = 359 nm ,

(5.23b)

H2 O2 + hν → H + HO2

λthreshold = 324 nm .

(5.23c)

1

5.2 Oxygen

| 279

It has long been assumed that channel (5.23a) is the only significant primary photochemical pathway at λ > 300 nm. However, the quantum yield is very low, resulting in a slow photodissociation with j on the order of 10−6 to 10−5 s−1 (resulting in a residence time of around a week). More important in the upper atmosphere is the reaction with OH: k 5.24 = 1.7 ⋅ 10−12 cm3 molecule−1 s−1 at 298 K. Reactions (5.24) and (5.19) together represent a net radical sink according to the budget equation OH + HO2 → H2 O + O2 : (5.24) H2 O2 + OH → H2 O + HO2 . Reactions (5.25) and (5.26) play a role only in the stratosphere when there is no significant competition with OH + A; k 5.25 = 1.48 ⋅ 10−12 cm3 molecule−1 s−1 and k 5.26 = 1.1 ⋅ 10−10 cm3 molecule−1 s−1 at 298 K: OH + OH → H2 O + O ,

(5.25)

OH + HO2 → H2 O + O2 .

(5.26)

H2 O is photolyzed in the upper atmosphere (outside the climate system): H2 O + hν → OH + H

λthreshold = 242 nm

(∆R H = 498 KJ mol−1 ) .

(5.27)

However, there is neither loss nor formation of water on Earth since the budget is zero (neglecting possible H2 loss in the upper atmosphere to space through diffusion). The aforementioned gas-phase radical reactions giving H2 O are unimportant in the climate system because of competing reactions between the radicals (H, OH, HO2 ) and other trace gases. However, in the upper atmosphere these reactions occur but are balanced by the back formation of H2 O. Only in a chemical regime with excess hydrogen (such as in space and likely only at an early time of chemical evolution and – of course – in a man-made chemical reactor) is H2 O net produced, establishing thermodynamic equilibrium between H2 , O2 , and H2 O. Unproven but not unlikely are the following reactions, where hydrogen polyoxides (see discussion in Chapter 5.2.5.5 on aqueous chemistry) could be short-lived intermediates of reactions (5.17), (5.26), and (5.19) (see also Table 5.7.): OH + O3 → HO4 → products (HO2 + O2 ) , OH + HO2 → H–O–O–O–H (H2 O3 ) → products (H2 O + O2 ) ,

(5.28) (5.29)

HO2 + HO2 → H–O–O–O–O–H (H2 O4 ) → products (H2 O2 + O2 ) ,

(5.30)

H2 O2 + O3 → H–O–O–O–O–O–H (H2 O5 ) → products (HO2 + OH + O2 ) .

(5.31)

Reaction (5.32) was proposed by McCarthy et al. (2012); see also aqueous chemistry eq. (5.122): OH + O2 󴀘󴀯 HO3 . (5.32)

280 | 5 Substances and chemical reactions in the climate system

5.2.3.2 Atmosphere with trace species Let us now consider the most important reactions of the Ox Hy species (Table 5.7) in air containing other trace gases.⁷ As mentioned, the most important species is the hydroxyl radical OH, which reacts with almost all gases but at very different rates. The decomposition of trace gases is not the aim of the discussion here, but rather we will consider the role of other molecules in odd oxygen recycling. By odd oxygen we mean the sum of all ROSs: O3 , OH, HO, H2 O2 , NO2 (later NO3 and N2 O5 will be added); in the aqueous phase, more species must be added (Table 5.7 and Chapter 5.2.5). The simplest example of radical recycling is given by atmospheric oxidation of carbon monoxide (there are no other important CO reactions in air); k 5.33 = 2.2 ⋅ 10−13 cm3 molecule−1 s−1 at 298 K: OH + CO → H + CO2 ,

(5.33)

or as gross reaction OH + CO + O2 → HO2 + CO2 due to the rapid combination of H with O2 to HO2 (reaction (5.1)). Reaction (5.33) is the only known OH splitting reaction. The mechanism proceeds via an additive intermediate: OH + CO 󴀘󴀯 HOCO → H + OCO . Because reaction (5.33) is faster than OH + O3 (5.17), ozone decay is enhanced (reaction (5.18) becomes relatively more important) in the presence of carbon monoxide, an almost abundant gas. This statement is only virtually in contradiction with the experience that biomass burning leads to O3 formation because CO (and organic compounds, as we will see later) in the presence of NOx results in net ozone formation. In competition with reaction (5.18), HO2 turns back to OH, whereas NO is oxidized, k 5.34 = 8.8 ⋅ 10−12 cm3 molecule−1 s−1 at 298 K: HO2 + NO → OH + NO2 .

(5.34)

NO is also quickly oxidized by ozone to NO2 , k 5.35 = 1.8 ⋅ 10−14 cm3 molecule−1 s−1 at 298 K: (5.35) O3 + NO → O2 + NO2 . These two reactions, together with reaction (5.15), show the role of NO x in oxygen chemistry, OH–HO2 recycling, and the net formation of O3 (Figure 5.5). There are two cycles, OH ↔ HO2 and NO ↔ NO2 , which are interlinked, consuming so-called

7 A complete description of radical reactions with the citation of original sources can be found in Leighton (1961). Many radicals have been proposed since the study of atomic reactions in combustion and explosive processes starting around 1925, but fast kinetic observations and intermediate detection became possible only in the 1940s with spectroscopic techniques. The stimulus for radical reactions was the recognition of photochemical air pollution in Los Angeles toward the late 1940s. The scientific literature in the early 1950s contains many studies on this topic.

5.2 Oxygen

|

281

RO CO, CH4, RH

OH

NO2 hν

products

O3

O3

HO2

NO

RO2 Fig. 5.5: Gas-phase net O3 production: HOx , ROx cycle, and NOx cycle; dotted lines denote competitive reaction HO2 + O3 and NO + O3 (for large NOx ).

ozone precursors (CO, CH4 , RH) and producing O3 . However, reactions (5.35), (5.17), and (5.18) are in competition with O3 , replacing the other trace species (dotted lines in Figure 5.5), which results in a net decay of ozone. Both cycles are interrupted when R5.18 ≫ R5.34 , which is given for a few tenths of 1 ppb NO: [NO] ≪

k 5.18 [O3 ] ≈ 10−2 [O3 ] . k 5.34

This concentration is the threshold between the ozone-depleting chemical regimes (in very remote air) and ozone-producing regimes (in NO x -enriched air). Another important reaction of the HO2 radical (with the exception of H2 O2 formation via reaction (5.19)) in NO-poor air is that with organic peroxy radicals gaining organic peroxides (eq. (5.56)). It also follows that H2 O2 formation is favored (and vice versa) in low-NO x and low-O3 environments, which are relatively restrictive conditions. As mentioned at the beginning of Chapter 5.2.3.1, OH can be lost by several reactions. The first type is the abstraction of H and forming reactive intermediates without recycling radicals (but possible further radical consumption in subsequent reactions to the final oxidation product), HA = NH3 , HNO2 , H2 S: HA

multistep

OH 󳨀󳨀󳨀󳨀󳨀→ A 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ products (e.g.NO, NO2 , SO2 ) . (−H2 O)

(5.36)

Another type of reaction is the addition of OH with the possible photolytic decomposition of the product back to OH but in competition with other pathways of HOB; B = NO, NO2 , and others, HOB = HNO2 , HNO3 , and others: hν

OH + B → HOB 󳨀󳨀→ OH + B .

(5.37)

282 | 5 Substances and chemical reactions in the climate system

The addition of OH to molecules gaining intermediate adducts with and without further radical recycling is possible; for example, D = SO2 : multistep

OH + D → HOD 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ products .

(5.38)

Most important are the reactions between OH and organic compounds where the first step also leads to H abstraction in accordance with reaction (5.36) but in subsequent steps to the formation of HO2 and other radicals, thereby continuing the radical chain: O2 (multistep)

OH + RH 󳨀󳨀󳨀󳨀󳨀→ R 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HO2 + products . (−H2 O)

(5.39)

Let us now consider in more detail reaction (5.39), beginning with the most simple but also most abundant hydrocarbon, methane CH4 . Reaction (5.40) is very slow (k 5.40 = 6.4 ⋅ 10−15 cm3 molecule−1 s−1 at 298 K), giving a residence time of about 10 years: OH + CH4 → H2 O + CH3 .

(5.40)

A low specific rate (large residence time), however, does not mean that this pathway is unimportant. On the contrary, because of the high CH4 concentration in air, nearly homogeneously distributed over the whole troposphere (Chapter 4.4.4 in Volume 2), CH4 controls to a large extent the background OH concentration and tropospheric net O3 formation. The methyl radical CH3 rapidly reacts with O2 , producing the methyl peroxy radical, k 5.41 = 1.2 ⋅ 10−12 cm3 molecule−1 s−1 at 298 K: CH3 + O2 → CH3 O2 .

(5.41)

Similar to HO2 (reaction (5.34)), CH3 O2 oxidizes NO; hence, we see that the first HOx radical cycle in Figure 5.5 overlaps with another RO x cycle, turning two molecules NO into NO2 per molecule of RH, k 5.42 = 7.7 ⋅ 10−12 cm3 molecule−1 s−1 at 298 K: CH3 O2 + NO → CH3 O + NO2 .

(5.42)

There are some (slow) competing reactions with eq. (5.42), which we will discuss in Chapter 5.2.4. But when the methoxy radical CH3 O is produced, reaction (5.43) rapidly proceeds and yields formaldehyde (HCHO) and HO2 , closing the HOy cycle, k 5.43 = 1.9 ⋅ 10−15 cm3 molecule−1 s−1 at 298 K: CH3 O + O2 → HCHO + HO2 .

(5.43)

Formaldehyde is the first intermediate in the CH4 oxidation chain with a lifetime longer than a few seconds. Formaldehyde is removed by photolysis (5.44) and also reacts with OH (5.45), k 5.45 = 8.5 ⋅ 10−12 cm3 molecule−1 s−1 at 298 K: HCHO + hν → H + HCO ,

(5.44)

HCHO + OH → H2 O + HCO .

(5.45)

5.2 Oxygen

| 283

The formyl radical HCO reacts rapidly with O2 (HCO is a carbon and not oxygen radical): (5.46) HCO + O2 → CO + HO2 . We see that methane oxidation results in a net gain of HO2 radicals, depending on the state of oxidation (HCHO, CO, and CO2 ): NO (multistep)

CH4 + OH + O2 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HCHO + HO2 + H2 O , (−NO2 )

NO (multistep)

CH4 + OH + 3 O2 + hν 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CO + 3 HO2 + H2 O , (−NO2 )

NO (multistep)

CH4 + 2 OH + 2 O2 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CO + 2 HO2 + 2 H2 O , (−NO2 )

NO (multistep)

CH4 + 2 OH + 3 O2 + hν 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CO2 + 4 HO2 + H2 O . (−NO2 )

(5.47) (5.48a) (5.48b) (5.48c)

The highest yield of HO2 is gained when HCHO is photolyzed (5.48a) instead of being oxidized by OH (5.48b and 5.48c). The gross budget of final CO oxidation into CO2 is CO + OH + O2 → CO2 + HO2 .

(5.49)

In the reaction chains (5.47) and (5.48) NO is turned into NO2 , which photolyzed with O3 formation according to NO2 + O2 + hν → NO + O3

(5.50)

and closing the NO 󴀗󴀰 NO2 cycle. Additional, HO2 in reactions (5.47) to (5.49) – note that only the pathway including HCHO photolysis (eq. (5.48a)) gains excess HO2 over OH – will ultimately in the presence of NO result in net O3 formation according to the gross reaction (5.51) HO2 + O2 + hν → OH + O3 . Therefore, adding all reactions in the conversion CH4 → CO (remember that after the initial step OH + CH4 all subsequent reactions are much faster) we obtain CH4 + 8 O2 + 4 hν → CO2 + 2 H2 O + 4 O3 .

(5.52)

Equation (5.52) represents the maximum yield of ozone from CH4 oxidation. No radical loss occurs due to radical chains and recycling. However, CH4 drops the radical concentration to lower values compared with an atmosphere without trace gases (Chapter 5.2.3.1). Definitive OH sinks are given by reactions of equation types (5.36) to (5.39); see sulfur and nitrogen chemistry later. The “perfect” ozone formation cycle (Figure 5.5) is based on the odd oxygen cycling shown in Figure 5.6. Not shown in Figure 5.6 are the O3 precursors (CO, CH4 , and RH), which maintain the OH ↔ HO2 cycle without consuming O3 . Because of the very slow photolysis, H2 O2 does not maintain the odd oxygen cycle; its formation already interrupts this cycle. Moreover, many competitive reactions (denoted by the dotted arrows in Figure 5.8) reduce net ozone formation.

284 | 5 Substances and chemical reactions in the climate system

O2

O3

O(3P)

NO

products

hν

O(1D)

OH

NO2

H2O

NO

HO2

H2O2 Fig. 5.6: Cycle of odd oxygen; dotted lines denote competitive reactions (not shown).

5.2.4 Reactive oxygen species II: RO, RO2 , and ROOH In reactions (5.41) and (5.42) over the CH4 oxidation chain we have already encountered RO and RO2 , the organic homologs to OH and HO2 radicals (Table 5.7). Any hydrocarbon can react analogously to CH4 ; we use the formula RCH3 (also in terms of RH): (5.53) RCH3 (RH) + OH → RCH2 (R) + H2 O . The fate of the alkyl radical R is to combine with O2 to form the alkyl peroxy radical RO2 (R–O–O∙ )⁸: RCH2 (R) + O2 → RCH2 O2 (RO2 ) . (5.54) Similar to HO2 , RO2 oxidizes NO to NO2 to form the alkoxyl radical R–O∙ : RCH2 O2 (RO2 ) + NO → RCH2 O(RO) + NO2 .

(5.55)

A number of reactions compete with reaction (5.55), mostly with other peroxy radicals. Reaction with HO2 leads to organic peroxides; the simplest is methylhydroperoxide CH3 OOH: RCH2 O2 (RO2 ) + HO2 → RCH2 OOH(ROOH) + O2 . (5.56)

8 See also Dibble and Chai (2017) for a critical review of the atmospheric chemistry of the alkoxy radical and Jackson and Hewitt (1999) for H2 O2 and organic peroxides.

5.2 Oxygen

| 285

Two alkyl peroxy radicals combine to give an alcohol and aldehyde: RCH2 O2 + RCH2 O2 → RCH2 OH + RCHO + O2 .

(5.57)

However, it should be noted that [NO] ≫ [HO2 ] > [RO2 ] when discussing the percentages of different pathways. Organic peroxides (the most important are CH3 OOH and C2 H5 OOH) are permanently found in air besides H2 O2 but in smaller concentrations. The alkoxyl radical gained in reaction (5.55) reacts with a comparable rate as in reaction (5.54) on the order of 10−11 to 10−12 cm3 molecule−1 s−1 giving an aldehyde and recycling HO2 : (5.58) RCH2 O(RO) + O2 → RCHO + HO2 . Aldehydes are very reactive substances. They react with OH by H abstraction (almost from the chain) to produce finally bicarbonyls, for example, dialdehydes and ketoaldehydes (the carbonyl group is denoted by >C=O). Nevertheless, more important is the photolysis of aldehydes and ketones that initiates radical chains. We have seen that the simplest aldehyde HCHO is photolyzed (reaction (5.44)) gaining H (which turns into HO2 ) and the formyl radical HCO, which further reacts with O2 to HO2 and CO (eq. (5.46)). Therefore, HCHO is an efficient radical source. In analogy, higher aldehydes photolyze and produce H atoms and acyl radicals RCO (R–C∙ =O), for example, acetyl CH3 CO. These radicals do not decompose like the formyl radical HCO, but add O2 , thereby giving a acyl peroxy radical R–C(=O)OO (eq. (5.60)), which is a precursor to peroxyacyl nitrates (PAN) (eq. (5.277)): RCHO + hν → RCO + H ,

(5.59)

RCO + O2 → RC(O)OO .

(5.60)

This acyl peroxy radical reacts in analogy to the RO2 radical, thereby oxidizing NO and giving an acyloxy radical (RC(O)O), further reacting with HO2 and forming acyl peroxide or adding NO x (Chapter 5.3.6.2): RC(O)OO + NO → RC(O)O + NO2 .

(5.61)

The acyl peroxy radical RC(O)O finally converts by reacting with HO2 to carboxylic acid (RCOOH) (Figure 5.7). Many of these species are radical reservoirs (especially peroxides but also nitro and nitroso compounds), which can be transported away from polluted areas and release radicals after photolysis, starting new radical chains, oxidizing trace species, and decomposing O3 . Acyl radicals are also given by the photolysis of ketones: RC(O)R + hν → RCO + R .

(5.62)

For HO2 recycling, the photolysis of olefins (R=R) and aldehydes (RCHO) is very important. Aldehydes produce a variety of primary radicals (HCO, RCO, and H) that retransform in multisteps back to HO2 (and to OH, see Figure 5.8). As we will see now,

286 | 5 Substances and chemical reactions in the climate system

OH

RH

O2

R

HO2

RO2

ROOH

NO (-NO2) h (-OH)

RO

h

O2

(-CO2)

O3

RCHO

R=R

RC(O)O2NO2

OH, h (-H)

NO2

h (-HCO) O2

RCO

RC(O)O2

h h

NO (-NO2) HO2

RCOOH

RC(O)R

RC(O)O

Fig. 5.7: Organic radical chemistry and fate of characteristic organic groups. RH hydrocarbon, R organic radical, RO2 organic peroxy radical, ROOH organic peroxide, RO organic oxy radical, RCHO aldehyde, RCOOH carboxylic acid, RC(O)R ketone, R=R olefin. Reactions between RO or RO2 and NO or NO2 are not included in this scheme.

O3

NO-NO2 / O3-O2 hν+H2O -O2

O3-O2

OH

CO-CO2

H2O2 HO2

O2

H

hν

SO2+O2+H2O -H2SO4

HO2

hν

HNOx

NOx

RCH3+O2

RCH2O2

hν-RCO

RCHO

NO-NO2

RCH2OOH

hν

O2

RCH2O

Fig. 5.8: Ox Hy gas-phase chemistry including all relevant trace gases (cf. Figure 5.4).

5.2 Oxygen

|

287

primarily low reactive hydrocarbons (RH), after initial oxidation by OH, produce a variety of more reactive intermediates that amplify net ozone formation (Figure 5.5). All organic oxy and peroxy radicals can also add NO and NO2 and form organic nitroso (–N=O) and nitro (–NO2 ) compounds (Chapter 5.3.6). These compounds provide a radical reservoir and can be photolyzed back to the original compounds.

5.2.5 Aqueous-phase oxygen chemistry Water (H2 O) is the most abundant molecule in space and was brough to Earth from space (i.e., not produced on Earth; for details see Volume 2). Liquid water (the aqueous phase) provides the fundaments of life. In Chapter 3.4, we discussed the unique physical and chemical properties of water. Table 3.4 shows data that explain its chemical stability. However, H2 O is chemically reactive, and Figure 5.9 and reaction (4.113) show the central role of H2 O in (biogeo-)chemical cycling between oxygen (O2 ), carbon dioxide (CO2 ), and hydrocarbons (C x Hy ). The water-splitting process proceeds in nature only in plants under the influence of light and enzymes. It is a model for future “green” or “sustainable” chemistry. Water provides fundamental species such as H+ and OH− (Chapter 4.4.1.1) and the hydrated electron H2 O− (Chapter 4.4.3). In our climate system, reaction (5.16) is the only natural gas-phase decomposition reaction of H2 O (1 O + H2 O → 2 OH), which is of crucial importance for follow-up radical production. The only natural source of singlet oxygen radicals is ozone photolysis (reaction (5.8b)), and the only significant source of ozone (under preindustrial conditions)⁹ is oxygen photolysis in the upper atmosphere. Hence, gas-phase chemistry is based on very few initializing reactions. Nevertheless the large chemical stability, we have seen that H2 O is chemically decomposed (reaction (5.16); see below for more examples) and

CO2

H

H2O

CH4

O

Fig. 5.9: Water-splitting process.

9 In the anthropogenic polluted atmosphere (and under certain limited natural sites were NO2 and organic compounds are available), ozone is also originated in the lower troposphere (see Chapter 5.2.3.2).

288 | 5 Substances and chemical reactions in the climate system

produced in many reactions (5.2c), (5.3), (5.23b), (5.24) to (5.26), (5.40), (5.45), (5.47) to (5.50), (5.52), and (5.53). However, it will not change the H2 O mixing ratio in a measurable amount and holds a steady state: H2 O (+O2 ) 󴀘󴀯 Hx Oy (+Ox ) . Reactive oxygen species (O3 , OH, HO2 , and H2 O2 ) produced in this way might enter the aqueous phase (surface water, cloud, fog, and rain droplets) and undergo further reactions. In the aqueous phase, however, many more pathways exist, which makes aqueous-phase oxygen chemistry essential for the climate system. H2 O2 and HO2 are readily soluble, and OH also shows significant solubility. Despite the low solubility of O2 , its large aqueous-phase concentration compared with that of trace species favors the recombination of many radicals with O2 such as in gaseous air. The solubility of O3 is low, but we have to consider that the uptake is not limited by dissolution but through mass transfer resulting from aqueous-phase reactions (Chapter 3.6.5.4). In natural surface waters, however, the scavenging of oxo radicals from air is very limited because of the diffusion-controlled uptake and its short lifetime in air. The absorption of O2 and O3 with subsequent light-induced radical formation is dominant (photosensitization, see Chapter 4.5.3). Hence it is likely that interfacial or surface water formation of hydrogen peroxide is more evident than gasphase production and absorption (Möller 2009a). For plants, however, uptake (dry deposition) of H2 O2 might have an important effect on their health, resulting in oxidative stress as described by Möller (1988, 1989). Table 5.8 shows the main oxygen chemistry in biological systems (enzymatic processes) but also occurring in abiotic environments (catalytic processes). Tab. 5.8: Basic Hx Oy reactions in aqueous phase. Catalase Fenton reaction dismutase Enzymatic reduction Deactivation Ozone decay

2 H2 O2 H2 O2 (+ FeII ) HO2 + O−2 (+ H+ ) O2 (+ e− ) O−2 (+ FeIII ) O3 + O−2 (+ H+ )

→ → → → → →

2 H2 O + O2 OH + OH− (+FeIII ) H2 O2 + O2 O−2 O2 (+FeII ) OH + 2 O2

Figure 5.10 shows that in water, under light influence (photosensitization) and in contact with air, all oxygen species listed in Table 5.7 can be produced. It can also clearly be seen that the presence of dioxygen (O2 ) and ozone (O3 ) opens up competing pathways for obtaining peroxo species. Principally, almost all gas-phase reactions also take place in the aqueous phase. Moreover, many additional reactions, not occurring in the gas phase, have to be considered in solution.

5.2 Oxygen

| 289

e-

H2O:

H-O(-)-H

H-O-H

(-OH-)

H O2

e-

O2:

H+

e-

-

O-O

O-O

H+ -

H-O-O

H-O-O

H-O-O-H e-

(-O2)

HO4-

H-O-O(-)-H

OH-

O3:

O-O-O

e-

O-O-O-

(-OH-)

(-O2)

O-

H+

H-O

H+

HO3

(-O2)

e−

H+

Fig. 5.10: Water, oxygen, and ozone redox chemistry (←→), including acid–base equilibria (←󳨀 →). The fate of OH is normally oxidation of other species (e.g., hydrocarbons) and the fate of H2 O2 is normally S(IV) oxidation. Note that some electron transfers are nonreversible.

Due to the fact that, in solution, concentrations of many chemical species are enlarged compared to the gas phase, the total rate of chemical conversion increases, making aqueous-phase chemistry very important in the environment. The formation of aquated electrons (Chapter 4.4.3) via photosensitization (Chapter 4.5.3) is obviously a natural process, yielding ROSs such as hydroperoxyl radical (HO2 ), hydrogen peroxide (H2 O2 ), and the hydroxyl radical (OH) via oxygen and ozone: e−

H+

e−

H+

e−

O2 󳨀󳨀→ O−2 󳨀󳨀→ HO2 󳨀󳨀→ HO−2 󳨀󳨀→ H2 O2 󳨀󳨀󳨀󳨀󳨀−→ OH , (−OH )

e−

H2 O

O3 󳨀󳨀→ O−3 󳨀󳨀󳨀󳨀→ O− 󳨀󳨀󳨀󳨀󳨀−→ OH . (−O2 )

(−OH )

5.2.5.1 Water chemistry Liquid water dissociates to a small percentage (0.00000556% – 1 L water contains 55.6 mol H2 O and produces 10−7 mol L−1 H+ ; see also Chapter 4.4.1.1): H2 O 󴀘󴀯 OH− + H+

or

H2 O + H2 O 󴀘󴀯 OH− + H3 O+ .

(5.63)

290 | 5 Substances and chemical reactions in the climate system The hydroxide ion OH− is the strongest known base in water and a one-electron donor according to OH− + X → OH + X− . For simplification, we disregard that H+ + H2 O → H3 O+ (it is conventional to use the symbol H+ ). In Chapter 4.4.3, we cited the wellknown H2 O decomposition by metallic Na. This reaction is the reason that alkali and earth alkali metals do not exist in elemental form on Earth. It is likely that at the beginning of the Earth’s chemical evolution metal hydrides such as NaH existed, produced by solar chemistry (such as metal nitrides). By contrast, the hydride ion H− does not exist freely. Let us assume its existence is short-lived and transient: H2 O

NaH(s) 󳨀󳨀󳨀→ Na+ + H− , −

+

H + H → H2 (g)

(5.64)

−

−

H + H2 O → H2 (g) + OH .

or

(5.65)

Therefore, the budget equation is NaH(s)+ H2 O → H2 (g)+ Na+ + OH− . Sodium and calcium are abundant elements, and at the beginning of chemical evolution, their most abundant forms were oxides: Na2 O and CaO. Oxygen in oxides is similar to the hydride ion that is nonexistent in aqueous solution, but let us again assume it existed as a short-lived transient anion O2− . Hence, the overall reactions were (see also eq. (4.143) Na2 O(s) + H2 O → 2 Na+ + 2 OH−

and

CaO(s) + H2 O → Ca2+ + 2 OH− ,

and

CaO(s) 󳨀󳨀󳨀→ Ca2+ + O2−

(5.66a)

which would proceed via H2 O

Na2 O(s) 󳨀󳨀󳨀→ 2 Na+ + O2−

H2 O

(5.66b)

and O2− + H+ → OH−

or

O2− + H2 O → 2 OH− .

(5.67)

According to the preceding reaction, OH− would be the corresponding weakest acid and, as a consequence, the hypothetical ion O2− would be the strongest base. However, reaction (5.67) is not an equilibrium and because of 2 H2 O 󴀘󴀯 OH− + H3 O+ , OH− is the strongest existing base and H3 O+ the strongest acid. All these reactions can produce alkalinity from water in accordance with the budget reaction e−

H2 O 󳨀󳨀→ H2 O− → H + OH− .

(5.68)

In the early state of the climate system, huge amounts of carbon dioxide (CO2 ) were found in the atmosphere as well as in the Earth because of degassing processes. This CO2 would react with alkaline aqueous solution (cf. with reaction (4.80)) in the sequence

CO2 (g)

CO2 (g) + OH− → HCO−3 ,

(5.69)

HCO−3 + CO2− 3

(5.70)

−

+ OH →

CO2− 3

+ H2 O 󴀘󴀯

2 HCO−3

+ H2 O , .

(5.71)

5.2 Oxygen

| 291

In this way, from solid hydrides and oxides together with water and atmospheric CO2 , in an early Earth, the initial composition of oceans can be explained as follows: CO2

H2 O

NaH(s) 󳨀󳨀󳨀󳨀→ Na+ + OH− 󳨀󳨀󳨀→ Na+ + HCO−3 , (−H2 ) H2 O

CO2

Na2 O(s) 󳨀󳨀󳨀→ 2 Na+ + 2 OH− 󳨀󳨀󳨀󳨀󳨀→ 2 Na+ + CO2− 3 . (−H2 O)

This inorganically produced carbonate could have provided the first feedstock for photosynthesis in water. Moreover, acid deposition (HCl and SO2 from volcanic exhalations) was buffered by bicarbonate in the early oceans: HCO−3 + SO2 (g) → CO2 + HSO−3 , HCO−3 + HCl(g) → H2 CO3 + Cl− 󴀘󴀯 H2 O + CO2 + Cl− . In all the foregoing reactions, we see that the two fundamental species of water, the ions H+ and OH− , act as reactive species. Their concentrations in neutral water (10−7 mol L−1 ) correspond to an order of magnitude in the ppm range, thereby by a factor of 103 larger than the comparable gas-phase concentrations of trace gases. This is one reason why aqueous-phase chemistry in air (clouds, fog, and precipitation) is so important for the quantification of air/volume-based total chemical conversion. Figure 5.11 shows most of the important oxygen species and reactions in water. The small box with the continuous line contains the chemical regime reduced in oxygen-free water. Because in natural waters oxygen is always dissolved, ROSs such as peroxides are produced and destroyed in waters under the influence of light (larger dotted box in Figure 5.11). But besides hydrogen (H+ ) and hydroxide ion (OH− ) another fundamental species of aqueous solutions exists, the hydrated electron e−aq (Chapter 4.4.3). For natural waters and hydrometeors, reaction (4.125a) is the key formation process of hydrated electrons, which reacts subsequently with dissolved oxygen: hν

aq

O2

W 󳨀󳨀→ W+ + e− 󳨀󳨀→ e−aq 󳨀󳨀→ O−2 . However, little is known about the rate of formation of superoxides in natural aqueous solution. It is clear that different photosensitizers (and mixtures of them) provide a large variety of photocatalytic oxygen activation. The formation of hydrated electrons can explain many processes such as autoxidation and corrosion (Chapter 4.5.3). It is clearly seen in Figure 5.11 that oxygen water chemistry is enhanced in the presence of O2 and O3 via parallel inputs of reactants. In the presence of oxygen, similar to the gas-phase reaction (5.1), a fast recombination of H with O2 follows: k 5.72 ≈ 2 ⋅ 1010 L mol−1 s−1 (Bielski et al. 1985): H + O2 → HO2 .

(5.72)

Reaction (5.72) occurs in an acid solution, whereas e−aq + O2 → O−2 (reaction (5.79)) proceeds in neutral and alkaline solutions.

292 | 5 Substances and chemical reactions in the climate system

H2O- ( e-aq ) e-

H2O (-OH-)

H+

OH-

e-

O2

O

e-

eH+

H

OH

O-

e-

(-OH-)

(-O2)

e-

H+

O2-

O3

O2

HO2

H+

H2O2-

e-

HO3

O3-

e-

HO2-

H2O2

H+

H2O2 (-O2)

O3 OHH+

H2O4

HO4-

Fig. 5.11: Aqueous-phase oxygen chemistry; HO3 , HO−4 , and H2 O4 short-lived intermediates. The box contains the oxygen-free water chemistry under radiolysis/radiation influence and the dotted box shows oxygen-containing water. e− electron donor; note that some pathways strongly depend on pH, i.e., whether the reactions occurs in alkaline or acid solution. The circle box represents a strong alkaline regime (pH > 10).

Water radiolysis is a well-established field of study just starting after the discovery of radioactive radiation (radium emanation). Without knowing the transient processes, the generic reaction equation radiation

2 H2 O 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ H2 O2 + H2

(5.73)

was established by Kernbaum (1909) during an investigation of the influence of β radiation (from RaCl2 ) on pure water (see Volume 2 for more historical details on H2 O2 formation). Haïssinsky and Magat (1951) first studied water radiolysis products such

5.2 Oxygen

|

293

as H, OH, and O− and proposed reaction (5.74). Reaction (5.75) was then confirmed years later: H2 O + γ → H2 O+ + e− −

e + n H2 O → +

(H2 O)−n +

λthreshold = 195 nm ,

,

H2 O → H + OH .

(5.74) (5.75) (5.76)

Hydrogen and hydrogen peroxide formation proceeds subsequently via H+ + e− → H (2 H → H2 ) and OH + OH → H2 O2 . Furthermore, H2 O2 again dissociates by radiation. Obviously, X-rays do not produce H2 O+ , and without O2 there is no peroxide (O−2 ) formation; for historic overviews on radiation chemistry and inorganic free radicals in solutions see Uri (1952), Hart (1959), Allen (1961), and Zimbrick (2002). Reaction (5.74) requires 8.8 eV of ionization energy and cannot occur under natural conditions in the climate system (Pozdnyakov et al. 2000). Alkaline solutions produce OH under UV irradiation and electrons (which in a subsequent step fix in finite-sized water clusters according to reaction (5.75)); however, in our climate system there is no liquid water where radiation smaller than 195 nm exists (cf. eq. (5.74): OH− + hν → OH + e− .

(5.77)

However, OH 󴀗󴀰 OH− interchange occurs via electron transfer in the aqueous phase (reactions (5.81), (5.108) and (5.111)). 5.2.5.2 Dioxygen and superoxide ion chemistry Singlet oxygen can be formed chemically, enzymatically, and photochemically. In the aqueous phase, specifically cells of organisms, singlet dioxygen (which is known to be cytotoxic) is produced photobiologically using organic dye as a sensitizer (eq. (5.10)) in identical reactions such as in the gas phase. Additionally, singlet dioxygen can be produced chemically in the aqueous phase: H2 O2 + OCl− → 1 O2 + H2 O + Cl− .

(5.78)

Hypochlorite plays a minor role in the atmosphere (Chapter 5.7.4), but hydrogen peroxide is ubiquitous in all natural systems, and hypochlorite is enzymatically produced in cells. Other chemical pathways in water include (Krinsky 1977) H2 O2 + O−2 → 1 O2 + OH + OH− H2 O2 + HO−2 → 1 O2 + H2 O + OH− OH + O−2 → 1 O2 + OH− The reaction of ozone with a number of biological molecules (cysteine, methionine, glutathione, albumin, uric acid, ascorbic acid) was found to produce singlet dioxygen in high yield (Kanofsky and Simal 1991). Thus, singlet dioxygen may be an important intermediate in the biochemical damage caused by ozone.

294 | 5 Substances and chemical reactions in the climate system

The atmospheric aqueous phase is a rich medium for chemical transformations of organic compounds, in part via photooxidants generated in droplets; the generation of 1 O2 is observed in all natural waters (Faust and Allen 1992, Kaur and Anastasio 2017). An important oxidant is the superoxide ion O−2 , which is gained via photosensitization (eq. (4.125a)); the reduction potential of the donor must be smaller than −0.33 V in neutral solution or −0.125 V in acid solution (Figure 5.13): O2 + e− → O−2 .

(5.79)

The limiting step (in terms of reduction potentials) (Figure 5.12) is the electron transfer to O2 from the photosensitizer. This means that an electron source adequate for the reduction of O2 will produce all the other reduced forms of oxygen (O−2 , HO2 , HOOH, HO−2 , OH) via reduction, hydrolysis (or proteolysis), and disproportionation steps (Figure 5.14). Thus, the most direct means to activate O2 is the addition of an electron (or hydrogen atom), which results in significant fluxes of several ROSs. The idea that an electron transfer to oxygen occurs was first proposed by Evans and Uri (1949) and was accepted by Leighton (1961) as a mechanism likely to be important e−

for PM: O2 (ads) 󳨀󳨀→ O−2 (ads). The superoxide anion O−2 (O–O− ) is the protolytic dissociation product of the weak acid (pKa = 4.9) hydrogen dioxide HO2 (hydroperoxyl radical). The name “superoxide” was first proposed by Neuman (1934) and Pauling (1979) for the potassium salt KO2 (during the burning of K in O2 ) but first detected as an ion in electrochemical investigations (Sawyer and Roberts 1966) and found to be a respiratory intermediate in aerobic organisms (Knowles et al. 1969). Surveys on superoxide chemistry include those by Sawyer and Gibian (1979), Sawyer (1991), and Hayyan et al. (2016). The su− − peroxide anion should not be confused with the peroxide dianion O2− 2 ( O–O ), which − is derived from peroxide but does not exist freely in aqueous solution. O2 is dominant in cloud and rainwater because of pH values normally around 4.5 (pK = 4.8) (Bielski et al. 1985): HO2 󴀘󴀯 H+ + O−2 . (5.80) The uptake of HO2 from air (Schwartz 1984) is an important source of O−2 besides photocatalytic formation. Only under acidic conditions (soils and cloud droplets) is the unprotonated HO2 dominant. Its main role is to carry and transfer electrons: reduction

H+

oxidation

󳨀󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀→ H2 O2 ←󳨀󳨀󳨀󳨀󳨀󳨀󳨀 HO2 ←󳨀→ O−2 ← 󳨀󳨀 O2 . It should be considered that almost all gas-phase reactions described in Chapter 5.2.3 also occur in aqueous solutions, for example, H2 O2 photolysis to OH radicals (5.23a) as first described by Urey et al. (1929); λthreshold < 379 nm. Another spontaneous radical formation in alkaline solution was proposed (Schroeter 1963, Walling 1957): O2 + OH− 󴀘󴀯 O−2 + OH .

(5.81)

5.2 Oxygen

-0.125

O2

1.51

HO2

0.714

H2O2

|

295

2.813

H2O + OH

0.695

2 H2O

1.763 1.229

-0.33

0.20

-0251

HO2-

O2-

O2

-1.985

2 OH-

OH + OH

-0.0649

0.867 0.401

0.506

O3

1.985

1.33

O2 + OH-

O2 + OH

O3

1.246

O2 + H2O

2.075

-0.892

O3 + H2O

2.813

O2 + OH

0.125

HO2 + O2

2 O2

-0.383

Fig. 5.12: Standard reduction potentials among Hx Oy species in aqueous solution (see also Table 4.14).

Finally, the following interesting pathway of O−2 formation from the photolysis of iron oxalate complexes was described by Zuo and Hoigné (1992): hν (λ 8), because then O−3 dominates over HO3 (remember that O− converts quickly into an OH radical). This is important for wastewater treatment; however, in natural atmospheric waters, pH < 6 and HO3 dominates. Before we summarize current knowledge about ozone decay in natural water, let us turn for a moment to early observations. It has long been known that ozone decays in alkaline solution. Schönbein (1844) found that ozone was removed from air after bubbling through alkaline solutions. This was proven quantitatively by Soret (1864), but Cossa (1867) found that O3 was not destroyed in pure KOH solution free of any organic substance. However, no mechanism was known (only the formation of O2 ) before Weiss (1935) first proposed the following three reactions, based on the observation that ozone decay is effective only in alkaline solution: O3 + OH− → O−2 + HO2 ,

(5.124a)

O3 + HO2 → 2 O2 + OH ,

(5.125)

O3 + OH → O2 + HO2 .

(5.126)

Equations (5.124a) and (5.125) do not represent elementary steps (see preceding discussion on intermediates such as O−3 and HO3 ): k 5.124a = 210 L mol−1 s−1 (Staehelin and

15 Sonntag and Gunten (2012) call it hydrotrioxyl radical. 16 Theoretical studies have shown that in the gas phase a reaction H + O3 → HO3 → OH + O2 occurs (Dupuis et al. 1986).

304 | 5 Substances and chemical reactions in the climate system Hoigne 1982), k 5.125 < 104 L mol−1 s−1 , k 5.126 = 1.1 ⋅ 108 L mol−1 s−1 (Sehested et al. 1984). In contrast to the important gas-phase reaction (5.17), the equivalent aqueousphase reaction (5.126) is at present not regarded as important. Hoigné and Bader (1976) reevaluated the importance of OH in the water ozonation process. Bahnemann and Hart (1982) and Staehelin and Hoigné (1982) estimated the reaction rate of (5.127) to be between 1 ⋅ 108 and 3 ⋅ 109 L mol−1 s−1 . Staehelin and Hoigné (1982), Sehested et al. (1983, 1984, and 1991), and Staehelin et al. (1984) added several reactions to the Weiss mechanism (eq. (5.124a) likely proceeds via HO−4 , see eq. (5.128)): O3 + OH− → O2 + HO−2

k 5.124b = 40 L mol−1 s−1 ,

O3 + HO−2 O3 + O−2

k 5.127 = 2.8 ⋅ 10 L mol s

→ O2 + OH →

O−3

+ O−2

+ O2

(5.124b)

6

−1 −1

,

(5.127)

9

−1 −1

.

(5.118)

k 5.118 = 1.6 ⋅ 10 L mol s

Evidently, only reaction (5.118) is fast enough for further consideration; the spontaneous alkaline ozone decay (nonradical and nonphotochemical) according to (5.124a) and (5.127) is too slow to obtain any atmospheric importance. 5.2.5.5 Hydrogen polyoxides The formation of H2 O2 in aqueous ozone decay has been controversial since being discussed by Schönbein; first Berthelot (1880)¹⁷ proposed the intermediate H2 O3. Some years later Mendeleev (1897) and Gräfenberg (1902, 1903) suggested the intermediate H2 O4 (Gräfenberg called it ozone acid H2 O ⋅ O3 ). H2 O4 has never been detected but Marshall and Rutledge (1959) and Kobozev et al. (1959) still speculated about its existence. Ardon (1965) proposed this intermediate in the so-called spontaneous ozone decay reaction: OH−

H+

H+

− 󳨀→ O3 󳨀󳨀󳨀→ HO−4 (󳨀 ← 󳨀󳨀 H2 O4 ) 󳨀󳨀󳨀󳨀→ HO2 󳨀󳨀→ H2 O2 . (−O2 )

(5.124c)

Hydrogen polyoxides H2 On (also called oxidanes) were now theoretically studied in the gas phase and in aqueous solution. Structures up to n = 4 were detected experimentally (Martins-Costa et al. 2011), Levanov et al. 2015): H2 O3 (trioxidane) and H2 O4 (hydrogen tetroxide). The formation and decay of H2 O3 were first proved in electronirradiated aqueous solution by Czapski and Bielski (1963). There is evidence for its existence in the atmospheric gas phase (Denis and Ornellas 2009) and in organisms¹⁸ (Wentworth et al. 2003). Its formation via O3 + H2 O2 → H2 O3 + 1 O2

(5.128)

17 Berthelot, M. (1880) Compt. Rend. 90, 656; cited after Plesničar (2005). 18 Antibodies are capable of catalyzing the oxidation of water by singlet dioxygen to generate H2 O2 and an oxidant with the signature O3 through HOOOH as key intermediate.

5.2 Oxygen

|

305

has been proved (peroxone process), but it is not clear whether it plays a role in the atmosphere (Nyffeler et al. 2004, Liebman and Greer 2014). It remains speculative as to whether hydrogen polyoxides play a role in atmospheric gas and aqueous-phase chemistry (Cerkovnik and Plesničar 2013). Bielski and Schwarz (1968) proposed the formation of H2 O3 : HO2 + OH → H2 O3 . (5.129) Another hydrogen polyoxide is suggested by Merényi et al. (2010b): H+

󳨀→ HO2 + O−2 󴀘󴀯 HO−4 󳨀 ← 󳨀󳨀 H2 O4 .

(5.130a)

This is competitive with (k 5.130b = 9.7 ⋅ 107 L mol−1 s−1 ): H+

󳨀→ HO2 + O−2 󳨀󳨀󳨀󳨀→ HO−2 󳨀 ← 󳨀󳨀 H2 O2 (−O )

(5.130b)

2

The following reactions were also suggested by Merényi et al. (2010a), k 5.132 ≈ k 5.133 : H+

󳨀→ HO−2 + O3 → HO−5 󳨀 ← 󳨀󳨀 H2 O5 , − HO5 → HO2 + O−3 ,

(5.132)

HO5 → 2 O2 + OH .

(5.133)

1

(5.131)

Interestingly, H2 O3 is more acidic (pK = 9.5) than H2 O2 (pK = 11.6), as shown theoretically (Plesničar 2005). Elliot et al. (2003) believe that the HO−3 anion may play a role in atmospheric processes, and its unusual long bond can expand our view of chemical bonding in oxygen-rich molecules. It can also be regarded as a weakly bonded van der Waals complex [O2 + OH− ]: H2 O3 󴀘󴀯 H+ + HO−3

pK = 5.4 .

(5.134)

The half-life of H2 O3 in water is about 20 ms (Plesničar 2005); it decays to singlet dioxygen and water as main (final) products; however, H2 O2 , O3 , and O also occur as intermediates: H2 O3 → 1 O2 + H2 O or

󳨀→ H2 O3 󳨀 HO−3 → 1 O2 + OH− . ← 󳨀󳨀 +

(5.135)

H

H2 O3 also decays proton-catalyzed: H2 O3 + H+ → H3 O+ + O2 .

(5.136)

In summarizing the proposed O3 decay¹⁹ reactions in solution, the intermediate O−3 forms via either reaction (5.118) or reaction (5.119) and quickly decays via several path19 Another species, HO+3 , is described by Cacace and Speranza (1994) as protonated O3 (O3 + AH+ 󴀘󴀯 A+HO+3 ). Analogeous H2 O+ (see eq. (5.76) and (5.521)) can be regarded as protonated OH. In eq. (5.118), (5.124)–(5.127), intermediate adducts in form of polyoxides appear, such as HO4 , HO5 , O−5 , HO−4 and HO−5 . Speculative we might assume protonated dioxygen (HO+2 ), see eq. (5.520), protonated oxygen (OH+ ) and protonated hydroperoxyl radical (H2 O+2 ). The protonated species could react according to HX+ + A− = HX + A.

306 | 5 Substances and chemical reactions in the climate system ways but gaining different ROSs such as OH, 1 O2 , H2 O2 , and HO2 : e−

H+

e−

H+

O3 󳨀󳨀→ O−3 󳨀󳨀→ HO3 󳨀󳨀→ HO−3 󳨀󳨀→ H2 O3 󳨀󳨀󳨀󳨀󳨀→ 1 O2 (−H2 O)

H+

H O

2 − − 󳨀→ O3 + O−2 󴀘󴀯 O−5 (󳨀 ← 󳨀󳨀 HO5 ) 󳨀󳨀󳨀󳨀→ O3 󳨀󳨀󳨀󳨀→ O 󳨀󳨀󳨀󳨀−→ OH ,

(−O2 )

(−O2 )

H+

OH−

(OH )

H+

− 󳨀→ O3 󳨀󳨀󳨀→ HO−4 [󳨀 ← 󳨀󳨀 H2 O4 ] → O2 + HO2 󳨀󳨀󳨀→ H2 O2 . −O2

The most important ozone reaction in slightly alkaline solution is O3 + O−2 (eq. (5.118)) with subsequent OH radical formation; however, in the presence of sulfurous acid (dissolved SO2 ), ozone is consumed while producing sulfate (eqs. (5.318) to (5.320)): HSO−3

H+

O3 󳨀󳨀󳨀󳨀→ O−3 󳨀󳨀→ HO3 󳨀󳨀󳨀󳨀→ OH . HSO3

(−O2 )

Nevertheless, the formation of H2 O2 from O3 in alkaline medium was shown to affect the direct formation of OH radicals. Thus, in the presence of O3 and electron donors, OH radicals with much higher yields are gained compared with those gained via O2 +e− and subsequent reactions (eq. (5.92)), as shown by Pichat et al. (2000) and Zhang et al. (2003). Finally, H2 O2 is produced in subsequent steps, likely via degradation of DOC,²⁰ where organic compounds in solution consume OH but recycle HO2 (as in the gas phase) (eq. (5.110)). Thus, Cossa’s remarkable early observations support the essential role of waterdissolved organic compounds (DOC or NOM) through reaction (5.110). It seems very likely that photosensitized electron transfer reactions (according to eq. (5.96)) to O2 , O3 , and H2 O2 , such as eqs. (5.79), (5.99), and (5.119), take place on all wetted surfaces providing ROSs. For example, dew provides a medium where all needed reactants are available. Hence, OM plays a crucial role as an electron donor as well as converter of OH into HO2 . Humic-like substances (HULIS) (also termed macromolecular compounds) were found in atmospheric aerosols (Havers et al. 1998) and in cloud water (Feng and Möller 2004), which were likely produced in atmospheric chemical processes from primary aromatic compounds and have chromophoric properties. Figure 5.13 summarizes the most important aqueous-phase oxygen reactions. In water treatment, UV radiation is often applied in a wavelength range of O3 formation (by O2 photolysis) (Stefan 2018). Therefore, as in the gas phase, the following relevant reactions occur in water: ozone photolysis under the formation of O(1 D) and subsequent fast O(1 D) + H2 O reaction, gaining OH radicals (eq. (5.16)); k = 1.8⋅1010 L mol−1 s−1 (Biedenkapp et al. 1970).

20 It is self-evident that this reaction provides efficient water treatment and cleaning (Mehrjouei et al. 2015).

5.2 Oxygen

| 307

OH, Fe3+

W

h

Fe(C2O4)+

O3 e-

H2O2

Fe3+

h

H2O2

OH

h

X,

Fe2+

O2-

Fe3+

HO2

eh

Fe(OH)2+

OH- (H2O)

O2

W

Fig. 5.13: Simplified main aqueous oxygen chemistry; W photosensitizer, X oxidizable species RH, N(III), S(IV), Cl− .

Similar to the gas phase, OH plays a central role as a key oxidant for many dissolved inorganic and organic species. Peroxides (H2 O2 and HO2 /O−2 ) play the role of OH generating and cycling. Organic photosensitizers in the presence of sunlight produce hydrated electrons or directly O−2 ; the formation of ROSs in natural waters at the interface with air is ongoing, thereby facilitating oxidation processes, including corrosion and autoxidation.

5.2.6 Multiphase oxygen chemistry In previous chapters, we considered either homogeneous gas-phase or aqueous-phase chemistry. However, the condensed aqueous phase exists only in interaction with the gas phase. As just mentioned, at the interface reactants meet from aqueous and gaseous sites and build up high concentrations to provide favorable conditions for chemical reactions; in recent years this has brought the term “interfacial chemistry” into fashion. Concerning Earth’s watery surface, processes are relatively simple to describe with respect to a plane interface and fluxes in both directions as emission and deposition. In a cloud, however, up to a few hundred droplets can be found within 1 cm3 . Thus, in a cloud, the specific surface-to-volume ratio is on the order of 0.3 m2 m−3 , but the aqueous volume-to-gas volume ratio (LWC) amounts to only 10−6 m3 m−3 . The volume between the droplets is termed the interstitial air. In Chapter 3.6.5, we talked about how, despite the low aqueous solution volume (LWC), chemical turnover

308 | 5 Substances and chemical reactions in the climate system

can be significant because of much faster reactions in solution and the fact that easily soluble gases are almost completely transferred to the droplet phase. Depending on the chemicals present, each phase provides different budget terms (sources and sinks). The chemistry in the aqueous phase depends on the concentrations of the reactants before droplet formation and their solubility. Because of different gas solubilities, the ratios among gas-phase species change and, hence, the significance of different competing pathways. One of the most important feedbacks of clouds in net ozone formation is a decoupling between OH–HO2 and NO–NO2 cycles (Figure 5.5). HO2 is far more scavenged than other species, which results in gaseous OH depletion (not recycling) and reduced NO to NO2 transformation, which results in a reduced net ozone formation in clouds.²¹ From the aqueous-phase chemistry of O3 we have learned that in-droplet O3 formation is unlikely and, once air is in contact with water, O3 is scavenged and decomposed. HO2 and OH radicals are also scavenged and consumed as well as produced in many aqueous-phase reactions. Whether the aqueous phase is a net sink or source of ROSs depends on the presence of consuming species (organic, sulfur, nitrogen, and halogen compounds). The general relationships among stabile oxygen species (O2 , O3 , H2 O2 , and H2 O) do not differ between the gas and aqueous phase (Figure 5.14). The short-lived radicals (HO2 /O−2 , OH) are the key oxidants generated from and turned back into “stable” oxygen species. Wetted surfaces and aqueous interfaces, respectively, are not only a sink for ozone but also a radical source: H+ +e− O3 (g) 󴀘󴀯 O3 (aq) 󳨀󳨀󳨀󳨀󳨀→ HO3 → OH + O2 . The most important insight, however, is the transfer of oxygen O2 into peroxo radicals and, ultimately, hydrogen peroxide: e−

H+

e−

H+

− 󳨀 − 󳨀󳨀→ O2 (g) 󴀘󴀯 O2 (aq) ← 󳨀󳨀 O2 󳨀 ←→ 󳨀󳨀 HO2 󳨀󳨀→ HO2 󳨀󳨀→ H2 O2 .

In the aqueous phase, hydrogen peroxide can either produce radicals, e−

H+

H2 O2 󳨀󳨀→ H2 O−2 󳨀󳨀→ H2 O + OH , or be decomposed (inactivated) into oxygen, 󳨀󳨀󳨀 → HO2 󳨀󳨀󳨀󳨀+→ O−2 󳨀󳨀󳨀󳨀−→ O2 . H2 O2 󳨀󳨀󳨀󳨀󳨀 + − −(H +e )

(−H )

(−e )

21 . . . and even in ozone depletion in the presence of SO2 (see later in Chapter 5.2.6.2).

5.2 Oxygen

| 309

Fig. 5.14: Chemical relationships between Ox and Ox Hy species.

The budget equation follows, which represents a water-splitting process similar to gasphase OH production from O3 : hν

O3 + H2 O 󳨀󳨀→ O2 + 2 OH . As shown, from ozone via OH, H2 O2 is also produced through the Fenton reaction. Moreover, it is seen that photocatalytic dioxygen reduction is less effective compared with O3 because many reactions scavenge superoxide (return it to O2 ) and OH formation requires a three-electron transfer, O2 + 3 e− + 2 H2 O → 3 OH− + OH , compared with the overall one-electron transfer step to O3 . Therefore, the presence of O3 will enhance all interfacial oxidation processes: O3 + e− + H2 O → OH− + OH . In what follows, all Oy and Hx Oy species are listed in relation to electron and proton transfers. Note that only oxygen (O2 ) and water (H2 O) are very stable, ozone (O3 ) and

310 | 5 Substances and chemical reactions in the climate system

hydrogen peroxide (H2 O2 ) are relatively stable, whereas all other species are unstable, occurring only as short-lived intermediates or not yet proved (such as O4 , O5 , H2 O5 ). e−

H+

e−

H+

e−

H+

e−

H+

e−

H+

e−

H+

e−

H+

e−

H+

e−

H+

e−

H+

O ←→ O− ←󳨀→ HO ←→ HO− ←󳨀→ H2 O O2 ←→ O−2 ←󳨀→ HO2 ←→ HO−2 ←󳨀→ H2 O2 O3 ←→ O−3 ←󳨀→ HO3 ←→ HO−3 ←󳨀→ H2 O3 O4 ←→ O−4 ←󳨀→ HO4 ←→ HO−4 ←󳨀→ H2 O4 O5 ←→ O−5 ←󳨀→ HO5 ←→ HO−5 ←󳨀→ H2 O5 Finally, the following list presents all likely reactions that occur in the gas and aqueous phases (note that in the climate system ions exist only in solution): H+ + e− → H H + H → H2 H2 + OH → H + H2 O O3

H + O2 → HO2 󳨀󳨀→ HO5 → OH + 2 O2 hν

H + O3 → HO3 󳨀󳨀→ OH + O2 󳨀→ O+O󳨀 ← 󳨀󳨀 O2 hν

󳨀→ O + O2 󳨀 ← 󳨀󳨀 O3 hν

H+

O− + O2 󴀘󴀯 O−3 (←󳨀→ HO3 → OH + O2 ) H+

O−2 + O2 󴀘󴀯 O−4 (←󳨀→ HO4 → HO2 + O2 ) O2 + O2 󴀘󴀯 O4 O2 + O3 󴀘󴀯 O5 H+

O−2 + O3 󴀘󴀯 O−5 (←󳨀→ HO5 → OH + 2 O2 ) H2 O

O−2 + O3 󴀘󴀯 O−5 󳨀󳨀󳨀󳨀→ O−3 (󳨀󳨀󳨀󳨀→ O− 󳨀󳨀󳨀󳨀󳨀−→ OH) (−O2 )

(−O2 )

(−OH )

OH + O2 󴀘󴀯 HO3 H+

OH + O−2 󴀘󴀯 HO−3 (←󳨀→ H2 O3 → H2 O +1 O2 ) OH + O3 󴀘󴀯 HO4 󴀘󴀯 HO2 + O2 H+

OH + O−3 󴀘󴀯 HO−4 (←󳨀→ H2 O4 → H2 O2 + O2 )

5.2 Oxygen

| 311

󳨀→ OH + OH 󳨀 ← 󳨀󳨀 H2 O2 hν

OH + HO2 󴀘󴀯 H2 O3 → H2 O + O2 HO2 + HO2 󴀘󴀯 H2 O4 → H2 O2 + O2 HO2 + O2 󴀘󴀯 HO4 HO2 + O3 󴀘󴀯 HO5 → OH + O4 (󴀘󴀯 O2 + O2 ) 5.2.6.1 Hydrogen peroxide H2 O2 is produced in the atmospheric gas phase only through a single pathway, specifically the HO2 radical recombination (eq. (5.19)). Its main role is oxidizing dissolved SO2 in hydrometeors to sulfate. Thus, aqueous-phase chemistry was considered a main sink (apart from dry deposition and scavenging) but rarely a source of H2 O2 , despite early findings of its heterogeneous and aqueous-phase production. Heikes et al. (1982) first suggested the idea of atmospheric aqueous-phase H2 O2 formation in cloud droplets. The in-droplet chemical formation of H2 O2 occurs much faster than in the gas phase. However, one must consider the liquid volume fraction (LWC) ratio as well as the occurrence of clouds to assess the share of in-droplet production in the total atmospheric budget. Liquid-phase H2 O2 is also formed from gasphase scavenging of H2 O2 and HO2 (Schwartz 1984) as well as via chemical reactions in the liquid phase, all based on the general reactions (5.88) and (5.94) where electron donors are given by different species, for example, O−2 itself (McElroy 1986) and TMIs (Gunz and Hoffmann 1990). Related to the volume of air, however, aqueous-phase production in connection with these radical mechanisms is small (about 10−7 ppb s−1 ) (Möller and Mauersberger 1990b, 1992) compared with the gas-phase production rate of about 10−5 ppb s−1 (Martin et al. 1997). All these findings emphasize the central role of H2 O2 in radical chains during biochemical, combustion, and air chemical processes. The fundamental role in H2 O2 environmental chemistry lies in the simple redox behavior among water and oxygen depending on the available electron donors and acceptors: reduced

oxidized

H2 O ←󳨀󳨀󳨀󳨀󳨀󳨀 H2 O2 󳨀󳨀󳨀󳨀󳨀󳨀→ O2 . This process is valid for aqueous and gaseous phases in all environmental media. The oxo and peroxo radicals provide reactive intermediates. Under atmospheric conditions, the self-reaction of the HO2 radical according to eq. (5.19c) is the most important gas-phase formation of H2 O2 (reviews: Gunz and Hoffmann 1990, Lee et al. 2000, Vione et al. 2003, Liebman and Greer 2014). H2 O2 is rather stable (Finlayson-Pitts and Pitts 1986) in the gas phase, i.e., it does not undergo fast photochemical and gas-phase reactions. The only important sinks in the boundary layer are dry deposition and scavenging by clouds (with subsequent aqueous-phase chemistry) and precipitation (wet deposition).

312 | 5 Substances and chemical reactions in the climate system

Thus, transport of H2 O2 over long distances is possible during essentially cloudfree conditions. H2 O2 will be completely and quickly consumed under SO2 -rich conditions. Hence, in the presence of clouds and rain, only under SO2 -poor conditions (see earlier discussion) is the net formation of H2 O2 likely to occur in the aqueous phase. By contrast, the HO2 radical (and in the aqueous phase, O−2 too) can undergo many competitive reactions that limit H2 O2 formation. Under NO-rich conditions, HO2 will be retransformed into OH (NO2 + HO2 → NO2 + OH) with decreasing H2 O2 yield. However, under NO-poor conditions (≪ 1 ppb), the reaction HO2 + O3 → OH + 2 O2 occurs and results in a diurnal inverse correlation (Ayers et al. 1996) between the short-term concentrations of O3 and H2 O2 . However, under NO-poor conditions, hydrocarbon oxidation by OH leads to the formation of organic peroxides by HO2 consumption. Thus, only under “medium NO” does gas-phase H2 O2 production reach its optimum. Gilge et al. (2000) have shown that under NO-limited ozone formation conditions, i.e., at each time step, more HO2 is produced than transformed by NO into NO2 and OH, and H2 O2 concentration increases. It is important to note that with increasing tropospheric ozone the concentration of hydrogen peroxide can – but need not – increase. Another pathway in the formation of HO2 that probably leads directly to H2 O2 proceeds via the ozonolysis of alkenes, which was investigated for many years. However, several open questions remain about the initial and product relationship. It is well known that the excited Criegee radical can produce OH and HO2 radicals (Neeb et al. 1998). The stabilized Criegee radical can react with water vapor to form α-hydroxyalkyl peroxides (RR’C(OH)OOH); Gäb et al. 1985, Becker et al. 1993). It was found²² that substituted Criegee radicals could directly produce H2 O2 , i.e., without the HO2 intermediate. The yield strongly depends on the alkene species and the water vapor pressure (Sauer et al. 1999). This path is independent of radiation and can be important in all situations where competition with the OH attack on alkenes is small, for example, under cloudy conditions, at night, and in winter. It can also be important in urban areas where high alkene emission occurs. Weinstein-Lloyd et al. (1998) believed that the increase of peroxides during photochemical periods in the USA was because of the ozonolysis of biogenic and human-made alkenes.²³ The most important atmospheric sink of H2 O2 is scavenging by cloud droplets and reaction with dissolved SO2 forming sulfate (Chapter 5.4.3.2). Modeling studies have shown that at low atmospheric SO2 concentrations (around 1 ppb) the droplet phase acts as a net source of H2 O2 (Möller and Mauersberger 1992), even without taking into account the photocatalytic formation according to eq. (5.96). Atmospheric SO2 definitively controls the source-sink relationship of H2 O2 in the aqueous phase. Möller (2009a) has shown for the first time by longer simultaneous H2 O2 monitoring in

22 The formation of H2 O2 from the boiling of organic ozonides was already described by Harries (1916). 23 This idea was first proposed by Möller (1989) to explain new-type forest decline by increasing H2 O2 .

5.2 Oxygen

|

313

Fig. 5.15: H2 O2 multiphase chemistry. Note that OH, HO2 /O−2 , and O3 can undergo competitive reactions with many substances (organic, sulfur, and nitrogen compounds) not shown here.

rain and air that in summer the net formation of H2 O2 occurs via the aqueous phase. Figure 5.15 shows the coupled air-aqueous oxygen chemistry with a focus on H2 O2 . Whereas H2 O2 in the gas phase is more like an oxidant reservoir (the slow photolysis only plays a role in the upper troposphere), in the aqueous phase it is included in intensive cycling between OH and HO2 . Thus, depending on the aqueous-phase pH, H2 O2 provides a variety of ROSs, partly scavenged from the gas phase and also produced in solution where dioxygen photocatalysis in the presence of photosensitizers occurs in a unique way for oxidation processes (Hoffmann 1990). It is likely that the morning wetted Earth’s surface (dew formation) provides an interface for photochemical reactive oxygen production. Summarizing the atmospheric H2 O2 sources, we can distinguish between the following processes: 1. direct emission (e.g., biomass burning), 2. photochemically initiated formation via the HO2 radical as a product of the photolysis of O3 and aldehydes; HO2 can either recombine into H2 O2 in the gas phase or react after scavenging in the liquid phase, 3. thermal direct formation in the gas phase via the ozonolysis of alkenes, 4. decay of O3 in (alkaline) aqueous solution, and 5. photosensitized formation (“photocatalysis”) via electron transfer onto O2 in the aqueous phase.

314 | 5 Substances and chemical reactions in the climate system

Most secondary formation pathways in gas and aqueous phases depend on ozone. There is only one path of light-independent formation (ozonolysis) and one way that is independent of oxidant precursors (aqueous-phase electron transfer to oxygen, eq. (5.87)). Over the past 20 years, many H2 O2 measurements have been carried out, but almost always (with very few exceptions) covering short-term measurement periods. The main findings of these studies are summarized as follows (Gunz and Hoffmann 1990 and references therein, Lee et al. 2000, Möller 2002, 2009a): – H2 O2 concentration is generally lower in the boundary layer (< 2 ppb) than in the free troposphere (2–8 ppb), whereas “typical” near-surface concentrations in summer are between 0.2 and 0.8 ppb. – H2 O2 concentration increases from the North Pole to the equator and rises dramatically around the equator and above Africa. – H2 O2 concentration drops in the gas phase during rainfall and within clouds (interstitial air). – Increased H2 O2 concentration has often been found close to clouds. – In remote areas, different diurnal variations were found with maxima between late afternoon and midnight. – H2 O2 concentration in winter is always significantly lower (factor ≤ 15). – H2 O2 concentration correlates with UV radiation. – In “NO-poor” areas, an inverse correlation exists between H2 O2 and O3 (in diurnal variation, not in seasonal variation). – H2 O2 concentration in urban areas is lower than in rural areas. – In the aqueous phase, an inverse correlation was found between H2 O2 and S(IV). 5.2.6.2 Ozone At a given site, ozone can have two different sources, its local in situ photochemical formation and its onsite transportation (vertical and horizontal). Local sinks of ozone include dry deposition (irreversible flux to ground) and chemical reactions in the gas phase, on aerosol particles, and in droplets. Air masses have a different potential to form and destroy ozone. Depending on the air mass type, the past and fate of ozone (in relation to the site) can be characterized by production or destruction (positive or negative budget). With changing air masses, a current ozone level can also drastically change. The atmospheric residence time of ozone, depending only on sink processes, is extremely variable. It amounts to a few days near the ground and several months in the upper troposphere. Thus, ozone can be transported over long distances in the free troposphere. Advective transport to a receptor site is therefore an important source of local ozone. The net rate of ozone includes three terms: chemical production P(O3 ) in the gas phase, a sink term S(O3 ) by chemical conversion and deposition, and a net transport

5.2 Oxygen

| 315

term T(O3 ), given by influx and outflow: (

d[O3 ] ) = P(O3 ) − S(O3 ) + T(O3 ) . dt

(5.137)

The chemical production term P(O3 ) is given by the OH to HO2 conversion reactions that represent rate-determining steps (see Figure 5.5 on the complete ozone formation cycle): P(O3 ) = (k 5.33 [CO] + k 5.40 [CH4 ] + ∑ k i [NMVOC]) [OH] .

(5.138)

i

Considering mean concentrations, ozone formation rates of 0.2–2 ppb d−1 in connection with CO and about 0.5 ppb d−1 in connection with CH4 follow. This is close to the net global mean ozone formation rates of 1–5 ppb d−1 found by modeling (Wang et al. 1998), suggesting that long-life carbon monoxide and methane are responsible for the global background ozone concentration. However, local and regional O3 net production rates of about 15 ppb d−1 are observed under cloud-free conditions in summer (Beck and Grennfelt 1994, Möller 2004). The in situ formation rate can quickly reach up to 100 ppb h−1 (Volz-Thomas et al. 1997). It is often neglected that the transport term in eq. (5.137) can be dominant in the morning following the breakdown of the inversion layer and vertical O3 mixing. Moreover, in the case of changing air masses, vertical fluctuations can “produce” O3 changes up to 10 ppb within a few minutes. At night, dry deposition might reduce near-surface ozone to zero. As discussed in Chapter 5.2.3.2, ozone production abruptly stops when NO becomes very small and the “catalytic” O3 destruction cycle (reactions (5.17) and (5.18)) works. Ozone is much less soluble in water compared with H2 O2 . Apart from that, the aqueous phase is an effective sink for O3 through reaction (5.104) and S(IV) oxidation (eqs. (5.318) to (5.320)). Moreover, because of the interruption of the NO to NO2 conversion cycle (Figures 5.5, 5.14, and 5.15) due to the higher solulibity (scavenging) of HO2 compared to OH, gas-phase ozone production decreases in clouds. However, ozone loss in clouds was almost disregarded before the 1990s. Only in the early 1990s did modelers (Lelieveld and Crutzen 1991, Möller and Mauersberger 1992, Liu et al. 1997) show that clouds could effectively reduce gas-phase ozone. Acker et al. (1995) found by long-term cloud chemistry monitoring that – depending on the transport characteristics – the interstitial air of clouds could have “ozone holes.” The main pathway of ozone decomposition in solution proceeds via OH formation, which turns either into H2 O2 (net H2 O2 formation was discussed in the previous chapter) or oxidizes organic substances when present. This is similar to the discussed “catalytic ozone destruction” in the remote atmosphere: O3 → OH → H2 O . In addition, in a polluted atmosphere, dissolved sulfur dioxide can react directly with O3 . Another indirect but very efficient pathway of irreversible O3 consumption via

316 | 5 Substances and chemical reactions in the climate system 0.9

O3 flux (in 10-9 mol L-1 s-1)

0.8 O3 + O2-

0.7 0.6 0.5

O3 + S(IV)

0.4 0.3 0.2 0.1 0 1

2

3

4

5

6

7

8

9

10

11

12

SO2 concentration (in ppb) Fig. 5.16: Modeled ozone flux (10−9 mol L−1 s−1 ) into the aqueous phase of a monodisperse stratiform cloud (droplet radius 5 μm, LWC 0.3 ⋅ 10−6 ), 30 ppb O3 for different gaseous SO2 concentrations, using a complex cloud chemistry model (Möller and Mauersberger 1995).

the aqueous and solid phases is combined with easily soluble NO y species (specifically NO3 , N2 O5 , and HNO3 , which are O3 reservoirs), which finally transform into dissolved nitrate (see next chapter). Figure 5.16 shows the destruction of O3 where cycling through OH dominates in alkaline solution (here adjusted because of the low availability of SO2 ). In a SO2 polluted atmosphere, the solution becomes acidic because of sulfurous acid formation and oxidation to sulfuric acid, and indirect O3 decay via OH plays no role. With decreasing atmospheric SO2 , the solution becomes less acidic and the rate of the O3 –S(IV) reaction decreases. Figure 5.16 shows modeling results illustrating this relationship. It is clearly seen that in remote air, droplets consume more O3 by reaction (5.104) than in polluted atmosphere through S(IV) oxidation. Other modeling groups (Johnson and Isakson 1993, Matthijsen et al. 1997, Liang and Jacob 1997) have confirmed that clouds can decompose O3 up to 100%, depending on pH, LWC, and the extension of the cloud system (in other words, the air volume a cloud occupies). Mauldin et al. (1997) carried out direct measurements in clouds and found that the OH concentration above the cloud was three to five times higher ((5–8)⋅106 cm−3 ) than under cloud-free conditions at the same altitude. Simultaneously, they found that O3 concentrations in clouds were about 25% lower than above clouds (30 ppb). Based on long-term monitoring at Mount Brocken (Harz, Germany), we generally found lower O3 concentrations under cloudy conditions than under comparable cloud-free conditions, on average 30% lower (Table 5.9). However, significantly lower interstitial O3 concentrations (“ozone holes”) were found only under special cloudy conditions such as no mixing (entrainment), no precipitating clouds, and long-scale cloud transportation (Acker et al. 1995).

5.2 Oxygen

| 317

Tab. 5.9: Statistical parameters for mean ozone concentrations in summer (mid-April until midOctober) and winter (mid-October until mid-April) and for cloud-free and cloudy conditions (“stationin-cloud”) at Mount Brocken, 1992–1997 (Harz Mountain, Germany) 1142 m a.s.l., 51.80° N, 10.67° E, based on monthly means (in ppb).

All events (ppb) Cloud-free (ppb) Station-in-cloud (ppb) LWC (in mg m−3 ) Station-in-cloud (%) Difference cloudy – cloud-free (ppb) Ratio cloudy/cloud-free

Winter

Summer

Year

26.3 ± 4 31.1 ± 5 21.1 ± 4 272 ± 22 59 ± 16 10.0 0.68

44.0 ± 3 47.1 ± 2 33.5 ± 3 272 ± 27 28 ± 10 13.6 0.71

34.2 ± 3 37.4 ± 4 26.8 ± 4 263 ± 63 45 ± 2 10.6 0.72

The mean (annual) background O3 concentration for Central Europe (reference year 1995 ± 5) was estimated to be 37 ± 5 ppb (winter 25 ppb and summer 47 ppb), where the following “sources” contribute (Möller 2004): – 10 ± 2 ppb stratospheric ozone with small seasonal variation (spring peak), – 6 ± 2 ppb “biogenic” ozone from natural VOC (including natural CH4 ) precursors with seasonally large variation (0–12 ppb), – 16 ± 2 ppb “human-made” ozone from oxidation of anthropogenic CH4 and CO, – 5 ppb of human-made “hot ozone” from anthropogenic NMVOC emissions with seasonal variation (0–15 ppb) and strong short-term variation (0–70 ppb). It was clearly shown that the “acute” air pollution problems stemmed from reactive NMVOC precursors (“hot ozone”), which contributed in fact only 5 ppb (25% of human-made contributions and 14% of total ozone) to the long-term average in the 1990s but resulted in large short-term variations. The “chronic” air pollution problem is due to methane oxidation (and partly by CO), contributing to a likely continuously increasing “base” ozone (50%). In Germany, and stepwise in all other European countries, the “hot” ozone problem was solved by the late 1990s. The problem of background ozone, connected with CH4 , cannot be solved due to the vital link between CH4 emission and food production. The reduction of “hot” ozone led to constant ozone levels or only minor ozone increases in the 1990s, but in the future, ozone can again rise baed on global CH4 emission increases.

5.2.7 Stratospheric oxygen chemistry Stratospheric chemistry (the stratosphere extends up to about 50 km in altitude) differs from that in the troposphere for three reasons: – Radiation below 300 nm is available for photodissociation that does not occur in the troposphere (Figure 5.17).

318 | 5 Substances and chemical reactions in the climate system

altitude (in km)

120

O2 Schumann continuum

80 O2 Schumann Runge bands O3 Hartley continuum 40

O2 + hν → O + O

O3 + hν

1O

+ O2

0 150

200

250

300

wavelength (in nm) Fig. 5.17: Penetration of solar UV radiation into the atmosphere as a function of wavelength and absorption by oxygen and ozone. The curve indicates the altitude at which incoming radiation is attenuated to about 1/10 of its initial intensity.

– –

Not all trace gases (those with a short lifetime) are either available or found only in very small concentrations (especially water; the stratosphere is very dry). There is no precipitation and no liquid cloud (but special polar stratospheric clouds, PSCs).

The following reactions are of crucial importance for the climate system because they result in continuous absorption of solar radiation below 300 nm (Figure 5.18): hν (λ≤ 300 nm)

O3 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ O(1 D) + O2 , hν (λ≤ 242 nm)

O2 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ O(3 P) + O(3 P) .

(5.8b and 5.8c) (5.13a)

Evidently, O3 formation (5.11) and reaction (5.139) follow, which has no relevance in the troposphere but is of crucial importance for O3 removal in the stratosphere: O(3 P) + O2 → O3 , O + O3 → O2 + O2 .

(5.11) (5.139)

5.2 Oxygen

| 319

There are other important differences between stratosphere and troposphere. Whereas the troposphere is heated from the bottom (i.e., Earth’s surface), the stratosphere heats from the top (i.e., by incoming solar radiation). This positive temperature gradient results in an extremely stable layering. Therefore, mixing and transport are much weaker than in the troposphere. At the bottom of the stratosphere, close to the tropopause, the lowest temperatures are found (200–220 K and at the poles down to ∼ 180 K), whereas temperature rises up to 270 K at 50 km. At each point of the stratosphere the temperature is determined by adiabatic radiation processes: O3 absorbs UV radiation and heats the air and CO2 absorbs IR radiation and cools the air. It is found that, in general, radiative equilibrium is not obtained at any latitude. Low latitudes constitute a heat source and high latitudes a heat sink in the stratospheric energy budget. It is shown that carbon dioxide is more important than water vapor in cooling the stratosphere (Ohring 1958). The chemical composition of the stratosphere (mixing ratios) with respect to the main constituents (N2 , O2 , CO2 , and CH4 ) remains constant but the pressure strongly decreases from about 200 hPa at 12 km to 1 hPa at 50 km altitude. The most important trace species is O3 ; in the layer between 15 and 30 km altitude, about 90% of atmospheric ozone is available. This is known as the ozone layer. The photolysis of oxygen was described many years ago by Chapman (1930). Attention was drawn to the stratospheric ozone by Bates and Nicolet (1950), who presented the idea of catalytic O3 decay. However, only through the implications of anthropogenic influences on the stratospheric ozone cycle by Crutzen (1971), Johnston (1971), Molina and Rowland (1974), and Stolarski and Cicerone (1974) have ozone-depleting processes attracted increased attention. Two of the previously listed reactions account for the catalytic decomposition of O3 : O + O3 → O2 + O2 O3 + hν → O + O2 2 O3 → 3 O2 By contrast, this decay is balanced by the formation of O3 according to O + O2 → O3 O2 + hν → O + O 3 O2 → 2 O3 The photolysis of O3 (eq. (5.8c)) does not lead to a net destruction of ozone. Instead, O is almost exclusively converted back to O3 (eq. (5.11)). However, because O2 dissociates to free oxygen atoms above about 30 km, below 30 km reaction (5.141) results in a net loss of odd oxygen (if the odd oxygen concentration is defined as the sum of the O3 and O concentrations). The budget between the photodissociation of O3 and its formation via eq. (5.11) is zero (steady state). Because the rate of reaction (5.11) decreases with altitude, whereas that of reaction (5.8c) increases, most of the odd oxygen below

320 | 5 Substances and chemical reactions in the climate system

60 km is in the form of O3 , whereas above 60 km it is in the form of O. Odd oxygen is produced by reaction (5.13a). It can be seen that reactions (5.11) and (5.8c) do not affect the odd oxygen concentrations but merely define the ratio of O to O3 . A significant fraction of the removal is caused by the presence of chemical radicals X, such as nitric oxide (NO), chlorine (Cl), bromine (Br), hydrogen (H), or hydroxyl (OH), which serve to catalyze reaction (5.140), termed cycle 1 (O + O3 → O2 + O2 ): X + O3 → XO + O2 ,

(5.140)

O + XO → X + O2 .

(5.141)

When k 5.141 > k 5.140 and substance X is not quickly lost by a termination reaction, the ozone decomposition flux according to cycle 1 becomes larger than follows only from reaction (5.139). Reaction (5.141) is generally faster than (5.140) because of the stronger radical characteristics (with the exception of hydrogen atoms) (Table 5.10). The species H and OH are natural (in contrast to halogens and nitrogen species) constituents of the stratosphere (but with lower concentrations than in the troposphere). Only the hydroxyl radical OH (no other XO species) can directly react with O3 (reaction (5.17)), providing another effective O3 decay cycle 2: OH + O3 → HO2 + O2 HO2 + O3 → OH + 2 O2 2 O3 → 3 O2 The reactive species, termed ozone-depleting substances (ODSs), come from different source gases such as H2 , H2 O, N2 O, CH4 , and halogenated organic compounds. It is noteworthy that changing the stratosphere with water (from aircraft) and hydrogen (H2 technology) results in ozone depletion. An important source of H2 O is methane, and a H2 O concentration maximum found at altitudes between 50 and 70 km results from CH4 oxidation: OH

O2

HO2

hν

O2

(−O2 )

(−OH)

(−HO2 )

CH4 󳨀󳨀󳨀󳨀󳨀→ CH3 󳨀󳨀→ CH3 O2 󳨀󳨀󳨀󳨀→ CH3 OOH 󳨀󳨀󳨀󳨀󳨀→ CH3 O 󳨀󳨀󳨀󳨀󳨀→ (−H2 O)

hν(+O2 )

O2

OH (+O2 )

(−HO2 )

(−HO2 )

(−HO2 )

HCHO 󳨀󳨀󳨀󳨀󳨀󳨀→ HCO 󳨀󳨀󳨀󳨀󳨀→ CO 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CO2 . An additional source of radicals (OH and HO2 ) generates the photolysis of O2 (eq. (5.13)), O3 (eq. (5.8)), and H2 O (eq. (5.27)) as well as CH4 , giving H (and subsequently HO2 ): (5.142) CH4 + hν → CH3 + H (λ > 230 nm) . Further considering the H2 O-production reactions OH + OH (eq. (5.25)) and OH + HO2 (eq. (5.26)) the gross reaction accounts for CH4 + 2 O2 → CO2 + 2 H2 O .

(5.143)

5.2 Oxygen

| 321

Tab. 5.10: Reaction rate constants for X + O3 (k5.140 ) and O + XO (k5.141 ) at 22 km altitude and 222 K (10−12 cm3 molecule−1 s−1 ); after DeMore et al. (1997). X

O

H

OH

NO

F

Cl

Br

I

k5.140 k5.141

8 –

140 22

1.6 30

2 6.5

22 27

29 30

17 19

23 120

XO

–

OH

HO2

NO2

FO

ClO

BrO

IO

About 90% of N2 O entering the stratosphere is photolyzed to N2 + O (eq. (5.170)); the remaining 10% reacts with O(1 D) to NO (eq. (5.170a)); the latter can then enter the ozone decay cycle. Halogens are most important for ozone depletion. In what follows we will see that NO y and halogen compounds produce condensed reservoir species such as ClONO2 and BrONO2 , which play a crucial role in the “ozone hole.” Precursors, such as halogenated organic compounds (halocarbons, CFCs), are photolyzed but also react with oxygen atoms (X = H, Br, F, and Cl): R–CX2 Cl + hν → R–CHX + Cl ,

(5.144)

R–CX2 Cl + O(1 D) → R–CHX2 O + Cl ,

(5.145a)

R–CX2 Cl + O( D) → R–CHX2 + ClO .

(5.145b)

1

The formation of ClO is dominant (about 60%). Reactions of halocarbons with OH are too slow to be important. Providing reactive species X and XO, cycle 1 (eqs. (5.140) and (5.141)) can run several thousand times before competing products (HOCl, HOBr, HOI, and nitrates) are produced. However, the ozone depletion cycles cannot explain the dramatic O3 depressions observed in Antarctica every spring (September to October) in the layer between 12 and 24 km because gas-phase chemistry (which stops in the Arctic winter such as at night) is a continuous process. The simple explanation is that radicals accumulate in a condensable matter, termed a PSC, which can form in different types at T < −80 °C. Type I consists of pure water, type II of nitric acid trihydrate (HNO3 ⋅ 3 H2 O), and type III a mixture (HNO3 /H2 SO4 /H2 O). These “clouds” provide a surface for heterogeneous chemistry and for the absorption and storage of so-called reservoir gases such as HCl, HBr, HI, ClONO2 , and others. Easily photodissociable species are Cl2 , ClNO2 , and HOCl (similar to the other halogen compounds). For example, the following reactions occur: HCl(s) + ClONO2 → Cl2 + HNO3 (s) , HCl(s) + N2 O5 → ClNO2 + HNO3 (s) ,

(5.146) (5.147)

ClONO2 + H2 O(s) → HOCl + HNO3 (s) ,

(5.148)

HOCl + HCl(s) → Cl2 + H2 O(s) .

(5.149)

322 | 5 Substances and chemical reactions in the climate system

PSC-HCl PSC-H2O

evaporation

PSC-HCl

HOCl

CFCs

HCl hν

PSC-H2O PSC-HCl

hν

hν

Cl2

ClONO2

OH

CH4

ClNO2

Cl hν

Cl2O2

O3 ClO

ClO PSC-HCl

hν

N2O

O3

NO

hν

O3

NO2 OH

hν

HNO3

NO2

NO3

hν

N2O5 PSC-H2O

CH4 PSC-H2O evaporation

PSC-HNO3

Fig. 5.18: Stratospheric multiphase chemistry.

In the Antarctic spring, PSCs evaporate and set free “active” halogen compounds (Cl2 + Cl + ClO + Cl2 O2 ; Figure 5.18). Most NO x is stored as HNO3 in solid PSCs and contributes little to O3 depletion. After ending the ozone hole period (at the end of November), PSCs almost evaporate and remain only as liquid sulfuric acid particles. Meanwhile, the “normal” gas-phase cycles of ozone depletion control the steady-state concentration.

5.3 Nitrogen Nitrogen, like carbon, is not one of the more abundant elements on Earth – its mean mass fraction is only about 0.002%; thus, oxygen is 23,000 times and carbon ten times more abundant (Table 5.1). In space, however, nitrogen is the fourth most abundant element (when not considering hydrogen and the noble gases); the ratios of O/N and C/N amount to about 10 and 5, respectively. The molecular nitrogen (N2 ) now present in Earth’s atmosphere is considered to have been there since the planet was first formed, 4.6 Gyr ago. Variation in the mass of O2 , CO2 , and H2 O, but not that of N2 , must have

5.3 Nitrogen

| 323

led to variation in total atmospheric pressure with time. The residence time of N2 in the atmosphere, relative to exchanges with and storage in crustal rocks, is estimated to be about 1 Gyr. The dissociation energy of the N≡N triple bond is very large (945.33 kJ mol−1 ); hence, molecular nitrogen is the most stable nitrogen compound. The formation of ammonia according to N2 + 3 H2 󴀘󴀯 2 NH3 is exothermic (92.28 kJ mol−1 ), but the initial N2 dissociation requires large amounts of activation energy. Industrial ammonia synthesis N2 + 3 H2 → 2 NH3 (Haber–Bosch process at about 200 bar and 500 °C in an iron oxide catalyst) is a copy of the enzyme-based reduction of molecular nitrogen by nitrogen-fixing bacteria. The photodissociation of N2 occurs at wavelengths smaller than 100 nm in the upper mesosphere (Richards et al. 1981, Wu et al. 1983). The reaction N2 + O2 󴀘󴀯 2 NO is endothermic (180.6 kJ mol−1 ) but in the gross budget N2 + 2.5 O2 → 2 HNO3 exothermic (30.3 kJ mol−1 ); again, the activation energy to split N2 under normal conditions in the climate system is not available (otherwise all atmospheric O2 would be converted into nitric acid and dissolved in the ocean). We live in an era with a surplus of ammonia (NH3 ) and ammonium (NH+4 ) in many parts of the world. The invention of the Haber–Bosch process, patented in 1908 by Fritz Haber (1868–1934) and commercialized by Carl Bosch (1874–1940), has made it possible to produce ammonia relatively cheaply in large quantities. In particular, the widespread use of ammonia and its derivatives as agricultural nitrogen fertilizers has substantially increased emissions of ammonia to the atmosphere, leading to a wide range of different environmental problems. These include the eutrophication of seminatural ecosystems, acidification of soils, formation of fine PM in the atmosphere, and alteration of the global greenhouse balance. Even though the atmosphere is 78% nitrogen (N2 ), most biological systems are nitrogen limited on a physiological timescale because most biota are unable to use molecular nitrogen (N2 ). Two natural processes convert nonreactive N2 to reactive N: lightning and biological fixation. Natural chemical fixation is due to lightning where NO is produced, similar to high-temperature industrial processes (Chapter 5.3.2). This source is small compared with biological fixation from N2 and is negligible for the biological nitrogen cycle but important for the atmospheric NO budget. The environmental importance of nitrogen, more precisely its role for life processes, lies in a wide range of oxidation states from N(−3) to N(+5), thereby promoting redox processes (Figure 5.19). It is the only element existing in all nine oxidation states (Tables 5.11 and 5.12): Reactive nitrogen is defined as any single nitrogen species with the exception of N2 and N2 O. It includes: – NO y (NO+NO2 +N2 O3 +N2 O4 +HNO2 +HNO3 +NO3 +N2 O5 +HNO4 +organic NOx + particulate NO−2 , and NO−3 ), – NHx (NH3 + NH+4 ), NH2 OH, and – Organically bonded N (mostly –NH2 but also –SCN and other structures or functional groups with special biochemical functions).

324 | 5 Substances and chemical reactions in the climate system

Fig. 5.19: Biochemical, soil chemical, and atmospheric chemical nitrogen oxidation and reduction in biosphere (nitrification, ammonification, and denitrification). Symbols for redox processes: −e: red, +e: ox, –H: ox (≡ e − H+), +H: red (≡ +H+ − e), –O: red (≡ +2 H+ − H2 O), +O: ox (≡ +H2 O − 2H); circles: gases; dotted boxes: intermediates. Tab. 5.11: Nitrogen compounds in different oxidation states (cf. Table 5.12). Oxidation state

−3

−2

−1

±0

+1

+2

+3

+4

+5

Compound

NH3

N2 H4

N2 H2

N2

N2 O

NO

N2 O3

NO2

N2 O5

Note that NO x = NO + NO2 and often is defined as NOz = NOy − NOx (Table 5.12). In addition to being important to biological systems, reactive nitrogen also dramatically affects the chemistry of the atmosphere. At very low NO concentrations, ozone (O3 ) is destroyed by reactions with radicals (especially HO2 ), although at higher levels of NO (larger than 10 ppt), there is a net O3 production (because HO2 reacts with NO to form NO2 ). The photolysis of NO2 (eq. (5.15)) is the only source of photochemically produced O3 in the troposphere. Although N2 O is not viewed as a reactive form of nitrogen in the troposphere, it adsorbs IR radiation and acts as a GHG. In the stratosphere, N2 O is oxidized to NOx and affects O3 concentrations.

5.3 Nitrogen

| 325

Tab. 5.12: Inorganic nitrogen species. Note: All H atoms can be partly or fully replaced by organic groups (R) forming organic nitrogen compounds (Table 5.13). Ox – oxidation state. Ox

Hydrides and oxides

Name

Oxoacids

Name

−3

NH3

Ammonia

–

–

−2

N2 H4 (H2 N=NH2 )

Hydrazine g

–

–

−1

N2 H2 (HN=NH) NH HN3 (H–N=N=N)

Diimine a, g Nitrene (or azane) c Hydrazoic acid b

HONH2 – –

Hydroxylamine – –

±0

N2 (N≡N)

Nitrogen

–

–

+1

N2 O

Dinitrogen monoxide

HNO (H–N=O) HON=NOH

Nitroxyl d, c g Hyponitrous acid e g

+2

NO

Nitrogen monoxide f

HNO2 (HONO)

Nitrous acid n

+3

N2 O3

Dinitrogen trioxide

HOONO H2 N2 O3

Peroxonitrous acid c, j

dioxide l

m

+4

NO2 N2 O4

Nitrogen Dinitrogen tetroxide

– HO–N(H)NO2 (OH)2 N–N(OH)2

– Hyponitric acid h Hydronitrous acid i, g

+5

NO3 N2 O5

Nitrogen trioxide c, k Dinitrogen pentoxide

HNO3 (HONO2 ) HNO4 (HOONO2 )

Nitric acid o Peroxonitric acid

a

Likely only intermediates in organisms, like the azo group (–N=N–) in organic compounds, also termed diazene, diimide. b Older name: hydronitric acid; IUPAC name: hydrogen acid. Likely only at workplaces and not in the environment. c Unstable (intermediate) radical; deprotonated form (conjugated base): nitroxyl ion NO− (oxonitrate(1–)). d IUPAC name: azanone; also called hydrogen oxonitrate and nitrosyl hydride. e Isomeric with nitramide H2 N − NO2 . f Old name: nitrous oxide. g Likely only intermediates in organisms, namely plants. h Does not exist freely, only as salt (termed Angeli’s salt). i Also termed nitroxylic acid; corresponding anion, known as nitroxylate, is N O4− . 2 4 j Peroxonitrite anion (ONOO− ) is a stable species in alkaline solution; IUPAC name: oxoperoxonitrate(1–). k Nitrate radical. l Old name: nitric oxide. m − Exists only as salt N2 O2− 3 (Angeli’s salt) – trioxodinitrate: O=N–N(O )2 . There are several isomers of H2 N2 O3 : hyponitric acid (O=)2 N–N(H)–OH, amino nitrate H2 N–O–N⊕ (=O)–⊖ O (1-oxodiazoxane 1-oxid), diazenediol HO–⊕ N(–OH)–O⊖ , N-hydroxonitramide ⊖ O–⊕ N(=O)–N(H)–OH. n Protonation of HNO2 led to H2 NO+2 , which dehydates to nitrosonium NO+ (nitrosyl cation). o Protonation of HNO led to H NO+ , which dehydates to nitronium NO+ (nitryl cation). 3 2 3 2

326 | 5 Substances and chemical reactions in the climate system NH3 is the major source of atmospheric alkalinity (NH3 + H2 O 󴀗󴀰 NH+4 + OH− ) and a source of acidity in soils. Deposited NH3 /NH+4 is nitrified in soils and water to nitrite NO−2 and, ultimately, to nitrate NO−3 , where two moles of H+ are formed for each mole of NH3 /NH+4 . Only a small part of atmospheric NH3 (≤ 5%) is oxidized by OH radicals, where a main product was estimated to be N2 O, thereby contributing around 5% to estimated global N2 O production. Thus, any change in the rate of formation of reactive nitrogen (and N2 O), its global distribution, or its accumulation rate can have a fundamental impact on many environmental processes. Most organic nitrogen compounds are derived from some of the aforementioned inorganic species, such as amines (–NH2 ), nitroso (or nitrosyl) compounds (–N=O), and nitro compounds (–NO2 ).

5.3.1 Natural occurrence and sources A total of 78.1 Vol-% of air contains dinitrogen (N2 ), and this corresponds to about 99% of all nitrogen on Earth. The other main forms of nitrogen are nitrate deposits and proteins in biomass, both representing the most oxidized N(+V) and most reduced N(–III) form of nitrogen and cycling through diverse oxides of nitrogen (Figure 5.19). In animals (including humans) and some plants, nitrogen is the third most common element (after hydrogen and carbon, excluding water as a molecule), occurring in the form of proteins. It is the –NH2 group (together with the carboxyl group –COOH), forming amino acids, that builds up proteins, large biological molecules that perform a vast array of functions within living organisms, including catalyzing metabolic reactions, replicating DNA, and transporting molecules from one location to another. Biological processes in soils, waters (including ocean), and even organisms themselves, together with inorganic conversions in media, produce a huge number of compounds (almost all presented in this book) found in environmental compartments and, depending on physical conditions, exchanged and transferred between soil, water, and air. The bacterial decomposition of animal excreta is the largest source of NH3 . In addition, but in much smaller quantities, many organic amines are emitted from animals. It is likely that natural ecosystems (forest, grassland) emit no or only small amounts of ammonia because normally there is a deficit of fixed nitrogen in landscapes. In contrast to sulfur species, there are no principal differences between natural and anthropogenic processes in the formation and release of reactive nitrogen species. Industrial nitrogen fixation (in separate steps: N2 → NH3 , N2 → NO x , NOx → HNO3 ) proceeds via the same oxidation levels as biotic fixation and nitrification, either by design in chemical industries (ammonia synthesis, nitric acid production) or unintentionally in all high-temperature processes, specifically combustion, as a byproduct due to N2 + O2 → 2 NO.

5.3 Nitrogen

| 327

On cultivated soils, as for NH3 , the primary NO source is N fertilizer application; natural soils have much less specific emissions. Denitrification (Chapter 6.1.4) is the direct way of producing molecular nitrogen (N2 ), dinitrogen monoxide (N2 O), and nitrogen monoxide (NO) (Figure 5.19). This path is parallel to the formation of ammonia/ ammonium (ammonification), and therefore it is assumed that all these compounds appear together, but in different quantities. Soil structure and pH, oxygen content, humidity, and temperature, but also radiation, are important parameters in determining emissions. N2 O emissions from soils under natural vegetation are significantly influenced by vegetation type, soil organic C content, soil pH, bulk density, and drainage, while vegetation type and soil C content are major factors for NO emissions. A soil emission similar to those of ammonia is proposed. The emission of N2 O is perhaps twice that, which is supported by the more direct chemical formation pathway during denitrification (Figure 5.19). In analogy to ammonia, microorganisms living in soils and plants assimilate both gases. As for ammonia, emission of NO and N2 O is considered to be a loss for the organisms, in contrast to emission of N2 by denitrification, closing the atmospheric cycle (> 100 Tg N yr−1 ). As for NO production during lightning, similar conversion processes occur in all combustion and high-temperature processes (see next Chapter 5.3.2). To a minor percentage, the fuel nitrogen content contributes to NO formation, but this pathway is relatively more important for biofuels. There is no less uncertainty in estimating anthropogenic NO emissions. While the fossil-fuel source is estimated at 20–25 Tg N yr−1 , total NO emissions are about 44 Tg N yr−1 .

5.3.2 Thermal dissociation of dinitrogen (N2 ) At high temperatures (T > 1000 °C), molecular nitrogen from air converts into NO. This happens in internal combustion engines, industrial and municipal combustion, and heating processes but not during biomass combustion (burning), which does not generate such high T. An important natural process is lightning. Depending on the flash energy, ambient air molecules dissociate and subsequently new molecules are produced according to air chemical conditions. Depending on the flash energy and the molecular dissociation energy, there is no other limit to decompose (and subsequently to synthesize) any molecule in the atmosphere. Because of the large dissociation energy in N2 , the initial step is dioxygen thermal dissociation (O2 󴀘󴀯 O + O) and a subsequent reaction of oxygen atoms with N2 : N2 + O → NO + N

k 5.150 = 1.8 ⋅ 1012 exp(−319/RT) ,

(5.150)

N + O2 → NO + O

k 5.151 = 6.4 ⋅ 10 exp(−26/RT) .

(5.151)

9

In steady state (d[N]/ dt = 0), it follows that d[NO] = 2 ⋅ k 5.150 [N2 ][O] . dt

(5.152)

328 | 5 Substances and chemical reactions in the climate system

A reaction chain follows where radical reaction eqs. (5.153) and (5.154) are rapid, whereas thermal molecular reaction eqs. (5.155)–(5.157) are slow; the radical reaction rates of eqs. (5.158) and (5.159) are slow due to a lower reaction probability: NO + N → N2 + O ,

(5.153)

NO + O → N + O2 ,

(5.154)

NO 󴀘󴀯 N + O ,

(5.155)

NO + NO → N2 O + O , NO + NO + O2 → 2 NO2

(5.156) −19

k 5.157 ≈ 2 ⋅ 10

.

(5.157)

For a small percentage, the formation of N2 O is possible, which can also effect NO formation: N2 + O + M → N2 O + M ,

(5.158)

N2 O + O → NO + NO .

(5.159)

This mechanism is valid for all high-temperature processes (lightning, metallurgical processes, glass production). The mechanism is known as the “thermal NO mechanism” or “Zeldovich mechanism.” In fuel-rich flames (hydrocarbon combustion) additional N + OH → NO + H (5.160) occurs. During the combustion of fossils fuels, CH, H, O, and OH radicals are produced, and the following reactions have been proposed (Fenimore mechanism): CH + N2 → HCN + N ,

(5.161a)

CH2 + N2 → HCN + NH .

(5.161b)

The different nitrogen products quickly oxidize to NO. Ultimately, the primary product is NO, which can then enter into further oxidation processes to NO2 (Chapter 5.3.5.1).

5.3.3 Ammonia (NH3 ) All nitrogen-fixing organisms are prokaryotes (bacteria). Some of them live independently of other organisms – the so-called free-living nitrogen-fixing bacteria. Others live in intimate symbiotic associations with plants or other organisms (e.g., protozoa). Biological nitrogen fixation can be represented by the following equation, in which 2 moles of ammonia are produced from 1 mole of nitrogen gas, at the expense of 12 moles of ATP (adenosine triphosphate, empirical formula: C10 H16 N5 O13 P3 ; ADP adenosine diphosphate) and a supply of electrons and protons using an enzyme complex called nitrogenase. This reaction is performed exclusively by prokaryotes (bacteria and related organisms): N2 + 6 H+ + 6 e− + 12 ATP → 2 NH3 + 12 ADP + 12 phosphate .

5.3 Nitrogen

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329

There is stepwise hydrogenation via diimine N2 H2 , an unstable intermediate, and hydrazine N2 H4 (diazene) to ammonia (azane): 2H

2H

2H

N2 󳨀󳨀→ N2 H2 󳨀󳨀→ N2 H4 󳨀󳨀→ 2 NH3 . Hydrazine is found in small concentrations in natural waters as a pollutant from industrial manufacturing. As mentioned, the technical formation of NH3 , to provide nitrogen fertilizers (chemical nitrogen fixation), is based on the Haber–Bosch process: 3 H2 + N2 󴀘󴀯 2 NH3 , Fe

Hads

Hads

Hads

󳨀󳨀→ 󳨀󳨀 󳨀→ 󳨀󳨀 󳨀→ 󳨀󳨀 󳨀→ N2 ← 󳨀󳨀 Nads 󳨀 ← 󳨀󳨀 (NH)ads 󳨀 ← 󳨀󳨀 (NH2 )ads 󳨀 ← 󳨀󳨀 (NH3 )ads 󴀘󴀯 NH3 . The following chain represents different groups derived from ammonia, whereas most compounds are derived from the amino group NH2 , for example, urea CO(NH2 )2 , amine RNH2 , hydrazine (NH2 )(NH2 ), acetamide CH3 CO(NH2 ), and hydroxylamine NH2 OH: ±H+

±H

NH+4 ←󳨀󳨀→ NH3 ←󳨀→ [NH2 ]∙ ammonium ammonia amide

±H

←󳨀→

±H

[NH]∙∙ ←󳨀→ [N]∙∙∙ imide nitride .

Ammonia²⁴ is relatively stable in air, and its importance lies in the formation of salts. Warburg (1914) first suggested the photodissociation of NH3 . The dissociation energy of ammonia using photolysis at 205 nm was determined to be 4.34 ± 0.07 eV (Amorim et al. 1996); thus, it is not relevant in the atmosphere (but was discussed in connection with the early atmosphere): NH3 + hν → NH2 + H .

(5.162)

The only gas-phase reaction of NH3 proceeds with OH, forming the amidogen (amide) radical NH2 ; k 5.163 = 1.6 ⋅ 10−13 cm3 molecules−1 s−1 : NH3 + OH → NH2 + H2 O .

(5.163)

Ennis et al. (2009) first detected the water amidogen radical complex (H2 O–NH2 ) as a reactive intermediate in atmospheric ammonia oxidation. The reaction of NH2 with O2 is slow (k < 6 ⋅ 10−21 cm3 molecule−1 s−1 at 298 K), making it unimportant in the

24 The origin of the word ammonia is often said to relate to the classical discovery of sal ammoniac near the Temple of Zeus Ammon, in the Siwa Oasis of the Lybian Desert. Pliny the Elder is often cited as the first to note the existence of hammoniacum (i.e., sal ammoniac), noting its occurrence near the Temple of Ammon. There are different stories on its origin about how sal ammoniac (NH4 Cl) was formed by solar distillation in the sands from the urine and dung of camels at the Siwa Oasis, and because of the nearby sea, sea salt (NaCl) was deposited. Sal ammoniac (in German Salmiak) was used for medical purposes and for incense in the temple ceremonies (Sutton et al. 2008).

330 | 5 Substances and chemical reactions in the climate system atmosphere. The products are not specified (NH2 O2 , NO + H2 O, OH + HNO). The reaction of NH2 with O3 is fast (Hack and Wagner 1981) and proceeds probably via NH2 O to hydroxylamine: RH

NH2 + O3 󳨀󳨀󳨀󳨀→ NH2 O 󳨀󳨀󳨀→ NH2 OH . (−O2 )

(5.164)

(−R)

The most likely fate of NH2 (Finlayson-Pitts and Pitts (2000) suggest a lifetime of about 2–3 s) is to react with NO x : k 5.165 (= k 165a +k 165b +k 165c ) = 1.6⋅10−11 cm3 molecule−1 s−1 at 298 K, with k 165a /k 5.165 = 0.9 and (k 165b + k 165c )/k 5.165 = 0.1: NH2 + NO → N2 + H2 O ,

(5.165a)

NH2 + NO → N2 H + OH ,

(5.165b)

NH2 + NO → N2 + H + OH .

(5.165c)

Reaction (5.165a) is considered a key step in the thermal DeNOx process and nitrosation²⁵ of amines (see also Chapter 5.3.6.1) (Miller et al. 1981). The mechanism of eq. (5.165a) remains unknown, but it was suggested that isomers of N2 H2 O (see for further details Chapter 5.3.5.2) occur as intermediates (HNNOH not isolated hydroxydiimide): OH

NH2 + NO → H2 NO–NO → HN=NOH 󳨀󳨀󳨀󳨀󳨀→ N=NOH 󳨀󳨀󳨀󳨀󳨀→ N2 . (−H2 O)

(−OH)

In the reaction with NO2 , channels (a) and (c) are the most probable; no evidence was found for the occurrence of channel (b) or the other exothermic channels leading to −1 N2 + 2 OH or 2 HNO: k 5.166 (= k 166a + k 166b + k 166c ) = 2.0 ⋅ 10−11 cm3 molecule−1 s at 298 K, where k 166a /k 5.166 = 0.25 and k 166c /k 5.166 = 0.75 over the temperature range 298–500 K: NH2 + NO2 → N2 O + H2 O ,

(5.166a)

NH2 + NO2 → N2 + H2 O2 ,

(5.166b)

NH2 + NO2 → H2 NO + NO .

(5.166c)

In summary, ammonia oxidation is negligible (5%) compared with the main fate of NH3 , particle formation via homogeneous nucleation (55%) and (wet and dry) deposition (40%); the numbers in parentheses represent the percentage of emitted NH3 . Thus, ammonia remains in its oxidation state −3, mainly seen as ammonium (NH+4 ) in air, and returns to soils and waters as ammonium, where it moves between the amino group (–NH2 ) in biomass and nitrate (NO−3 ) through nitrification and ammonification.

25 The term nitrosation is interchangeable with nitrolysation; the same holds for nitroso- or nitrosyl compounds (Table 5.13). Both terms refer to a process of converting organic compounds into nitroso derivatives, i.e., compounds containing the R–NO functionality. The reagent is called a nitrosating agent, i.e., HNO2 , N2 O3 , and NO+ .

5.3 Nitrogen

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331

In air (and exhaust gases), gaseous NH3 combines with HCl as well HNO3 to form a gas–solid equilibrium (called gas-to-particle conversion): NH3 (g) + HCl(g) 󴀘󴀯 NH4 Cl(g) 󴀘󴀯 NH4 Cl(s) , NH3 (g) + HNO3 (g) 󴀘󴀯 NH4 NO3 (s) .

(5.167a) (5.167b)

NH3 is easily soluble but a weak base: NH3 + H2 O 󴀘󴀯 NH+4 + OH−

pK = 4.75 .

(5.168)

After dissolution in hydrometeors (clouds, rain), ammonia neutralizes acids, specifically sulfuric acid (H2 SO4 ) and nitric acid (HNO3 ); in earlier times, before air pollution, the main salt in rainwater was (NH4 )2 CO3 mixed with NaCl. Today, the most abundant salt in background atmospheric aerosol is ammonium sulfate (NH4 )2 SO4 or hydrogen sulfate NH4 HSO4 . It is formed during homogeneous SO2 oxidation in air to SO3 and subsequent condensation to particulate sulfuric acids, taking up gaseous NH3 . Now, after drastic SO2 abatement. replacement of sulfate by nitrate is observed. In Chapter 5.3.5.2, the fate of ammonium nitrite in evaporating water droplets will be discussed; see eqs. (5.213)–(5.216). In aqueous solution, ammonia is oxidized according to eq. (5.163) with a rate constant k = 9.7 ⋅ 107 L mol−1 s−1 (Hickel and Sehested 1992). The product, aminyl radical NH2 , reacts, in contrast to the gas phase, with O2 very quickly to form the aminylperoxo radical NH2 O2 with a rate constant k ≈ 9 ⋅ 108 L mol−1 s−1 (Laszlo et al. 1998). NH2 O2 deprotonates and isomerizes and finally forms NO in solution: O2

NH3 + OH 󳨀󳨀󳨀󳨀󳨀→ NH2 󳨀󳨀→ NH2 O2 → HNOOH 󳨀󳨀󳨀󳨀󳨀→ NO , (−H2 O)

NH2 O2 +

O−2 󳨀󳨀󳨀󳨀→ (−O2 ) O2

(−H2 O)

NH2 O−2 󳨀󳨀󳨀󳨀󳨀→ (−H2 O)

− O2

NO 󳨀󳨀→ O=N–O–O− (peroxonitrite) ,

NH2 O−2 󳨀󳨀→ O=N–O–O− + HO2

(or NO3 + HO−2 ) .

Hydroxylamine (NH2 OH) is found in small concentrations in natural waters because it is known as an intermediate in the biological oxidation of ammonia to nitrite by ammonia-oxidizing bacteria and in the dissimilatory sulfate reduction (Lees 1952). However, abiotic hydroxylamine conversion is also described (e.g., Soler-Jofra et al. 2016 and references therein); its reaction with nitrous acid is decribed in Chapter 5.3.5.2. NH2 OH reacts fast in aqueous solution with OH and superoxide ion O−2 (Bors et al. 1977) to NO by an unknown mechanism. Based on electrochemical studies of the kinetics of reduction (final product NH3 ) and oxidation (final products N2 , N2 O, NO, NO−2 ) of NH2 OH in aqueous solution (Möller and Heckner 1971, 1972, 1974), the following mechanism can be derived, which is basically supported by the investigation of autoxidation of hydroxylamine by Hughes and Nicklin (1971). An aqueous diffusion coefficient is determined to be Daq = 2.54 ⋅ 10−5 cm2 s−1 and pKa = −5.5 of proto-

332 | 5 Substances and chemical reactions in the climate system

nated hydroxylamine (Möller and Heckner 1972); see also eq. (5.224) for the formation of hyponitrous acid H2 N2 O2 from nitroxyl HNO and eq. (5.226) for its fate: NH2 OH + H+ 󴀘󴀯 NH3 OH+

(pK = 5.5)

OH

OH

(−H2 O)

(−H2 O)

O

H+

→ H2 N2 O2 󳨀󳨀→ HN2 O−2 󳨀󳨀󳨀󳨀󳨀−→ N2 O NH2 OH 󳨀󳨀󳨀󳨀󳨀→ HNOH 󳨀󳨀󳨀󳨀󳨀→ HNO 󳨀 (−OH )

HNOH

HNOH 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ N2 (−2 H2 O)

HNOH + HNO → N2 + OH + H2 O O−2

e−

H2 O

NH2 OH 󳨀󳨀󳨀󳨀→ NH2 OH− 󳨀󳨀󳨀󳨀󳨀−→ NH2 󳨀󳨀→ NH−2 󳨀󳨀󳨀󳨀󳨀−→ NH3 (−O2 )

(−OH )

(−OH )

5.3.4 Dinitrogen oxide (N2 O) Dinitrogen oxide²⁶ is a biologically important gas and rather stable in the troposphere. It only undergoes either uptake by soils and vegetation or transport to the stratosphere, where it photodissociates up to 90%; however, photolysis is effective only for λ < 240 nm: N2 O + hν (λ < 240 nm) → N2 + O . (5.169) Another pathway is via attack of singlet oxygen (k 5.170 = 1.2 ⋅ 10−10 cm3 molecules−1 s−1 ): N2 O + O(1 D) → 2 NO ,

(5.170a)

N2 O + O( D) → N2 + O2 .

(5.170b)

1

N2 O contributes to the greenhouse effect. At present this contribution is still negligible, but after energy conversion (stop of CO2 emission), it could become a problem because of likely further increasing N2 O emissions from agriculture (together with CH4 emissions from agriculture).

5.3.5 Inorganic nitrogen oxides and oxoacids (NOy ) Nitrogen forms oxides with the formula NOn (n = 1, 2, 3) and N2 On (n = 1, 2, 3, 4, 5, 6); N2 O was discussed in the previous section, whereas N2 O6 and N4 O n (n = 1, 2) play no role under environmental conditions. Here we present nitrogen monoxide (NO),²⁷ nitrogen dioxide (NO2 ), nitrogen trioxide (NO3 ), and dinitrogen pentoxide

26 The common names laughing gas and nitrous oxide for N2 O should not be used. 27 The common name nitric oxide for NO should no longer be used.

5.3 Nitrogen

| 333

(N2 O5 ). Several oxoacids exist from nitrogen; of importance for the environment are only nitrous acid (HNO2 ) and nitric acid (HNO3 ) (from which the anions nitrite NO−2 and nitrate NO−3 are derived), and as intermediates H3 NO (hydroxylamine NH2 OH) and nitroxyl (HNO). In contrast to the corresponding oxoacids of sulfur (H2 SO3 and H2 SO4 ), HNO2 and HNO3 occur as molecular gas in air. It is useful to distinguish between groups (the termination of NO x is also practical). Most in situ analyzers based on chemiluminescence measure the sum of NO+NO2 and only a two-channel technique can be used to detect separately NO and NOx , where the difference is interpreted as NO2 . The following definitions may be given: NOx = NO + NO2 , NO y = NO x + NO3 + N2 O5 + HNO2 + HNO3 + organic N + particulate N , NO z = NO y − NO x . Therefore, NO y represents the sum of all nitrogen with the exception of ammonia (and amines), N2 O, and N2 . 5.3.5.1 Gas-phase chemistry NO2 and NO play crucial roles in the ozone formation cycle and ROS chemistry (Chapter 5.2.3.2). The former provides the source of atomic oxygen (eq. (5.15)) and the latter cycles the HO2 radical back to OH (eq. (5.34)) for continuous “burning” of ozone precursors such as CO, CH4 , and NMVOC (Figure 5.5): NO2 + hν → NO + O,

(5.15)

NO + HO2 → NO2 + OH ,

(5.34)

NO + O3 → NO2 + O2 .

(5.35)

Reaction (5.34) probably proceeds via peroxonitrous acid (HNO3 ) as a short-lived intermediate (the acid has never been detected, not to be confused with nitric acid HO–N(=O)2 ): NO + HO2 󴀘󴀯 O=N–O–O–H → O=N=O + OH . In Figure 5.7, the following competing reaction to eq. (5.34) is included: NO + RO2 → NO2 + RO .

(5.171)

The aging of air masses in terms of oxidation state is often described by ratios such as NO y /NOx . It can clearly be seen that during the day the ratio NO2 /NO depends on radiation and O3 concentration. At a close distance to a strong NO source (e.g., intersections and freeways), O3 can be totally depleted through reaction (5.35). This is also termed “ozone titration.” NO2 carries oxygen and releases it via photodissociation. This was observed by the fact that O3 concentration at suburban sites is often greater than that at urban sites, leading to the following definition of Ox : Ox = O3 + NO2 .

334 | 5 Substances and chemical reactions in the climate system

Ox represents the sum of odd oxygen and should be roughly constant for suburban and urban sites, as found by Kley et al. (1994). NO x reacts with ClO (see also Chapter 5.7.3): NO + ClO → NO2 + Cl , NO2 + ClO → ClONO2 .

(5.172) (5.173)

NOx forms equilibrium with dimers: NO + NO2 󴀘󴀯 N2 O3 (ON–NO2 ) ,

(5.174)

NO2 + NO2 󴀘󴀯 N2 O4 (O2 N − NO2 ) .

(5.175)

Both dimers (they are more soluble than NO and NO2 ) were discussed as precursors to the formation of the corresponding oxoacids in solution (Möller and Mauersberger 1990a). However, compared with other pathways and because of their very low gasphase concentrations, they were assessed as negligible; N2 O3 might still play a role as an interfacial intermediate (see subsequent discussion). N2 O3 is the anhydride of nitrous acid (N2 O3 + H2 O = 2 HNO2 ). The gas-phase equilibrium constant KN2 O3 = [NO][NO2 ]/[N2 O3 ] = 1.91 atm at 298 K suggests that N2 O3 is negligible in air. By contrast, KN2 O4 strongly depends on temperature (0.0177 at 273 K and 0.863 at 323 K) (Chao et al. 1974) but is not considered in with respect to the atmosphere (except in plumes). The biological role of nitrogen oxides will be briefly discussed in Chapter 5.3.5.2. Under atmospheric conditions, the formation of NO2 is relevant only through reactions (5.34) and (5.35). Reactions involving dioxygen might have importance only under extremely high NO x concentrations (such as in exhaust systems and biological cells) and are negligible under atmospheric conditions: k 5.176 = 2.0 ⋅ 10−38 cm6 molecule−2 s−1 at 298 K: NO + NO + O2 → 2 NO2 .

(5.176)

Equation (5.176) does not represent an elementary reaction; it is a multistep mechanism involving NO3 or the dimer (NO)2 . This NO3 (O=NOO) is an isomer to the nitrate radical O=N=O(O) and the first step in NO oxidation. It is clear that this very unstable peroxo radical will almost decompose by quenching to NO + O2 , which results in a slow reaction probability (we will encounter this reaction later in biological systems): NO

NO + O2 󴀘󴀯 O–O–N=O ←󳨀→ O=N ⋅ ⋅ ⋅ O–O–N=O → NO2 + NO2 . Since NO2 is the precondition for near-surface ozone formation and thereby triggering ROS chemistry, any primary NO2 emission (e.g., diesel cars) is of crucial importance for changing the atmospheric ROS budget because there is no ROS consumption in NO–NO2 conversion. The next higher nitrogen oxide, only a short-lived but extremely important atmospheric intermediate, is NO3 (directly derived from nitrate

5.3 Nitrogen

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ions via electron loss and also called nitrate radical), an important nighttime oxidant (Brown and Stutz 2012): k 5.177 = 3.5 ⋅ 10−17 cm3 molecule−1 s−1 at 298 K: NO2 + O3 → NO3 + O2 .

(5.177)

The lifetime of NO3 is very short and is much shorter during the day because of effective photodissociation (quantum yield 1.0 for λ ≤ 587 nm); at wavelengths less than 587 nm, NO3 radical dissociation is predominantly to NO2 + O(3 P): NO3 + hν → NO + O2 3

NO3 + hν → NO2 + O( P)

λthreshold ≥ 714 nm ,

(5.178a)

λthreshold = 587 nm .

(5.178b)

Orlando et al. (1993) suggested photodissociation rates at Earth’s surface, for an overhead Sun and in a wavelength range 400–700 nm, of j(NO2 + O) = 0.19 s−1 and j(NO + O2 ) = 0.016 s−1 . Moreover, collision with NO x removes NO3 : k 5.179 = 2.6 ⋅ 10−11 cm3 molecule−1 s−1 at 298 K and k 5.180 = 3.6 ⋅ 10−30 (T/300)−4.1 [N2 ]cm3 molecule−1 s−1 over the temperature range 200–300 K: NO3 + NO → 2 NO2 ,

(5.179)

NO3 + NO2 → N2 O5 .

(5.180)

Hence, at night NO3 accumulates (daytime concentrations are negligible) and plays a role similar to OH in H abstraction, whereas stable HNO3 is produced as the final product of NO oxidation (NO → NO2 → NO3 → HNO3 ): NO3 + RH → HNO3 + R .

(5.181)

The specific reaction rates with different hydrocarbons are generally lower (about three to four orders of magnitude) compared with OH + RH, but the high nighttime NO3 concentration can balance it out and provide absolute rates comparable to OH. Of high importance is the fast reaction of NO3 with isoprene and α-pinene (k > 3 ⋅ 10−12 cm3 molecule−1 s−1 ; see Wayne et al. 1991 for more details on atmospheric NO3 chemistry). Reaction (5.181) is only one way of producing nitric acid in gas phase (Eqs. (5.182) and (5.188)). N2 O5 is the anhydride of HNO3 , but it reacts absolutely negligibly in the gas phase with H2 O: k 5.182 < 1⋅10−22 cm3 molecule−1 s−1 : N2 O5 + H2 O → 2 HNO3 .

(5.182)

In a certain sense, N2 O5 is in (dynamic) equilibrium with NO2 and NO3 according to the fast reaction (no kinetic is known) eq. (5.183). It is remarkable that until now no measurements of N2 O5 have existed, but extensive measurements of NO3 have, from which indirect conclusions on N2 O5 were drawn: N2 O5 + M → NO2 + NO3 + M .

(5.183)

336 | 5 Substances and chemical reactions in the climate system

NO3 and N2 O5 will be quantitatively scavenged by clouds and precipitation to form HNO3 and NO−3 , respectively (see next chapter). Some reactions of N2 O5 with sea salt were studied, producing gaseous nitryl chloride from NaCl (and similarly with NaBr and NaI) (Finlayson-Pitts and Pitts 2000), which is a daytime Cl oxidant source (Thornton et al. 2010): N2 O5 (g) + NaCl(s) → ClNO2 (g) + NaNO3 (s) . (5.184) NO2 also reacts rapidly with sea salt to produce gaseous nitrosyl chloride (Schroeder and Urone 1974): 2 NO2 (g) + NaCl(s) → ClNO(g) + NaNO3 (s) .

(5.185)

Measured and predicted ClNO2 can reach high levels (in a range of 1 ppb) in several areas across the Northern Hemisphere, especially during winter, and can account for a sizeable fraction of the NO y budget (Sarwar et al. 2014 and references therein). The cycling of nitrogen oxides and chlorine (see also Chapter 5.7.3) through nitryl chloride (ClNO2 ) is of global relevance. It effectively extends the lifetime of NO2 , allowing it to produce more ozone and to be transported by air currents away from its primary source. Moreover, in both reactions, the significance consists of the possible subsequent photolytic release of Cl (or related halogen) radicals, which can enter, for example, into O3 destruction cycles: ClNO + hν → NO + Cl ,

(5.186)

ClNO2 + hν → NO2 + Cl .

(5.187)

In summary, we present the NOy chemistry in the following line (see Chapter 5.7.3 for more details on NOy – chlorine chemistry): O3

O3

NO2

particulate Cl−

hν

NO,hν

M

(−NO3 )

hν

󳨀→ 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀→ 󳨀󳨀 󳨀→ NO 󳨀 ← 󳨀󳨀 NO2 󳨀 ← 󳨀󳨀 NO3 󳨀 ← 󳨀󳨀 N2 O5 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀−󳨀󳨀󳨀→ NO2 󳨀󳨀→ Cl + NO2 . We now turn to the formation of nitrogen oxoacids. As noted, nitric acid is the final product formed from NO3 and N2 O5 via phase transfer as well as from NO2 in a fast reaction with OH; k 5.188 = 3.3⋅10−30 (T/300)−3.0 [N2 ]cm3 molecule−1 s−1 over the temperature range 200–300 K (about 6.0 ⋅ 10−11 cm3 molecule−1 s−1 at 298 K): NO2 + OH + M → HNO3 + M .

(5.188)

The reaction of OH with NO2 to form nitric acid (HONO2 ) is an effective chain-termination step in atmospheric chemistry because HOx and NOx are sequestered in the reservoir species, nitric acid. Besides nitric acid, HOONO (peroxonitrous acid) can be formed in reaction (5.188) according to Golden and Smith (2000); however, it will decay into several products. The photodissociation of HNO3 is negligible, and the fate of nitric acid is tied up with scavenging, dry deposition, and formation of particles in accordance with eqs. (3.118) and (3.122), which are also finally deposited.

5.3 Nitrogen

|

337

The reaction with OH is too slow to be important in the lower troposphere, k 5.189 = 1.5 ⋅ 10−13 cm3 molecule−1 s−1 at 298 K and 1 bar of air: HNO3 + OH → NO3 + H2 O .

(5.189)

NO2 also reacts with HO2 to produce peroxonitric acid HOONO2 (HNO4 ); it follows formally an equilibrium constant of 2⋅10−11 at 298 K (k 5.190+ = 1.8⋅10−31 (T/300)−3.2 [N2 ] cm3 molecule−1 s−1 and k 5.190− = 1.3 ⋅ 10−20 [N2 ]cm3 molecule−1 s−1 ): N2

NO2 + HO2 ← 󳨀→ HNO4 , HNO4 + hν (λ < 1184 nm) → NO2 + HO2 .

(5.190) (5.191)

This acid is very unstable and decomposes immediately; only in the upper troposphere at low temperatures is a certain accumulation and formation of NO2 + HO2 possible. Furthermore, photolysis produces all breakdown species: OH, HO2 , NO, and NO2 . Let us now turn to the formation of nitrous acid. In the atmosphere, its formation by OH radicals is quickly followed by photodissociation (similar to HNO4 ); over the temperature range 200–400 K and quantum yield 1.0 throughout the wavelength range 190–400 nm at 298 K: M(N2 ,O2 )

NO + OH 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HNO2

k 5.192 = 7.4 ⋅ 10−31 (T/300)−2.4 [N2 ]cm3 molecule−1 s−1 , (5.192)

HNO2 + hν → NO + OH

λthreshold = 578 nm ,

(5.193a)

HNO2 + hν → H + NO2

λthreshold = 361 nm ,

(5.193b)

HNO2 + OH → NO2 + H2 O

k 5.194 = 6.0 ⋅ 10−12 cm3 molecule−1 s−1 .

(5.194)

Gaseous HNO2 in ambient air was first measured by Perner and Platt (1979) using differential optical absorption spectroscopy (DOAS). Recent measurements indicate that HNO2 also plays a much larger role in the reactive nitrogen budget of rural sites than previously expected (Acker and Möller 2007 and references therein). The formation of nitrous acid (HNO2 ) via heterogeneous and interfacial pathways (see next chapter) provides a source (especially in the morning after sunrise) to produce OH radicals parallel to the photolysis of O3 (eq. (5.8b)) and HCHO (eq. (5.44)). From measurements it was derived (Acker et al. 2005) that HNO2 accounts for about 30–42% of radical production in air close to the ground, similar to contributions from the photolysis of HCHO and O3 . Figure 5.20 shows the significant difference between nocturnal and daytime NOy chemistry. Note that HNO3 formation proceeds through very different pathways. The interrelationships can be characterized as the following chains: Daytime chemistry:

NO 󴀘󴀯 NO2 → HNO3 ,

Night-time chemistry:

HNO2 ← NO2 󴀘󴀯 NO3 → HNO3 .

338 | 5 Substances and chemical reactions in the climate system

Fig. 5.20: Gas-phase NOy chemistry during the day and at night.

5.3.5.2 Aqueous and interfacial chemistry NO3 , N2 O5 , and HNO3 are quantitatively scavenged by natural waters. Nitric acid is a strong acid and thereby fully dissociated (Table 4.10), whereas nitrous acid is roughly 50% dissociated in hydrometeors: HNO3 → NO−3 + H+ , HNO2 󴀘󴀯

NO−2

+

+H

(5.195) pKa = 3.3 .

(5.196)

When N2 O5 (the anhydride of nitric acid) sticks to any water’s surface, it is completely and quickly converted into nitrate ions: N2 O5 + H2 O → 2 NO−3 + 2 H+ . The nitrate radical NO3 can react with all electron donors in accordance with eq. (5.197) and is therefore a strong oxidant: NO3 + e− → NO−3 .

(5.197)

NO3 reacts with dissolved hydrocarbons (according to the gas-phase reaction (5.181)), but reactions with chloride and sulfite predominate (the fate of Cl radicals is described in Chapter 5.7.4 and that of sulfite radicals in Chapter 5.4.3.2): NO3 + Cl− → NO−3 + Cl NO3 + HSO−3

→

NO−3

+ HSO3

k 5.198 = 9.3 ⋅ 106 L mol−1 s−1 , 9

−1 −1

k 5.199 = 1.7 ⋅ 10 L mol s

.

(5.198) (5.199)

The nitrate ion can be photolyzed; however, in the bulk water phase, the reaction is very slow (j ≈ 10−7 s−1 ). The photodecomposition of NO−3 into OH and NO x species

5.3 Nitrogen

| 339

within and upon ice was discussed over the past decade and can be crucial to the chemistry of snowpacks and the composition of the overhead atmospheric boundary layer (Dubowski et al. 2002, Chu and Anastasio 2003 and references therein), λ > 300 nm and pH < 6: NO−3 + hν → NO−2 + O(3 P) , NO−3

+

+ H + hν → NO2 + OH .

(5.200) (5.201)

Warneck and Wurzinger (1988) found that channels (5.200) and (5.201) contribute 10% and 90%, respectively, but that nitrate photolysis is generally too slow (a lifetime of about 7 days) to be significant in the atmosphere. The significance of reaction (5.200) lies in the subsequent ozone formation (O(3 P) + O2 ). However, more important is the photolysis of nitrite yielding OH: NO−2 + H+ + hν → NO + OH .

(5.202)

In the absence of radical scavengers, atomic oxygen can react with nitrate: NO−3 + O(3 P) → NO−2 + O2

k 5.203 = 2 ⋅ 108 L mol−1 s−1 .

(5.203)

For exactly 200 years it was known that nitrous gases in contact with water produced nitrous acid (Volume 2, Chapter 2.6.6). Raschig (1904) showed that when passing N2 O3 (NO + NO2 ) into liquid water, only HNO2 is formed: NO + NO2 + H2 O → 2 HNO2 .

(5.204)

Other more “exotic” formation pathways of HNO2 in the condensed phase include possible inorganic reactions similar to biogenic denitrification and nitrification processes, for example, from NO (Figure 5.19). Hence, it cannot be excluded that NO is directly associated with HNO2 formation via the aqueous phase despite its very low solubility, which can be increased because of N2 O3 formation (adduct ON–NO2 from NO + NO2 ). The atmospheric importance is that primary emitted NO produces via the condensed phase without consumption of oxidants HNO2 and, finally, OH radicals. When passing NO2 through water, nitrous as well as nitric acid is produced; thus, N2 O4 (adduct O2 N = NO2 from NO2 + NO2 ) is interpreted as a “mixed” anhydride of nitrous and nitric acid: NO2 + NO2 + H2 O → HNO2 + HNO3 .

(5.205)

Reactions (5.204) and (5.205) were proposed to proceed at wetted surfaces, first shown by Akimoto et al. (1987) as an artifact OH source via HNO2 photolysis in smog chamber studies. Kessler (1984) first studied the nocturnal increase of HNO2 due to surface formation without knowing a formation mechanism. Acker et al. (2000) suggested HNO2 formation in clouds because of the large surface provided for heterogeneous

340 | 5 Substances and chemical reactions in the climate system

Fig. 5.21: N2 O4 and N2 O3 interfacial reaction to HNO2 and HNO3 (adapted from Möller 2003).

processes. The heterogeneous hydrolysis of NO2 , which is believed to occur with the same mechanism during the day as at night, was investigated in numerous field and laboratory studies on many different surfaces (references in Acker and Möller 2007). Soils, buildings, roads, and vegetation can hold water in sufficient amounts to promote heterogeneous reactions during the day. Accordingly, different heterogeneous formation pathways were postulated. For example, HNO2 can be formed from NO2 suspended on a reducing soot surface as indicated by Ammann et al. (1998). However, only a very small fraction of the surface of fresh soot particles acts with a high reaction probability, proceeding to a very fast termination (e.g., see discussion in Trick 2004). Until now, the chemical formation mechanism has not been well understood and no kinetics is available (cf. Figure 5.21). According to eq. (5.204), nitrous acid can accumulate in surface water during the night and is released in the gas phase due to water evaporation, whereas nitric acid remains absorbed on the surface. Although formation on ground surfaces is expected to be the main source, it seems likely that under certain circumstances – when atmospheric aerosol or fog droplets provide sufficient surface area – they could also supply an additional surface for the heterogeneous formation of HNO2 . A process with dinitrogen tetroxide (N2 O4 ) after the adsorption of NO2 and steric rearrangement as a key intermediate was proposed by Finlayson-Pitts et al. (2003) and Möller (2003) (Figure 5.21). Whereas the interpretation of observed nighttime HNO2 formation rates is mainly based on eq. (5.204), this “classical” heterogeneous HNO2 formation is too slow to account for the observed atmospheric daytime HNO2 mixing ratios. From midday measurements above a mixed deciduous forest canopy near Jülich (Germany), Kleffmann et al. (2005) calculated a missing daytime source of ∼ 500 ppt h−1 . To evaluate reaction (5.204) as a potential candidate for HNO2 generation, the authors estimated a mean HNO2 source strength of 8 ppt h−1 , 64 times less efficient than required.

5.3 Nitrogen

| 341

It is surprising that the idea to transfer a simple electron transfer mechanism according to eq. (5.79) to NO2 in atmospheric chemistry was not proposed before 2005²⁸: H+

󳨀→ NO2 + e− → NO−2 󳨀 ← 󳨀󳨀 HNO2

(5.206)

George et al. (2005) found that the photoinduced conversion of NO2 into HNO2 on various surfaces containing photosensitive organic substrates might exceed the rate of reaction (5.204) by more than one order of magnitude, depending on the substrate. A high conversion yield for NO2 reduction according to reaction (5.206) by photochemically activated electron donors present in films of humic acid was observed by Stemmler et al. (2006). Meanwhile, Acker and Möller (2007) and Acker et al. (2008) showed that this photochemically driven conversion was common to many surfaces “rich” in partly oxidized aromatic structures and, therefore, is a major candidate for a daytime HNO2 source at interfaces. Vertical measurements using a small aircraft (and other measurements using towers and long path absorption techniques) all showed significant vertical HNO2 gradients in the lower portion of the boundary layer, indicating the ground surface as a significant HNO2 source (Zhang et al. 2009b and references therein). Thus, for the first time atmospheric HNO2 concentrations were measured, with values ranging from 4 to 17 pptv in the FT and from 8 to 74 pptv in the boundary layer, suggesting that an in situ HONO production rate of 57 ppt h−1 would be required in the FT. Because the concentration varied little with the time of day, this suggests that in situ HNO2 production was photochemical in nature and that the ambient HONO concentration was in a near photosteady state. However, the net budget of reactions (5.192) and (5.193) only contributes less than 10% to the measured concentration. The remaining 90% of the needed in situ HNO2 production could be derived from photoenhanced processes on aerosol particles involving NO2 . He et al. (2006) and Zhou et al. (2003) proposed the photolysis of HNO3 /nitrate, but this process seems to be too limited (the preceding discussion concerns HNO3 photolysis on ice). Other proposed sources, such as photolysis of nitrophenols (Bejan et al. 2006), cannot explain the HNO2 concentration because of the very small ambient concentrations of nitrophenol (Zhang et al. 2009b, Acker and Möller 2007). Kleffmann (2007) confirmed that a hitherto unknown photochemical HNO2 source explains the large daytime HONO concentrations and proposed the photolysis of nitroaromatic compounds. However, evidence of strong photochemical in situ HNO2 production in the FT would result in significant implications with respect to the cycling of reactive nitrogen in the troposphere and the OH budget. Gustafsson et al. (2006) showed experimentally under laboratory conditions the reduction of NO2 to HNO2 when aerosol containing TiO2 was present. As mentioned

28 In air pollution treatment, it was known long before that NOx was photocatalytically converted on a TiO2 catalyst surface finally to HNO2 and HNO3 (Hoffmann et al. 1995, Fujishima et al. 1999).

342 | 5 Substances and chemical reactions in the climate system

previously, H2 O2 is formed on desert sand, which contains TiO2 (Kormann et al. 1988). Beaumont et al. (2008) detected H2 O2 when reducing NO2 onto TiO2 particles. Combining oxygen and nitrogen chemistry via heterogeneous (or interfacial) photochemistry would explain all experimental results. The aerosol particles provide OM with chromophoric properties or inorganic matter with photochromic properties. Many oxides (and partly sulfides) of transition state metals (Wo, No, Ir, Ti, Mn, V, Ni, Co, Fe, Zn, and others) have been characterized as being able to support photosensitization (Granqvist 2002). All these observations lead to the conclusion (Acker et al. 2005, 2008, Acker and Möller 2007) that NO2 undergoes photosensitized conversion by single-electron transfer according to eq. (5.206) and similar to those of O2 (eq. (5.79)) and O3 (eq. (5.119)) at all wetted surfaces. Despite the fact that photosensitizers seem to be ubiquitous, theirspecific abundance in natural waters and aerosol particles varies, so the potential to provide electrons can vary, and this explains the different ratios of HNO2 /NOx (Acker and Möller 2007) found in different regions. Moreover, the importance of RH as a precondition of forming water films on the surface can clearly be seen. Figure 5.22 shows the cycle between NO x and HNO2 via the condensed phase. In Figure 5.22, the nitrate chemistry is included; however, it is likely that we can neglect this and conclude that

e-, O2OH

hν

NO2(g)

NO2

H2O2

NO2-

W

HNO2(g)

?

hν (-OH)

hν (-O)

NO3-

O, H2O2

OH (-OH-) O3(g)

NO(g)

hν

OH(g) Fig. 5.22: Photocatalytic NO2 conversion in condensed phases (natural waters, hydrometeors, and aerosol particles); (g) gas phase.

5.3 Nitrogen

| 343

the following is the main pathway: O3

e− ,O−2

ads

H+

− 󳨀󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀→ NO(g) 󳨀󳨀󳨀󳨀→ NO2 (g) 󳨀󳨀→ NO2 (ads) ← 󳨀󳨀 NO2 󳨀󳨀→ HONO(aq) (−O2 )

OH (−OH− )

evaporation

hν

󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HONO(g) 󳨀󳨀→ NO + OH . The multiphase net budget in view of ozone is its conversion via the aqueous phase into OH, whereas NO 󴀗󴀰 NO cycles: e− +hν

O3 + H+ 󳨀󳨀󳨀󳨀󳨀→ OH + O2 . As seen from the budget equation, there is a chemical consumption of H+ + e− (≡ H) in the aqueous phase. Because of the condition of electroneutrality and mass conservation, there are two ways to close the budget: – providing H (H+ + e− ) means abstraction of H from any organic substance, releasing an organic radical R, or – providing H+ at the cost of strong acids (H2 SO3 , H2 SO4 , HNO3 ) and e− from organic photosensitizer W, releasing an anion (e.g., HSO−3 and NO−3 ) and an organic cation W+ . It seems therefore that photosensitized interfacial reduction of NO2 is unalterably interlinked with the oxidation of organic compounds²⁹: hν (multistep)

(NO2 + RH)aq 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ (HNO2 + R)aq , hν (multistep)

(NO2 + W + H+ + HSO−3 )aq 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ (HNO2 + WHSO3 )aq . Besides photosensitized reduction of NO2 according to eq. (5.206), several ions can transfer an electron and form nitrite radicals; for the fate of the HSO3 radical see Chapter 5.4.3.2, k 5.207 = 4.5 ⋅ 109 L mol−1 s−1 (Løgager and Sehested 1993) and k 5.208 = 1.2 ⋅ 107 L mol−1 s−1 (Clifton et al. 1988): NO2 + O−2 → NO−2 + O2 , NO2 +

HSO−3

→

NO−2

+ HSO3 .

(5.207) (5.208)

Nitrite is quickly converted back (oxidized) to NO2 by OH radicals, k 5.209 = 2 ⋅ 1010 L mol−1 s−1 : NO−2 + OH → NO2 + OH− . (5.209) Reaction (5.209) proceeds via peroxonitrite ONOO− as intermediate (see also eqs. (5.232b) and (5.233); in analogy to eq. (5.188), NO2 reacts with OH in solution to form peroxonitrous acid (ONOOH); k = 4.5 ⋅ 109 L mol−1 s−1 (Løgager and Sehested 1993). Aqueous-phase nitrite (apart from unique decay processes; see below) is in equilib29 It would be a new research task to search for organic sulfur and nitrogen compounds at atmospheric interfaces and their possible relevance for health and particle formation.

344 | 5 Substances and chemical reactions in the climate system

rium with aqueous HNO2 , which transfers to the gas phase after droplet evaporation, where it is photolyzed. From this sequence the following budget equations result: Aqueous and gaseous phase:

e− +hν

NO2 + H+ 󳨀󳨀󳨀󳨀󳨀→ NO + OH .

The pathway via the aqueous phase shows a smaller stoichiometry to OH than the budget from the pure gas-phase cycle of reactions (5.15), (5.11), (5.8b), and (5.16): hν

Gas-phase: NO2 + H2 O 󳨀󳨀→ NO + 2 OH . The overall budget also depends on the interfacial conditions. Let us again remark that the significance of such net budgets of OH formation depends on the primary NO2 sources; from primary NO, the formation of NO2 consumes an equivalent amount of ozone, which is again equivalent to 2 OH (eq. (5.16)), gaining the budget NO = NO. It is remarkable that the multiphase process shows only 50% of the OH budget compared to the exclusively gas-phase process: hν

Gas-phase process:

O3 + H2 O 󳨀󳨀→ 2 OH

Multiphase process:

O3 + e− + H+ 󳨀󳨀→ O2 + OH

hν

Acid solutions favor HNO2 formation and desorption and thereby reduce nitrite oxidation (note that HNO2 formation from NO2 is a reducing step in an aerobic environment). Therefore, alkaline conditions and high oxidation potential lead to nitrate formation (Damschen and Martin 1993)³⁰: NO−2 + H2 O2 → NO−3 + H2 O NO−2

+ O3 →

NO−3

+ O2 1

k 5.210 = 4.6 ⋅ 103 L mol−1 s−1 , −1 −1

k 5.211 = 5.0 ⋅ 10 L mol s 5

.

(5.210) (5.211a)

Reaction (5.211a) proceeds with 96% yield, but peroxynitrite (2.6%) and OH radicals (8%) are also formed (Naumov et al. 2010). The latter are generated in the course of the reactions toward peroxonitrite and upon its decay (ONOOH → NO2 + OH) (Løgager and Sehested 1993). They also result from the reaction of ozone with nitrite by electron transfer (see reaction (5.123) for the fate of O−3 ): NO−2 + O3 → NO2 + O−3 .

(5.211b)

Reactions (5.210) and (5.211) are relatively slow compared with the oxidation of dissolved SO2 , which it must be assumed also occurs in the presence of NOx (Chapter 5.4.3.2); H2 O2 will therefore exclusively react with HSO−3 and O3 with SO2− 3 . Mudgal et al. (2007) studied the very slow autoxidation (NO−2 + O2 ) of nitrous acid according to 2 HNO2 + O2 → 2 HNO3 .

(5.212)

30 A good compilation of aqueous-phase chemical reactions and equilibria can be found in Williams et al. (2002) and Herrmann et al. (2005).

5.3 Nitrogen

| 345

It has been proposed that HNO2 is dimerized with intermediate peroxo formation and, hence, a complicated steric arrangement (cf. Figure 5.21), which would likely explain the very high acceleration of the reaction rate under freezing conditions (Takenaka et al. 1996, 1998): O2

2 HNO2 󴀘󴀯 (HNO2 )2 󳨀󳨀→ HO2 N–O–O–NO2 H → 2 HNO3 . The author’s own experimental studies have also shown that nitrite in rainwater and cloud water samples can persist for hours and even days, whereas S(IV) is oxidized within minutes. Therefore, it is very likely that nitrite is predominantly accumulated in atmospheric droplets and at interfaces and transferred back to the gas phase as HNO2 . Figure 5.23 shows the key photochemical and electron transfer reactions in the multiphase oxygen–nitrogen system. The link from nitrogen to oxygen proceeds only in the gas phase via photolysis of NO2 (to O3 ) and HNO2 (to OH) – there is no ROS formation in the aqueous phase from dissolved NOy (neglecting the already discussed nitrate photolysis), but NOy plays a crucial role in both phases in the cycling of ROSs.

Fig. 5.23: Principal reactions in oxygen and nitrogen multiphase chemistry. Dotted lines: phase equilibrium and transfer, respectively; double arrow: protolytic equilibrium; e− electron transfers, O symbol for odd oxygen in terms of different oxidants. Note: behind the solid arrows are mostly complex multistep pathways.

346 | 5 Substances and chemical reactions in the climate system

Let us now turn to an interesting pathway for combining ammonium and nitrite chemistry. Likely in the early nineteenth century it was already known that ammonium nitrite is a “natural” substance found in air.³¹ Certainly, ammonium (NH+4 ) and nitrite (NO−2 ) are important species in dew. Jöns Jakob Berzelius (1779–1848) found in 1812 that aqueous solutions of NH4 NO2 decomposed, and Marcellin Berthelot (1827– 1907) stated in 1875 that concentrated solutions decomposed quickly under the formation of N2 where the presence of acids accelerated this process (Berthelot 1880). We already mentioned that dew water is very common and likely hitherto an underestimated interfacial chemical pathway in linking the biosphere and atmosphere, bringing emission and deposition together. Several photosensitized oxidation processes produce reactive substances, and especially under drying (in other words evaporation) conditions high concentrations of solutes occur. Takenaka et al. (2009) studied the chemistry of the aqueous solution of salts during drying especially with respect to dew. He found that drying dew droplets containing NH+4 and NO−2 evaporated not only HNO2 (which becomes OH production, as discussed earlier) but also N2 , NO, and NO2 . The gross reactions had already been described in the 1930s (Gmelin 1936a and references therein): NH+4 + NO−2 → N2 + 2 H2 O , 2 HNO2 + NO−2

→

NO−3

(5.213)

+ 2 NO + H2 O ,

2 HNO2 → NO + NO2 + H2 O .

(5.214) (5.215)

Schmid and Pfeifer (1953) proposed that reaction (5.213) proceeds via the following steps; see also eq. (5.165a) on the DeNOx process: NH3 + HONO 󳨀󳨀󳨀󳨀󳨀→ H2 N=NO → HNNOH 󳨀󳨀󳨀󳨀󳨀→ N2 (−H2 O)

(−H2 O)

with a more detailed acid-catalyzed mechanism: HCl

NH3

(−H2 O2 )

(−HCl)

HNO2 󳨀󳨀󳨀󳨀󳨀󳨀→ NOCl 󳨀󳨀󳨀󳨀󳨀→ H2 N=NO → HN=NOH 󳨀󳨀󳨀󳨀󳨀−→ HN+2 → N2 + H+ . (−OH )

Already Audrieth (1930) had proposed as intermediates HN=NOH (hydroxydiimide) and the tautomer H2 N–NO (nitrosamine³²). Casewit and Goddard (1982) proposed several isomers of N2 H2 O:

31 Alchemists did collect dew (see Mutus Liber) in large amounts and distilled it to find the “materia prima”; it is likely that they also mentioned the “explosive” character of the residual salt – ammonium nitrite (Möller 2008); see also Volume 2. 32 Casewit and Goddard (1982) called it nitrosamide. NH2 NO is the inorganic parent compound of organic nitrosamine R2 NNO. Nitramide is NH2 NO2 , a structural isomer of hyponitrous acid and the parent compound of organic nitramides. NH2 NO2 is a colorless solid and was first synthesized by J. Thiele and A. Lachmann in 1894 (Ueber das Nitramid. Berichte der deutschen chemischen Gesellschaft 27, 1909–1910).

5.3 Nitrogen

H–N=N–OH N=N(H)OH HN=N(=O)H H2 N–N=O

|

347

hydroxydiimide (hydroxy–1,2–diazene 1)³³ hydroxy–1,1–diazene diimide–N–oxide nitrosamine

None of these compounds were ever isolated and characterized, but they exist as organic derivates; several are believed to be intermediates in processes involving the reduction of nitrogen oxides to molecular nitrogen and water.³⁴ It is likely that the nitrosonium ion (NO+ ) plays a role as intermediate in the reaction between ammonia and nitrous acid, gaining nitrosamine as intermediate: NH3 + NO+ 󴀘󴀯 (NH3 NO)+ 󴀘󴀯 (H2 N=NOH)+ 󴀘󴀯 H2 N=NO + H+ .

(5.216)

NO+ forms in very small concentrations from nitrous acid in strong acid solution when HNO2 reacts as a base; the nitrous acidium ion H2 NO+2 was verified by direct observations (Burrey et al. 1983): H+

+ + 󳨀→ HNO2 + H+ 󴀘󴀯 H2 NO+2 󳨀 ← 󳨀󳨀 NO + H3 O

pKa = −7 .

(5.217)

Alternatively, we can formulate the following equilibria (HNO2 acts as a weak base): HNO2 󴀘󴀯 OH− + NO+ , +

(5.218a)

+

HNO2 + H3 O 󴀘󴀯 NO + 2 H2 O , +

−

HNO2 + H2 O 󴀘󴀯 NO + OH .

(5.218b) pK = 6.6

(5.218c)

The adduct NH3 NO+ (NH3 + NO+ ) in eq. (5.216) is a tautomer with NH2 NOH+ and NH2 NHO+ , where the tautomerization transition states proceeds via H-atom mobilization (Deláez et al. 2008). NH2 NOH+ represents protonated nitrosamine: NH2 NO + H+ 󴀘󴀯 NH2 NOH+ . Nitrosamine further isomerizes via H-atom migration to a conformer of hydroxydiimine (HNNOH) that finally decays to N2 : H2 N=NO → HN=NOH 󳨀󳨀󳨀󳨀󳨀−→ HN+2 󳨀󳨀󳨀󳨀+→ N2 . (−OH )

(−H )

(5.219)

Takenaka et al. (2009) found that droplet size (smaller accelerate decomposition), pH, nitrite/ammonium ratio, and the drying speed determine reaction channels and ultimately the yield of N2 , N2 O, NO, and NO2 versus evaporation of simply NH3 and HNO2

33 Named by Hantzsch and Reddelien (1921) oxydiimine and described as nonexistent (as diimine HN=NH), which decays – if formed as intermediate – to N2 . 34 Another N2 H2 O2 compound was described as a likely intermediate, nitroso hydroxylamine HO– N(H)–NO, that converts internally to hyponitrous acid HO–N=N–OH (Hantzsch and Reddelien 1921).

348 | 5 Substances and chemical reactions in the climate system

or the residual formation of NH4 NO3 . Reaction (5.215) is the inverse of reaction (5.204) and proceeds via N2 O3 (Burrey et al. 1983); N2 O3 is also called nitrosyl nitrite and N2 O4 as nitryl nitrate: 2 HNO2 󳨀󳨀󳨀󳨀󳨀→ O=N–NO2 (N2 O3 ) 󴀘󴀯 NO + NO2 (−H2 O) H+

NO−2

HNO2 󳨀󳨀󳨀󳨀󳨀→ NO+ 󳨀󳨀󳨀→ O=N–NO2 (N2 O3 ) → N2 O + O2 . (−H2 O)

(5.220) (5.221)

The reactions of NO and NO2 with water (eqs. (5.204) and (5.205)) were interpreted as an interfacial steric arrangement of hydrated N2 O3 and N2 O4 , respectively, with internal electron transfers and rearrangement. However, we have seen that the aqueous chemistry of nitrogen dioxide (NO2 ) is triggered through electron transfer (eqs. (5.206)–(5.208)) gaining nitrite ions and nitrous acid, which can be further oxidized to nitrate. It is remarkable that nothing is found in the air-chemistry literature on the aqueous-phase chemistry of nitrogen monoxide (NO). In textbooks on inorganic chemistry (e.g., Wiberg et al. 2001) it is noted that NO does not react with water. However, in older literature (Gmelin 1936a) we find that NO slowly reacts with water under the generation of HNO2 , N2 , and N2 O. It has been speculated that NO combines with OH− via H2 N2 O2 (hyponitrous acid, an isomer of nitramide)³⁵ formation, which decays to N2 O, or that NO directly combines with H2 O to generate H2 N2 O3 (oxo hyponitrous acid), which decays to HNO and HNO2 . The dimerization of HNO to H2 N2 O2 was also proposed, but detailed mechanisms were unknown (see below). The intermediate existence of HNO in HNO2 reduction as well as NH3 or NH2 OH (hydroxylamine) oxidation is well established (Heckner 1977). Ignaro et al. (1993) described the following reaction chain: O

NO

2 󳨀󳨀→ NO 󳨀󳨀→ OONO ← 󳨀󳨀 ONOONO → 2 NO2 (N2 O4 ) .

According to eq. (5.205), NO2 + NO2 (N2 O4 ) convert into HNO2 and HNO3 . However, nitrate is not found in the “reaction” NO + H2 O (Ignaro et al. 1993), and the precise mechanism is not well understood but could be represented in the following manner: NO + NO 󴀘󴀯 ON–NO 󴀘󴀯 2 NO2 , H2 O

NO2 + NO 󴀘󴀯 N2 O3 󳨀󳨀󳨀→ 2 NO−2 + 2 H+ .

35 Hyponitrite was discovered by Edward Divers (1837–1912) in 1871 by treating a solution of nitrate by sodium (Divers 1871). This was first done by Schönbein in 1861 (Erdmann’s Journal für praktische Chemie 34, 202), obtaining nitrite. Divers further reduced nitrite by metallic sodium, finally obtaining a stable, difficultly soluble crystalline salt, first called “salt of nitrous oxide.” He called the corresponding acid hyponitrous acid (HNO), and he also found that the acidified heated solution evolved dinitrogen oxide (N2 O) according to 2 HNO = N2 O + OH2 . Interestingly, he named H2 N2 O2 “hyponitroso-nitrous acid.”

5.3 Nitrogen

| 349

The last reaction proceeds in the following way (see below for chemistry of nitrosonium NO+ ), i.e., we regard dinitrogen trioxide as nitrosyl nitrite where NO+ exists only as a short-lived intermediate: NO2 + NO 󴀘󴀯 N2 O3 = [O=N–O⊖ –⊕ N=O] 󴀘󴀯 NO−2 + NO+ . The subsequent hydrolysis of NO+ is the inverse reaction to eq. (5.221); eq. (5.222) explains why nitrosonium is a strong acid (cf. also eq. (5.218)): NO+ + H2 O → HNO2 + H+ .

(5.222)

Alternatively to eq. (5.222), NO+ reacts with the hydroxide ion (eq. (5.236)). With the findings that NO (one of the smallest and simplest molecules) is an important signaling molecule in biological chemistry and its inactivation is unique with respect to other signaling molecules in that it depends solely on its nonenzymatic chemical reactivity with other molecules (Miranda et al. 2000), an explosion in NO solution chemistry started to appear in the 1990s. Until recently, most of the biological effects of nitric oxide were attributed to its uncharged state (NO), yet NO can also exist in a reduced state as nitroxyl³⁶ (HNO and its protolytic form, the nitroxyl anion NO− ) and in an oxidized form as nitrosonium ion (NO+ ) (Hughes 1999, Fukuto et al. 2005, Doctorovich et al. 2011): NO+ [N≡O]+ 󴀘󴀯 NO [N=O] 󴀘󴀯 NO− [N=O− ] 󴀘󴀯 HNO [H–N=O] . Interconversion of NO− , NO, and NO+ can take place under cellular conditions, so all three species must be considered in order to account fully for the biological activity of nitric oxide (Hughes 1999). Thus, unlike NO, HNO can target cardiac sarcoplasmic ryanodine receptors to increase myocardial contractility and can interact directly with thiols and is resistant to both scavenging by superoxide (O−2 ) and tolerance development (Irvine et al. 2008). Under laboratory conditions, the nitroxyl radical HNO is produced from Angeli’s salt Na2 N2 O3 (which is produced from hydroxylamine and organic nitrates; the corresponding hyponitric acid does not freely exist): H+

N2 O2− 󳨀→ HNO + NO−2 . 3 󳨀

(5.223)

HNO quickly dimerizes to hyponitrous acid³⁷ H2 N2 O2 (HO–N=N–OH, also called nitroxylic acid, which is isomeric with nitramide H2 N–NO2 ), which includes an electronic rearrangement and H shift, k 5.224 = 1.8 ⋅ 109 L mol−1 s−1 (Hughes 1999): HNO + HNO → H2 N2 O2 (HO–N=N–OH) .

(5.224)

36 Good reviews on the chemistry and biology of HNO can be found in Bonner and Hughes (1988), Mirande (2005), and Doctorivic et al. (2017). 37 First shown by Angeli (1908).

350 | 5 Substances and chemical reactions in the climate system

Hyponitrous acid is also obtained in the reaction between hydroxylamine and nitrous acid (Soler-Jofra et al. 2016)³⁸: NH2 OH + HNO2 → H2 N2 O2 .

(5.225)

H2 N2 O2 slowly decomposes (dehydrates) in aqueous solution into dinitrogen oxide and water (cf. Figure 5.19 with respect to nitrification), k 5.226 = 8 ⋅ 106 L mol−1 s−1 : H2 N2 O2 󳨀󳨀󳨀󳨀+→ HONNO− → N2 O + OH− . (−H )

(5.226)

Hence, N2 O can be regarded as an anhydride of hyponitrous acid. Note that dinitrogen oxide N2 O is a tautomer: ⊖ N=N⊕ =O and N≡N⊕ –O⊖ . HNO also adds NO and generates the anionic radical of the NO dimer (Lymar et al. 2005), k 5.227 = 5.8 ⋅ 106 L mol−1 s−1 , which further reacts with NO (k 5.228 = 5.4 ⋅ 109 L mol−1 s−1 ) to form the long-lived N3 O−3 , which finally decomposes into N2 O and nitrite (k 5.229 = 3 ⋅ 102 s−1 ): HNO + NO → O=N–N=O− (N2 O−2 ) + H+ , N2 O−2

−

+ NO → O=N–N(O)–N=O N3 O−3

→ N2 O

+ NO−2

(N3 O−3 )

(5.227) ,

.

(5.228) (5.229)

The nitroxyl anion NO− is the conjugated base of the very weak acid nitroxyl HNO (pKa = 11.4), when both species are in their ground states, 1 HNO and 3 NO− (Shafirovich and Lymar 2002): (5.230) HNO 󴀘󴀯 NO− + H+ . As for other electron receptors (such as NO2 and NO3 ), NO is easily reduced, and we assume that the electron source is the hydrated electron or a conduction band electron (Lymar et al. 2005): NO + e− → NO− . (5.231) Superoxide also forms NO− by the near diffusion-controlled reaction of nitric oxide (NO) and superoxide ion (O−2 ) (Huie and Padmaja 1993): NO + O−2 → NO− + O2

k 5.232a = 6.7 ⋅ 109 L mol−1 s−1 .

(5.232a)

NO− forms peroxonitrite with O2 (not to be confused with nitrate NO−3 ) (Shafirovich and Lymar 2002): NO− + O2 → O=N–OO−

k 5.233 = 2.7 ⋅ 109 L mol−1 s−1 .

(5.233)

Reactions (5.231) and (5.233) can be combined into one step: NO + O−2 → O=N–OO−

k 5.232b = k 5.232a .

38 First shown by Wislicenus (1893), who also showed that it decayed to N2 O + H2 O.

(5.232b)

5.3 Nitrogen

| 351

Peroxonitrite ion is essentially stable,³⁹ but its protonated form, peroxonitrous acid (ONOOH, pKa = 6.5 to 6.8), decomposes rapidly via the homolysis of the O–O bond to form NO2 , NO−3 , NO−2 , OH, and O− radicals depending on the pH (Løgager and Sehested 1993, Merényi et al. 1999, Goldstein and Merényi 2008). Peroxonitrite is a potent oxidant that converts with CO2 via nitroperoxo carbonate (ONOOCOO− ) to nitrate (Fukuto et al. 2000), k 5.234a = 3 ⋅ 104 L mol−1 s−1 : H2 O

ON–OO− + CO2 → O=N–O–O–COO− 󳨀󳨀󳨀→ HCO−3 + NO−3 + H+

(5.234a)

Around 1/3 of this intermediate proceeds to form NO2 and carbonate ion radicals (CO−3 ) in the bulk of the solution (Goldstein and Merényi 2008): ON–OO− + CO2 → O=N–O–O–COO− → NO2 + CO−3 .

(5.234b)

We now turn to nitrosonium (NO+ ) (sometimes also called nitrosyl cation), which is very short-lived in aqeous solution (3 ⋅ 10−10 s). If the formation of NO+ were possible under atmospheric conditions (e.g., at highly concentrated particle and water interfaces), the subsequent step would be the formation of nitrosyl chloride (ClNO), an important species in gas-phase chemistry. The likely importance of this pathway lies in the photolysis of ClNO, which yields reactive Cl radicals: NO+ + Cl− → ClNO .

(5.235)

Nitrosonium reacts fast with hydroxide ions to form nitrous acid: NO+ + OH− → HNO2 .

(5.236)

Reactions with organic compounds are known by the replacement of an H atom: NO+ + RH → R–NO + H+ .

(5.237a)

Nitrosonium ions react with secondary amines to generate nitrosamines, many of which are cancer-inducing agents at very low doses (see also eq. (5.254)): NO+ + R2 –NH → R2 –N–NO + H+ .

(5.237b)

We cannot exclude the possibility that NO+ is produced from electron holes: NO + W+ (h+vb ) → NO+ .

(5.231b)

Whereas nitrosonium (NO+ ) is well decribed as a nitrating agent in aqueous solution (i.e., electrophilic aromaric nitration), another species, the nitronium ion (NO+2 : O=N=O+ ) has been less investigated despite the fact that its existence has been known 39 Decomposition of peroxonitrite (ONOO− ) in acidic aqueous solution leads to 1 O2 and NO− (or HNO depending on pH) according to Khan et al. (2000). However, Merényi et al. (2000) confirmed the mechanism already proposed by Mahoney (J. Am. Chem. Soc. 1970, 92, 4244–4245) that the decomposition of ONOOH yields about 30% NO2 and OH radicals.

352 | 5 Substances and chemical reactions in the climate system

(also called nitryl cation) for over a hundred years, specifically in organic synthesis. Heal et al. (2007) proposed that NO+2 partitioned with N2 O5 in the aqueous phase to explain the presence of nitrophenols in the atmospheric gas phase, in clouds and rainwater (see also Chapter 5.3.5.2); however, its formation had not yet been verified experimentally: N2 O5 (g) 󴀘󴀯 N2 O5 (aq) 󴀘󴀯 [O2 NO⊖ –⊕ NO2 ] → NO−3 + NO+2 .

(5.238)

Nitronium reacts relatively slowly with water but very quickly with phenols (Heal et al 2007): NO+2 + H2 O → NO−3 + 2 H+ NO+2

or

+ Ph → products

NO+2 + OH− → NO−3 + H+ ,

(5.239)

−1

(5.240)

12

k ≈ 10

−1 −1

L mol s

.

Its reactivity increases with protonation (i.e., in strong acids) (Olah et al. 2009); cf. with reaction (5.221): HNO2 + H+ 󴀘󴀯 NO2 H+2 [HO–⊕ N–OH] (󴀘󴀯 NO+ + H2 O) HNO3 + H+ 󴀘󴀯 NO3 H+2 [HO–⊕ N(=O)–OH] (󴀘󴀯 NO+2 + H2 O) It is also known from chemistry textbooks that concentrated sulfuric acid and nitric acid produce nitronium (in equlibirium): HNO3 + H2 SO4 󴀘󴀯 NO+2 + HSO−4 + H2 O .

(5.241)

In reaction (5.241), the salt nitronium hydrosulfate (NO2 HSO4 ) does exist. Fuming nitric acid (i.e., at a higher concentration than 90%) contains substantial quantities of dissolved nitrogen oxides – NO, NO2 , N2 O, and N2 O4 – leaving the solution with a reddish-brown color (because of concentrated NO2 ). Dinitrogen pentoxide (N2 O5 ) – the anhydride of nitric acid (HNO3 ) – can be regarded as nitronium nitrate, but only as solid compounds, whereas gaseous N2 O5 is molecular: N2 O5 [(O=)2 N–O–N(=O)2 ] = [NO+2 –NO−3 ] We will encounter this later in a dicussion on the reaction between HNO3 and N2 O5 with sea salt (NaCl) (Chapter 5.7.2). According to the following heterogeneous pathway, nitrate is reduced to nitrite: Cl−

NaCl

HNO3 + HNO3 󳨀󳨀󳨀󳨀󳨀󳨀 󳨀󳨀󳨀󳨀→ NO+2 󳨀󳨀→ ClNO2 (aq) 󴀘󴀯 ClNO2 (g) 󳨀 󳨀󳨀󳨀󳨀→ NaNO2 (s) (−Cl2 ) (−NO−3 −H2 O) The formation of nitroxyl (NO− ), nitronium (NO+2 ), and nitrosonium (NO+ ) ions is believed to occur in reactions between nitric acid and N2 O3 : N2 O3 + HNO3 → [[NO− ] − [NO+2 ] + HNO3 ] → HNO + N2 O5 , +

N2 O3 + HNO3 → [[NO

] − [NO−2 ]

+ HNO3 ] → HNO2 + N2 O4 .

(5.242a) (5.242b)

5.3 Nitrogen

| 353

NO+2 and NO+ react with chloride to nitryl and nitrosyl chloride: NO+2 + Cl− → ClNO2 , +

(5.476)

−

NO + Cl → ClNO .

(5.235)

These reactions are unimportant under normal conditions in the environment; however, at interfaces created when, for example, NOy sticks to sea salt and organic particles as well as during the evaporation of droplets, high concentrations can occur, yielding nitryl and nitrosyl halides (eqs. (5.184) and (5.185)) as well as nitroaromatic compounds. Dinitrogen trioxide (N2 O3 ) can be reduced in two steps: e−

N2 O3 󳨀󳨀→ NO + NO−2 ,

(5.243a)

2 e−

N2 O3 󳨀󳨀󳨀→ N2 O2− 3 (dianion of N2 O3 : Angeli’s salt) .

(5.243b)

Biochemical routes for the formation of nitroxyl ions are shown in Figure 5.24 but without considering inorganic or nonenzymatic solution chemistry. In cells, reactions of NO with haems,⁴⁰ thiols (R–SH), and metals to form metal nitrosyl complexes (Me– RSH (-RSSR)

NOH

RSNO

NOH

RSH

HONNOH

N2O

N3O3-

NO

(-Men-1)

e-

RNO

MeNO (-H+)

(-NO2-) H+

NO2-

Men

NO (-OH-)

N2O2-

eNO

NO-

NO2

R O2

(-NO 2) NO

ONOO

ONOONO

O2O2

ONOO-

CO2 (-HCO3-)

NO3-

Fig. 5.24: Biological NOx chemistry; adapted and simplified from Fukuto et al. (2000). Dotted arrow: multistep process, Me TMI, RSH organic sulfide (–SH thiol group), RSSH disulfide, ONOO (an isomeric form of the nitrate radical NO3 ), ONOO− (ONOOH) peroxonitrous acid, HON=NOH (H2 N2 O2 ) hyponitrous acid, N2 O−2 (O=N–N–O− ) radical anion of NO dimer, N3 O−3 (O=N–N–O–NO− ) trimer radical 2− anion (not to be confused with Angeli salt N3 O2− 4 : [O2 N–N–NO2 ] ).

40 Compounds of iron complexed in a porphyrin (tetrapyrrole) ring differ in side chain composition. Haems are prosthetic groups of cytochromes and are found in most oxygen carrier proteins.

354 | 5 Substances and chemical reactions in the climate system NO) as carriers of NO+ at a physiological pH and nitrosation (formation of S-nitrosothiols) is of large biological significance. NO can be added to iron complexes and enter into internal electron transfer, thereby forming electropositive nitrosyl ligands: Me n+ + NO → [Me n+ –NO] ↔ [Me(n+)−1 − NO+ ] .

(5.244)

The nitrosation of thiol compounds proceeds directly via N2 O3 and indirectly through metallic nitrosyl ligands: RSH + N2 O3 → RS–NO + HNO2 , RSH + [Me –NO] → RS–NO + Me n+

(n+)−1

(5.245) +

+H .

(5.246)

The nitrosothiol quickly decomposes by cuprous, thereby transforming nitroxyl back to nitric oxide (Nelli et al. 2000): RS–NO + Cu+ → RS− + NO + Cu2+ .

(5.247)

An important role of NO lies in the interchange between oxyhemoglobin⁴¹ Hb(Fe–O2 )2+ and methemoglobin⁴² Hb(FeIII ), which is the primary mechanism by which the movement and concentration of NO are controlled in vivo. Because of NO lipid solubility, it can enrich high concentrations. The following reactions illustrate the conversion among NO, NO2 , and nitrite and nitrate (Fukuto et al. 2000, Huang et al. 2005): Hb(FeII )2+ + HNO2 → Hb(FeIII )3+ + NO + OH− , II 2+

Hb(Fe ) Hb(Fe ) II

Hb(Fe –O2 ) Hb(Fe –O2 )

2+

2+

+ NO → Hb(Fe –NO)

+ NO−2 2+

II 2+

II

II

→

+ NO →

+ NO2 →

III 3+

(5.248a)

,

Hb(Fe ) + NO2− (hyponitrite) 2 III 3+ − Hb(Fe ) + NO3 , Hb(FeIII –O2 )3+ + NO−2 ,

(5.248b) ,

(5.248c) (5.248d) (5.248e)

Figure 5.25 summarizes the main routes in multiphase NO x –NO x chemistry. In air, odd oxygen tends to accumulate in NOx and NO y but is in a photo-steady state between oxygen and nitrogen species. This condensed phase acts as a sink of oxygen gas-phase species, mainly in the form of NO z (HNO3 , NO3 , N2 O5 ). It is obvious that NOx can transfer either nonphotochemical (via NO + NO2 reaction, not shown in Figure 5.25) or photosensitized to nitrite, which might return to the gas phase as HNO2 and photolyzed to OH and NO. N(III) oxidation in solution to nitrate is relatively slow and not important as an oxidant consumer. Not shown in Figure 5.25 is the decomposition of NH4 NO2 (comproportionation of NH3 and HNO2 ) into gases (N2 , NO, NO2 , N2 O) during the evaporation of droplets (dew, fog, clouds).

41 Also called oxygenated hemoglobin oxyHb. 42 Also called deoxyhemoglobin deoxyHb.

5.3 Nitrogen

gas phase

N2O

hν

NO

NOCl

OH O3

NO2

hν

NO

interface

N2O e- (-OH)

N2

HNO3

HNO2 OH

NOCl

W+ Cl-

H+

NO HNO

N2O

e-

NO-

NO+

HNO

transport and transfer multistep conversion

| 355

NO

RH O3

NO3

hν

NO3

e-

hν (-OH) e-

NO2-

N2O5

NO, M

NO2 OX

NO2

N2O5 H2O

NO3-

H+

HNO2 aqueous phase

Fig. 5.25: Multiphase NOx –NOy chemistry (main pathways); OX oxidants (OH, H2 O2 ); not included is the N2 O3 chemistry, which might have importance at night for nitrite formation in solution and at interfaces.

Nitrate photolysis is too slow in bulk solution but can have significance under special climatic conditions (snow and ice surface) and at aerosol particle surfaces. Interestingly, a new aspect has potential significance for nitrosonium anions NO+ that mainly produce nitrosyl chloride (ClNO) but could also react with organic compounds (nitrosation). The role of aqueous-phase oxidant formation, specifically OH radicals through photosensitized electron transfer processes onto different nitrogen oxides and oxygen species, is shown in Figure 5.26 (to avoid overloading this scheme, the OH-consuming reactions and intermediates are not shown; see also Figures 5.10, 5.13, and 5.15). Photosensitizers (W) play a key role in providing surface electrons or hydrated electrons after illumination for the reduction of molecules transferred from the gas phase onto wetted surfaces (natural waters, hydrometeors, and aerosol particles). N2 O provides a direct pathway for OH production (not yet included in atmospheric models). Similarly, reduction of ozone proceeds directly to OH. Reduction of O2 is less efficient and takes place through peroxides. As shown in Chapter 5.2.5, all ROSs (O−2 , HO2 , H2 O2 , OH) can be found in solution but dependent on pH and redox potentials. A new pathway – adapted from biological chemistry – could be the NO-nitrite cycle having relevance for permanent OH production. Much experimental evidence for HNO2 formation from the photoconversion of NO2 in condensed phases is available, but this pathway is not

356 | 5 Substances and chemical reactions in the climate system

hν

W

N2O(g)

NO(g)

NO2(g)

O2(g)

O3(g)

N2O(ads)

NO(ads)

NO2(ads)

O2(ads)

O3(ads)

e- (-N2)

hν

O-

W + + eOH- (-W)

e-

NO-

hν (+H+) 2 NO

H+

e-

NO2-

hν (+H+)

NO3-

hν (+H+)

e-

O2-

e-

O3-

hν (+H+)

OH

transport and transfer multistep conversion

Fig. 5.26: Solution and interfacial photosensitized electron transfer processes of N2 O, NOx , and Ox yielding OH radicals; not included are oxidant-consuming processes. W – any photosensitizer such as organic chromophoric substances and inorganic semiconductors.

a net source of OH because in the first step of NO to NO2 conversion, ozone (or HO2 ) is consumed (note the budget equation in the gas phase: 2 O3 +H2 O → OH+HO2 +2 O2 ): e− +H+

hν

NO + O3 (or HO2 ) 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ NO2 󳨀󳨀󳨀󳨀󳨀→ HONO 󳨀󳨀→ NO + OH . (−O2 or −OH)

This widely discussed process only shifts (because of the much faster photolysis of HNO2 compared with that of O3 ) the photo-steady states and changes the reservoir distribution of species. Now, considering the interfacial chemistry between NOy species and particulate NaCl (e.g., sea salt; see Chapter 5.6.2 for details) we summarize in what follows the interconversion processes NOy 󴀘󴀯 NOx (x = 1, 2 and z = 2, 3); they are well described for NO y = N2 O5 but likely occur also for NO2 , HNO3 , and N2 O3 : particulate Cl−

hν

(−NO3 )

(−Cl)

N2 O5 󴀘󴀯 [O2 N⊕ –⊖ NO3 ] 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀−󳨀󳨀󳨀→ ClNO2 󳨀󳨀󳨀󳨀→ NO2 particulate Cl−

hν

(−NO2 )

(−Cl)

N2 O3 󴀘󴀯 [ON⊕ –⊖ NO2 ] 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀−󳨀󳨀󳨀→ ClNO 󳨀󳨀󳨀󳨀→ NO

5.3 Nitrogen

NO2 ↑ (−Cl) ClNO2 +

|

357

hν

particulate Cl−

N2 O3 󴀘󴀯 [ON⊖ –⊕ NO2 ] 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→

NO− H+ ↓ HNO

HNO 󳨀󳨀󳨀󳨀󳨀→ N2 O (−H2 O)

particulate Cl−

hν

2 NO y 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀−󳨀󳨀󳨀→ ClNOx 󳨀󳨀󳨀󳨀→ NO x (−Cl) (−NOz ) particulate Cl−

hν

(−NO2 )

(−Cl)

2 NO2 󴀘󴀯 [O2 N⊕ –⊖ NO2 ] 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀−󳨀󳨀󳨀→ ClNO2 󳨀󳨀󳨀󳨀→ NO2 Moreover, we can conclude that the textbook knowledge (Finlayson-Pitts and Pitts 2000, Möller 2014), that nitric acid (HNO3 ) is an ultimate sink for inorganic ROS (O3 and OH) as well as NO x , is no longer valid. The importance of NO y lies in the reservoir behavior of HNO3 and, thus, the long-range transportation of “stored” NO2 and ROSs (via NO2 photolysis and Cl attack on organic compounds): particulate Cl−

hν

2 HNO3 󴀘󴀯 [NO+2 + NO−3 + H2 O] 󳨀󳨀󳨀󳨀󳨀󳨀−󳨀󳨀󳨀󳨀󳨀→ ClNO2 󳨀󳨀󳨀󳨀→ NO2 (−Cl) (−NO3 −H2 O)

5.3.6 Organic nitrogen compounds Nitrogen is an essential element in life and, thus, in biogeochemical cycling (Chapter 6.1.4). In biomass, nitrogen is almost in a reduced state in organic molecules, derived from ammonia NH3 . The main building block is the amino group –NH2 , occurring in its simplest organic compounds, amines (Chapter 5.3.6.1 and Table 5.13). In biomass, amino acids =C(NH2 )C(=O)OH are the building blocks of peptides (which are polymers of amino acids with the C–N(H)–C central group), and next are proteins, which are polymers of more than 50 amino acids that have enormous diversity in structure and functions. Additionally, nitrogen is found heterocyclically (mainly in nucleic acids) in biomolecules. Oxidized nitrogen (such as organic nitrites and nitrates) should be absent in organisms and expected only because of reactions between organic compounds and NO x /NOy (Chapter 5.3.6.2). Direct emissions are less likely because of large N-containing biomolecules, almost nonvolatile, and after degradation highly water soluble. Biomass burning was identified as the source of organic nitrogen, but this is probably already in a decomposed form such as HCN or CH3 CN. The simplest amine is methylamine CH3 NH2 , whose global emission from animal husbandry was estimated by Schade and Crutzen (1995) in 1988 to be 0.15 ± 0.06 Tg N. Almost three-quarters of these emissions consisted of trimethylamine-N. Other sources were marine coastal waters and biomass burning.

358 | 5 Substances and chemical reactions in the climate system

Tab. 5.13: Organic nitrogen species: functional groups of environmental importance. Structure –NH2 =NH ≡N –N=N– –N=N+ X− –NHNH2 –N3 –C≡N –N=C=O –C(=O)NH2 –N=O and + N=O –O–N=O –N(=O)O or –NO2 –O–NO2 =N–N=O

Name

Formula/symbol amine) a

Amino group (primary Secondary amine Tertiary amine Azo group Diazonium Hydrazine, diazine Acide Cyano group (nitrile) Isocyanate Amide Nitroso group (nitrosyl) Nitrite Nitro group (nitryl) Nitrate Nitrosamine

RNH2 R2 NH R3 N RNNR RN+ X− RNHNH2 RN3 RCN RNCO RC(O)NH2 RNO RONO RNO2 RONO2 R2 NNO

a Amines are derived from ammonia by replacement of an H atom through an organic residue R; amides

contain an acyl group R–C(=O)–, so they are derivates of carboxylic acids: R–C(=O)–NH2 (primary amide) and R1 –C(=O)–N(R2 )H (secondary amide), where R2 is often given by CH3 and the compound is called N-methyl-(acyl)-amide.

Nothing is known about natural emissions of amines. Several anthropogenic sources (traffic, fertilizer production, paper mills, rayon manufacturing, and the food industry) have been identified. Possible amine emissions along with scrubbed flue gas from CO2 capture facilities (using amine-washing solutions) were recently studied. Other simple degradation products of amino acids and peptides are amides, which consist of the building block R–C(=O)NH2 . The simplest molecule is formamide HC(=O)NH2 . Amides are derivates of carboxylic acids (R(O)OH), where the hydroxyl group (–OH) is replaced by the amino group (–NH2 ). Nitriles with the cyano group –CN are potential biomass combustion products from degraded biomolecules. 5.3.6.1 Amines, amides, and nitriles Amines have been detected in ambient air, specifically close to industrial areas, livestock habitations, and animal waste and wastewater treatments (Grönberg et al. 1990, Schade and Crutzen 1995, Ge at al. 2011). In connection with CCS (carbon capture and storage, see Volume 2), intensive studies were recently carried out on amine emission and degradations (e.g., Nielsen et al. 2010, Ge et al. 2011). Currently, very limited information is available for the land-atmosphere emissions and deposition processes of amines (Hertel et al. 2013). For the first time measurements of amines and ammonia were conducted on a rural forested site in the Southeast USA (Youl et al. 2014), but only trimethylamine (1–15 ppt; other amines were below

5.3 Nitrogen

| 359

detection limits) and NH3 (up to 1–2 ppb) were found, whereas at a moderately polluted Ohio site, amines were found in greater abundance (in ppt): methylamine (1–4), trimethylamine (4–10), diethylamine (10–50) and C5–amines (10–100), ammonia up to 6 ppb (interestingly, no dimethylamine was detected). Amides (dimethyl formamide) were also detected in air (Howard 1990), whereas other amides were found to be emitted in industrial processes (acetamide, acrylamide). Yao et al. (2016 and references therein for more measurements) found in urban Shanghai much higher values for C1 and C2 amines (16–40 ppt), whereas C4 –C5 amines were lower (3–15 ppt); trimethylamine was also low (1 ppt); in contrast, concentrations of amides were higher (14– 35 ppt for C5 and C6 and 170–780 ppt for C3 –C4 , whereas C2 was low, at about 1 ppt). It is concluded that amides are of secondary origin from primary industrial emissions. Amides are not gaseous; only formamide is liquid and all higher amides (from acetamide) are solid. Hence, primary emission is very unlikely, and molecular detection in air can only be explained by conversion from amines (see below). Up to C3 , amines are gaseous and highly volatile. They are Lewis bases (somewhat more basic than NH3 ) and water-soluble (without longer carbon chains), thereby forming salts; the cation NR3 H+ is called aminium: NR3 (g) + HNO3 (g) 󴀘󴀯 NR3 HNO3 (s) .

(5.249)

Therefore, the acidity of individual particles can greatly affect gas/particle partitioning, and the concentrations of amines, as strong bases, should be included in estimations of aerosol pH (Pratt et al. 2009). The general fate of amines is similar to that of ammonia, i.e., reaction with OH. They do not photolyze. Because the C–H bond energy is smaller than that of the N–H bond, OH predominantly abstracts H from C–H (Chapter 5.6.4) forming bifunctional compounds (e.g., amides R–C(=O)–NH2 ; see following discussion for more on their fate); in what follows the conversion of methylamine to formamide is shown: O2

OH

H3 C–NH2 󳨀󳨀󳨀󳨀󳨀→ H2 C–NH2 󳨀󳨀→ H2 C(–O–O)–NH2 (−H2 O) NO

O2

(−NO2 )

(−HO2 )

󳨀󳨀󳨀󳨀󳨀→ H2 C(−O) − NH2 󳨀󳨀󳨀󳨀󳨀→ HC(= O) − NH2 In the less likely case of N–H abstraction the following radicals are formed: CH3 NH2 + OH → CH3 NH + H2 O ,

(5.250)

(CH3 )2 NH + OH → (CH3 )2 N + H2 O .

(5.251)

The further fate is not explicitly known, but molecular rearrangements or the addition of O2 , NO x , and NO3 is possible: NO

O2

(−NO2 )

(−HO2 )

CH3 NH + O2 → CH3 N(H)O2 󳨀󳨀󳨀󳨀󳨀→ CH3 N(H)O 󳨀󳨀󳨀󳨀󳨀→ CH3 N=O (nitrosyl) . (5.252)

360 | 5 Substances and chemical reactions in the climate system

From secondary amines, azo compounds or organic hydrazines (derived from the inorganic parent compound hydrazine, N2 H4 ) can be given: 2(CH3 )2 N → (CH3 )2 NN(CH3 )2 ,

(5.253)

(CH3 )2 N + NO → (CH3 )2 N–NO

(nitrosamines: R2 NNO) ,

(5.254)

(CH3 )2 N + NO2 → (CH3 )2 N–NO2

(nitramines: R2 NNO2 ) .

(5.255)

They also photolyze quickly back to R2 N and NO x in the gas phase (hence, they are enriched in air during the night). Nitrosamines are of high interest because of their cancerogenic properties. They were found to be everywhere, but almost always in small concentrations. As good electron donors, they are easily oxidable in solution, acquiring derivatives of hydroxylamine (NH2 OH): (CH3 )2 N + H2 O2 → CH3 N–OH + H2 O .

(5.256)

In water, tertiary amines form quaternary ammonium compounds, for example, with methyl halogenides. In aqueous solution, secondary (aliphatic and aromatic) amines react with nitric acid HNO2 (specifically the nitrosonium ion NO+ ), as already mentioned (reaction (5.237b)) to generate nitrosamines: (CH3 )2 NH + HNO2 → CH3 N–NO + H2 O .

(5.257)

In water, amines undergo more decomposition than in the gas phase and accumulate in the condensed phase. Even simpler is the formation of aromatic nitroamines (Ar – aryl, e.g., C6 H5 ), which reform by internal rearrangement (Fischer–Hepp rearrangement) of the nitroso group into nitroamine: Ar–NHR + HNO2 󳨀󳨀󳨀󳨀󳨀→ Ar–NR–NO → ON–Ar–NHR . (−H2 O)

(5.258)

The rate of all nitrosation (nucleophilic substitution) increases with the basicity of the released group X: Y−

X–NO 󳨀󳨀→ [X⋅ ⋅ ⋅NO⋅ ⋅ ⋅Y]− → Y–NO + X− .

(5.259)

For amines (HY = HNR2 ) this reaction is equal to eq. (5.257) – there is an equilibrium HNR2 󴀘󴀯 H+ + R2 N− ; however, the direct nitrosation agent is not nitrous acid (ON–OH) but the protonized form ON–OH+2 with measurable rates only for pH < 1. Other excellent nitrosation agents are nitrosamines itself (OH–NR2 ) and dinitrogen trioxide N2 O3 (ON–NO2 ): NO–NO2 (N2 O3 ) + RNH2 → R–NH–NO + HNO2 .

(5.260)

Dimethyl formamide is expected to exist almost entirely in the vapor phase in ambient air and react with photochemically produced hydroxyl radicals in the atmosphere (Howard 1990): (CH3 )2 C(O)NH2 + OH → (CH3 )2 C(O)NH + H2 O .

(5.261)

5.3 Nitrogen

| 361

Further dimerization led to imides or imido compounds (–C(=O)NH2 ), which quickly react with OH (Barnes et al. 2010). Formamide (HC(O)NH2 ) is the simplest amide in air. The following main or dominant products have been identified and so are final products of amine oxidation: Isocyanic acid O=C=NH Methyl isocyanate O=C=NCH3 N-formylformamide HN(C(O)H)2 N-formyl-N-formamid N–CH3 (C(O)H)2 In the aqueous phase, tertiary amines react with H2 O2 to form amine oxides (Singh et al. 2006), which act as surfactants and can be of importance in cloud droplets: −

R3 N + H2 O2 → R3 N(+) –O + H2 O .

(5.262)

In solution amines also react easily with chlorine (see also Chapter 5.7.4): RNH2 + HOCl → RNHCl + H2 O .

(5.514)

Organic cyanides (nitriles) react with OH according to the general C–H abstraction, probably leading ultimately to the formation of CN radicals, which turn into HCN by reaction with hydrocarbons (Goy et al. 1965): CH3 CN + OH → CH2 CN + H2 O ,

(5.263)

CN + RH → HCN + R .

(5.264)

HCN is an easily soluble but weak acid (pKa = 9.2), forming many salts (cyanides): HCN 󴀘󴀯 H+ + CN− .

(5.265)

Hydrogen cyanide or hydrocyanic acid (HCN) is found in air, water, and soils (Ghosh et al. 2006). It is emitted from several thousand plant species, including many economically important food plants, which synthesize cyanogenic glycosides and cyanolipids. Upon tissue disruption, these natural products are hydrolyzed, liberating the respiratory poison hydrogen cyanide. This phenomenon of cyanogenesis accounts for numerous cases of acute and chronic cyanide poisoning of animals, including humans (Poulton 1990). The –C≡N group (as well as thiocyanate or, in older terminology, rhodanide –S–C≡N) is the simplest organic nitrogen bond (a building block of biomolecules) and already produced in interstellar chemistry (Volume 2). In air, HCN is insignificantly destroyed by OH (k = 3 ⋅ 10−14 cm−3 molecule−1 s−1 ) into the CN radical. HCN cycles back to vegetation and soils through dry and wet deposition and is biologically taken up. Therefore, cyanides are ubiquitously found but in concentrations far from poisonous. 5.3.6.2 Organic NO x compounds The direct natural emission of oxidized organic nitrogen compounds is unknown. Therefore, organic nitrites and nitrates are produced in the decomposition process of

362 | 5 Substances and chemical reactions in the climate system

hydrocarbons (Chapter 5.6.4) where different oxo and carbon (alkyl) radicals can add NO (leading to nitrites) and NO2 (leading to nitrates) (Figure 5.7): CH3 O + NO + M → CH3 ONO + M

k 5.266 = 3.3 ⋅ 1011 cm3 molecule−1 s−1 , (5.266)

CH3 O + NO2 + M → CH3 ONO2 + M

k 5.267 = 2.1 ⋅ 1011 cm3 molecule−1 s−1 . (5.267)

Organic nitrites and nitrates are easily photolyzed: CH3 ONO + hν → CH3 O + NO ,

(5.268)

CH3 ONO2 + hν (λ < 703 nm) → CH3 O + NO2 ,

(5.269a)

3

CH3 ONO2 + hν (λ < 394 nm) → CH3 ONO + O( P) .

(5.269b)

Organic peroxy radicals also add NO, where the intermediate CH3 OONO rearranges to a nitrate CH3 ONO(O): C2 H5 OO+NO+M → CH3 ONO2 +M

k 5.270 ≤ 1.3⋅1013 cm3 molecule−1 s−1 . (5.270)

However, in reaction eq. (5.271) between RO2 and NO2 (Niki et al. 1978) the peroxyalkyl nitrate (not to be confused with peroxyacyl nitrates; see eq. (5.277)) decomposes back by collision: C2 H5 OO + NO2 + M → C2 H5 OONO2 + M , C2 H5 OONO2 + M → C2 H5 O2 + NO2 + M

(5.271) −1

k 5.272 = 4.5 s

.

(5.272)

NO reacts with the methyl radical to form formaldehyde and nitroxyl (however, recall that in air, CH3 + O2 is absolutely predominant): CH3 + NO → HCHO + HNO

k 5.273 = 2 ⋅ 1013 cm3 molecule−1 s−1 .

(5.273)

The methoxy radical CH3 O can react with NO2 , in contrast to O2 (eq. (5.43)), to generate nitrous acid; however, both reactions are very slow and therefore not of interest in air: CH3 O + NO2 → HCHO + HNO2

k 5.274 = 2.1 ⋅ 1013 cm3 molecule−1 s−1 . (5.274)

Alkyl nitrite is photolyzed back to the initial molecules in reaction (5.266); the photolytic lifetime is only 10–15 min (Seinfeld and Pandis 1998). Organic nitrates also photodissociate, where reaction (5.276a) is the dominant pathway; reaction (5.276b) includes internal rearrangement: CH3 ONO + hν → CH3 O + NO ,

(5.275)

RONO2 + hν → RO + NO2 ,

(5.276a)

󸀠

RONO2 + hν → R CHO + HNO2 ,

(5.276b)

RONO2 + hν → RONO + O .

(5.276c)

5.4 Sulfur |

363

Peroxyacyl nitrates (PANs) were intensively studied as NO x reservoirs because they form in photochemical processes but are relatively stable and decompose thermally, thereby providing long-range transport of nitrogen and regaining organic radicals. They are yielded from the peroxyacyl radical RC(O)OO, which is produced via RC(O) + O2 , where the former carbon radical is obtained from photolysis or OH attack of aldehydes (eq. (5.386)): RC(O)OO + NO2 󴀘󴀯 RC(O)OONO2 .

(5.277)

Peroxyacyl nitrates can also decompose as follows: RC(O)OONO2 → RC(O)O + NO3 ,

(5.278a)

RC(O)OONO2 → RC(O) + O2 + NO2 .

(5.278b)

In aqueous solution, alkyl peroxy radicals ROO react with NO2 and NO similar to the gas phase (eqs. (5.270) and (5.271)), forming alkyl peroxynitrates and alkyl peroxynitrites (Goldstein et al. 2005). Whereas the nitrates accumulate, the nitrites decompose, mostly to form an alkyl nitrate, RONO2 . Many nitration reactions proceed on a surface and in a condensed phase (waters, droplets, and particles) (Heal et al. 2007). In clouds (Mount Brocken monitoring station), we found nitrophenols (Lüttke et al. 1997, 1999). The nitrating properties of N2 O3 (NO + NO2 ) and N2 O5 are obviously seen from the structure, transferring –NO2 , –N=O, and –O–N=O: O=N–O–N=O N2 O3 N2 O5 (O)O=N–O–N=O(O)

5.4 Sulfur In our climate system, sulfur ranks fourth in terms of total mass (Table 5.14). After oxygen and nitrogen, sulfur (and later phosphorus) is an important constituent of biomolecules with specific properties in the form of functional groups. As for other life-essential elements, sulfur occurs predominantly in its most stable chemical compound, as sulfate dissolved in oceans. As for nitrogen, biogenic redox processes are essential to turn sulfur from its highest oxidation state +VI (sulfate) to its lowest –II (sulfide); no natural abiotic reduction is possible. Organisms need sulfur in the form of thiols RSH and sulfides R2 S. Thiols are (like alcohol ROH) weak acids, but stronger than alcohols. Thiols easy oxidize into sulfides (this reaction is the main function in biological chemistry), so thiols provide hydrogen for the reduction of other molecules (the dissociated form RS– acts as an electron donor): oxidation

󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀→ 2 RSH 󳨀 ← 󳨀󳨀 RS–SR + 2 H . reduction

364 | 5 Substances and chemical reactions in the climate system

Tab. 5.14: Reservoirs or pools of elements in the climate system. Note: without consideration of the lithosphere where O (as oxides), C (as carbonates), S (as sulfides), and P (as phosphates) occur in dominant or significant amounts (cf. Table 5.2). Element

Mass (in 1019 g element)

Atmosphere

Ocean and waters

Oxygen Hydrogen Nitrogen Sulfur Carbon Phosphorus

12,620 1,500 442 128 4 15 a

O2 (1%) H2 (negligible) N2 (100%) COS (negligible) CO2 (negligible) PH3 (negligible)

H2 O (99%) H2 O (100%) NH+4 /NO−3 (negligible) SO2− 4 (100%) HCO−3 /CO2− 3 (100%) PO3− 4 (negligible)

a

Only in the lithosphere based on O/P ratio, after Clarke (1920).

The following scheme shows the biological cysteine sulfur turnover (Gupta and Carrol 2014) (see Table 5.16 for names of compounds): RSO2 H ↓ RSO3 H

←

RSOH

←

RSH

→

RSSR

→

← RS(=O)2 S(=O)2 R ← RS(=O)S(=O)2 R ←

RSS(=O)R ↓ RSS(=O)2 R

There are many organic sulfur compounds in nature, but all probably exist in a higher oxidation state than S(–II), such as sulfides (including disulfides) and thiols, because they are oxidized after their release from organisms (see Table 5.16 for different functional sulfur groups). Carbonyl sulfide O=C=S (commonly written COS) is the most abundant sulfur compound naturally occurring in the atmosphere. Before 1970 hydrogen sulfide H2 S was believed to be the major emitted species, but it is almost completely oxidized before escaping from anoxic environments into the atmosphere. In the natural environment, dimethyl sulfide (CH3 )2 S (DMS) is the most important sulfur species because of its high emission levels and contribution to climate-relevant atmospheric particulate sulfates. With industrialization, sulfur dioxide (SO2 ) became the key pollutant and the most important sulfur species in air (Möller 1977). At present, after the introduction of flue gas desulfurization, NO x replaced SO2 in air in terms of its chemical significance. However, concerning atmospheric background submicron aerosols, sulfates remain dominant and important in climate control. It is a subtle irony that too much SO2 abatement leads to the disappearance of cooling sulfate aerosol, which intensifies the greenhouse effect. The atmospheric chemistry of sulfur is simpler than that of nitrogen in two aspects. First, the number of stable species in air is smaller,⁴³ and second, the variety of interactions in the environment is less – almost all effects come from sulfate, such

43 The number of possible intermediates (often hypothetical) is huge (Tables 5.16, 5.17, and 5.23), especially in aquatic environments.

5.4 Sulfur |

365

as acidity and radiation scattering. In the oxidation line to sulfate, oxidants are consumed: H2 O 4O O → SO3 (󳨀󳨀󳨀→ H2 SO4 ) H2 S 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ SO2 󳨀 (−2 H2 O)

Because SO2 is formed (and emitted) from sulfides contained in fuels during combustion processes, five O atoms are needed to produce one sulfate. These are two atoms of oxygen more than for nitrate (HNO3 ) formation from air nitrogen (N2 ). The idea that SO2 plays a role in the ozone formation cycle by transferring OH to HO2 has always been not regarded (reactions (5.295) and (5.296)); however, the rate of OH → HO2 conversion through SO2 is low compared to that of other O3 precursors of interest. There is also another irony of fate: in the past, when SO2 concentrations in urban areas were so high that they contributed to O3 formation, nothing was known about the mechanism of tropospheric ozone formation.

5.4.1 Natural occurrence and sources Like nitrogen, sulfur is an important element in biomolecules with specific functions. In contrast to nitrogen, where the largest pool is the atmosphere (molecular N2 ), for sulfur the largest pool is the ocean (as dissolved sulfate); both components are chemically stable. Elemental sulfur (which forms cyclic octatomic molecules with the chemical formula S8 ) was found in huge deposits in Italy (Sicily), Poland, Japan, and the USA. At present, elemental sulfur reservoirs are almost all depleted. Industrial sulfur is now produced from H2 S, which occurs in natural gas (desulfurization is essential in gas treatment) and from sulfide mineral ores (where SO2 is a byproduct of roasting). In the atmosphere, carbonyl sulfide (COS) represents the major sulfur component (despite its small emissions but due to its long residence time). Similarly to nitrogen and carbon, the sulfur content in the lithosphere is small because of degassing volatile sulfur compounds in the early history of the Earth. Primordial sulfides and elemental sulfur are almost all oxidized in the atmospheric turnover (Canfield 2004). Moreover, humans have extracted them by mining from the lithosphere to such an extent that the remaining resources are negligible now. The great “role” of life again is the reduction of sulfate (S6+ ) to sulfide (S2− ). Volcanism is an important source of sulfur dioxide (SO2 ) and promotes the formation of a strong acid (H2 SO4 ) that may play an important role in weathering. The possible average annual volcanic contribution of SO2 to the free acidity budget (in terms of H+ ) is about on the same order of magnitude as that from CO2 (the huge atmospheric CO2 concentration compared with that of SO2 is compensated due to the low Henry’s law constant of CO2 and the low acidity constant of H2 CO3 ). Consequently, the dominant anthropogenic SO2 emission since the Industrial Revolution has resulted in significant acidification of many parts of the world. More than 90% of SO2 emissions is related to the combustion of fossils fuels (coal and oil with an approximate share of two-thirds and one-third, respectively), primarily

366 | 5 Substances and chemical reactions in the climate system

metal smelting (Cu, Zn, Mn, and Ni) and sulfuric acid production (only in the past). Air pollution in the industrialized world has undergone drastic changes in the past 50 years. Until World War II, the most important urban air pollutant was sulfur dioxide combined with soot from the use of fossil fuels in heat and power production. By the turn of the century, almost everything that was known in the 1950s about the causes of smoke and its elimination had already been said, but hardly anything had been done to reduce the smokiness of cities. Although SO2 concentrations in the air of cities were in a range of 1–10 mg m−3 around 1900, they dropped to the upper range of micrograms per cubic meter (several hundred) by the 1950s and at present are in the lowest range of micrograms per cubic meter (5–10), close to the remote background values on the order of 0.5 to 4 μg m−3 . In 1980, flue gas desulfurization (FDG) was introduced stepwise with different degrees in industrialized countries; FDG works with an efficiency of about 95%. Global anthropogenic sulfur emissions increased until around 1980. Different estimates in the period 1975–2000 show large variations between 65 and 85 Tg S yr−1 , with a maximum around 1985 of approximately 70 Tg S yr−1 . Newer estimates show a relative stability throughout the decade of the 1980s and a 25% decline from 1990 to 2000 to a level not seen since the early 1960s. The decline is evident in North America, at present in China, but most significantly in Europe. The combustion of fossil fuels has increased continuously up to the present. China’s maximum SO2 emission occurred in 2005 (16.5 Tg SO2 –S) and decreased to 14 Tg in 2010 (contributing to one-third of worldwide emissions). SO2 emissions from India increased from 1.7 (1990) to 5 (2010) Tg S yr−1 . Biogenic sources emit so-called reduced sulfur compounds, which are in an oxidation state of S2− , for example, hydrogen sulfide (H2 S), dimethyl sulfide (DMS) and dimethyl disulfide (DMDS), carbon disulfide (CS2 ), and carbonyl sulfide (COS).⁴⁴ Plants emit DMS and COS (like other organic compounds) predominantly by respiration (Table 5.15).

5.4.2 Reduced sulfur: H2 S, COS, CS2 , and DMS In chemistry textbooks, carbon disulfide and carbonyl sulfide are treated as carbon compounds. In the climate system, the contribution of CS2 and COS to the carbon budget is negligible, and both species play no role in carbon chemistry. Moreover, COS only decomposes in the stratosphere because of its chemical stability. Most tropospheric COS is removed by dry deposition (plant assimilation and uptake by microorganisms in soils). Crutzen (1976) suggested that COS was a contributor to the stratospheric sulfate layer (Junge layer). However, at present it is assumed that it plays a

44 Some authors use the formula OCS, which also represents the molecular structure O=C=S.

5.4 Sulfur |

367

Tab. 5.15: Natural sulfur emissions; after Möller (2003). Source

Emission (Tg S a−1 )

Emitted compound

Volcanism Soils and plants Wetlands Biomass burning Ocean

10 (±5) 1–4 2 2–3 36 (±20)

SO2 , H2 S, COS (?) H2 S, DMS, COS, CH3 SH H2 S, DMS, COS, CS2 SO2 , COS DMS, H2 S, COS, CS2

Compounds

Emission (Tg S a−1 )

DMS SO2 H2 S CS2 COS

35 (±20) 12 (±6) 3 (±2) 1 (±1) 1 (±0.5)

Total

50 (±25)

minor role in the stratospheric sulfur budget. Stratospheric chemistry is simple. Either it photodissociates into CO and S, which subsequently form CO2 and SO2 , or it reacts slowly with OH to form CO + SO or CO2 + HS. All sulfur species ultimately oxidize to H2 SO4 , which is important in the formation of PSCs (Chapter 5.2.7). SO and HS are short-lived intermediates, which also occur in the oxidation of CS2 and H2 S: k 5.279 = 7.6 ⋅ 10−17 cm3 molecule−1 s−1 , k 5.280 < 4 ⋅ 10−19 cm3 molecule−1 s−1 , and k 5.281 = 3.7 ⋅ 10−12 cm3 molecule−1 s−1 : SO + O2 → SO2 + O ,

(5.279)

HS + O2 → products (HSO2 , HO2 + S, H + SO2 ) ,

(5.280)

HS + O3 → HSO + O2 .

(5.281)

The radicals HSO and HSO2 quickly decompose (with O3 and O2 ) into several other radicals (HS, SO, HSO2 , and OH; k = 6 ⋅ 10−14 cm3 molecule−1 s−1 ); finally, SO2 is produced. Atomic sulfur oxidizes quickly, k 5.282 = 2.1 ⋅ 10−12 cm3 molecule−1 s−1 ): S + O2 → SO + O .

(5.282)

The only important (and very fast) reaction of CS2 happens via OH radicals, k 5.283 = 2.5 ⋅ 10−11 cm3 molecule−1 s−1 and k 5.284 = 2.8 ⋅ 10−14 cm3 molecule−1 s−1 : CS2 + OH + M → HOCS2 + M , HOCS2 + O2 → products (CO, CS, SO, COS) .

(5.283) (5.284)

The CS radical reacts in two channels, k 5.285 = 2.9 ⋅ 10−19 cm3 molecule−1 s−1 : CS + O2 → CO + SO ,

(5.285a)

CS + O2 → COS + O .

(5.285b)

368 | 5 Substances and chemical reactions in the climate system

CH3SCH3 abstraction

addition

OH (-H2O), NO3 (-HNO3)

OH

CH3S(OH)CH3

CH3SCH2

O2 (-HO2)

O2

CH3SCH2OO

CH3S(O)CH3 (B)

NO (-NO2)

OH

CH3S(O)(OH)CH3

(- HCHO)

CH3SCH2O O2 (-HO2)

O2 (-HO2)

O2 (-HO2)

CH3S(O2)CH3 (C) CH3 + CH3S(O)OH (D)

CH3SCHO (A)

OH

hν (-CO), OH (-CO)

CH3S(O)(OH)2

CH3S

O2 (-HO2)

O2

M CH3S(O)O

CH3SOO

CH3S(O)2OH (E)

NO (-NO2) O2

CH3SO O2

CH3S(O)OO CH3S(O2)OO

CH3 + SO2

NO (-NO2)

CH3S(O)2O

CH3 + SO3

H2O

H2SO4

Fig. 5.27: DMS oxidation, simplified on main routes; after Berresheim et al. (1995), Berresheim (1998), and Finlayson-Pitts and Pitts (2000).

It is self-evident that O reacts with O2 to give O3 and CO forms CO2 via OH attack. The oxidation of H2 S is also relatively fast (2–3 day lifetime) and finally produces SO2 : H2 S + OH → HS + H2 O .

(5.286)

Analog OH reacts with methanethiol (methyl mercaptan) CH3 SH (k = 3.3 ⋅ 10−11 cm3 molecule−1 s−1 ). A very important reduced sulfur species in our climate system is DMS. Many studies have been carried out to clarify the oxidation mechanisms shown in Figure 5.27. The fate of radical intermediates such as CH3 O, SO, and CH3 was described earlier, but many other radicals can only be grouped together under the term “product” on

5.4 Sulfur | 369

Tab. 5.16: Organic sulfur compounds. Sulfenes and sulfenic acids are extremely unstable and convert into disulfides and sulfinic acids. The open bond (–) is connected with alkyl or aryl residues R. Note that sulfane is the systematic name for H2 S and should never be used for organic sulfur; HSn S are polysulfanes and RSn R are polysulfides. Note that many organic sulfur-nitrogen compounds exist being essential in biochemistry. Structure

Formula

Name of compound

–S–H –S– –S–S– >S=O and >S+ –O− –CH(=S=O) >S=S >S(=O)2 >C=S(=O)2 –S(=O)–S– –S–S(=O)2 – –S(=O)–S(=O)2 – –S(=O)2 –S(=O)2 – –S–OH –S(=O)–OH –S(=O2 )–OH

RSH R2 S R2 S2 R2 SO RCHSO R2 S2 R2 SO2 R2 CSO2 R2 S2 O R2 S2 O2 R2 S2 O3 R2 S2 O4 RSOH RSO2 H RSO3 H

Thiol (thio group sh) a Sulfide f Disulfide e Sulfoxide (sulfinyl group SO) Thioaldehyde s-oxide g Thiosulfoxide h Sulfone (sulfonyl group SO2 ) Sulfene b Thiosulfinic acid Thiosulfanate Disulfide trioxide Disulfone Sulfenic acid c Sulfinic acid Sulfonic acid (sulfo group) d

Also called mercaptan (old); R–S– is also called the sulfenyl (or, synonymously, sulfanyl) group, RS+ sulfenylium ion, RS∙ sulfenyl radical, R3 S+ sulfonium compound. b Note that S is double-bonded with a C atom in contrast to sulfone; S,S-dioxide, thioaldehydes or thioketones. c Tautomer: –S(=O)–H. d Sulfonic acid is a hypothetical acid with the formula H–S(=O )–OH. This compound is a tautomer 2 of sulfurous acid HO–S(=O)–OH, but it is less stable and would likely convert to that very quickly if it were formed. Although this compound is unimportant, there are many derived compounds with the formula R–S(=O)2 –OH for various R. These may then form salts or esters called sulfonates. e A disulfide bond is a single covalent bond derived from the coupling of thiol groups. The linkage is also termed an SS-bond or disulfide bridge. The overall connectivity is therefore C–S–S–C. The terminology is almost exclusively used in biochemistry and bioorganic chemistry. f Once called thioether. g Once called sulfines (obsolete). h Once called sulfanes (obsolete). a

the right-hand side of the equation. Many molecules found in the reaction scheme can be identified from Table 5.16. Figure 5.27 only shows the OH attack; in addition, NO3 (nitrate radical) was described as a very effective oxidizer. OH initiates two channels: the H abstraction and the addition: k 5.287 = 4.8 ⋅ 10−12 cm3 molecule−1 s−1 and k 5.288 = 2.2 ⋅ 10−11 cm3 molecule−1 s−1 : DMS + OH → CH2 SCH3 + H2 O ,

(5.287)

DMS + OH → CH3 S(OH)CH3 .

(5.288)

370 | 5 Substances and chemical reactions in the climate system

Two more channels that break down the DMS molecule are known to form CH3 S + CH3 OH and CH3 + CH3 SOH. Because of the nocturnal NO3 attack on DMS (H abstraction channel), its lifetime is short (only about 1 day). It is remarkable that via the abstraction channel only sulfate is seen at the end, whereas in the OH addition channel, many stable organic sulfur species, such as methanesulfonic acid or methanesulfonate (MSA) and dimethylsulfoxide (DMSO), as well as dimethylsulfone (DMSO2 ), can be identified. The further fate of these compounds is to transfer to the aqueous phase (clouds and precipitation). It is known that organic sulfide (here DMS) can also be simply oxidized to sulfoxide (here DMSO) and further to sulfone in solution: CH3 SCH3 (DMS) + H2 O2 → CH3 S(O)CH3 (DMSO) + H2 O , O

→ CH3 (O)S(O)CH3 (DMSO2 ) . CH3 S(O)CH3 󳨀

(5.289) (5.290)

Although DMSO is the major product of aqueous-phase DMS oxidation (and is ubiquitously found in all aquatic environments), minor amounts of methanethiol CH3 SH, dimethyldisulfide CH3 SSCH3 (DMDS), MSA, and DMSO2 have been observed (Lee and de Mora 1999 and references therein). DMSO was first detected in a marine environment by Andreae (1980). DMSO2 will oxidize in droplets such as MSA, which is found (together with DMSO) in clouds and precipitation water with a distinct seasonal variation (Munger et al. 1986, Ayers et al. 1986, Brimblecombe and Shooter 1987, Adewuyi 1989, Sciare et al. 1998). The rate of DMS oxidation was observed to increase in the presence of humic substances as well as model substances that could act as photosensitizers. This again is a remarkable observation supporting the notion that in aquatic environments oxidizing agents (where OH plays the key role) are photoenhanced (reaction (5.79)). It was found (see references in Lee and de Mora 1999) that besides the formation of DMSO2 , DMSO also reacts in the following chain (CH3 SO2 H – methanesulfuric acid): OX

OX

DMSO 󳨀󳨀→ CH3 SO2 H 󳨀󳨀→ MSA A number of studies on the oxidation of H2 S with O2 in natural waters were conducted in the laboratory and the field (Chen and Morris 1972, Hoffmann and Lim 1979, Millero 1986, Millero et al. 1987, Zhang and Millero 1993, Brezonik 1994), but only one study is known to have an atmospheric relevance (Hoffmann 1977). With respect to the sediment chemistry of natural waters and the pollution treatment of wastewater, H2 S (aut)oxidation was of interest long before. It was found that the process is in the first order with respect to H2 S. Trace metals (especially Fe and Mn) increase the rate of ox2− idation, and sulfate (SO2− 4 ), thiosulfate (S2 O3 ), and elemental sulfur were detected as products. From the water bottom to the surface, the H2 S oxidation rate increases. This is attributed to a larger amount of dissolved oxygen as well as additional oxidants such as hydrogen peroxide (Hoffmann 1977, Millero 2006) and ozone closer to the interface. The oxidation of intermediate sulfite (HSO−3 ) is discussed in Chapter 5.4.3.2.

5.4 Sulfur

| 371

Atmospheric H2 S concentrations are significant only near their sources. Therefore, considering the much larger significance of DMS and SO2 in the sulfur cycle, aqueousphase H2 S oxidation has never been considered in cloud and precipitation chemistry models. H2 S is only slightly soluble (Table 3.2) and partly dissociates: pK a = 7 (the second dissociation with pKa ≈ 13 can be neglected): H2 S 󴀘󴀯 HS− + H+ .

(5.291)

In the studies cited previously, only gross reaction equations are given. However, with modern knowledge, we can speculate about aqueous oxygen chemistry and photocatalytic-enhanced redox processes (Chapter 5.2.5) that reactive oxidants such as OH, O3 and H2 O2 will elementarily react with HS− (in the autoxidation process all these species are slowly produced from O2 ), similarly to the sulfite oxidation (Chapter 5.4.3.2): (5.292) HS− + OH(O3 , H2 O2 ) → HS + OH− (O−3 , H2 O−2 ) . The HS radical (in solution it dissociates to a very small extent into H+ + S− ; thus, unstable S− could donate its electron and produce sulfur) can react in analogy to the gas-phase reaction (5.281) with O3 gaining HSO but also with OH forming S: HS(S− ) + OH → S + H2 O(OH− ) , HS + O−2

→

S + HO−2

.

(5.293) (5.294)

Elemental sulfur becomes colloidally stable in S8 molecules but can also add to sulfite and form thiosulfate, which also loses sulfur via disproportionation into H2 S and sulfate: 2− H2 O S + SO2− 󳨀󳨀→ H2 S + SO2− 4 3 → S2 O3 󳨀 In hydrometeors and interfacial waters, however, sulfur reacts with oxygen (reaction (5.282)) via SO2 to form hydrogen sulfite HSO−3 . Thiosulfate is an important intermediate in biological sulfur chemistry from both sulfate reduction and sulfide oxidation. Many hypothetical so-called lower sulfuric acids (Table 5.17) might appear as intermediates or in the form of radicals (such as SOH, HSO, HSO2 , HSS, and HS, as seen from the structure formulas) in the oxidation chain from sulfide to sulfate: HS− → S → HSO−3 → SO2− 4 The role of these intermediates and organosulfur compounds as antioxidants (due to radical scavenging) has been known for many years (Kulich and Shelton 1978, 1991).

5.4.3 Oxides and oxoacids: SO2 , H2 SO3 , SO3 , and H2 SO4 Sulfur forms oxides of the composition SOm (m = 1, 2, 3, and 4). We have already encountered sulfur monoxide (SO) as an intermediate in the oxidation of reduced sulfur

372 | 5 Substances and chemical reactions in the climate system

Tab. 5.17: Oxoacids of sulfur and isomeric forms (hypothetically); after Holleman-Wiberg (2007). Note: Many are unstable intermediates or exist only as anions in solution. Structure

Formula

Name (acid)

Name (salt)

HS(=O)–OH HS(=O)2 –OH (HO)2 S=O (HO)2 S(=O)2 HO–S(=O)2 –OOH HS–S(H) = O HS–S(= O)–OH (HO)2 S=S(=O) HO–S(=O)–S(=O)–OH HO–S(=O)2 –O–S(=O)–OH HO–S(=O)2 –S(=O2 )–OH HO–S(=O)2 –O–S(=O2 )–OH HO–S(=O2 )–OO–S(=O2 )–OH

H2 SO2 H2 SO3 H2 SO3 H2 SO4 H2 SO5 H2 S2 O H2 S2 O2 H2 S2 O3 H2 S2 O4 H2 S2 O5 H2 S2 O6 H2 S2 O7 H2 S2 O8

Sulfinic acid Sulfonic acid a Sulfurous acid Sulfuric acid Peroxomonosulfuric acid b Thiosulfoxyl acid Thiosulfurous acid c Thiosulfuric acid Hyposulfurous acid d Disulfurous acid e Dithionic acid f Disulfuric acid h Peroxodisulfuric acid i

Sulfinate g Sulfonate g Sulfite Sulfate Peroxomonosulfate Thiosulfinate Thiosulfite Thiosulfate Hyposulfite d Disulfite Dithionate Disulfate Peroxodisulfate

a

Only as intermediate. Also termed Caro’s acid. c Disulfur(I)acid, anhydride: S O (disulfur monoxide); tautomers: HO–S–S–OH (dihydroxy disulfane) 2 and S–S(OH)2 (thiothionyl hydroxide). d Also termed dithionous acid (salt: dithonite or hydrosulfite). e Also termed pyrosulfurous acid. f Generic name: thionic or polythionic acids H2 SnO6 (n = 2 . . . 6), also named disulfanic acid. g Only as organic compounds. h Also termed pyrosulfuric acid; generic. i Also called Marshall’s acid. b

compounds. Environmentally important are only sulfur dioxide (SO2 ) and sulfur trioxide (SO3 ). Sulfur forms three oxoacids of the composition H2 SOn (n = 3, 4, and 5), six of the composition H2 S2 On (n = 3, 4, 5, 6, 7, and 8), and several acids of the composition H2 S n Om (Table 5.17). However, in the atmosphere only sulfurous acid (H2 SO3 ) and sulfuric acid (H2 SO4 ), with the corresponding anhydrides sulfur dioxide (SO2 ) and sulfur trioxide (SO3 ), are of importance. Apart from minor global (but locally it can be a significant source) contributions from metallurgical processes, anthropogenic SO2 derives exclusively from the combustion of fossil fuels, mainly coal; the only natural source of SO2 is given by volcanic activities.⁴⁵ In air, we have to consider gas-phase SO2 oxidation and the subsequent gas-to-particle conversion to sulfuric acid and sulfate PM (see also Chapter 3.6.2).

45 Field measurements have provided evidence that acid sulfate soils, when drained, oxidize sulfides and might emit SO2 , globally contributing about 3 Tg S yr−1 (Macdonald et al. 2004).

5.4 Sulfur |

373

Some acids (or anions) exist only as intermediate. As stated previously, the primary emission of burning (sulfur containing) fuels is SO2 ; however, it is known that around 2–5% of sulfur emissions occur already as SO3 . Once SO3 is formed, it converts quickly into particles of sulfuric acid (smaller than 10 nm), much less of which can be removed by flue gas desulfurization than SO2 . Therefore, the relative percentage of SO3 to SO2 is drastically increased in modern coal-fired power plants and might cause “blue plumes.” In the gas phase, SO2 oxidizes only by OH radicals, followed by gas-toparticle conversion to sulfuric acid and sulfate PM. The main route of S(IV) oxidation is through the aqueous phase, where cloud droplet evaporation provides submicron aerosol particles containing sulfate, as illustrated in the following scheme: H2 O

󳨀󳨀 󳨀→ SO2 (󳨀 ← 󳨀󳨀 H2 SO3 )

OX

󳨀󳨀→

H2 O

󳨀󳨀 󳨀→ SO3 (󳨀 ← 󳨀󳨀 H2 SO4 )

↕

↓

aqueous-phase S(IV)

OX

󳨀󳨀→

→ particulate sulfate ↕

aqueous-phase S(VI)

5.4.3.1 Gas-phase SO2 oxidation From all gas-phase reactions studied since the 1950s (Katz and Gale, 1971; see Möller 1980 and references therein), OH remains the sole component for SO2 oxidation: k 5.295 = 1.3 ⋅ 10−12 cm3 molecule−1 s−1 , k 5.296 = 4.3 ⋅ 10−13 cm3 molecule−1 s−1 , and k 5.297 = 5.7 ⋅ 104 s−1 (50% RH). Therefore, it is seen that reaction (5.295) determines the overall rate of conversion: SO2 + OH + M → HOSO2 + M ,

(5.295)

HOSO2 + O2 → HO2 + SO3 ,

(5.296)

SO3 + H2 O → products (sulfate clusters) . 106

(5.297)

cm−3 ,

molecules the SO2 lifetime Assuming a mean OH radical concentration of is about 10 days. Therefore, dry deposition and uptake by clouds and precipitation are important removal pathways (Chapter 5.4.4). 5.4.3.2 Aqueous-phase sulfur chemistry As seen from Figure 4.16, the reservoir distribution of SO2 strongly depends on aqueous-phase pH. Sulfurous acid H2 SO3 is not known as a pure substance (similar to H2 CO3 ); several isomeric forms have been spectroscopically detected. Therefore, the symbol SO2 ⋅aq is often used; the equilibrium eq. (5.298) lies fully on the left-hand side (K5.298 < 10−9 ). Sulfurous acid, however, is largely dissociated with pK5.299 = 2.2 and pK5.300 = 7.0, k 5.300+ = 3.1 ⋅ 103 s−1 : SO2 + H2 O 󴀘󴀯 SO2 ⋅ aq 󴀘󴀯 H2 SO3 , H2 SO3 󴀘󴀯 HSO−3

󴀘󴀯

HSO−3 + H+ , + SO2− 3 +H .

(5.298) (5.299) (5.300)

374 | 5 Substances and chemical reactions in the climate system

Because of the complication with H2 SO3 , dissolved SO2 can be directly associated with bisulfite, k 5.301+ = 6.3 ⋅ 104 s−1 (Graedel and Weschler 1981): SO2 + H2 O 󴀘󴀯 HSO−3 + H+ .

(5.301)

SO2 reacts directly with hydroxide ions: k 5.302 = 1.1 ⋅ 1010 L mol−1 s−1 (Boniface et al. 2000): (5.302) SO2 + OH− → HSO−3 . S(IV) denotes the sum of all dissolved sulfur species in this oxidation state +4, SO2 + H2 SO3 + HSO−3 + SO2− 3 , whereby [H2 SO3 ] → 0. Sulfite forms adducts with dissolved aldehydes, of which the most important is α-hydroxymethanesulfonate (HMS), which is stable against oxidation, pK5.303b = 3.4 (Warneck 1989): HCHO + HSO−3 → HCH(OH)SO−3 (HMS) , H+

− − 󳨀 󳨀→ HCHO + SO2− 󳨀󳨀 HMS . 3 → HCH(O) (SO3 ) ←

(5.303a) (5.303b)

However, competitive formaldehyde produces a hydrate, which is unable to add onto sulfite: (5.304) HCHO + H2 O 󴀘󴀯 CH2 (OH)2 . HMS is the anion of the strong hydroxymethanesulfonic acid (HMSA), which is fully dissociated (Munger et al. 1984). The second dissociation step to HCH(O)− (SO−3 ) corresponds to a weak acid with pKa ≈ 10 (Sörensen and Anderson 1970). HMS slowly decomposes into the initial substances, thereby sometimes describing eqs. (5.303) and (5.305) as being in equilibrium with K5.303/5.305 = 6.6 ⋅ 109 , k 5.305 = 7.7 ⋅ 10−3 s−1 (Möller and Mauersberger 1995): HCH(OH)SO−3 (HMS) → HCHO + HSO−3 .

(5.305)

Often formaldehyde hydration is also included in the equilibrium (Deister et al. 1986): K = [CH2 (OH)SO−3 ]/[CH2 (OH)2 ][HSO3 ] = 3.6 ⋅ 106 L mol−1 .

(5.306)

In alkaline solution, HMS decomposes, k 5.307 = 3.7 ⋅ 10−3 L mol−1 s−1 : HCH(OH)SO−3 + OH− → CH2 (OH)2 + SO2− 3 .

(5.307)

The only oxidation of HMS proceeds via OH attack (Buxton et al. 1996): HCH(OH)SO−3 + OH → CH2 (OH)2 + SO−3 .

(5.308)

From all three HMS sinks (oxidation, alkaline decomposition, and decay), only eq. (5.305) is considered to be important (Möller and Mauersberger 1995). Sulfite also forms adducts with other aldehydes such as benzaldehyde, methylglyoxal, acetaldehyde, and hydroxyacetaldehyde (Olson et al. 1988, Olson and Hoffmann 1988, 1989).

5.4 Sulfur |

375

Tab. 5.18: Reaction rate constants for HSO−3 + H2 O2 . k in 107 L2 mol−2 s−1

Reference

35.0 2.6 4.7 2.4 8.0 9.5 2.1 9.1 ± 0.5

Hoffmann and Edwards (1975) Penkett et al. (1979) Martin and Damschen (1981) McArdle and Hoffmann (1983) Kunen et al. (1983) Lee at al. (1986) Lagrange et al. (1993) Maaß et al. (1999)

Because of the importance of SO2 and sulfate in the atmosphere, the oxidation pathways in solution have been studied extensively and typically been subdivided as follows: – by peroxides (H2 O2 and ROOH), – by ozone O3 , – by oxygen (autoxidation), – by oxygen with participation of TMIs (so-called catalytic oxidation), – by radicals (OH, NO3 , Cl and others), and – by other oxidants (e.g., HNO4 , HOCl). Decades of SO2 research have produced almost only gross reaction rates for S(IV) + H2 O2 such as those first studied by Mader (1958) and later recognized as being atmospherically important by Hoffmann and Edwards (1975) and Penkett et al. (1979): k 5.309 = (5.3±2.7)⋅107 L2 mol−2 s−1 recommended by Möller and Mauersberger (1995) (Table 5.18). Instead of H2 O2 , also peroxoacetic acid (Lind et al. 1987), methylhydroperoxide, peroxomonosulfuric acid (Betterton and Hofmann 1988), and other oganic peroxides (Drexler et al. 1991) have been studied as oxidants: − (d[S(IV)]/ dt = (d[S(VI)]/ dt = RH2 O2 = k 5.309 [H+ ][HSO−3 ][H2 O2 ] .

(5.309)

Louis Jacques Thénard (1777–1857) recognized that one O is only weakly bonded in H2 O2 and that the molecule easily decomposes (Thénard 1819).⁴⁶ Remarkably, soon after its discovery it was known that H2 O2 oxidizes sulfurous acid into sulfuric acid without the formation of free oxygen (Gmelin 1827), a mechanism recognized to be important in air chemistry almost 150 years later (Möller 1980) as the most important pathway in the oxidation of dissolved SO2 in hydrometeors: + HSO−3 + H2 O2 → SO2− 4 + H + H2 O .

46 This (wrong) statement is based on the often generally accepted reaction scheme A + H2 O2 → AO + H2 O. However, H2 O2 cannot transfer O (like O3 ); the only way to do this is by decomposing it according to H2 O2 + e− + H+ → OH + H2 O; in a subsequent reaction, OH is the oxidizer.

376 | 5 Substances and chemical reactions in the climate system

It is remarkable that the exact mechanism of the S(IV)−H2 O2 reaction is not known in detail; several authors (Lagrange et al. 1993 and references therein) have proposed the formation of the intermediate ion HO2 SOO− as a rate-controlling step (peroxomonosulfite HO–S(=O)–OO− , an unknown substance). The subsequent proton-catalyzed rearrangement into sulfate could explain the pH dependence (rate increase with H+ ); however, it is hard to understand how HOOH (H2 O2 ) might transfer a single O atom or the whole peroxo group (–O–O–). H O ... O

O HO S

+H2O2 O

HO S

+H+

HO S O ... O

O

O

O O

HO S OH (H2SO4) O

H

Möller (2009a) proposed that a single electron transfer occurs in the sense of another Fenton-like reaction (eq. (5.97)) as the initializing step: HSO−3 + H2 O2 → HSO3 + H2 O−2 .

(5.310)

The fate of H2 O−2 is well known: OH + OH− (eq. (5.101)). Note that OH yield is stoichiometric to H2 O2 and thereby provides OH concentrations orders of magnitude larger than by the phase transfer of gaseous OH (the “radical” oxidation by OH was described as slow) (Möller 1980). Figure 5.28 shows a generalized scheme of S(IV) oxidation, depending on pH. Ermakov et al. (1997) considered that the radical chain mechanism is most likely respon-

Fig. 5.28: General S(IV) oxidation in alkaline and acidic solution. Electron acceptors: H2 O2 , O3 , O2 , − OH, NO3 , Cl, Fe3+ , Mn2+ , Cu2+ ; electron donors: Fe2+ , Mn+ , Cu+ , HSO−3 , SO2− 3 , OH .

5.4 Sulfur |

377

Tab. 5.19: Rate constants of reactions of sulfite with radicals. k in L mol−1 s−1

Reaction OH + HSO−3 OH + HSO−3 OH + SO2− 3 SO−4 + HSO−3 SO−4 + SO2− 3 SO−4 + HSO−3 + SO−5 + SO2− 3 +H SO−5 + HSO−3 SO−5 + SO2− 3 NO3 + HSO−3 NO3 + SO2− 3 Cl−2 + HSO−3 Cl−2 + SO2− 3

→ → → → → → → → → → → → →

H2 O + SO−3 OH− + HSO3 OH− + SO−3 − + SO2− 4 + SO3 + H − SO2− + SO 4 3 HSO−5 + SO−3 HSO−5 + SO−3 SO−4 + H+ + SO2− 4 SO−4 + SO2− 4 NO−3 + SO−3 + H+ NO−3 + SO−3 2 Cl− + SO−3 + H+ 2 Cl− + SO−3

2.7 ⋅ 109 4.6 ⋅ 109 5.5 ⋅ 109 6.8 ⋅ 108 3.1 ⋅ 108 8.6 ⋅ 103 2.15 ⋅ 105 3.6 ⋅ 102 5.5 ⋅ 105 5.6 ⋅ 103 3.0 ⋅ 108 1.7 ⋅ 108 6.2 ⋅ 107

Buxton et al. (1996) Buxton et al. (1996) Neta and Huie (1985) Buxton et al. (1996) Buxton et al. (1996) Buxton et al. (1996) Buxton et al. (1996) Buxton et al. (1996) Buxton et al. (1996) Exner et al. (1992) Exner et al. (1992) Jacobi (1996) Herrmann et al. (1996)

sible for S(IV) oxidation. The existence of the sulfite radical HSO3 and its role in biological damage (whereby the subsequently produced peroxosulfate radical SO−5 is a much stronger oxidant) has long been known (Neta and Huie 1985). Many molecules, radicals, and metal ions react with sulfite and bisulfite in a one-electron oxidation (Table 5.19); A – electron acceptor (see also Figure 5.28): HSO−3 + A → SO−3 + H+ + A− ,

(5.311a)

SO−3

(5.311b)

SO2− 3

+A→

−

+A .

The sulfite radical SO−3 reacts quickly with oxygen to form the peroxosulfate radical, k 5.312 = 2.5 ⋅ 109 L mol−1 s−1 (Buxton et al. 1996): SO−3 + O2 → SO−5 .

(5.312)

The peroxosulfate radical SO−5 reacts primarily with sulfite (HSO−3 and SO2− 3 ) in different pathways to form peroxomonosulfate (HSO−5 ) and the final product sulfate − − 5 (SO2− 4 ), generating sulfur radicals (SO3 and SO4 ) (Figure 5.29), k 5.313a = 5.5 ⋅ 10 L mol−1 s−1 , k 5.313b = 3.6 ⋅ 102 L mol−1 s−1 , k 5.313c = 8.6 ⋅ 103 L mol−1 s−1 (Buxton et al. 1996): − 2− SO−5 + SO2− 3 → SO4 + SO4 ,

SO−5 SO−5

+ +

HSO−3 HSO−3

→ →

HSO−5 HSO−5

+ SO−3 + SO−3

(5.313a)

,

(5.313b)

.

(5.313c)

At this state, the pathway splits from the sulfate radical SO−4 and peroxomonosulfate (HSO−5 ); the latter decomposes with sulfite (HSO−3 and SO2− 3 ) into sulfate, k 5.314 = 7.1 ⋅ 106 L mol−1 s−1 (Betterton and Hofmann 1988): 2− + HSO−5 + HSO−3 (or SO2− 3 ) → 2 SO4 + 2 (or 1)H .

(5.314)

378 | 5 Substances and chemical reactions in the climate system

reaction rate in mol L-1 s-1

100 10-2

S(IV) + O3

10-4 S(IV) + H2O2 10-6 10-8 10-10 10-12 2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

pH Fig. 5.29: Dependence of the reaction rates of the reaction S(IV) + H2 O2 and S(IV) + O3 on pH.

The sulfate radical reacts similarly with sulfite but regenerates sulfite radicals, k 5.315a = 3.2 ⋅ 108 L mol−1 s−1 (Betterton and Hofmann 1988): 2− − + SO−4 + HSO−3 (or SO2− 3 ) → SO4 + SO3 + H .

(5.315a)

With nitrate ions the sulfate radical is in equilibrium with sulfate and the nitrate radical (Løgager et al. 1993): SO−4 + NO−3 󴀗󴀰 SO2− 4 + NO3 .

(5.315b)

Hence, a radical chain is established where in the initial step sulfite ions can also be transformed into sulfite radicals by other sulfur radicals (SO−4 and SO−5 ). Of less importance are radical–radical reactions. We mentioned first dimerization to relatively 2− 8 −1 −1 stable dithionate (S2 O2− 6 ) and peroxodisulfate (S2 O8 ), k 5.316 = 1.8 ⋅ 10 L mol s , 8 −1 −1 8 −1 −1 k 5.317a = 1.8 ⋅ 10 L mol s , k 5.317b = 7.2 ⋅ 10 L mol s (Herrmann et al. 1995): SO−4 + SO−4 → S2 O2− 8 ,

(5.316)

SO−5 + SO−5 → S2 O2− 8 + O2 ,

(5.317a)

SO−5

(5.317b)

+

SO−5

→

2 SO−4

+ O2 .

Peroxodisulfate (a strong oxidant) decays back in aqueous solution by homolysis to sulfate radicals. There are several competing reactions in this radical sulfur oxidation mechanism (not noted here) because the chain e− +H+

e− +H+

e−

SO−5 󳨀󳨀󳨀󳨀󳨀→ HSO−5 󳨀󳨀󳨀󳨀󳨀→ SO−4 󳨀󳨀→ SO2− 4 (−H2 O)

also proceeds by all available electron donors such as reduced TMI (5.327) and (5.334), O−2 (5.329) and (5.336), OH− (5.332), and Cl− (5.328). Furthermore, there are described transfers of sulfur radicals by ROSs such as H2O2 (5.331), HO2 ((5.330) and (5.335)), and

5.4 Sulfur | 379

OH (5.333), whereby OH acts as H abstractor (formation of H2 O) and the ionic species acts as electron donor according to H2 O2 󳨀󳨀󳨀󳨀+→ HO−2 󳨀󳨀󳨀󳨀−→ HO2 󴀘󴀯 O−2 󳨀󳨀󳨀󳨀−→ O2 . (−H )

(−e )

(−e )

Remember (Chapter 5.2.3) that other ROSs, oxidizing sulfite in an initial step, undergo conversions and provide the important superoxide O−2 (pKHO2 /O−2 = 4.5): e−

H2 O2 󳨀󳨀→ H2 O−2 → OH + OH− e−

H+

e−

H+

O3 󳨀󳨀→ O−3 󳨀󳨀→ HO3 → OH + O2 O−2

H+

O2 󳨀󳨀→ O−2 󳨀󳨀→ HO2 󳨀󳨀󳨀󳨀→ HO−2 󳨀󳨀→ H2 O2 (−O2 )

Note the large differences in reaction rate constants independently of whether sulfite or bisulfite is the reagent. This makes the overall process strongly dependent on pH. This pH dependence, however, is much more subtle because the sulfur radicals (sulfite, sulfate, and peroxomonosulfate) undergo acid–base equilibria, which likely is on the left-hand side because the hydrogenated species are strong acids: H+

󳨀→ SO−3 󳨀 ← 󳨀󳨀 HSO3 H+

󳨀→ SO−4 󳨀 ← 󳨀󳨀 HSO4 H+

󳨀→ SO−5 󳨀 ← 󳨀󳨀 HSO5 Parallel to all possible starting reactions of the type (5.311), the direct nucleophilic attack of oxygen species (O3 , OH, and HO2 ) might be possible (interestingly, sulfite provides OH 󴀗󴀰 HO2 recycling): 2− → O2 + SO2− O3 + SO2− 4 , 3 → [OOO–SO3 ]

O3 + HSO−3

−

→ [OOO–SO3 H] → O2 +

HSO−4

(5.318) ,

H2 O

O3 + SO2 → [OOO–SO2 ] 󳨀󳨀󳨀󳨀→ SO3 󳨀󳨀󳨀󳨀+→ HSO−4 , (−O2 )

(−H )

O2

(5.319) (5.320)

2− 󳨀󳨀󳨀󳨀󳨀→ SO2− OH + SO2− 4 , 3 → [HO–SO3 ]

(5.321)

2− HO2 + SO2− 󳨀󳨀󳨀󳨀󳨀→ SO2− 4 . 3 → [HOO–SO3 ]

(5.322)

(−HO2 )

(−OH)

The rate law eq. (5.323) has been confirmed by many experimental studies (Table 5.20). The reaction of ozone with S(IV) is assumed to be a nucleophilic attack to all S(IV) species (Erickson et al. 1977): RO3 = (k a [SO2 ] + k b [HSO−3 ] + k c [SO2− 3 ])[O3 ] .

(5.323)

380 | 5 Substances and chemical reactions in the climate system Tab. 5.20: Reaction rate constants for S(IV) + O3 in nucleophilic mechanism. 104 ka

105 kb

109 kc

Reference

0 2.2 2.4

3.1 3.2 3.7

2.2 1.0 1.5

Erickson et al. (1977) Hoigné et al. (1985) Hoffmann (1986)

Tab. 5.21: Reaction rate constants for S(IV) + O3 in radical mechanism. k in 10−4 L1/2 mol−1/2 s−1

Reference

1.45 1.4–3.5 1.9 1.23 1.65 1.27

Penkett et al. (1979) Maahs (1983) Martin (1984) Nahir and Dawson (1987) Lagrange et al. (1993) Botha at al. (1994)

Using the expressions for the protolysis equilibrium and simplification for pH > 3, we get (5.324) RO3 = (k b + k c Kb [H+ ]−1 )[S(IV)][O3 ] , where Kb is the equilibrium constant of the second dissociation (HSO−3 󴀘󴀯 SO2− 3 ). This expression is identical to the rate law proposed by Maahs (1983), even though he proposed the radical mechanism instead of the nucleophilic one. A general rate law can be derived from studies suggesting the radical mechanism (Table 5.21): RO3 = k[H+ ]−1/2 [S(IV)][O3 ] .

(5.325)

Now comparing the pseudo-second-order rate constants 1 k for the nucleophilic reaction (5.324) and 2 k for the radical reaction (5.325) mechanism RO3 (nucleophil) = 1 k [S(IV)] [O3 ] 2

RO3 (radical) = k [S(IV)] [O3 ]

with

1

k = k b + k c Kb [H+ ]−1

with

2

+ −1/2

k = k[H ]

,

and

(5.326a) (5.326b)

we come to the noteworthy conclusion that the difference is numerically insignificant (Table 5.22) and that all experimental studies strongly agree with the kinetics, although without clarifying the mechanism. Figure 5.29 shows the strong influence of pH on both the H2 O2 (dominant in acidic solution) and O3 (dominant in alkaline solution) pathways. Accepting the radical mechanism theory, the reaction rate of the sulfite radical formation (eq. (5.311)) determines the overall rate. Amplification of the S(IV) oxidation is given by the subsequent formation of radicals (OH, O−2 , SO−4 , SO−5 ) that further react with sulfite or bisulfite (Figure 5.28). It is impossible to regard the S(IV) oxidation under natural conditions (i.e., outside laboratory conditions) in the sense of a definite

5.4 Sulfur | 381

Tab. 5.22: Comparison of pseudo-second-order rate constants of S(IV) + O3 reaction in nucleophilic (1 k) and radical (2 k) mechanisms depending on pH. k in L mol−1 s−1

pH = 3

pH = 4

⋅ 105

1k

4.3 6.0 ⋅ 105

2k

pH = 5

⋅ 106

1.0 ⋅ 107 0.6 ⋅ 106

1.3 1.9 ⋅ 106

mechanism because all reactive species (producing A to E in the following scheme) are available, but in different concentrations and superposed, making sulfate formation very complex and dependent on the redox state and the pH of the solution as well as the radiation and photosensitizers.

SO4 B

SO23

A

(HSO3)

O2

SO3

C

SO25

SO24

D

E

HSO5 All conversions through species A to E can proceed through sulfur radicals (sulfite, peroxomonosulfate, and sulfate) as well as via many other species, whereas some of them are permanently abundant and others are produced via photochemical processes. Only coupled gas–aqueous-phase models comprising the whole chemistry can describe the very complex S(IV) oxidation in hydrometeors. The following list of reactions only includes the most important steps; for further reactions see, for example, CAPRAM; for references on reaction rates, given in L mol−1 s−1 , see Möller and Mauersberger (1995) or Möller (2003). 3+ 3+ 2+ 9 SO−4 + Fe2+ (Mn2+ , Cu+ ) → SO2− 4 + Fe (Mn , Cu ) k 5.327 (Fe) = 4.1 ⋅ 10 , (5.327)

SO−4 + Cl− → SO2− 4 + Cl

SO−5

SO−4 + O−2 SO−4 + HO2 SO−4 + H2 O2 SO−4 + OH− SO−4 + OH 2+ 2+ +

→ → → → →

SO2− 4 + SO2− 4 + SO2− 4 + SO2− 4 + HSO−5 +

k 5.328 = 2.5 ⋅ 108 ,

(5.328)

k 5.329 = 4 ⋅ 10 ,

(5.329)

9

O2 +

H + O2 +

H + HO2 OH

9

(5.330)

7

(5.331)

7

k 5.332 = 1.4 ⋅ 10 ,

(5.332)

k 5.333 = 1 ⋅ 10

,

(5.333)

k 5.330 = 3.5 ⋅ 10 , k 5.331 = 1.2 ⋅ 10 , 10

+ Fe (Mn , Cu ) + H

→ HSO−5 + Fe3+ (Mn3+ , Cu2+ ) SO−5 + HO2 → HSO−5 + O2 SO−5

+ O−2

+ H2 O →

HSO−5

−

+ OH + O2

k 5.334 (Fe) = 4.3 ⋅ 107 , (5.334) k 5.335 = 1.7 ⋅ 109 ,

(5.335)

k 5.336 = 2.3 ⋅ 10 .

(5.336)

8

382 | 5 Substances and chemical reactions in the climate system

Tab. 5.23: Ions and radicals of oxo of sulfur (instead of “hydrogen,” “bi-” is also used in the names of protonized forms). Ion

Radical

Name

HSO−3 SO2− 3 HSO−4 SO2− 4 HSO−5 SO2− 5

HSO3 SO−3 HSO4 SO−4 HSO5 SO−5

Hydrogen sulfite Sulfite Hydrogen sulfate Sulfate Hydrogen peroxomonosulfate Peroxomonosulfate

a

Acid

Name

H2 SO3

Sulfurous acid

H2 SO4

Sulfuric acid

H2 SO5

Peroxomonosulfuric acid a

HO3 S–O–OH.

Reactions (5.330) and (5.331) proceed likely via the intermediate hydroperoxyl cation HO+2 and hydrogen peroxide cation H2 O+2 , respectively. Dithionate (S2 O2− 6 ) and peroxodisulfate (S2 O2− ) have never been detected in clouds and rainwater. Dithionate 8 2− slowly disproportionates (into SO4 + SO2 ) and peroxodisulfate hydrolyzes in acid solution (into HSO−5 + SO2− 4 ). Table 5.23 lists all higher oxidized sulfur species of interest in the climate system.

5.4.4 Multiphase sulfur chemistry Because of the relatively slow gas phase of SO2 oxidation, aqueous-phase oxidation in clouds contributes to 80–90% of sulfate formation in the northern midlatitudes, and 10–20% of SO2 oxidation proceeds via OH radicals in the gas phase (Langner and Rodhe 1991, Möller 1980, 1995). The in-droplet S(IV) oxidation rate is related to the volume of air using the general eqs. (3.173) and (3.178)⁴⁷ in terms of (

d[sulfate] ) = −k[SO2 ]gas = RT ⋅ LWC ⋅ k aq [S(IV)] . dt air

(5.337)

In clouds having mean daytime conditions of LWC and concentrations of H2 O2 and O3 , the SO2 lifetime is ≤ 1 h, and sulfate production can reach 8 ppb h−1 . This is by a factor of 100 higher than the maximum gas-phase production (Table 5.24). On a yearly basis, however, we need statistical information on the occupancy of the PBL by clouds and occurrence of clouds to calculate the mean aqueous-phase S(IV) oxidation. Any error in k aq is insignificant compared with the uncertainty of cloud statistics. The atmospheric SO2 residence time strongly depends on the event-related cloud and precipitation statistics. As shown in Figure 4.16, only the scavenging of sulfur dioxide depends so strongly on changing the pH in the range 6 to 8; hydrometeors normally

aq

aq

47 We set Fchem = Fdiff .

5.4 Sulfur |

383

Tab. 5.24: SO2 oxidation (percentage of pathway a ) and sulfate formation rates (% h−1 ) for Central European conditions; data from Möller (1995) and Möller and Mauersberger (1992). Pathway

Summer day

liquid phase gas phase

75.8 1.4

O3 H2 O2

0.3 99.6

a

Summer night 8.1 0.0013 2.2 87.3

Winter day 11.3 0.22 65.5 26.7

Winter night 4.4 0.0002 24.1 34.7

the difference to 100% is given by other not listed pathways such as radicals and catalytic TMI.

have pHs between 4 and 6 and natural waters between 7 and 8. The key questions with respect to climate-relevant sulfate formation are as follows: – What is the percentage of gas-to-particle sulfate formation in the very low submicron range? – What percentage do cloud processes contribute to sulfate formation in the upper submicron range? – How much nonoxidized sulfur is deposited (dry as SO2 and wet as S(IV))? – How much sulfur is on average dissolved in clouds and thereby not climate relevant? The last question is important because the percentage of atmospheric SO2 oxidation determines the “climate-active” sulfate as particulate sulfate in air (often global climate models assume a simple conversion factor as a percentage of SO2 emissions). Figure 5.30 shows a scheme of multiphase atmospheric sulfur chemistry. The values are derived from many field studies and modeling attempts and are representative of Central Europe. It is noteworthy that the number of studies with in situ measurements of S(IV) in hydrometeors (rain, clouds, and fog) is very limited (because of the instability of S(IV) and a complicated measurement technique) (Möller 2003). Normally in rainwater only sulfate is detected because much time passes from field sampling to laboratory analysis. In situ field measurements, however, support the theoretical assumption that in fresh rainwater S(IV) contributes about 30% to total sulfur. In other words, the percentage of wet deposited SO2 (in-cloud and subcloud) is significant but might vary depending on the gas-phase SO2 concentration and droplet pH. These findings support the conclusion that on average less than 50% of emitted SO2 is converted into sulfate in air. Sulfur dioxide is the most important consumer of atmospheric hydrogen peroxide (H2 O2 ) and ozone (O3 ) via the aqueous phase; therefore, it limits the oxidation capacity of the atmosphere. However, it is (or was) the main cause of environmental acidification (“acid rain”). Acid formation (acidifying capacity) is inextricably linked with oxidation capacity.

384 | 5 Substances and chemical reactions in the climate system

vertical transport 20% gas-to-particle conversion 20%

gaseous SO2 35%

particulate sulfate nucleation 80%

in-cloud scavenging oxidation ~ 70% wet removal ~ 10%

evaporation 80%

in cloud dissolved SO2 and sulfate cloud layer

wet removal 20%

subcloud layer gas-to-particle conversion 10%

65%

gaseous SO2

100% emission

20%

>2/3 sub-cloud scavenging

70% dry deposition

particulate sulfate

< 1/3 wet deposition (30% S(IV) + 70% S(VI))

dry deposition

Fig. 5.30: SO2 multiphase chemistry (after Möller 1995, 2003); percentage related to each box as budget.

5.5 Phosphorus After oxygen, nitrogen, and sulfur, phosphorus is the next most important life-essential element, but, in contrast to the other listed elements, it does not naturally occur as an element in nature. Moreover, phosphorus (according to textbook knowledge) only occurs in nature in derivatives of phosphoric acid. Phosphorus (white) was first produced as an element (but not recognized as an element) by the German alchemist Hennig Brand (c. 1630–1692) in Hamburg in 1669 from the heating of distillated urine remaining in sand. Bernhardt Siegfried Albinus (1697–1770) isolated phosphorus from the charcoal of mustard plants and cress, confirmed by Andreas Sigismund Marggraf (1709–1782) in 1743, and Scheele in 1769 likely found it from bone (Kopp 1931). Antoine Laurent de Lavoisier (1743–1794) recognized P as an element. It is believed that all original phosphates came from the weathering of rocks. Phosphate ions enter into organic combinations largely unaltered. From phosphoric acid H3 PO4 many esters are formed simply by the exchange of H through organic residuals. It was thought that phosphorus could cycle in the atmosphere only as phosphate bound to aerosol particles such as pollen, soil dust, and sea spray. Like nitrogen,

5.5 Phosphorus |

385

chemical forms of P were found in an oxidation state −3 to +5. It is generally accepted that, in contrast to O, S, N, and C, the phosphorus cycle does not contain redox processes (i.e., it remains in the state of phosphate) or volatile compounds (i.e., the atmosphere is excluded from the P cycle). In continental rainwater, Lewis et al. (1985) found phosphate in such concentrations that it could not be explained by the scavenging of particulate phosphorus and concluded that it was a terrestrial source of a volatile P compound. First Glindemann and coworkers (Glindemann et al. 2005a and references therein) detected monophosphane PH3 (formerly phosphine, also called hydrogen phosphide) in air in a concentration range of pg m−3 to ng m−3 . Close to identified emission sources (paddy fields, water reservoirs, and animal slurry) reported concentrations are significantly higher. Glindemann et al. (2003) found for the first time PH3 in remote air samples (low ng m−3 range) in the high troposphere of the North Atlantic. In the lower troposphere, PH3 is observed at night in the 1 ng m−3 range, with peaks of 100 ng m−3 in populated areas. During the day, the concentration is much lower (in the pg m−3 range). Monophosphane⁴⁸ has a low water solubility, H = 8.1 ⋅ 10−3 L mol−1 atm−1 (Williams et al. 1977), which is about three times less than the Henry’s law constant for NO2 . PH3 cannot be photolyzed in the troposphere but reacts quickly with OH (much faster than OH + NH3 ): PH3 + OH → PH2 + H2 O

k 5.338 = 1.4 ⋅ 10−11 cm3 molecule−1 s−1 .

(5.338)

The literature is lacking of studies on atmospheric PH3 oxidation in detail. In PH3 + O2 explosions, the radicals PH2 and PO were detected (Norrish and Oldershaw 1961), and PO has also been found in interstellar clouds. According to chemistry textbooks, PH3 burns to phosphorus pentoxide P4 O10 , which in contact with water ultimately turns into orthophosphoric acid: 2 H2 O

2 H2 O

2 H2 O

P4 O10 󳨀󳨀󳨀󳨀→ H4 P4 O12 󳨀󳨀󳨀󳨀→ 2 H4 P2 O7 󳨀󳨀󳨀󳨀→ 4 H3 PO4 .

(5.339)

According to Glindemann et al. (2003, 2005a), the final product of PH3 oxidation in air is the phosphate ion, but nothing is known about the reaction steps. We can only further speculate that the oxidation proceeds in solution or interfaces, i.e., in cloud and aerosol layers, and this might explain why PH3 is found in the upper troposphere. As we have discussed, it is not the solubility that controls the “washout” but the interfacial chemistry for low-soluble species. PH3 is a very weak base (PH3 + H2 O 󴀗󴀰 PH+4 + OH− ; pKb ≈ 27 compared with 4.75 for NH3 ), but the phosphonium ion is known in solid salts, for example with chloride (PH3 + HCl 󴀘󴀯 PH4 Cl). On the other hand, PH3 is a weak but stronger acid 48 P forms many compounds with hydrogen according to the general formula Pn Hn+m (n in whole numbers, m = 2, 0, −2, −4, . . . ), but few compounds have been isolated, of which the most important are PH3 and P2 H4 , which are both volatile and self-igniting at high concentrations.

386 | 5 Substances and chemical reactions in the climate system than NH3 (PH3 󴀗󴀰 PH−2 + H+ ; pKa about 29). Because PH3 mixing ratios are 10–100 times lower than those of NH3 , it is likely that during inorganic gas-to-particle conversion in the late morning (SO2 → H2 SO4 ) ammonium and phosphonium are taken up by the evolving particulate phase. The equilibrium is generally on the left-hand side (PH3 ), but because of acid excess and dynamic processes, it might be shifted to salt formation. Moreover, in the condensed phase, a strong oxidation regime can stepwise oxidize PH3 /PH+4 by OH to phosphate. This process can better explain the observed daytime decrease of PH3 concentrations and the relatively high PH3 concentrations in the upper and remote atmosphere. However, to acquire the PO3− 4 ion, a very complex P chemistry has to be assumed, including all oxidants of interest (O−2 , OH, O3 , H2 O2 ). We can speculate that alternate OH attacks abstract H from P and subsequent O3 attacks add oxygen onto P according to the known chain of oxoacids: +

H H

P

H

H phosphonium

0

H O

P

H

H phosphaneoxide

_

O O

P

H

H phosphinate

2-

O O

P

O

3-

O O

O

P

H

O

phosphonate

phosphate

Fine PM might be transported and release PH3 , whereas particulate acidity decreases and so explains why PH3 seems to be ubiquitous in air. Moreover, PH2 probably returns to PH3 via H abstraction from hydrocarbons in the gas phase: PH2 + RH → PH3 + R .

(5.340)

In biomass, phosphorus is as important as ATP and ADP for providing energy transfers and in DNA and RNA, where phosphate interlinks the nucleosides. In bones and teeth, it is found as calcium phosphates (approximately 85% of phosphorus in the body). In contrast to nitrogen, plants do not reduce phosphate. However, PH3 (and likely P2 H4 ) exist in air and are emitted from decomposing biomass under anaerobic conditions. Even exotic formation via lightning, shown by simulated lightning in the presence of OM, which provides a reducing medium, was suggested by Glindemann et al. (2004), but this is hard to accept under atmospheric conditions. Natural rock and mineral samples release trace amounts of phosphine during dissolution in mineral acid. Strong circumstantial evidence has been gathered on the reduction of phosphate in rock via mechanochemical or “tribochemical” weathering at quartz and calcite/marble inclusions (Glindemann et al. 2005b). However, this can also be because of traces of phosphides in rocks, which produce PH3 in acidic hydrolysis. Although phosphorus could be expected to occur naturally as a phosphide, the only phosphide in the Earth’s crust is found in iron meteorites as the mineral schreibersite (Fe, Ni)3 P, in which cobalt and copper might also be found (WHO 1988). Many papers have suggested that PH3 forms by microbial processes in soils and sediments, but no bacteria responsible or any chemical mechanism is known (Zhu

5.6 Carbon | 387

et al. 2007). This question arose 40 years ago, but Burford and Bremner (1972) could not confirm earlier evidence for the evolution of phosphine through the microbial reduction of phosphate in waterlogged soils. They also showed that phosphine was sorbed by soil constituents and might not escape to the atmosphere if produced in soils. Recently, PH3 was detected at surprisingly high concentrations in the marine atmosphere (Zhu et al. 2007). The measurement technique to detect these low PH3 concentrations became available around 1993; therefore, the absence of evidence of PH3 previously is no longer evidence of PH3 absence. It seems that only as yet unknown microbial processes where phosphate is used as an oxygen source under anaerobic conditions (similar to the sulfate reduction) might explain PH3 formation. This remains an open field of research and needs more specific microbial studies. Organophosphanes PR3 , where R = alkyl or aryl (e.g., triphenylphosphine oxide OPPh3 and trimethylphosphine oxide OP(CH3 )3 ), are known to form metal complexes and were found in fungi (Holland et al. 1993). Organophosphanes are easily oxidized to the corresponding phosphane oxide OPR3 , which are considered the most stable organophosphorus compounds. The identification that organophosphines are responsible for the “typical smell” when touching metals (Glindemann et al. 2006) might provide evidence for these compounds in the human body. Ignis fatuus, a phosphorescent light that for centuries has been seen over marshy ground and around graveyards at night (ghostly lights), is now known to be caused by the spontaneous combustion of gases emitted by decomposing OM where phosphanes act as a “chemical match.”

5.6 Carbon Carbon is among the main group 4 (tetrele) elements in the periodic table of the elements; it possesses affinities comparable to electropositive and electronegative elements (to the left and right of the periodic system). It is the harmonic balanced affinity of carbon to electropositive and electronegative elements as well that provides the largest quantity of different chemical compounds with all other elements in the periodic system. Carbon is very central in the group of elements. No group (carbon, silicon, germanium, tin, and lead) shows more differences: carbon is a nonmetal, and lead, the final item in this group, is a typical metal showing no similarity with carbon. The similarities between the elements increase from the middle group to the beginning groups (alkali and earth-alkali metals) and ending group (halogens). Space consists of 98% hydrogen (3/4) and helium (1/4); of the remaining 2%, threequarters is composed of just two elements, oxygen (2/3) and carbon (1/3). Based on the molar ratios, a formula for a “space molecule” would be about H2600 O3 C2 . It is logical that, with regard to compounds, water (H2 O), hydrocarbons (Cx Hy ), and CO2 are the most abundant molecules in space.

388 | 5 Substances and chemical reactions in the climate system

The huge reservoir of CO2 (including water-dissolved bicarbonate) supports the maintenance of life in the form of omnipresent plants and animals and carbon cycling. Without life, there would be no carbon cycle on Earth. However, this is also true of all other elements: chemical processes cannot reduce carbonate, nitrate, sulfate, and phosphate in the environment. Deep in the Earth, however, we cannot exclude – even hypothesizing the existence of elemental carbon – reducing chemical regimes, transforming elements between different oxidation states on geological timescales. The separation between inorganic and organic carbon chemistry (and compounds) is not strongly fixed. In nature, the synthesis of organic compounds only occurs in the living cells of plants and animals, where only plants are able, through photosynthesis, to link the organic world with the inorganic, i.e., by using CO2 as feedstock. Nature provides OM in a large variety of food, materials, and energy carriers. So far, the extraction of these natural compounds has been limited to the biological carbon cycle (i.e., limited to renewable sources), and problems have only arisen because of local limits on the carbon supply and local waste loadings. Only because of the exhaustion of fossil fuels are humans again encountering the same general problems, but now on a global scale. Thousands of organic compounds used as chemicals by humans have been described in relation to properties and environmental fate in air, soil, and water (Howard 1990, Mackay et al. 2006, Verschueren et al. 2009). However, the detailed atmospheric chemistry is almost unknown and has been studied for only a few hundred substances. The general fate of organic carbon in the climate system is mineralization, i.e., oxidation back to CO2 or carbonate and water. In Chapter 5.2.3.2, we presented the elementary steps in CH4 oxidation, ultimately, to CO2 : OH

O2

NO

O2

OH or hν

(−NO2 )

(−HO2 )

(−H2 O or −H)

CH4 󳨀󳨀󳨀󳨀󳨀→ CH3 󳨀󳨀→ CH3 O2 󳨀󳨀󳨀󳨀󳨀→ CH3 O 󳨀󳨀󳨀󳨀󳨀→ HCHO 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HCO (−H2 O) OH

OH

(−H2 O)

(−H)

󳨀󳨀󳨀󳨀󳨀→ CO 󳨀󳨀󳨀→ CO2 Table 1.2 shows that CO2 , CH4 , and CO are the main carbon compounds in air, roughly in a ratio of 1000:10:1. It is noteworthy that these ratios also express roughly the ratios of the chemical lifetime of these species in the atmosphere (τCH4 ≈ 10 years). In the preceding reaction chain, there are two competitive pathways. At low NO concentrations, CH3 O2 will react with HO2 to form methyl peroxide CH3 OOH, which mainly transfers to the aqueous phase but can also be photolyzed into CH3 O + OH. Formaldehyde (HCHO) will also be scavenged; thus, hydrometeors (and, ultimately, natural waters) are an important sink for reactive carbon intermediates. Organic acids probably only form in aqueous solutions. For the CO2 budget, these play no role in the conversion percentage of CH4 and NMVOC to CO2 . The natural atmospheric CO2 concentration is determined by the difference between global photosynthesis and respiration, whereby the ocean plays the role of regulator (Volume 2). It was discussed in Chapter 5.2.6.2 that both CO and CH4 (because of its OH → HO2 conversion, see pre-

5.6 Carbon |

389

ceding scheme) determine the regional and global tropospheric net O3 production, whereas NMVOC contributes to local and mesoscale additional O3 formation. Within these photochemical conversions, organic oxidized nitrogen compounds are formed (Chapter 5.3.6), which (at high concentrations) were blamed for human health problems. An important group of organic compounds are semivolatile compounds (SVOCs) such as polycyclic aromatic hydrocarbons (PAHs), polychlorinated biphenyls (PCBs), polychlorinated dibenzo-p-dioxins (PCCD), and dibenzofurans. They can be transported and redistributed on a global scale; current knowledge about the sources of SVOCs is lacking (Bandowe and Meusel 2017, Lammel et al. 2009). In the following sections, we will summarize the basic principles of carbon chemistry relating to atmospheric chemistry; the reader is encouraged also to refer to textbooks on organic chemistry, biogeochemistry, and biochemistry.

5.6.1 Organic carbon and chemistry The question may arise as to why organic matter is composed of carbon and not of silicon. The answer is simple and twofold: (a) silicon is too heavy to create organisms that would be mobile against Earth’s gravity and (b) only carbon can provide gaseous molecules in the most electronegative state (CH4 ) and the most electropositive state (CO2 ). Nevertheless, the nonorganic world, the “fundament” of life, is composed of solid SiO2 . The diversity of silicon compounds is no less than that of carbon. However, most of the silanes, the counterpart of hydrocarbons (in other words, hydrosilicon), are unstable, and the variety of molecules with unsaturated bonding is much less than for carbon. The ability to create element chains, rings, and networks (in two and three dimensions) is similar for carbon and silicon and explains why these elements are the basic matter of materials, more soft for organic and more rigid for inorganic materials. Previously we mentioned (for details see Volume 2) that a primary source of organic molecules on Earth was space. Hence, we must first address what “organic” means in chemistry because in the colloquial language it is equated with “life.” The term derives from όργανον (Greek) and organum (Latin), meaning tool, device, or voice, and was first used in the seventeenth century in France with various derived forms and expanded senses (organe, organiser, organisme, organisation, organique). “Organic” compounds were known for centuries but were not distinguished from “inorganic” matter. A systematic classification of chemistry was made that divided matter into mineral, vegetable, and animal according to its origin by the French chemist Nicolas Lémery (1645–1715), who wrote Cours de chymie (1675, cited after Kopp 1931). First Lavoisier found systematically that vegetable matter was composed of C, H, and O and that in animal matter additionally N and P are present. According to Walden (1941), the first use of the term “organic chemistry” is now attributed to the Swedish

390 | 5 Substances and chemical reactions in the climate system

chemist Jöns Jacob Berzelius, who called it “organisk kemie” in a book published in 1806. After Lavoisier’s revolutionary book (Lavoisier 1789) Traité élémentaire de chimie (1789), Berzelius wrote the first textbook Lärbok i kemien (1817–1830) in six volumes. It was soon published in French (1829) still with the now traditional title Traité de chimie minerale, vegetale et animale in eight volumes with the subtitle “Chimie organique” (part 2 – 3 volumes). In Germany the first handbook, subtitled “Organische Verbindungen,” was the third volume of Handbuch der theoretischen Chemie (1819) by Leopold Gmelin (1788–1853), later rearranged into separate volumes of inorganic and organic chemistry (from 1848). With the publication of this book, it was believed that OM (also termed “organized”) could not be synthesized from its elements and that a special force, the vital force, was needed for its production. However, organic molecules can be produced by processes not involving life. Friedrich Wöhler (1800– 1882) destroyed the theory of vital force by the synthesis of urea in 1828), an event generally seen as a turning point. Liebig (Organic chemistry in its application to agriculture and physiology, 1840) defined the task of organic chemistry as follows: The object of organic chemistry is to discover the chemical conditions which are essential to the life and perfect development of animals and vegetables, and, generally, to investigate all those processes of organic nature which are due to the operation of chemical laws. (Opening words in Part I: “Of the chemical processes in the nutrition of vegetables”).

This definition is still very much focused on the original idea that all “organic” is definitely equal to “life,” despite the fact that it was written by Liebig after Wöhler’s rejection of the “vital force” in association with organic compounds. Gmelin (1848) wrote that carbon is the only element never missing and hence it is the only essential constituent in an organic compound. There has been no change in the definition since that time: the lexical database WordNet (Princeton University) defines organic chemistry as . . . the chemistry of compounds containing carbon (originally defined as the chemistry of substances produced by living organisms but now extended to substances synthesized artificially).

According to this definition it appears, however, that (for example) carbon dioxide is an organic compound. It was convenient to distinguish between inorganic and organic carbon compounds to explain the cycles between the biosphere and the atmosphere. On the other hand, when we state that there is a prime chemistry considering a limited number of elements and an unlimited (or at least immense) number of molecules in defined numeric relationship between the elements (including carbon), there is no need to separate chemistry into inorganic and organic chemistry. In contrast to the countless number of “organic” carbon compounds, the number of “inorganic” carbon compounds is rather small (of course, we count here only simple compounds found in nature), Table 5.25.

5.6 Carbon | 391

Tab. 5.25: Different simple inorganic carbon compounds. Name

Formula

Comments

Oxides

CO CO2 H2 CO3 H2 C2 O6 CS2 COS CCl4 C2 Cl6 C2 Cl4 C2 Cl2 COCl2 HCN HSCN Ca2 C

Carbon monoxide (Chapter 5.6.3) Carbon dioxide (Chapter 4.4.1.6 and 5.6.3) Carbonic acid (Chapter 4.4.1.6) Oxalic acid (Chapter 5.6.6) Carbon disulfide (Chapter 5.4.2) Carbonyl sulfide (Chapter 5.4.2) Carbon tetrachloride (Chapter 5.7.1) Dicarbon hexachloride Dicarbon tetrachloride Dicarbon dichloride Carbonyl chloride Hydrocyanic acid (Chapter 5.3.6.1) Rhodanic acid Calcium carbide b

Oxoacids Sulfides Halogens a

Nitriles Rhodanides Carbides a b

Here given as an example of chlorine but exchangeable by F, Br, and I. As an example of many metallic carbides; unstable against water.

Tab. 5.26: Most important functional groups in environmentally relevant organic compounds; R – organic residue (e.g., alkyl or aryl). Symbol

Formula

Name

Examples of compounds

ROR ROH RO2 R2 CO R(O)H RCOOH RNH2 RNO2 RCN RSO3 H

–O– –O–H –O–O– >C=O =O –C(=O)(–OH) –N(–H)2 –N(=O)2 –C≡N –S(=O)2 (–OH)

Alkoxy Hydroxy Peroxy Oxo (keto), carbonyl Oxo (formyl) Carboxy Amino Nitro Cyano Sulfo

Ether Alcohols, phenols, sugar Peroxides Aldehydes, ketones Aldehydes (also RCHO) Carboxylic acids Amines, amino acids Nitrophenol Nitriles Sulfonamides

It seems that a useful condition for specifying an “organic” compound is the proviso for the given definition that there must be at least one C–H bond in the molecule. The simplest organic compounds are hydrocarbons, consisting of only carbon and hydrogen, often symbolized as HC; the simplest “organic” molecule is methane, CH4 . The specific chemical role of organic molecules, however, is given by functional groups; the most important are listed in Table 5.26. The functional groups determine the chemical reactivity – the reactive influence of the carbon residue is much less significant. Here we deal only with H–C and H–C–O compounds; nitrogen, sulfur, and halogen organic compounds are treated in the relevant element sections.

392 | 5 Substances and chemical reactions in the climate system

Classification of organic chemistry can be done according to the functional groups (Table 5.26) or via compound classes: Aliphatic compounds: Acyclic and cyclic, but not aromatic; can be saturated, joined by single bonds (alkanes), or unsaturated, with double bonds (alkenes) or triple bonds (alkynes). Besides hydrogen, other elements can be bound to the carbon chain, the most common being oxygen, nitrogen, sulfur, and chlorine. Alicyclic compounds: Three or more atoms of the element carbon are linked together in a ring; the bonds between pairs of adjacent atoms may all be of the type designated single bonds, or some of them may be double or triple bonds, but not aromatic. Aromatic compounds: Compounds based on the benzene ring (phenyl as the most basic aryl group), including polycyclic aromatic compounds. Heterocyclic compounds: Characterized by the fact that some or all of the atoms in their molecules are joined in rings containing at least one atom of an element other than carbon. The environmentally very important groups of heterocyclic compounds are natural products, a chemical compound or substance produced by a living organism – that is, found in nature. Heterocyclic compounds include many of the biochemical material essential to life. For example, nucleic acids, the chemical substances that carry the genetic information controlling inheritance, consist of long chains of heterocyclic units held together by other types of materials. Many naturally occurring pigments, vitamins, and antibiotics are heterocyclic compounds, as are most hallucinogens. Modern society is dependent on synthetic heterocyclic species for use as drugs, pesticides, dyes, and plastics. Another important class of natural product comprises terpenes (which are emitted in huge amounts by vegetation into the atmosphere) and steroids. The interested reader should consult textbooks on organic chemistry. In the following sections, we only deal with aliphatic and aromatic compounds. To get an idea of how much the biosphere emits, see Table 5.27 (note that secondary formation means chemical formation in air from other NMVOCs). In the atmosphere, five categories of VOCs can be detected (Table 5.28). The two largest classes are the aliphatic (alkanes, cycloalkanes, alkenes) and aromatic hydrocarbons. The third class of compounds is terpenes, emitted from plants (isoprene is dominant). Chlorinated hydrocarbons make up a fourth class, and oxygenated compounds (aldehydes, ketones, alcohols, acids) constitutes the remaining class (not quantified by the measurements presented in Table 5.28). From aircraft measurements carried out in summer 1994 in Saxony-Anhalt (Germany) we have the following data: the following five compounds represent 65% of all measured (35) VOCs: methane (25–35%), ethane (19–15%), ethene (8–10%), propane (7–10%), and benzene (4–5%), emphasizing the importance of C1 –C3 compounds.

5.6 Carbon | 393

Tab. 5.27: Average global annual emission of organic substances in Tg yr−1 . – no date available, 0 no emission; note the large uncertainty in the data (see also Volume 2 for more data and references). Substance

Natural emission Vegetation

Ocean

Biomass burning c

500 120–200 150–200 37 34 30–40 0

5 0 10–27 – – – –

– – 3–9 – 3–10 – –

– 15 12 5 0 4 4 4

– – – – 1–10 – – –

5 – – – 15–30 – – –

0 0 30–40 0 1600 40 40– 100 – 0 0 0 0 0 0 0

– – –

1 3–12 0

7–30 10–30 2–19

0 0 0

15–60 5–25 10–30

–

95

–

50–200

Isoprene Monoterpenes Methanol Acetaldehyde Formaldehyde Acetone Glyoxal Carboxylic acids Propene Propane i-pentane Methane Ethane Ethene i-butane Alkanes Alkenes Aromatic Compounds Total a

750–1150

Secondary formation

Anthropogenic emission

0 0 4 – – – 0 0 – – – 350 – – –

Total a

– – 240 – – 95 – – – – – 500–600 b – – – – – – 450–4800 d

a

Not the sum – independent estimates. Including wetlands. c Biomass burning is almost anthropogenically caused. d Total anthropogenic 100 (50–200) and total biogenic 1200 (400–4600). b

Tab. 5.28: Concentrations of organic compounds (52 species were detected a , C3 –C10 ) in the atmosphere of Berlin (suburb, July 1998); in ppb (only n-hexane, toluene, and benzene were in the ppb range; the other listed compounds were in the range 100–800 ppt and not listed compounds 10–100 ppt). Class of compounds compounds (benzene, toluene, xylene, and others) b

Aromatic Alkanes (n-hexane, n-butane, propane, n-heptane, n-nonane, cyclohexane, and others) Alkenes (butenes, pentenes, propene, hexenes) Isoprene Terpenes (α-pinene, β-pinene) a b

Ethane, ethene, and ethyne were not measured. Compounds in order of decreasing concentration.

c 8.2 4.5 4.0 0.8 0.2

394 | 5 Substances and chemical reactions in the climate system

5.6.2 Elemental carbon and soot Elemental carbon exists naturally as graphite (hexagonal C structure) and diamond (tetrahedral C structure). In graphite, very small amounts of fullarenes, where C60 molecules are most known, were detected. We have clear evidence that unoxidized carbon exists at depths between 150 and 300 km in the form of diamonds. We know diamonds come from there, because it is only in this depth range that the pressures would be adequate for their formation. Diamonds are known to have high-pressure inclusions that contain CH4 and heavier hydrocarbons, as well as CO2 and nitrogen. The presence of at least centimeter-sized pieces of very pure carbon implies that carbon-bearing fluids exist there, and that they must be able to move through pore spaces at that depth, so that a dissociation process may deposit the pure carbon selectively, a process akin to mineralization processes as we know them at shallower levels. The fluid responsible cannot be CO2 , since this has a higher dissociation temperature than the hydrocarbons that coexist in the diamonds; it must therefore have been a hydrocarbon that laid down the diamonds such as methane (CH4 ). Elemental carbon is chemically extremely stable. Only at high temperatures does C react with other elements and burn with O2 (well known for centuries⁴⁹). Another phenomenon is the self-ignition of coal, but locally the neccessary increased temperature must rise, and several processes have been proposed. This process of self-oxidation until self-ignition needs time and is only possible in condensed coal stocks – when burning in deposits, it can occur over centuries (e.g., Stepanov and Andrushchenko 1990). However, this ignition was always initiated by humans who interrupted the chemical regime of the deposit through contact with atmospheric oxygen. In the environment, soot is a phenomenon that is as old as the culture of fire. Humans predominantly cause biomass burning, and “natural” burning caused by lightning strikes has always been negligible. Therefore, soot is largely an artifact of nature (Table 5.29). A large fraction of PM is soot, the historic symbol of air pollution. For centuries, until the end of the twentieth century, when the combustion of fossil fuels, sulfur dioxide, and soot (smoke), the so-called smoke plagues, was the key issue in air pollution. Coal was used in cities on a large scale from the beginning of the Middle Ages, and this “coal era” has not yet ended. In most parts of the world until the 1960s, coal was the primary source of energy for electricity generation, industry, and domestic heating. Air purification devices were practically nonexistent. This led to high levels of air pollution, particularly in cities, with soot, dust, sulfur dioxide, and nitrogen oxides. Winter smog, particularly the notorious episodes in London during the 1950s, had se49 The traditional Japanese Shou Sugi Ban technique makes wood (paradoxically) fire-resistant by charring it with fire. Today it is still used for fashion, and users probably do not know that the carbonized surface is much more flame-resistant than the former wooden surface.

5.6 Carbon | 395

Tab. 5.29: Soot types. Soot origin

Characteristics

Wood combustion soot

Large OC fraction, usually only 20% BC; lignin-derived substances with OC

Biomass burning soot

Similar to wood soot but OC fraction larger, up to 90%

Coal combustion

soot a

Different from biomass burning soot; large BC and EC fractions, mainly in coarse mode

Diesel soot

OC may approach 50%, the remainder is BC and EC; smallest size fraction, 3–20 nm, consists of oil nanodroplets, accumulation mode (50–250 nm) contains EC and OC, and the coarse mode is EC due to coagulation

Aviation soot

Includes undefined OC fraction up to 300 nm

a

This soot was important in the past from household coal heating and steam locomotives; lowefficiency coal-fired power plants are still widely used in India and Brasilia and may also produce large soot emissions.

rious effects on health as well as on building materials and historic monuments. The soot problem (and almost that of sulfur dioxide) seems to have been solved at present; the problem of climate change due to carbon dioxide remains unsolved, however. There was a long dispute in the literature about the definition of soot, which is also called elemental carbon (EC), black carbon (BC), and graphitic carbon. Surely, soot is the best generic term to refer to impure carbon particles resulting from the incomplete combustion of a hydrocarbon. The formation of soot depends largely on fuel composition. It spans carbon from graphitic (EC) through BC to organic carbon fragments (OC, POM). The answer to the question of what is soot varies from person to person. A general definition was given by Popovicheva et al. (2006): “Soot is a carbon-containing aerosol resulting from incomplete combustion of hydrocarbon fuel of varying stoichiometry, defined by the ratio of fuel to oxygen.”

Soot not only possesses the properties of BC and EC fractions commonly associated with soot but also includes the organic fraction (OM). It is largely the chosen combustion conditions that dictate the soot properties. Each of the available methods (optical, thermal, and thermo-optical) refers to a different value; it remains a simple question of definition. Hence, comparing different soot methods is senseless. The atmospheric implications of soot include: – It provides the largest surface-to-volume ratio for heterogeneous processes. – It forms the most complex structural nanoparticles. – It carries (toxic) organic substances. – It warms the atmosphere through light absorption.

396 | 5 Substances and chemical reactions in the climate system

Soot aerosol consists of harmful substances, such as adsorbed PAHs as well as their hydroxylated and nitro-substituted congeners, which have significant carcinogenic and mutagenic potential. New research has found that the sooty brown clouds caused primarily by the burning of coal and other organic materials in India, China, and other parts of South Asia might be responsible for some of the atmospheric warming that had been attributed to GHGs. A lot is known on the direct and indirect climate impact of atmospheric soot, the absorption of gases, possible heterogeneous processes, and water-soot interactions, but nothing is known about the fate of soot, especially elemental carbon. The latest IPCC report ranks BC as the second most important climate-warming agent, after CO2 (IPCC 2013). Brown carbon (organic carbon aerosol that absorbs at UV and visible wavelengths) may also contribute significantly to climate forcing. Studies on the chemistry of NOy , O3 , SO2 , and many other species on soot have been carried out in recent decades and have shown that soot might provide a reactive surface in air. However, their surface chemistry was assessed to be insignificant in the budget of chemical species compared with gas-phase and liquid-phase processes, mainly because of the limited PM surface-to-air volume ratio. Many studies suggest that direct ozone loss on soot aerosol is unlikely under ambient conditions in the troposphere (Disselkamp et al. 1999, Nienow and Roberts 2006). Without a doubt, the large OC fraction in “soot” will undergo “aging” by oxidation. Decesari et al. (2002) showed that the water-soluble organic compounds (WSOCs) produced from the oxidation of soot particles increased rapidly with ozone exposure and consisted primarily of aromatic polyacids that are found widely in atmospheric aerosols and are frequently referred to as macromolecular humic-like substances (HULIS). However, we can only speculate that ROSs such as O3 and OH can react with carbon to form CO: C + OH → CO + H ,

(5.341)

C + O3 → CO + O2 .

(5.342)

This process is extremely slow and can result in a chemical lifetime of hundreds or more years under environmental conditions. It is known that surfaces covered with photocatalytically active TiO2 obviously remain “clean” with respect to soot pollution, whereas reference surfaces become (and remain) black. As discussed earlier, under these photocatalytic conditions, large OH concentrations might be produced locally. Total BC emissions were given as being between 5.8 and 8.0 Tg C yr−1 (Haywood and Boucher 2000, Bond et al. 2004). Bond et al. (2004) estimated 8.0 Tg for black carbon and 33.9 Tg for organic carbon, where the contributions of fossil fuel, biofuel, and open burning were estimated as 38%, 20%, and 42%, respectively, for BC and 7%, 19%, and 74%, respectively. The uncertainty ranges were 4.3–22 Tg yr−1 for BC and 17–77 Tg yr−1 for OC. The fate of the approximately 8 Tg BC yr−1 widely dispersed around the globe is deposition in oceans and soils. It is known that coal can survive

5.6 Carbon | 397

in soils for hundreds of years and can improve soil structure and water budgets. The survival of soot from atmospheric coal combustion in the Middle Ages can still be seen at old churches and it is a cultural question to regard it admiringly as patina or as dirty pollution.

5.6.3 Inorganic C1 chemistry: CO, CO2 , and H2 CO3 5.6.3.1 Gas-phase chemistry As stated at the very beginning, it does not make much sense to distinguish between inorganic and organic chemistry. However, we follow a convention here. Sulfur, nitrogen, and halogen compounds of carbon are treated in their respective sections. Here we present two oxides and carbonic acid. Carbon monoxide (as a product of incomplete biomass and fossil fuel burning processes) oxidizes by OH radicals directly to CO2 : (5.343) CO + OH → CO2 + H . This is the only known reaction where OH dissociates (however, cf. eq. (5.341)). The fate of H is known; hence, CO is an important converter, OH → HO2 (CO is one of the precursors of tropospheric ozone; see Chapter 5.2.3.2): O2

CO

OH 󳨀󳨀󳨀󳨀󳨀→ H 󳨀󳨀→ HO2 . (−CO2 )

Carbon dioxide accumulates in the atmosphere (Volume 2) due to ongoing increases in emissions and missing sinks: There is no inorganic chemical process that can reduce CO2 in air (photosynthesis is balanced by respiration and mineralization), and wet and dry removal is negligible (likely balanced by volcanic CO2 emissions) due to carbonate saturation of the Earth’s surface. Atmospheric CO2 is in equilibrium with dissolved CO2 , but DIC also increases (Chapter 4.4.1.6). 5.6.3.2 Aqueous chemistry CO2 is slightly soluble in water; the ratio between atmospheric and water-dissolved CO2 is described by the Henry equilibrium, which depends only on temperature. The “true” equilibrium is given through subsequent chemical reactions, leading to higher solubility of CO2 in water. Dissolved carbon dioxide forms bicarbonate via different equilibrium steps (Chapter 4.4.1.6): H2 O

− 󳨀󳨀󳨀→ 2− 󳨀󳨀󳨀 󳨀󳨀 󳨀󳨀 → CO2 (g) 󴀕󴀬 CO2 (aq) ← 󳨀 HCO3 󳨀 ←󳨀󳨀󳨀 󳨀 CO3 + + (−H )

(−H )

In aqueous solution, especially in cellular environments, the carbonate radical anion (CO−3 ) is produced from the reaction between the ubiquitous carbon dioxide and peroxonitrite (ONOO− ), which is an unstable intermediate (Figure 5.24 and eq. (5.234b))

398 | 5 Substances and chemical reactions in the climate system

in biological NO reduction and first forms as a CO2 adduct, nitrosoperoxo carboxylate, which then decomposes: CO2 + ONOO− → ONOOCO−2 → CO−3 + NO2 .

(5.234b)

Carbonate radicals react with many organic compounds (Chen and Hoffmann 1973, Umschlag and Herrmann 1999) in a general H abstraction reaction (competing with OH), k 5.344 = 104 to 107 L mol−1 s−1 : CO−3 + RH → HCO−3 + R .

(5.344)

It is a strong acid (i.e., the radical HCO3 fully dissociates), with pKa = −4.1, and a strong oxidizing agent, with E°(CO−3 /CO2− 3 ) = 1.23 ± 0.15 V (Czapski et al. 1999, Armstrong et al. 2006, Medinas et al. 2007), which likely exists as the dimer-adduct 3− 2− CO−3 ⋅ CO2− 3 (CO3 )2 and H(CO3 )2 (Wu et al. 2002). Its importance in natural waters is likely limited because it is produced in radical reactions such as those in the following list (k 5.345a = 3.9 ⋅ 108 L mol−1 s−1 , k 5.345b = 1.7 ⋅ 107 L mol−1 s−1 , k 5.346 = 4.1 ⋅ 107 L mol−1 s−1 , k 5.347 = 2.6 ⋅ 106 L mol−1 s−1 ; CAPRAM model) and reacts back to carbonate. − − CO2− 3 + OH → CO3 + OH ,

HCO−3 + OH → CO−3 + H2 O , HCO−3 + NO3 → CO−3 + H+ + NO−3 , − − − − + CO2− 3 (HCO3 ) + Cl2 → CO3 + 2 Cl (+H ) , − − 2− CO2− 3 + SO4 → CO3 + SO4 .

(5.345a) (5.345b) (5.346) (5.347) (5.348)

It also reacts with TMIs (k 5.349 = 2 ⋅ 107 L mol−1 s−1 ) and with peroxides (k 5.350 = 6.5 ⋅ 108 L mol−1 s−1 ), which represent radical termination as one-electron transfers. Reactions (5.350a) and (5.351) also represent H abstraction reactions: k 5.351 = 4.3 ⋅ 105 L mol−1 s−1 (Draganic et al. 1991): 3+ 3+ 2+ CO−3 + Fe2+ (Mn2+ , Cu+ ) → CO2− 3 + Fe (Mn , Cu ) ,

CO−3

+ HO2

CO−3 + O−2 CO−3 + H2 O2

→ HCO−3 + O2 , → CO2− 3 + O2 , → HCO−3 + HO2

(5.349) (5.350a) (5.350b)

.

(5.351)

Reactions (5.350a) and (5.351) likely also proceed via HO+2 (→ H+ + O2 ) and H2 O+2 (→ H+ +HO2 ), respectively. The following fast reaction obviously transfers intermolecular O− : NO2 → NO−3 (similar reactions with respect to NO → NO−2 and O2 → O−3 are not described in the literature), k 5.352 = 1 ⋅ 109 L mol−1 s−1 (Lilie et al. 1978): CO−3 + NO2 → CO2 + NO−3 .

(5.352)

5.6 Carbon

| 399

An analogous reaction (O− transfer) with ozone is slow and implies the intermediate H+

O−4 (←󳨀→ HO4 ): k 5.353 = 1 ⋅ 105 L mol−1 s−1 (Sehested et al. 1983): CO−3 + O3 → CO2 + O2 + O−2 .

(5.353)

Another interesting species is given by the carbon dioxide anion radical CO−2 , which is an efficient reducing agent in two ways, electron transfer and radical addition. It is produced from aquated electrons (Hart and Anbar 1970), k 5.354 = 4 ⋅ 109 L mol−1 s−1 (CAPRAM): (5.354) CO2 + e−aq → CO−2 . The CO−2 radical is also gained from the oxidation of formate ions (Todres 2008), which act as an efficient OH scavenger: HCOO− + OH → CO−2 + H2 O .

(5.355)

The ultimate fate of this radical is in electon transfer to oxygen gaining a superoxide ion: CO−2 + O2 → CO2 + O−2 k 5.256 = 2.4 ⋅ 109 L mol−1 s−1 . (5.356) In a Fenton-like reaction, hydrogen peroxide is destroyed via the following reaction sequence (cf. eq. (5.101)): CO−2 + H2 O2 → CO2 + H2 O−2 (→ OH + OH− ) .

(5.357)

It is added to organic radicals and double bonds (Morkovnik and Okhlobystin 1979): CO−2 + RCH(OH) → RCH(OH)COO− , CO−2

−

+ R–CH=CH–R → RCH(COO )–CH–R .

(5.358) (5.359)

It disproportionates and dimerizes to oxalate (Morkovnik and Okhlobystin 1979): CO−2 + CO−2 → CO2− 3 + CO , CO−2

+ CO−2

−

→ O(O)C–C(O)O

(5.360a) −

(oxalate) .

(5.360b)

Basically, these processes represent a path to sustainable chemistry in the future for CO2 air capture and CO2 reduction to fuels (Fujita 1999, Wu 2009). Two-electron steps with adsorbed CO2 are favored compared to reaction (5.354), whose reduction potential amounts to −1.0 V: 2 H+ +2 e−

CO2 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HCOOH +

−

+

−

2 H +2 e

CO2 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CO + H2 O 6 H +6 e

CO2 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CH3 OH + H2 O

E = −0.61 V , E = −0.53 V , E = −0.38 V .

400 | 5 Substances and chemical reactions in the climate system

In aqueous solution, some metal–ligand complexes form CO2 adducts, which internally undergo a two-electron step: H+

󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ MIII –L . MI –L + CO2 → MI –L(CO2 ) 󴀘󴀯 MIII –L(CO2− 2 )󳨀 −(CO, HCOOH, H2 O)

(5.361)

Thus, one of the best routes to remedy the CO2 problem is to convert it to valuable hydrocarbons using solar energy in “photocatalytic farms” (Chapter 5.3.2 in Volume 2). Finally, another radical is produced from carbon monoxide (CO), the carbon monoxide anion CO− (Hart and Anbar 1970), which very quickly reacts with water to give the formyl radical HCO: CO + e−aq → CO− ,

(5.362)

−

−

CO + H2 O → HCO + OH .

(5.363)

The formyl radical HCO in solution can be considered the conjugated acid of CO− . It undergoes very rapid hydration according to HCO + H2 O → HC(OH)2 .

(5.364)

According to McElroy and Waygood (1991), the hydrated formyl radical HC(OH)2 does not measurably dehydrate back to HCO. Raef and Swallow (1966) showed that the hydrated form is given directly from eqs. (5.362) and (5.363) (recall that e−aq + H2 O ≡ H2 O− ): H+

󳨀⇀ CO + e−aq + H2 O → HC(OH)O− 󳨀 ↽ 󳨀󳨀 HC(OH)2 .

(5.365)

The hydrated formyl radical HC(OH)2 is a strong reducing species. It was detected as an intermediate in the reaction of hydrated formaldehyde (H2 C(OH)2 ) with OH (eq. (5.366)), which is also oxidized by H2 O2 to formic acid (or the formate anion, respectively): H2 C(OH)2 + OH → HC(OH)2 + H2 O , HC(OH)2 + H2 O2 → HCOOH + H2 O + OH .

(5.366) (5.367)

A possible propagation mechanism involves HC(OH)2 + OH− → HCOOH + e−aq + H2 O .

(5.368)

HCO further dimerizes⁵⁰ to glyoxal (HCO)2 ; see eq. (5.393). In Chapter 5.6.6, we will see that C2 species are produced in the aqueous phase by carbonylation (reactions with

50 Woods et al. (2013) proposed the direct HCO dimerization in interstellar atmosphere to form glyoxal, which further reduces to glycolaldehyde: (HCO)2 + H → CH2 (O)CHO and CH2 (O)CHO + H → CH2 OHCHO.

5.6 Carbon |

401

HCO) and carboxylation (reactions with CO−2 ). With hydroxyl, it oxidizes very fast to formaldehyde: HC(OH)2 + OH → HCHO + H2 O

k = 3.5 ⋅ 109 L mol−1 s−1 .

(5.369)

Finally, the self-reaction of the hydrated formyl radical is also fast in solution: HC(OH)2 + HC(OH)2 → 2 HCHO + 2 H2 O

k = 1.4 ⋅ 109 L mol−1 s−1 .

(5.370)

5.6.4 Hydrocarbon oxidation and organic radicals Here we deal with the general radical oxidation of hydrocarbons and will encounter important organic ROSs⁵¹; see also Chapter 5.2.4, Table 5.30, and Figure 5.7; inorganic ROSs (OH, HO2 , and H2 O2 ) were already encountered in the section on oxygen, Chapter 5.2.3. The C–H bond is divided into four types, each having slightly different bond energies: Formula

Name

Comment

R–CH3 R–CH2 –R R–CH=CH–R (C2 H5 ) − CH3

Alkylic Allylic Vinylic Benzylic

Terminal C atom Midsized C atom C atom is linked with a double bond C atom has a bond with an aromatic ring

Alkanes (CH4 is the basic compound) are chains of carbons bound with single atomic bond; the C–H bond (the line symbolizes a σ electron pair) can be destroyed by several radicals (but not photodissociated) – it remains an alkyl group RCH2 (cf. eq. (5.53)), where R can be any kind of organic residue: RCH3 (RH) + OH(NO3 , Cl) → RCH2 (R) + H2 O(HNO3 , HCl) .

(5.371)

In the atmosphere, the OH radical is dominant; at night, the NO3 radical might be important, and in soils and waters, chlorine is important. The terminal CH3 group is favored for any radical attack, but less likely is a midsized CH2 group: RCH2 R + OH(NO3 , Cl) → RCHR + H2 O(HNO3 , HCl) .

(5.372)

51 Organic radicals and compounds are spelled variously in the literature. The different use of oxo and oxy was mentioned in the heading of Table 4.3; this is also true of peroxo and peroxy (some authors also use peroxyl). However, the alkoxy group is R–O– and the alkoxyl radical is R–O∙ ). Whereas some authors write names as one word, e.g., alkylperoxy, we generally write it as two: alkyl peroxy. However, acyloxy is general written as one word. Another example relates to the order of words: peroxy acyl versus acyl peroxy.

402 | 5 Substances and chemical reactions in the climate system

Tab. 5.30: Organic radicals. Note: In some cases R = H (for C1 species). Shorthand symbol

Formula

Name

R Ph RO RO2 – – RCO RCO3 RCO2 –

R–C∙ H2 –∙ C6 H5

Alkyl a Phenyl (aryl – general aromatic residue) alkoxyl b Alkyl peroxy Alkenyl c Alkenyl peroxy Acyl d Acyl peroxy Acyloxy e Criegee radical

R–C(H2 )–O∙ R–C(H2 )–O–O∙ R–CH=C∙ R–CH=C–O–O∙ R–C∙ (=O) R–(O=)C–O–O∙ R–(O=)C–O∙ R–(H)C∙ –O–O∙

a

If R = H, CH3 (methyl). Derived from alcohol ROH. c H C=CH vinyl, H C=CH–CH allyl, H C–CH –CH=CH 1–bytenyl. 2 2 2 3 2 d If R = H, HCO (formyl), if R=CH , acetyl; derived from carbonyl group –CHO (generally >C=O). 3 e This radical is derived directly from carboxylic acid RCOOH. b

The generic formula for alkanes is C n H2n+2 (n number of carbon atoms). Ethane C2 H6 (H3 C–CH3 ) consists of two methyl groups; for propane C3 H6 the structure formula H3 C(CH2 ) n−2 CH3 holds. Alkenes contain one (or more) double bonds; the position of the double bond is different from butene forming isomers. The position of the double bond is identified by a number: (1)–butene and (2)–butene. Alkane Methane Ethane Propane Butane Pentane Hexane

Alkene CH4 C2 H6 C3 H8 C4 H10 C5 H11 C6 H14

– Ethene Propene Butene Pentene Hexene

Structure of isomers C2 H4 C3 H6 C4 H8 C5 H10 C6 H12

C=C C–C=C C–C–C=C C–C–C–C=C C–C–C–C–C=C

C–C=C–C C–C–C=C–C C–C–C-C=C–C

C–C–C=C–C–C

For the three first alkanes and C2 –C3 alkenes only a linear structure is possible, but for butane and butene branched structure occurs, called isomers. Linear molecules have the prefix n– (n–butane) and the branched molecules i– (i–butane). All alkanes and alkenes are insoluble in water. The alkanes C1 to C4 (methane, ethane, propane, and butane) are gaseous, C5 to C17 (n-pentane to n-heptadecane) are liquid, and higher alkanes are solid. The liquid alkanes and alkenes are volatile and found in air. The chemistry of the double bond is described in Chapter 4.2.1. Natural gas mainly consists of CH4 , but C2 to C6 are also found (Table 5.31). Crude oil contains volatile compounds (1–3%), 20–60% light liquids (petrol and kerosene, boiling point 40–140 °C), 10–20% heavy naphthas and diesel (boiling point

5.6 Carbon | 403

Tab. 5.31: Chemical composition of natural gas (in vol-%). Compound

Mean

Range

CH4 C2 H6 C3 H8 C4 H10 C5 H12 C6 H14 N2 CO2 H2 S He H2

∼ 95 ∼ 2.5 ∼ 0.2 ∼ 0.2 ∼ 0.03 ∼ 0.01 ∼ 1.3 ∼ 0.02 ∼ 0.2 ∼ 0.1 ∼ 0.01

62–97 1–15 0–7 0–3 < 0.2 < 0.1 1–25 1–9 [RO2 ] in air (it can be different in other media such as biota) in terms of the percentages of different pathways. Organic peroxides (the most important are CH3 OOH and C2 H5 OOH) are constantly present in air, like H2 O2 but in smaller concentrations. In the case of a midsized radical attack (eq. (5.374)), the subsequent peroxy radical RO2 rearranges, forming a ketone (see further eq. (5.62) for the photolysis of ketones): RCH(O2 )R → RC(=O)R + OH .

(5.374)

In the case of terminal alkoxyl radicals (eq. (5.55)), followed by reaction (5.56), the most dominant subsequent reaction is with O2 (eq. (5.58)), forming an aldehyde RCHO and the hydroperoxyl radical (the atmospheric importance of this reaction lies simple in the transfer OH → HO2 ): RCH2 O(RO) + O2 → RCHO + HO2 .

(5.58)

In an urban environment, the addition of NO x (x = 1, 2) to alkoxyl radicals forms harmful alkyl nitrites (–NO) and nitrates (–NO2 ) (see eq. (5.266) and (5.267)): RO + NO x → RONO x .

(5.375)

The C–H bond in the methane (CH4 ), alkyl (–CH3 ), and allylic (>CH2 ) groups of organic compounds cannot be photodissociated under environmental conditions, but the H atom is abstracted by radical attack, mostly by OH. The methyl (CH3 ) and alkyl (R) radicals follow several reaction pathways, but in the presence of oxygen, aldehydes and ketones are formed. This oxygenation increases the reactivity and water solubility of the products.

5.6.5 Organic C1 chemistry: CH4 , CH3 OH, HCHO, HCOOH Most of the organic C1 chemistry is presented elsewhere; see Chapters 5.2.3.2 and 5.2.4 on the role of organic compounds during tropospheric O3 formation and OH 󴀘󴀯 HO2 cycling. In Chapter 5.2.3.2, we described the oxidation chain of CH4 and the formation of important radicals such as methyl (CH3 ), methyl peroxy (CH3 O2 ), methoxy (CH3 O), formyl (HCO), and the important intermediate formaldehyde HCHO. But ultimately, methane is oxidized to CO2 (reactions (5.40)–(5.46) and (5.33)): OH

O2

NO

O2

(−NO2 )

(−HO2 )

CH4 󳨀󳨀󳨀󳨀󳨀→ CH3 󳨀󳨀→ CH3 O2 󳨀󳨀󳨀󳨀󳨀→ CH3 O 󳨀󳨀󳨀󳨀󳨀→ HCHO (−H2 O) hν+O2

O2

OH+O2

(−HO2 )

(−HO2 )

(−HO2 )

HCHO 󳨀󳨀󳨀󳨀󳨀→ HCO 󳨀󳨀󳨀󳨀󳨀→ CO 󳨀󳨀󳨀󳨀󳨀→ CO2

5.6 Carbon

| 405

The methyl peroxy radical CH3 O2 reacts preferentially with NO ((eq. (5.42)), but under NO-limited conditions it also reacts with HO2 to form methyl hydroperoxide CH3 OOH (the second channel (5.376b) is less important) and with itself to form methanol CH3 OH and formaldehyde (eq. (5.377)). CH3 O2 + HO2 → CH3 OOH + O2 ,

(5.376a)

CH3 O2 + HO2 → HCHO + H2 O + O2 ,

(5.376b)

CH3 O2 + CH3 O2 → CH3 OH + HCHO + O2 .

(5.377)

Methyl hydroperoxide photolyzes quickly, CH3 OOH + hν (λ < 640 nm) → CH3 O + OH ,

(5.378)

or reacts with OH (Anglada et al. 2017), k 5.379 = (2–4)⋅10−12 cm3 molecule−1 s−1 : CH3 OOH + OH → CH3 O2 + H2 O

(68%) ,

(5.379a)

CH3 OOH + OH 󳨀󳨀󳨀→ CH2 OOH → HCHO + OH (32%) .

(5.379b)

H2 O

When the methoxy radical CH3 O is produced, reaction eq. (5.43) proceeds rapidly and yields formaldehyde. The importance of organic peroxides lies in the role of oxidant reservoirs in the troposphere, i.e., after formation they can be transported to other sites and again provide ROSs. Let us finally consider methanol oxidation in air. Because C–O and O–H bonds are much stronger than the C–H bond, OH attack happens preferably on C–H (at higher carbon chains preferably at the α–C–H), k 5.380 = 7.7 ⋅ 10−13 cm3 molecule−1 s−1 and k 5.381 = 1.3 ⋅ 10−13 cm3 molecule−1 s−1 , i.e., about 85% of methanol occurs via reaction (5.380): CH3 OH + OH → CH2 OH + H2 O ,

(5.380)

CH3 OH + OH → CH3 O + H2 O .

(5.381)

The fate of the methoxy radical CH3 O is known (eq. (5.43)), and CH2 OH also yields the same products: k 5.382 = 9.7 ⋅ 10−12 cm3 molecule−1 s−1 : CH2 OH + O2 → HCHO + HO2 .

(5.382)

Hence, methanol oxidation yields formaldehyde according to the budget OH+O2

CH3 OH 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HCHO . (−H2 O−HO2 )

Formaldehyde (IUPAC name methanal) quickly converts during the day to CO (eqs. (5.44) and (5.45)) but also transfers to the aqueous phase, where it hydrates (eq. (5.304)) or reacts with S(IV) (eq. (5.303)). In aqueous solution, methanol quickly oxidizes similarly to the gas phase mechanisms to formaldehyde, which (together with scavenged

406 | 5 Substances and chemical reactions in the climate system

HCHO) further oxidizes to formic acid (methane acid), likely via an OH adduct (the following reaction is speculative): O2

HCHO + OH → H2 C(O)OH 󳨀󳨀󳨀󳨀󳨀→ HC(O)OH .

(5.383)

(−HO2 )

Numerous measurements have shown that in the gas phase [HCHO] > [HCOOH] and in hydrometeors [HCHO] < [HCOOH]. Formic acid was first isolated in 1671 by the English researcher John Ray (1627–1795) from red ants (its name derives from the Latin word for ant, formica). Considering methane acid as a transient between inorganic and organic carbon, the carbonyl group –C(O)OH provides the huge class of organic acids RCOOH, and the formate HCOO− gives the class of esters HCOOR and RCOOR:

OH O=C

NH2 O=C

OH carbonic acid

NH2 O=C

OH carbamic acid

C1 O=C

NH2 urea

C1 phosgene

From carbonic acid (H2 CO3 = CO2 + H2 O) important derivatives are derived: carbamic acid (or carbamates,⁵² which also provides a class of organic carbamines substituting H for organic R), urea, and halogenated substitutes (such as phosgene). Urea is the “symbol” linking inorganic with organic chemistry; thus, there are two IUPAC names: diaminomethanal (as organic compound) and carbonyl diamide (as inorganic compound). Figures 5.31 and 5.32 summarize the C1 chemistry in the gas and aqueous phases. Whereas CH4 is very slowly oxidized in air (but yields methyl peroxide as ubiquitous compound), methanol and particularly formaldehyde quickly oxidize (the latter also photodissociates) to inorganic CO and, ultimately, CO2 . As shown in Chapter 5.2.3, HCHO provides a net source of radicals. In what follows, we summarize the most important conclusion on C1 chemistry: – Whereas CH4 is very slowly oxidized in air (but provides methyl peroxide as an ubiquitous compound), methanol and particularly formaldehyde quickly oxidize (the latter also photodissociates) into inorganic CO and, ultimately, CO2 . – HCHO provides a net source of radicals. – The formation of formic acid is likely negligible in the gas phase. – But methanol, formaldehyde, and formic acid (all produced or emitted in huge quantities from biogenic sources) will be scavenged and allow for more efficient oxidation, ultimately with an accumulation of formic acid, but partly until it mineralizes to CO2 and, most interestingly, furnishes a pathway in the formation of highly reactive bicarbonyls such as glyoxal and oxalic acid (Volkamer et al. 2005). 52 They are formed during CO2 capture from (flue) gases using aqueous amine solutions.

5.6 Carbon | 407

CH3OOH HO2 (-O2) NO (-NO2)

CH3O2

O2 (-HO2)

CH3O OH (-H2O)

O2

CH3

CH3OH

OH (-H2O)

CH2OH

O2 (-HO2)

HCHO

OH+O2 (-HO2)

HCOOH

hν (-H) OH (-H2O)

OH (-H2O)

HCO

CH4

O2

CO

(-HO2) OH + O2 (-HO2)

CO2 Fig. 5.31: C1 gas-phase chemistry.

CH3OOH HSO3OH + O2

CH3OH

H2O

HCHO

H2C(OH)2

-H2O-HO2 OH (-H2O) e- + H2O

CO

(-OH-)

OH (-H2O)

H2O

HCO HCO

(HCO)2

H2O2

HC(OH)2 H+

HC(OH)O-

(- 2H 2O)

OH + O2

HCOOH

(-H2O-HO2)

CO2

OH (+CO2- + H2O)

(COOH)2

e-

CO2-

CO2- (-CO32-)

Fig. 5.32: C1 aqueous-phase chemistry. (HCO)2 – glyoxal, (COOH)2 – oxalic acid; dotted line – multistep process.

408 | 5 Substances and chemical reactions in the climate system 5.6.6 C2 chemistry: C2 H6 , CH3 CHO, C2 H5 OH, CH3 COOH, and (COOH)2 5.6.6.1 Gas-phase chemistry Alkanes (also known as paraffins), with the general formula Cn H2n+2 , represent CH2 chain blocks with methyl ends. They generally produce first an aldehyde by oxidation of the terminal carbon atom with OH and then a bicarbonyl (here glyoxal from ethane) at the other end of the chain (here C2 ): OH+NO+O2

OH+NO+O2

(−H2 O−NO2 −HO2 )

(−H2 O−NO2 −HO2 )

H3 C–CH3 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ H3 C–C(O)H 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ (C(O)H)2 .

(5.384)

Acetaldehyde CH3 CHO (similar to formaldehyde) photolyzes and oxidizes through OH attack. Other photolysis pathways (to CH4 + CO or CH3 CO + H) are important above 300 nm in the troposphere: CH3 CHO + hν → CH3 + HCO ,

(5.385)

CH3 CHO + OH → CH3 CO + H2 O .

(5.386)

CH3 CO (which is not RO but a carbon radical ∙ CO) adds O2 (eq. (5.60)) and produces PAN (eq. (5.277)), but also in a competitive reaction as RO2 radical it oxidizes NO and afterwards decomposes (from the methyl peroxy radical CH3 O2 ultimately formaldehyde is produced): NO

CH3 C(O)O2 󳨀󳨀󳨀󳨀󳨀→ CH3 C(O)O ,

(5.387)

(−NO2 ) O2

NO

O2

(−CO2 )

(−NO2 )

(−HO2 )

CH3 C(O)O 󳨀󳨀󳨀󳨀󳨀→ CH3 O2 󳨀󳨀󳨀󳨀󳨀→ CH3 O 󳨀󳨀󳨀󳨀󳨀→ HCHO .

(5.388)

Alcohols yield (acetic) acid: k 5.389 = 2.8 ⋅ 10−12 cm3 molecule−1 s−1 . Acetic acid is likely stable in the gas phase and transferred to hydrometeors: O2

C2 H5 OH + OH 󳨀󳨀󳨀󳨀󳨀→ CH3 CHOH 󳨀󳨀󳨀󳨀󳨀→ CH3 C(O)OH (90%) ,

(5.389a)

C2 H5 OH + OH 󳨀󳨀󳨀󳨀󳨀→ CH2 CH2 OH (5%) ,

(5.389b)

(−H2 O)

(−HO2 )

(−H2 O)

O2

C2 H5 OH + OH 󳨀󳨀󳨀󳨀󳨀→ CH3 CH2 O 󳨀󳨀󳨀󳨀󳨀→ CH3 CHO (5%) . (−H2 O)

(−HO2 )

(5.389c)

The radical adduct CH2 CH2 OH reacts similarly to ethene + OH (see below) and forms glycolaldehyde⁵³ (IUPAC name 2-hydroxyethanal): OH+NO+O2

CH2 CH2 OH 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ HOCH2 CHO . (−H2 O−NO2 −HO2 )

(5.390)

The lifetime of glycolaldehyde in the atmosphere is about 1 day for reaction with OH and more than 2.5 days for photolysis, although both wet and dry deposition are other

53 Glycolaldehyde has two isomers: methyl formiate HCOOCH3 and acetic acid CH3 COOH.

5.6 Carbon | 409

important removal pathways (Bacher et al. 2001). Primary products of OH attack and photolysis are mainly HCO and CH2 OH (cf. eq. (5.386)). We will see later that glycolaldehyde is the main product of the OH + C2 H2 (ethine) reaction. However, the α-hydroxy alkoxyl intermediate might also decompose (the oxidation of glycolaldehyde gives HCHO and CO as final products): HOCH2 CH2 O → HCHO + CH2 OH .

(5.391)

Finally, the CH2 OH radicals react with O2 to give HCHO and HO2 (eq. (5.382)). Thus, C2 is broken down into C1 species. Figure 5.33 shows schematically the C2 gas-phase chemistry. It is obvious that there is no ethanol formation or acetic acid decomposition, whereas acetaldehyde provides many pathways back to C1 chemistry. Glycolaldehyde is a highly water-soluble product from several C2 species (ethene, acetaldehyde, and ethanol); other bicarbonyls, however, are likely to be produced preferably in solution. C2H4

PAN

CH3COOH OH

C2H5OOH

OH

HOCH2CHO OH

C2H5OH

HO2

C2H5O2 OH

C2H6

NO2

CH3CO

O2

OH

NO (-NO2)

CH3C(O)O2

NO (-NO2)

OH

CH3CHO

CH3C(O)O

hν (-HCO)

O2 (-CO2)

OH

CH3

(CHO)2

O2

CH3O2

hν

HCO, CO, HCHO, HCOOH

HCHO

Fig. 5.33: C2 gas-phase chemistry. C2 H5 OOH – acetyl peroxide, HOCH2 CHO – glycolaldehyde, C2 H6 – ethane, C2 H4 – ethene; dotted line – multistep process. OH reactions involve a subsequent step with O2 (and HO2 formation).

410 | 5 Substances and chemical reactions in the climate system

CH3O2 + CO2

OH

CH3CH2OH

OH

(-H2O)

CH3CHO

OH (-H2O)

O2

(-H2O)

CH3C(O)

CH3C(O)O2

H2O2 (-2 H2O) OH

CH2CH2OH

CH3COOH

CH2COOH

O2

O2CH2COOH

products

O2

(CHO)2

OHC-CH2OH

(COOH)2 H+

hν

C2O42-

HCO

OH (-OH-)

C2O4-

O2 (-O2-)

CO2

Fig. 5.34: C2 aqueous-phase chemistry.

5.6.6.2 Aqueous chemistry The aqueous phase produces other C2 species but also decomposes them (Figure 5.34). By contrast, in aqueous solution from C1 , C2 species can be produced, as shown by the formation of glyoxal from the formyl radicals (eq. (5.393)); the latter is an often found species in solution. From methanol and formaldehyde dicarbonyls are produced via carbonylation in aqueous phase: OH

HCO

CH3 OH 󳨀󳨀󳨀󳨀󳨀→ CH2 OH 󳨀󳨀󳨀→ OHC–CH2 OH (−H2 O) OH

(glycolaldehyde) ,

HCO

HCHO 󳨀󳨀󳨀󳨀󳨀→ HCO 󳨀󳨀󳨀→ OHC–CHO (glyoxal) . (−H2 O)

(5.392) (5.393)

Furthermore, from methanol and formic acid the corresponding acids gained through carboxylation (in reaction with the CO−2 radical) are as follows: OH

CO−2

CH3 OH 󳨀󳨀󳨀󳨀󳨀→ CH2 OH 󳨀󳨀󳨀→ HOCH2 –CO−2 (−H2 O) OH

CO−2

HCOOH 󳨀󳨀󳨀󳨀󳨀→ COOH 󳨀󳨀󳨀→ COOH–CO−2 (−H2 O)

(glycolic acid) , (oxalic acid) .

(5.394) (5.395)

Ethanol C2 H5 OH oxidizes in a multistep process in solution to acetaldehyde: OH+O2

CH3 CH2 OH 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CH3 CHO . (−H2 O−HO2 )

(5.396)

5.6 Carbon | 411

This starting H abstraction can also go with other H acceptors such as SO−4 , NO3 , Cl−2 , Br−2 and CO−3 (see, for example, the CAPRAM model). Further oxidation of the aldehyde is similar in elementary steps to acetic acid: OH+O2

CH3 CHO 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CH3 COOH . (−H2 O−HO2 )

(5.397)

Acetic acid further oxidizes in a first step to yield the CH2 COOH radical; in the absence of O2 , it can dimerize to succinic acid COOH(CH2 )2 COOH (Garrison et al. 1959): O2

OH

CH3 COOH 󳨀󳨀󳨀󳨀󳨀→ CH2 COOH 󳨀󳨀→ O2 CH2 COOH . (−H2 O)

(5.398)

This peroxy radical can then yield glycolic acid, glyoxylic acid, oxalic acid, HCHO, and CO2 (Garrison et al. 1959). The peroxyacetyl radical (ACO3 ) – the precursor of PAN – is produced from the oxidation of acetaldehyde. It forms with HO2 peroxyacetic acid CH3 C(O)OOH, which is also detected in air in small concentrations: OH

O2

HO2

CH3 CHO 󳨀󳨀󳨀󳨀󳨀→ CH3 C(O) 󳨀󳨀→ CH3 C(O)O2 󳨀󳨀󳨀󳨀→ CH3 C(O)OOH . (−H2 O)

(−O2 )

(5.399)

As for other peroxy radicals, it can transfer O onto other dissolved species (NO → NO2 ) and then decompose them (finally, the methyl peroxy radical forms HCHO): O2

NO

CH3 C(O)O2 󳨀󳨀󳨀󳨀󳨀→ CH3 C(O)O 󳨀󳨀→ CH3 O2 + CO2 . (−NO2 )

(5.400)

In aqueous solution, organic peroxy radicals can also react with bisulfite, gaining the sulfite radical and organic peroxide ROOH: HSO−3

RO2 󳨀󳨀󳨀󳨀󳨀−→ ROOH . (−SO3 )

(5.401)

Glyoxal (CHOCHO or (CHO)2 ) is one of the simplest multifunctional compounds found in the atmosphere and is produced by a wide variety of biogenically and anthropogenically emitted organic compounds (Ortiz et al. 2006). One current model estimates global glyoxal production to be 45 Tg yr−1 , with roughly 50% due to isoprene photooxidation, whereas another estimates 56 Tg yr−1 , with 70% produced from biogenic precursors (Galloway et al. 2009 and references therein). CHOCHO is destroyed in the troposphere primarily by reaction with OH radicals (23%) and photolysis (63%), but it is also removed from the atmosphere through wet (8%) and dry deposition (6%) (Myriokefalitakis et al. 2008). Glyoxal sulfate has also been detected in filter samples: CHO–C(OH)–O–SO−3

(glyoxal sulfate)

COOH–C(H)–SO−3

(glycolic acid sulfate)

In diluted aqueous solution, glyoxal exists as a dihydrate CH(OH)2 CH(OH)2 , which is quickly and reversibly formed (Schweitzer et al. 1998). The aqueous-phase photooxi-

412 | 5 Substances and chemical reactions in the climate system

dation of glyoxal is a potentially important global and regional source of oxalic acid and secondary organic aerosol (Fu et al. 2009) and could account for a missing SOA source in budgets. The gas-phase photolysis of glyoxal produces two HCO radicals as the most important pathway under atmospheric conditions. Tadić et al. (2006) estimated jobs = 1.0 ⋅ 10−4 s−1 . Although glyoxal has a very low effective quantum yield (Φeff = 0.035 ± 0.007), photolysis remains an important removal path in the atmosphere. Oxalic acid is the most abundant dicarboxylic acid (DCA) found in the troposphere, yet there is still no scientific consensus concerning its origins or formation process. Concentrations of oxalic acid gas at remote and rural sites range from about 0.2 ppb to 1.2 ppb with a very strong annual cycle showing high concentrations during the summer periods. Oxalate was observed in clouds at air-equivalent concentrations of 0.21±0.04 μg m−3 to below-cloud concentrations of 0.14 μg m−3 , suggesting an incloud production as well (Crahan et al. 2004). Oxalic acid is the dominant DCA, and it constitutes up to 50% of total atmospheric DCAs, especially in nonurban and marine atmospheres. The large occurrence in the condensed phase led Warneck (2003) to suggest that oxalate does not solely originate in the gas phase and condense into particles (Figure 5.35). Hence, hydroxyl radicals might be responsible for the aqueous-phase acethylene (g)

HC CH

O glyoxal (g)

glyoxal, hydrated (aq)

O ║ ║ HC–CH

O OH ║ HC–CH OH O

glyoxylic acid, hydrated (aq)

OH ║ HC–CH

HO

H2C=CH2

O ║ HO–C(H)2–CH

ethylene (g)

glycolaldehyde (g)

H HO–C(H)2–C–OH

glycolaldehyde hydrated (aq)

H O ║ HO–C(H)2–COH

glycolic acid, hydrated (aq)

OH

O oxalic acid (aq)

O ║ ║ HC–CH

HO

OH

Fig. 5.35: Proposed reaction pathway for formation of oxalic acid in cloud water; after Warneck .(2003)

5.6 Carbon

| 413

Tab. 5.32: C1 and C2 carboxylic acids, after Holleman-Wiberg (2007). Formula

Structure

Name of acid

Name of salt

Methanol a Formic acid Carbonic acid Peroxocarbonic acid

Methanolate Formate Carbonate Peroxocarbonate

Acetic acid d Glycolic acid e Dihydroxyacetylene Glyoxylic acid f Oxalic acid Dicarbonic acid Peroxodicarbonic acid

Acetate Glycolate Dihydroxyacetylate Glyoxalate Oxalate Dicarbonate Peroxodicarbonate

Mono carboxylic acids H4 CO H2 CO2 H2 CO3 H2 CO4

H3 COH HC(O)OH C(O)(OH)2 C(O)(OH)OOH b

Dicarboxylic acids H4 C2 O2 H4 C2 O3 H2 C2 O2 H2 C2 O3 H2 C2 O4 H2 C2 O5 H2 C2 O6

CH3 C(O)OH HOCH2 C(O)OH HOC≡COH b, c HOC–C(O)OH HO(O)C–C(O)OH HO(O)C–O–C(O)OH b HO(O)C–O–O–C(O)OH b

a

Very weak acid forming. Only as salts. c Isomer with nonacidic glyoxal O=CH–CH=O (ethandial). d IUPAC name: ethanoic acid; other names: methanecarboxylic acid, acetyl hydroxide. e IUPAC name: 2–hydroxyethanoic acid; other name: hydroxoacetic acid. f IUPAC name: oxoethanoic acid; other names: oxoacetic acid, formylformic acid (ubiquitous in nature in berries). b

formation of oxalic acid from alkenes. Of the different DCAs (oxalic, adipic, succinic, phthalic, and fumaric), only the dihydrate of oxalic acid, enriched in particles in the upper troposphere, acts as a heterogeneous ice nucleus (Zobrist et al. 2006). Ubiquitous organic aerosol layers above clouds with enhanced organic acid levels were observed, and field data suggest that aqueous-phase reactions that produce organic acids, mainly oxalic acid, followed by droplet evaporation, are the source (Sorooshian et al. 2007). Organic acids (Table 5.32) are ubiquitous components in the troposphere of urban and remote regions of the world. Organic acids contribute significantly to rainwater acidity in urban areas (Pena et al. 2002) and account for as much as 80–90% of the acidity in remote areas (Andreae et al. 1988). Keene and Galloway (1984) were the first to demonstrate that formic and acetic acid concentrations are highly correlated in rainwater. Organic acid concentrations in rainwater vary both spatially and temporally. Concentration variations in the gas and aqueous phases were attributed to seasonal variations in biogenic emissions.

414 | 5 Substances and chemical reactions in the climate system

5.6.7 Alkenes, alkynes, and ketones Besides alkanes, C2 carbon comprises two other classes, alkenes and alkynes. The double bond C=C is stronger than the simple C–C bond but paradoxically is more reactive. The most simple compound is ethylene (ethene) CH2 =CH2 . Alkenes are produced in so-called elimination reactions, mainly by the dehydration (–H2 O) of alcohols and dehydrohalogenation (–HX) of alkyl halides: H3 C–CH2 OH → H2 C=CH2 + H2 O .

(5.402)

Alkenes add OH and provide a radical adduct (which reacts further as shown in reaction (5.390)): H2 C=CH2 + OH → CH2 CH2 OH . (5.403) In contrast to alkenes (also known as olefins), which are important compounds in nature, alkynes (also termed alkines) –C≡C– are relatively rare in nature but highly bioactive in some plants. The triple bond is very strong with a bond strength of 839 kJ mol−1 . Ethylene C2 H2 (commonly known as acetylene) is generally considered to be produced only by human activities with an average tropospheric lifetime on the order of 2 months, allowing this compound to reach remote areas as well as the upper troposphere. Thus, the presence of C2 H2 in the open oceanic atmosphere is commonly explained by its long-range transport from continental sources together with CO originating from combustion. Both species are strongly correlated in atmospheric observations, offering constraints on atmospheric dilution and chemical aging. In effect, its mixing ratio is typically in the range 500–3000 ppt in inhabited countries compared with 50–100 ppt in remote oceanic areas. Xiao et al. (2007) used a model to estimate a global source of 6.6 Tg yr−1 . However, Kanakidou et al. (1988) do not exclude an oceanic source. The destruction of acetylene in the atmosphere occurs only by reaction with OH radicals (Siese and Zetzsch 1995). Typical products are HO2 and glyoxal (CHO–CHO), but SOA formation (Volkamer et al. 2009) is also found under laboratory conditions. The polymerization of C2 H2 after radiolysis has long been known: M (multistep)

HC≡CH + OH 󴀘󴀯 (HC=CHOH)∗ 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ CH2 CHO .

(5.404)

CH2 CHO is the alkyl radical, which would form if OH did not attack the C–H of the carbonyl group (cf. eq. (5.396)) but the CH3 group (what is much less probable). This radical adds O2 and forms glyoxal, but SOA formation is also found under laboratory conditions: M (multistep)

CH2 CHO + O2 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ (CHO)2 + OH .

(5.405)

5.6 Carbon | 415

Alkenes are the only class of organic compounds that react in the gas phase with ozone (the often cited DOC decomposition by O3 is almost a result of secondary ROS formation from O3 in solution). This occurs by O3 addition in a reaction known as ozonolysis and has been known for more than 100 years (Fisher and Dussalt 2017): O

R1

R3

R1

O

O

C

C

R3

O3 C=C R2

R4

R2

R1 R2 C=O + R3 R4 •COO•

(a)

R1 R2 •COO• + R3 R4 C=O

(b)

R4

(5.406) The reaction rate increases with increasing carbon numbers, ranging between 10−18 −1 and 10−14 cm3 molecule−1 s . Considering the O3 concentration is larger by a factor of > 105 than that of OH, the absolute rate of ozonolysis, even for lower alkenes (C1 –C4 ), is about 10% of the OH addition. Hence, at night ozonolysis is an important pathway. For higher alkenes such as isoprene and terpene, the atmospheric lifetime is only in the range of minutes. Because of the steric consideration, the probability of each pathway (a) and (b) amounts to 50%. The ozonide intermediate decomposes with the formation of a ketone and biradicals (>∙ C–O–O∙ ), called Criegee radicals (Criegee 1948), which then stabilize and decompose. Criegee intermediates are produced in the ozonolysis of unsaturated hydrocarbons in the troposphere, and understanding their fate is a prerequisite for modeling climate-controlling atmospheric aerosol formation. Although some experimental and theoretical rate data are available, they are incomplete and partially inconsistent, and they do not cover the tropospheric temperature range. Long et al. (2016) consider two different types of reaction mechanisms for bimolecular reactions: – addition-coupled hydrogen transfer, and – double hydrogen atom transfer (DHAT). The simplest Criegee intermediate CH2 OO is termed carbonyl oxide, which reacts rapidly with NO2 (k = 4.4 ⋅ 10−12 cm3 molecule−1 s−1 ) by adduct formation, almost exclusively forming nitro-peroxy radicals ∙ OOCH2 NO2 (Vereecken and Ngyen 2017). These will react as other alkyl peroxy radicals in the atmosphere, ultimately generating CH2 O and regenerating NO2 in most reaction conditions. For the example of propene, the following products are produced (Finlayson-Pitts and Pitts 2000,

416 | 5 Substances and chemical reactions in the climate system

Neeb et al. 1998): M

(C(H)HOO) ∗ 󳨀→ HCO + OH (37–50%) ,

(5.407a)

∗ M

(5.407b)

∗ M

(5.407c)

∗ M

(5.407d)

∗ M

(5.407e)

(C(H)HOO) 󳨀→ CO + H2 O (12–23%) , (C(H)HOO) 󳨀→ CO2 + H2 (23–38%) , (C(H)HOO) 󳨀→ CO2 + 2 H (0–23%) , (C(H)HOO) 󳨀→ HCOOH (0–4%) .

The produced OH and HO2 (the latter as a subsequent product from primary H) react additionally with the alkenes and yield a huge spectrum of products. Most important is SOA formation (known as blue haze from biogenic emissions of tropical forests). The stabilized Criegee radical reacts with various major species (H2 O, SO2 , NO, NO2 , CO, RCHO, and ketones). In reaction with water vapor, direct H2 O2 can also be formed (Sauer et al. 1999): RH∙ COO∙ + H2 O → RC(O)OH (carboxylic acid) + H2 O ,

(5.408a)

H

.

.

RH COO + H2O

RC(O)OH + H2O

R C O O H

(5.408b)

OH

(5.409)

RCHO + H2O2

This is an important source of secondary organic acids; reaction eq. (5.408a) is an intramolecular rearrangement via H2 O–collision intermediate. The hydroxyperoxide was identified as an intermediate. The following are competing conversions to aldehyde: RH∙ COO∙ + (NO, NO2 , CO) → RCHO + (NO2 , NO3 , CO2 ) . (5.410) The reaction with SO2 proceeds via an adduct that decays to sulfuric acid:

.

.

RH COO + SO2

O R(H)C

O O

S=O

H2O

RCHO + H2SO4

(5.411)

Nitrate radicals also react with alkenes by addition, which results in a variety of different compounds such as hydroxynitrates, nitrohydroperoxides, and hydrocarbonyls (Wayne et al. 1991). Another class of atmospherically important compounds are ketones (alkanones), which are almost exclusively of biogenic origin. The simplest is acetone, which is ubiquitous in air. With the exception of acetone, higher ketones react preferably with OH

5.6 Carbon | 417

at any carbon atom by H abstraction. With subsequent O2 addition the fate of RO2 is known, forming either aldehyde (–C(=O)H) at a terminal carbon or ketone (>C=O) in the middle of the chain. The photolysis of acetone (Emrich and Warneck 2000) produces the acetyl radical CH3 CO, whose fate is described after reaction eq. (5.386); for the fate of methyl CH3 see eq. (5.41): CH3 C(O) CH3 + hν → CH3 C=O + CH3 .

(5.412)

5.6.8 Aromatic compounds Aromatic compounds play a key role in the biochemistry of all living things, serving many biochemically important functions. Aromatic hydrocarbons (arenes) can be monocyclic or polycyclic (PAH). The simplest aromatic compound is benzene C6 H6 , which is similar to the simplest alkane, methane CH4 . Figure 5.36 shows some simple arenes. In contrast to alkenes, benzene is very stable (see Chapter 4.2.1 on chemical bonding), that is, it is very stable against OH attack. Because they are so stable, these rings tend to form easily and, once formed, tend to be difficult to break in chemical reactions. The basic benzene structure forms many derivatives where the functional groups serve specific “functions” in biochemistry (e.g., acidity, odor, smell, reactivity). The four aromatic amino acids histidine, phenylalanine, tryptophan, and tyrosine each serve as one of the 20 basic building blocks of proteins. Further, all five nucleotides (adenine, thymine, cytosine, guanine, and uracil) that make up the sequence of the genetic code in DNA and RNA are aromatic purines or pyrimidines. The haems (biomolecules) contain an aromatic system with 22π electrons. Chlorophyll also has a similar aromatic system. Aromatic compounds are released into the atmosphere by combustion (i.e., gasoline and diesel engines), gasoline evaporation, solvent usage, and spillage. Biofuel and biomass burning are the second largest sources of aromatics. From litter, aromatic hydrocarbons are important common contaminants of soils and groundwater. Certain crops and coniferous trees were found to emit toluene (White et al. 2009), but the overall impact of biogenic toluene emissions is probably minor compared to the anthropogenic and pyrogenic sources. Anthropogenic emissions provided the largest source of aromatics (23 TgC yr−1 ) and biomass burning from the GFAS inventory (Global Fire Assimilation System) the second largest (5 TgC yr−1 ). The simulated chemical production of aromatics accounts for 5 TgC yr−1 . The atmospheric burden of aromatics amounts to 0.3 TgC. The main removal process of aromatics is photochemical decomposition (27 TgC yr−1 ), and during wet and dry deposition they are responsible for a removal of 4 TgC yr−1 (Cabrera-Perez et al. 2016). However, biogenic emissions of simple aromatics could be equal in importance to anthropogenic emissions (Misztal et al. 2015). Typical benzene and toluene mixing ratios fall in a 0.1–10 ppt range. Estimated lifetimes are 2 days for toluene and 2 weeks for benzene (Koppmann 2008).

418 | 5 Substances and chemical reactions in the climate system CH3

OH

NH2

toluene

phenol

aniline

CH3

CH3

CHO

CH3 CH3 p-xylene

m-xylene

benzaldehyde

CH3 CH3

o-xylene NO2

naphtalene COOH

COOH

OH nitrobenzene

benzoic acid

OH OH gallic acid

Fig. 5.36: Some important arenes.

PAHs are a class of several hundred compounds that share a common structure of at least three condensed aromatic rings. PAHs may be formed during natural processes such as incomplete combustion of organic materials such as coal and wood or during forest fires. PAHs are released during industrial activities such as aluminum, iron, and steel production in plants and foundries, waste incineration, mining, or oil refining. PAHs have also been detected at low levels in cigarette smoke and motor vehicle emissions. They are persistent organic pollutants and are slow to degrade in the environment. Benzo[a]pyrene (BaP) is commonly used as an indicator species for PAH contamination, and most of the available data refer to this compound. Substituted arene compounds react faster with OH, for example, methylbenzenes such as toluene, p–xylene, and 1,3,5–trimethylbenzene. The degradation chemistry of aromatic VOCs remains an area of particular uncertainty. What is clear is the attack on the methyl group because it turns into an aldehyde (toluene → benzaldehyde). How-

5.6 Carbon |

419

ever, about 90% of the OH attack is directed at the ring, generating an adduct called a hydroxycyclohexadienyl radical (Becker et al. 1999): OH H

This can further react in different channels; first, it can yield benzene oxide C6 H5 O, which is in equilibrium with oxepine – from which through photolysis phenols are gained, for example, α-cresol from toluene: oxepin

benzene oxide

O

O

Because benzene oxide has a conjugated but not localized radical carbon atom, O2 addition is another pathway; toluene gives the following peroxide, which is linked in a ring: CH3 OH O H

O

This intermediate peroxide decays during opening of the ring into butendial and methylglyoxal. Methylglyoxal and glyoxal were identified as the main components: (methylglyoxal)

(butendial) •O OH O HC O

CH CH

C

H

H

C

C

O CH2

O2 ( HO)2

HC O

CH CH

CH

HC

O

O

C

CH3

(5.413)

The variety of products is large; often bi- and polycarbonyls are found, which were proposed as producers of SOA and which transfer to the aqueous phase. However, it has also been found that during new particle formation in forested areas the OM mass fraction significantly increases but that the CCN efficiency is reduced by the low hygroscopicity of the condensing material (Dusek et al. 2010).

420 | 5 Substances and chemical reactions in the climate system

5.6.9 Is the atmospheric fate of complex organic compounds predictable? In recent years, the availability of kinetic and mechanistic data relevant to the oxidation of VOCs has increased significantly, and various aspects of the tropospheric chemistry of organic compounds have been reviewed extensively, in particular concerning ozone formation (Calvert et al. 2015). We have a good generic VOC mechanism for the OH-initiated oxidation of organic compounds that becomes progressively less accurate with increasing carbon number and functionalization (with oxygen) and especially at low NOx . What we do know is summarized in the master chemical mechanism,⁵⁴ which is a crucial link between laboratory kinetics and the reduced mechanisms used in large-scale models. The simple enumeration of the possible branching pathways in the oxidation of large (C5 and larger) organic compounds is bound to fail. One reason is simply the number of possible reaction pathways open to a large molecule, including radical attack at numerous sites as well as photolysis and isomerization. However, it is often argued that we need these mechanisms to predict ambient radical budgets and ratios, to predict ozone generation and removal, and to predict organic aerosol production as well as organic aerosol aging in both vapor and condensed phases. Do we really need these mechanisms? When 90% of the radical budget and ozone formation is well described by the available mechanisms and models from the past 15–20 years, what would bring about any improvement when considering the main uncertainty, the quantity of the emission of organic species (which is within a factor of two or more)? Nevertheless, science is unlimited, and new generations of atmospheric chemists will (probably) accumulate more and more insights into atmospheric organic chemistry. The question of whether we need better mechanisms is therefore wrong. But the answer to whether atmospheric organic chemistry is predictable is definitively no.

5.7 Halogens (Cl, Br, F, and I) Among the halogens (main group 7 of the periodic table of the elements) are fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At). The radioactive At is the rarest element on Earth. The name halogens (Greek) comes from “salt makers” (halides such as fluorides and chlorides, for example). Due to their high eletronegativity, halogens form anions, F− , Cl− , Br− , and I− ; only iodine also forms polyhalides such as I−3 . Chlorine, bromine, and iodine occur in elementary form only in the atmosphere at very small concentrations and are very reactive.

54 The Master Chemical Mechanism (MCM – University of Leeds) is a near-explicit chemical mechanism describing the degradation of CH4 and 142 VOCs in the troposphere. The organic component of the version MCMv3 contains around 12,600 reactions and 4500 chemical species.

5.7 Halogens (Cl, Br, F, and I) | 421

Tab. 5.33: Emission of chlorine compounds (in Tg Cl yr−1 ); see Volume 2 for reference. Substance

Ocean

Soils

Biomass burning

Fossil fuel burning

Other artificial emissions

CH3 Cl CHCl3 CH3 CCl3 C2 Cl4 C2 HCl3 CH2 Cl2 CHClF2

0.46 0.32 – 0.016 0.020 0.16 –

0.0001 0.0002 – – – 0.0003 –

0.640 0.0018 0.013 – – – –

0.075 – – 0.002 0.003 – –

0.035 0.062 0.572 0.313 0.195 0.487 0.080

Total organic

1.0

0.0006

0.65

0.08

1.7

6.3 c

4.6 d

2d

Total inorganic

1785 a

15 b

a

Sea salt including release of HCl (50) and ClNO2 (0.06). Soil dust chloride. c HCl and particulate chloride. d HCl. b

There is a reservoir of chlorine (and other halogens) in the ocean and sea salt in the form of NaCl from which HCl can be released. However, the ocean has been identified as a source of many organic halogen compounds (Table 5.33), and newer insights provide evidence for halogenated compounds in soils (Chapter 5.7.1). The ocean acts as both a source and a sink for methyl halides, where algae are responsible for the production of halogenated organic compounds with surface photochemical processes most likely breaking them down into simple species (similar to DMS production – thereby correlations have often been found) (O’Dowd et al. 1995). The natural emission of volatile organic chlorine (CH3 Cl is dominant) lies in the Tg range per year (Table 5.33) and those of CH3 Br only in the kt range (Yvon-Lewis et al. 2004), but the net CH3 I oceanic emission to the atmosphere is 0.2 Tg (Bell et al. 2002), whereas rice paddies, wetland, and biomass burning only contribute small amounts (Lee-Taylor et al. 2005). Unexpectedly, during Saharan dust events, methyl iodide mixing ratios were observed to be high relative to other times, suggesting that the dust-stimulated emission of methyl iodide had occurred (Williams et al. 2007).⁵⁵ Most of the attention paid to halogens has focused on their effects on the stratospheric ozone layer (Chapter 5.2.7). Simpson et al. (2015) provide an overview on tropospheric halogen chemistry. Table 5.34 lists the chlorine compounds that have been detected in nature but do not all exist in all phases (natural waters, hydrometeors, and air-gas phase) (Simpson et al. 2015). From bromine and iodine are derived HX, HOX, HOXO2 , and HOXO3 but 55 Of course, experiments (Williams et al. 2007) that involve adding collected dust to seawater as well as adding H2 O2 rapidly produced CH3 I, another example in line with photoenhanced radical aqueous chemistry.

422 | 5 Substances and chemical reactions in the climate system

Tab. 5.34: Important chlorine compounds in the environment (note that most of the compounds also exist from bromine and iodine). Name a

Formula Element Cl2 Hydrogen

Dichlorine halides b

HCl

Hydrogen chloride c

Oxides Cl2 O (Cl–O–Cl) m Cl2 O3 (O–Cl–Cl(=O)2 ) ClO3 (Cl(=O)3 ) ClO2 (O=Cl=O) Cl2 O4 (Cl–O–Cl(=O)3 ) Cl2 O6 ((O=)2 –Cl–O–Cl(=O)3 ) Cl2 O7 ((O=)3 –Cl–O–Cl(=O)3 )

Dichlorine monoxide Dichlorine trioxide d Chlorine trioxide e Chlorine dioxide Chlorine perchlorate Dichlorine hexoxide f Dichlorine heptoxide g

Oxoacids HOCl HClO2 (HO–Cl=O) HClO3 (HO–Cl(=O)2 HClO4 (HO–Cl(=O)3

Hypochlorous acid Chlorous acid Chloric acid Perchloric acid

Ions Cl− OCl− ClO−2 (− O–Cl=O ClO−3 (− O–Cl(=O)2 ClO−4 (− O–Cl(=O)3 ClO+ ClO+2 (O=Cl⊕ =O) ClO+3 (O=Cl⊕ =(O)2 )

Chloride Hypochlorite Chlorite Chlorate Perchlorate Chlorosyl anion h (also called chloronium) Chloryl anion h Perchloryl anion h

Radicals Cl Cl−2 ClO ClO2 (Cl–O–O) ClO4 (O–Cl(=O)3

Chlorine atom Dichlorine anion radical Chlorine monoxide Chloroperoxo radical Chlorine tetroxide

5.7 Halogens (Cl, Br, F, and I) | 423

Tab. 5.34: (continued) Formula

Name a

Peroxides Cl2 O2 (Cl–O–O–Cl) HClO2 (HO–O–Cl) HClO3 (HO–O–Cl=O) HClO4 (HO–O–Cl(=O)2 )

Chlorine peroxide i Peroxohypochlorous acid (− OOCl peroxohypochlorite) Peroxochlorous acid (− OOClO peroxochlorite) Peroxochloric acid (− OOClO2 peroxochlorate)

Halogen nitrogen compounds ClONO2 ClNO ClNO2

Chlorine nitrate Nitrosyl chloride Nitryl chloride

Halogen carbon compounds CCl4 CHCl3 CH2 Cl2 CH3 Cl

Carbon tetrachloride Trichloromethane j (TCM) Dichloromethane k (DCM) Chloromethane0

Halogen sulfur compounds SF6 a

Sulfur hexafluoride

Given as example for Cl compounds. In English (in contrast to German where generic specific meanings exist and here proposed in English terms) halogen or halogenic acid is the general name for all acids (HCl, HOCl, HClO2 , HClO3 ). c Common name: hydrochloric acid (gas). d Isomeric with Cl–O–Cl(=O) . 2 e Exist only as dimer Cl O . 2 6 f Red fuming liquid: chloryl perchlorat [ClO2 ⊕ –ClO4 ⊖ ]. g Anhydride of perchloric acid. h Derived from hypochlorite, chlorite, and chlorate, resp. i Dimer of ClO. j Common name: chloroform. k Common name: methylen chloride. l Common name: methyl chloride. m Resonance structures O–Cl–Cl (14%), ⊖ O–Cl–Cl⊕ (70%), and O=Cl⊕ –Cl⊖ (16%). b

424 | 5 Substances and chemical reactions in the climate system

not HOXO; chlorous, chlorine, and perchloric acids are not known in pure forms (iodine acid is a stable white solid). In atmospheric gas phase, acids such as HCl, HBr, HI, HClO, HBrO, HIO3 , HClO4 , HBrO4 , and HIO4 exist, as do all of their oxides and radicals. In the aqueous phase Br− , Br−2 , BrO− , BrO−2 , BrO−3 , I− , I−2 , IO− , IO−2 , and IO−3 exist. Moreover, peroxohalogen acids, where O is exchanged by the peroxo group O–O, also exist as an intermediate in redox processes; peroxo acids are discussed as part of stratospheric chemistry. Several interhalogens are known and might exist in air (such as iodine chloride). HF exists in air only in the condensed phase (PM) despite its being primarily emitted as a gas. SF6 is exclusively from anthropogenic sources (it is used for air dispersion tracer experiments). It is extremely stable with one of the longest known lifetimes, 3200 years.

5.7.1 Chlorine in the environment Chlorine is one of the most abundant elements on the Earth’s surface. Until recently, it was widely believed that all chlorinated organic compounds were xenobiotic, that chlorine did not participate in biological processes, and that it was present in the environment only as chloride. However, over the years, research has revealed that chlorine takes part in a complex biogeochemical cycle, that it is one of the major elements of soil OM, and that the amount of naturally formed organic chlorine present in the environment can be counted in tons per square kilometer (Öberg 1998). More than 4000 organohalogen compounds, mainly containing chlorine or bromine but a few with iodine and fluorine, are produced by living organisms or are formed during natural abiogenic processes, such as volcanoes, forest fires, and other geothermal processes. The ocean is the single largest source of biogenic organohalogens, which are biosynthesized by myriad seaweeds, sponges, corals, tunicates, bacteria, and other marine life. Terrestrial plants, fungi, lichen, bacteria, insects, some higher animals, and even humans also account for a diverse collection of organohalogens (Gribble 2003). The abundance of chlorine in the lithosphere seems not to be well established – in the literature it is found in a range from 0.013% to 0.11%; Clarke (1920) suggested 0.045%. With the last value, we obtain a total mass of chlorine (using the mass of the lithosphere) of 2.2⋅1022 g, which is comparable to the chloride dissolved in the oceans (2.6 ⋅ 1022 g). Elemental chlorine is one of the most reactive species and therefore not found in nature, with the exception of small volcanic emissions. Inorganic chlorine in the form of chloride (and like other halogens such as fluorine, bromine, and iodine) is therefore stored in seawater and salt stocks from former oceans. Hence, the formation of sea salt (Chapter 5.7.2) is the dominant source of particulate chloride and gaseous HCl due to subsequent heterogeneous reactions (Chapter 5.7.4). Reactive halogen compounds (X, XO, X2 , XY, OXO, HOX, XONO2 , XNO2 , where X, Y = Cl, Br, I) – in particular halogen oxides – are present in various domains throughout the troposphere. The principal precursors of reactive Cl and Br are Cl− and Br− in sea

5.7 Halogens (Cl, Br, F, and I) | 425

salt aerosol (SSA). Reactive I, in contrast, is derived mainly from organic iodine compounds produced in and emitted from the ocean and possibly from I2 . The total load of chlorine in the atmosphere (particulate chlorine, gaseous inorganic chlorine, and organohalogens) is estimated to be 23 Tg Cl, including 8.4 Tg Cl reactive gases; CH3 Cl contributes 43%, CH3 CCl3 29%, and HCl/Cl2 7% (Khalil et al. 1999). Historically, reactive halogens were recognized to be of importance for stratospheric chemistry and (specifically Cl, ClO, and ClOOCl, for example) were blamed for Arctic ozone depletion, whereas the sources of chlorine atoms are poorly understood (Keil and Shepson 2006). The Cl atom reacts similarly to OH (e.g., in the oxidation of VOCs). However, the photolysis of HCl is too slow (even in the stratosphere) to provide atomic Cl. Thus, the only direct Cl source from HCl is due to its reaction with OH, but with a low reaction rate constant (Rossi 2003). There are several chemical means of producing elemental Cl (and other halogens) from heterogeneous chemistry (Chapter 5.7.4); in the troposphere, the photolysis of organochlorine compounds is not very important, with a few exceptions (Chapter 5.7.3); see Faxon and Allen (2013) for a review of chlorine chemistry.⁵⁶ Besides HCl, volcanic plumes contain ClO and OClO. In air above salt lakes (Dead Sea, Great Salt Lake in the USA) ClO, IO, OIO, I2 , and BrO have been detected, likely released from salt stocks due to some “bromine explosion” mechanism (Chapter 5.7.3). Perchlorate (ClO−4 ) was detected on Mars (NASA’s Phoenix Lander Mission) in soil samples in a range of 0.5–0.6 wt % ClO−4 (Hecht et al. 2009) on the order of one magnitude higher than Cl− . On Earth, natural perchlorate is rare and is found only in the driest places, such as unusually arid deserts and the stratosphere. The highest concentrations – comparable to those on Mars – were found in the Atacama Desert in Chile (0.04–0.57%) together with nitrate ores (Ericksen 1981), see also Catling et al. (2010) and references therein. Perchlorate in the Atacama can be definitively attributed to an atmospheric source (such as nitrate, see also Volume 2). Together with ClO−4 , high concentrations (0.04–0.14%) of iodate (IO−3 ) were found also in Atacama saltpetre (Ericksen 1981). The most important reservoirs of inorganic iodine are HOI and IONO2 , and for bromine they are BrONO, HOBr, and BrCl in the atmosphere. Global emission of HCl from coal combustion and from waste incineration was estimated to be 4.6 Tg Cl yr−1 and 2 Tg Cl yr−1 , respectively (McCulloch et al. 1999), whereas HCl emissions from sea salt and biomass burning was estimated to be 50 Tg Cl yr−1 and 6 Tg Cl yr−1 , respectively (Volume 2).⁵⁷ Thornton et al. (2010) estimated, by measurements and modeling, the global Cl source from photolysis (reaction

56 From a historical viewpoint, see the excellent review “Atmospheric chemistry of chlorine compounds” (1976), National Research Council Chlorine and Hydrogen Chloride. Washington, DC: The National Academies Press, 282 pp. 57 Note the different values given for HCl formation from sea salt (Table 5.33 and text) between 7.6 and 400 Tg Cl yr−1 expressing the large uncertainty (see discussion in Volume 2).

426 | 5 Substances and chemical reactions in the climate system eq. (5.187)) of nitryl chloride (ClNO2 ) to be 8–22 Tg Cl yr−1 , whereas ClNO2 is produced nocturnally, especially in polluted areas, according to reaction eq. (5.185). The global methane sink due to reaction with Cl atoms (reaction eq. (5.445)) in the marine boundary layer could be as large as 19 Tg yr−1 ; see Chapter 5.7.4 for the Cl formation process via bromine autocatalysis. As seen from Table 5.33, some volatile organochlorine compounds are emitted both naturally and anthropogenically. More than 200 chlorinated gases were identified in air (Graedel 1979, Graedel et al. 1986b), and more than 1000 organic chlorine compounds were identified in nature (Öberg 2002). As mentioned previously, today more than 4000 compounds are known from natural processes (Gribble 2004). It is now an established fact that natural organohalogens are a normal part of the chlorine cycle in the environment (Khalil and Rasmussen 1999). The group of reactive gases consists of chloromethane or methyl chloride (CH3 Cl), chloroform (CHCl3 ), phosgene (COCl2 ), dichloromethane (CH2 Cl2 ), chlorinated ethylenes (C2 HCl3 , C2 Cl4 ), chlorinated ethanes (CH4 Cl2 , C2 H2 Cl4 ), from natural and artificial sources (cf. Table 5.33). The long-lived or unreactive gases are the chlorofluorocarbons (CCl2 F2 , CCl3 F, C2 Cl3 F3 , C2 Cl2 F4 , C2 ClF5 , CCl3 F) and carbon tetrachloride (CCl4 ). These are all of human origin and will no longer be produced because of the Montreal Protocol and its amendments (international agreements to phase out global production of compounds that can deplete the stratospheric ozone layer) (Montreal Protocol 2000); see also Chapter 5.2.7. Synthesized organic chlorine compounds were widely used as solvents, cleaning materials, pesticides, pharmaceuticals, and plastics. In organic chemical synthesis, chlorinated compounds (mostly via radical attack of elemental chlorine) are used for other synthesis because Cl is easily exchangeable with other functional groups. Many halogenated compounds belong to the category of persistent organic pollutants (POPs). Because organochlorine compounds are lipophilic, they accumulate in the organs of animals and can have effects when they exceed a certain threshold. Pesticides such as dichloro-diphenyl-trichloroethane (DDT), which is the best known, are banned in many countries. It seems that chlorinated (or generally halogenated) organic compounds play very special roles as biomolecules. Halogenated natural products are medically valuable and include antibiotics (chlorotetracycline and vancomycin), antitumor agents (rebeccamycin and calichemycin), and human thyroid hormone (thyroxine). Halogenation is essential to biological activity and chemical reactivity of these compounds and often generates versatile molecular building blocks for chemists working on synthetic organic molecules (Gribbles 2004). The organic chlorine in soil was originally suggested to be of anthropogenic origin, resulting from the atmospheric transport and deposition of human-made chlorinated compounds. However, the total atmospheric deposition of organic chlorine in remote areas can only explain a small fraction of the organic chlorine found in soil. Furthermore, it was derived from those soil constituents that originate from the period before industrialization, which also contain organic chlorine. Very little is known about the biogeochemical cycling (e.g., formation, mineralization, leaching) of chlorinated

5.7 Halogens (Cl, Br, F, and I) | 427

OM in soil. For example, the net formation of organic chlorine in spruce forest soil is closely related to the degradation of OM. The ecological role of this formation is so far unknown, but recent findings suggest (Öberg 2002) that the amount of organically bound halogens in soil increases with decreasing pH, and that production seems to be related to lignin degradation, in combination with studies suggesting that the production of organochlorine compounds is a common feature among white-rot fungi. This makes it tempting to suggest a relationship between lignin degradation and production of organohalogens. These relations may result from an enzymatically catalyzed formation of reactive halogen species as outlined in what follows. Öberg (2002) enlightens four paradoxes that spring up when some persistent tacit understandings are viewed in the light of recent work as well as earlier findings in other areas. The paradoxes are that it is generally agreed that – Chlorinated organic compounds are xenobiotic, even though more than 1000 naturally produced chlorinated compounds were identified. – Only a few, rather specialized, organisms are able to convert chloride to organic chlorine, even though it appears the ability among organisms to transform chloride to organic chlorine is more the rule than the exception. – All chlorinated organic compounds are persistent and toxic, even though the vast majority of naturally produced organic chlorine are neither persistent nor toxic. – Chlorine is mainly found in its ionic form in the environment, even though organic chlorine is as abundant or even more abundant than chloride in soil. Considering the important role of chlorine⁵⁸ in organic synthesis, it is a small step to assume that the evolution of the metabolisms of organisms (especially animals) results in the use of chloride, which is transformed into Cl atoms used in specific organosynthesis reactions and also provide functional molecules. Again, hydrogen peroxide (cf. eq. (5.78)) and hydroxyl (cf. eq. (5.111)) play a central role in oxidizing chloride in aqueous solution: H2 O2

H+ +Cl−

(−H2 O)

(−H2 O)

HCl ←󳨀󳨀󳨀󳨀→ HOCl ←󳨀󳨀󳨀󳨀→ Cl2

and OH + Cl− → OH− + Cl .

(5.414)

The ubiquitous role of chloride (as dissolved sodium chloride) in animal and human cells and blood plasma is manifold. As just discussed, it provides Cl for organosynthesis and to control electrolytic properties such as osmosis (a process where water molecules move through a semipermeable membrane from a dilute solution into a more concentrated solution), for nutrient and waste transport, as well as to provide electrical gradients (based on conductivity) for information transfer through neurons.

58 . . . and other more reactive halogens; but Cl is only industrially used due to its cheap production from electrolysis.

428 | 5 Substances and chemical reactions in the climate system

5.7.2 Formation of sea salt and chlorine degassing Various physical processes generate SSAs, especially the bursting of entrained air bubbles during whitecap formation, resulting in a strong dependence on wind speed (see Volume 2 for more deails). Sea salt particles cover a large size range (about < 0.5 μm to > 10 mm diameter) and have a correspondingly wide range of atmospheric lifetimes. SSAs have multiple impacts (besides other PM categories) on atmospheric properties: responding to climate by optical properties (Mahowald et al. 2006), providing CCNs (McGovern et al. 1999, Clarke et al. 2006), being a heterogeneous surface for multiphase chemical reactions, for example, SO2 oxidation (Luria and Sievering 1991), and serving as a source for reactive chlorine (Finlayson-Pitts et al. 2003). The circulating amounts of sea salt are immense (Figure 5.37) and provide chloride (together with sodium) to all parts of the world. Globally, large amounts of fine sea salt (i.e., not removed by sedimentation) are to be assumed to be emitted into the free troposphere and available for degassing processes between 100 and 800 Tg yr−1 as Cl (e.g., Erickson and Duce 1988, Möller 1990). These values are based on total sea salt chloride emissions on the order of 5000 Tg yr−1 . Erickson et al. (1999) estimated (based on global modeling) the integrated annual production of sea salt chloride (Cl− ) to be substantially smaller, at 1785 Tg Cl yr−1 (this is the latest estimation found in the literature) and the subsequent HCl flux to be only 7.6 Tg Cl yr−1 . Due to its ready solubility in water, Cl− is found in all natural waters and is finally transported back to the oceans. < 20 (?)

cloud water R ≤ 0.86

cloud water

mixed aerosol

gaseous HCl

200-400 fine aerosol R = 1.2-2.2

~ 200

~ 50 (?)

sea salt R = 1.2-2.2

D

200-300 (?) W

~150

~ 5000 D

ocean

rain water R ~1.16

500-800

rain water ≤ 50 (?) coarse aerosol R = 0.9-1.5 R ~ 0.86 ~ 150-350

?

gaseous HCl

~ 5500 S

D

60-90

W

~3

S

river run-off ~ 200

continent

Fig. 5.37: The global inorganic chlorine cycle (data from Möller 1990, 2003). S – source, W – wet deposition, D – dry deposition, R – Na/Cl ratio.

5.7 Halogens (Cl, Br, F, and I) |

429

Loss of chlorine from marine PM was observed more than 65 years ago and attributed to surface reactions (acidification) by acids produced from gaseous SO2 and its oxidation onto sea salt particles (e.g., Junge 1954, Duce 1969, Hitchcock et al. 1980): NaCl(s) + H2 SO4 → NaHSO4 (s) + HCl(g) .

(5.415)

This results in chloride deficit in atmospheric aerosol particles. However, the Cl− deficit in atmospheric aerosol particles seems to have been known for even longer and was explained by Cauer (1949) through HCl degassing. McInnes et al. (1994) have shown that in the marine remote boundary layer, Cl depletion from individual particles is highly variable, in a range from submicrometer- to above micrometer-sized particles. Only in the past 15 years has evidence been found that SSA also occurs in the very fine fraction below 250 nm (down to 10 nm) depending on the sea state (Nilsson et al. 2001, Geever et al. 2005, Clarke et al. 2006). Polluted air masses may result in a complete loss of chloride (Roth and Okada 1998). During their study in northern Finland in summer 1996, Kerminen et al. (1998) found that the fraction of chloride lost from SSAs increased with decreasing particle size for all samples. They also estimated the average contribution from sulfate (after subtraction of (NH4 )2 SO4 ), nitrate, and selected organic anions (methanesulfonate, oxalate). The overall calculated loss was very close to 100% for submicrometer particles (up to 1.8 μm), about 43–65% for particles up to 7.5 μm and slightly less for particles in the range 7.5–15 μm, and seems to depend on the air transport time over continental areas and the concentration of SSAs in air. The acid replacement according to eq. (5.415) was described by Brimblecombe and Clegg (1988) as equilibrium, HX(g) 󴀘󴀯 HX(aq) 󴀘󴀯 H+ (aq) + X− (aq)

− (X = HSO−4 , SO2− 4 , NO3 ) , (5.416)

H+ (aq) + Cl− (aq) 󴀘󴀯 HCl(g) ,

(5.417)

and argued that only for strong acids (e.g., H2 SO4 , HNO3 ) with Heff > 10−3 mol L−1 atm−1 does reaction (5.418) take. Remember that H2 SO4 does not exist (in contrast to HNO3 ) in molecular form in air; hence, its formation from interfacial SO2 oxidation was presumed to carry reaction (5.415): NaCl(p) + H+ (p) → Na+ (p) + HCl(g) .

(5.418)

In what follows we will discuss in detail that some NO y species might react with particulate NaCl (or Cl− ) gaining primarily Cl atoms and subsequently HCl (x = 1, 2 and z = 2, 3): 2 NOy

hν

RH

(−NaNOz )

(−NOx )

(−R)

NaCl(p) 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ ClNO x (g) 󳨀󳨀󳨀󳨀󳨀→ Cl 󳨀󳨀󳨀→ HCl(g) .

(5.419)

Cl degassing observed also from continental PM is mainly believed to occur by gaseous HNO3 adhering to particles (Pakkanen 1996, Keene and Savoie 1998, Zhuang et al. 1999, Yao et al. 2003, Xiu et al. 2004, Wai and Tanner 2004). Guimbaud et al. (2002)

430 | 5 Substances and chemical reactions in the climate system

studied this acid displacement in the laboratory to be diffusion limited in the gas phase. In other words, after uptake, all HNO3 taken up is readily displaced as HCl in the gas phase. Because of recrystallization, nitrate can replace all chloride even in the deeper layers of sea salt crystals (Finlayson-Pitts et al. 2003). In Figure 5.37, the measured ratio Rmeas = [Na]/[Cl] is given for different chlorine reservoirs; in seawater Rseawater = 0.86 (molar ratio; mass ratio 0.56). Thus, deviations to higher values indicate Cl loss. However, over continents and in polluted air masses, so-called excess chloride may occur, which is mainly caused by human activity (coal combustion, waste incineration, salt industry). This excess chloride can be calculated according to eq. (5.420); however, there are two preconditions: (a) that there are no sodium sources other than sea salt and (b) that the local reference value of Rsea salt is known. In older literature, instead of Rsea salt , authors used the seawater bulk value Rseawater = 0.86: [Cl− ]excess = [Cl− ]seasalt (

[Na+ ]sample Rseasalt − 1) = [Cl− ]sample − . Rsample Rseasalt

(5.420)

The Cl loss x (in %) in a sample can be calculated according to x = 100 (1 −

0.86 ) , Rseasalt

(5.421)

where Rsea salt is the reference value at a given site. Möller (1990, 2003) estimated, based on experimental data for sea salt entering the Northern European continent, Rsea salt = 1.16, which corresponds to x = 26% mean Cl loss. Taking into account that sea salt is already depleted in Cl to a large extent (50–75%) when entering the continents (and will be further depleted by acid reaction during transport over the continents), the HCl flux from acid degassing must be much larger than the foregoing estimate by Erickson et al. (1999) and could be 200–400 Tg yr−1 (Figure 5.37). It is worth noting that, despite large differences in the estimates of the tropospheric inorganic chlorine budget, the freshwater-to-ocean transport of chloride agrees with the 220 Tg estimated by Graedel and Keene (1996, 1999). This run-off is due to wet deposition of fine SSAs transported to the continents, which is to a large extent Cl depleted. At this moment, keeping the following sections on gas-phase and aqueous-phase chemistry of halogens in mind, we return to NaCl degassing chemistry. Besides the “simple” HCl degassing due to the acidification of sea salt particles (or any kind of chloride-containing atmospheric particles), we have seen already with eqs. (5.184) and (5.187) the formation of nitryl and nitrosyl chloride from reactions between solid NaCl and gaseous N2 O5 and NO2 , respectively. Reaction (5.235) shows the formation of ClNO from NO+ + Cl− . Hence, we can speculate that NO+ (and NO+2 ) are the key species (Chapter 5.3.5.2) in gaining ClNO (and ClNO2 ). Finally, after degassing of these compounds, subsequent photolysis results in the formation of Cl atoms (see next section for Cl chemistry). Schroeder and Urone (1974) first mentioned the importance of the NO2 + NaCl reaction as a source of ClNO. However, the formation of ClNO (Cl–N=O)

5.7 Halogens (Cl, Br, F, and I) |

431

had already been investigated by Robbins et al. (1959). These authors proposed the formation of HCl secondary from primary ClNO formation (its photolysis was not yet known): NaCl(s) + 2 NO2 (g) → NaNO3 (s) + ClNO ClNO + H2 O → HCl + HNO2 Likely Cauer (1939) first proposed a mechanism of Cl degassing from sea salt, later confirmed by Yeatts and Traube (1949): O3 (g) + Cl− (aq) → O2 (g) + ClO− ClO− + 2 H+ + Cl− → Cl2 + H2 O Eriksson (1959, 1960) argued that this reaction is too slow to become apparent in the atmosphere. It is remarkable that already in the early nineteenth century ClNO formation was observed when nitric acid affects powdered NaCl (Davy 1831).⁵⁹ Lunge and Pelet (1895)⁶⁰ investigated the reaction between HCl (or NaCl + H2 SO4 ) and HNO3 in solution and proposed the following processes⁶¹: HCl + HNO3 󴀘󴀯 ClNO2 + H2 O ClNO2 + NO → ClNO + NO2 ClNO2 + 2 HCl → ClNO + Cl2 + H2 O Hence, we can summarize chlorine degassing from sea salt particles in air simply via Cl− + NO+ → ClNO Cl− + NO+2 → ClNO2 whereby NO+ and NO+2 are obtained from different NO y compounds, NO2 , N2 O3 (NO + NO2 ), N2 O5 (NO2 + NO3 ), and HNO3 . Likely under acid- or water-catalyzed processes, internal electron transfer occurs: (N2 O5 )O2 N–O–N(=O)2 → O2 N⊕ –O⊖ –NO2 → NO+2 + NO−3 (N2 O3 )ON–O–N(=O)2 → ON⊕ –O⊖ –NO → NO+ + NO−2 (N2 O4 )O=N–O–N(=O)2 → ON–O⊖ –⊕ NO2 → NO−2 + NO+2 Furthermore, HNO2 might form NO+ (eq. (5.217) and HNO3 can formally be seen in equilibrium with nitronium (see also eq. (5.239)) and nitrate, the composites of N2 O5 : HNO3 + HNO3 󴀘󴀯 NO+2 + NO−3 + H2 O 59 E. Davy (1831) Philosophical Magazine 9, 355; Proceedings of the Royal Society 3, 27 (cited after Gmelin 1927). 60 Lunge, U. L. and Z. Pelet (1895) Zeitschrift für angewandte Chemie 8, 3 (cited after Gmelin 1927). 61 Note that a mixture of concentrated HCl and HNO3 is called aqua regia (dissolves gold), where ClNO, ClNO2 , and free Cl occur as reactive species.

432 | 5 Substances and chemical reactions in the climate system

whereas the process particulate Cl−

hν

N2 O5 (g) → N2 O5 (aq) 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀−→ ClNO2 󳨀󳨀󳨀󳨀󳨀→ Cl (−NO2 ) (−particulate NO3 )

(5.422)

is currently (including many measurements of nitryl chloride at different sites around the world) under consideration for modeling of ozone formation and the radical budget in the morning hours (because of nocturnal N2 O5 chemistry). N2 O3 chemistry (occurring day and night) is not considerd in the atmospheric chemistry community despite the fact that the reaction between N2 O3 and HCl has been known for a long time as double substitution and was recently investigated again (Rosadiuk 2015): HCl + N2 O3 → ClNO + HNO2 Therefore, the pathway particulate Cl−

hν

N2 O3 (g) → N2 O3 (aq) 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀−→ ClNO 󳨀󳨀󳨀󳨀󳨀→ Cl (−NO) (−particulate NO2 )

(5.423)

is recommended to include in models of atmospheric chemistry. Moreover, nitrite (or nitrous acid) is formed, being a source for OH radicals after photolysis (eq. (5.193a). In the N2 O5 pathway, NO2 can subsequently produce O3 (eq. (5.15) and subsequent reaction eq. (5.11)). The importance of Cl atoms for attacking organic compounds is evident in these mechanisms, in addition to OH from HNO2 photolysis and later in the day from O3 photolysis, thereby providing additional free radicals (x = 1, 2 and z = 2, 3); NO y = NO2 , HNO3 , N2 O3 and N2 O5 : 2 NOy

hν

RH

(−NaNOz )

(−NOx )

(−R)

NaCl(p) 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ ClNOx (g) 󳨀󳨀󳨀󳨀󳨀→ Cl 󳨀󳨀󳨀→ HCl(g) .

(5.424)

5.7.3 Gas-phase chemistry In this and the following section, we will treat mainly chlorine chemistry, despite the fact that the literature is full of bromine and iodine atmospheric chemistry (the interested reader is encouraged to conduct a search on it); see Saiz-Lopez et al. (2012) for a review. We start with a brief overview on general reactions and cycles (X, Y = Cl, Br, I). Organic and inorganic halogen species will be rapidly photolyzed to form halogen atoms (R – organic residue): RX (and XY) + hν → R (and Y) + X .

(5.425)

The halogen atoms will most likely react with ozone (99% of Br reacts with O3 ): X + O3 → XO + O2 .

(5.426)

5.7 Halogens (Cl, Br, F, and I) | 433

Halogen atoms are regenerated (photolysis is important for X = I and Br but to a minor extent for Cl) through XO + hν → X + O ,

(5.427)

XO + NO → X + NO2 ,

(5.428)

XO + YO → X + Y + O2 ,

(5.429a)

XO + YO → OXO + Y ,

(5.429b)

XO + YO → XY + O2 .

(5.429c)

Reaction with hydroperoxyl radical and aldehydes turns the atoms back into hydrogen halides: X + HO2 → HX + O2

(X = Cl, Br, and I) ,

X + HCHO → HX + CHO (X = Cl and Br) .

(5.430) (5.431)

The only relevant (but slow) gas phase converting hydrogen halides back to the atoms is the reaction with hydroxyl: HX + OH → X + H2 O .

(5.432)

Besides HX, other key species are HOX and XONO2 (the latter in polluted air): XO + HO2 → HOX + O2 ,

(5.433)

XO + NO2 → XONO2 .

(5.434)

Photolysis of HOX leads to a photo-stationary state between XO and HOX, with [HOX]/[XO] ranging from 1 to 10: HOX + hν → X + OH .

(5.435)

Halogen nitrates are rapidly converted back by photolysis: XONO2 + hν → XO + NO2 .

(5.436)

Finally, gaseous species can enter interfaces of aerosol particles, cloud droplets, icy surfaces, and so forth, entering into aqueous or heterogeneous reactions: XONO2 + H2 O(aq) → HNO3 + HOX ,

(5.437)

XONO2 + HY → HNO3 + XY ,

(5.438)

XNO2 (g) + NaX(s) → NaNO2 (s) + X2 (g) ,

(5.439)

N2 O5 + NaX(s) → NaNO3 (s) + XNO2 (g) , NO3 (g) + NaX(s) → NaNO3 (s) + X(g) .

(5.440) (5.441)

434 | 5 Substances and chemical reactions in the climate system

Based on our present knowledge, fluorine chemistry is unimportant for the troposphere because F (if formed) very rapidly reacts to HF, which subsequently turns heterogeneously into stable fluorides, with even SiO2 turning into fluorosilicates (SiF2− 6 ). We have recently learned that huge amounts of gaseous hydrochloric acid (HCl) and probably ClNO x are being permanently released from sea salt above the oceans as well as the continents. However, hydrogen halides (HCl, HBr, HI) react with OH but relatively slowly (only HI reacts quickly): k 5.422 = 7.8 ⋅ 10−13 cm3 molecule−1 s−1 , k HI = 7.0 ⋅ 10−11 cm−3 molecule−1 s−1 : HCl + OH → H2 O + Cl .

(5.442)

The photolysis of HCl is too slow (even in the stratosphere) to provide atomic Cl. Gaseous HCl is in equilibrium with particulate chloride. In summer 2006 (12–30 June) we studied the Cl partitioning (Möller and Acker 2007) during a campaign at the research station Melpitz near Leipzig (Germany, 51°32 N, 12°54 E; 87 m a.s.l.). For the first time, HNO3 and HCl in the gas phase and chloride and sodium in the particle phase were measured at high time resolution, together with a number of other atmospheric components (in the gas and particulate phases) as well meteorological parameters. On most of the 19 measurement days the HCl concentration showed a broad maximum around noon/afternoon (on average 0.1 μg m−3 ) and much lower concentrations at night (0.01 μg m−3 ), with a high correlation with HNO3 . The data support that – HNO3 is responsible for Cl depletion in continental air. – There is an increase in the Na/Cl ratio due to faster HCl removal during continental air mass transport. – On average 50% of total Cl exists as gas-phase HCl. The time series for HCl and HNO3 are shown in Figure 5.38, exhibiting a pronounced diurnal variation with usually low nocturnal values and high values during the day, reaching a maximum around noon. Remarkably, even the fine structure in temporal variation is identical for HCl and HNO3 , resulting in a high correlation: [HCl] = 0.001 + 0.05[HNO3 ]

r2 = 0.79 ;

n = 800

On average, 83% Cl depletion, calculated by Cldepl = 1 − Rsea /Rsample , were observed in PM with only slight variation (Figure 5.38), attributable mainly to the diurnal cycle. The results demonstrate the important role of continental Cl degassing by an acid replacement process, very likely only driven by gaseous HNO3 . Chlorine atoms, even if present in the troposphere in small concentrations, can have a significant effect on tropospheric oxidation and can impact the production of ozone in urban environments. Atomic Cl is extremely reactive toward VOCs, with rate coefficients that are, with a few exceptions, at least an order of magnitude larger than those of hydroxyl radicals (OH). In addition, Cl reacts rapidly with some compounds,

5.7 Halogens (Cl, Br, F, and I) | 435

HCl (in μg m-3)

concentration (in μg m-3)

HNO3 5 4 3 2 1 0

1.0 0.8 0.6 0.4 0.2 0.0

1.4 1.0 0.6 0.2 0.0 15

17

19

21

23

25

27

29

date (day of June 2006) Fig. 5.38: Time series of HNO, HCl, and particulate sodium (Na+ ) and chloride (Cl− ) at Melpitz, June 2006.

such as alkanes, with which OH is relatively unreactive. Recent measurements of anthropogenically derived photolabile Cl precursors (ClNO2 and Cl2 ) identify a mechanism by which anthropogenic pollution contributes to the production of Cl. The detection of these species in midcontinental areas has expanded the potential impact of Cl to tropospheric oxidation chemistry. Even in the presence of strong photochemical sources, predicted ambient Cl concentrations are small (< 106 atoms cm−3 ). The spatially and temporally averaged (i.e., hemispheric to global scale over months to years) concentrations in the marine boundary layer were estimated to be on the order of 103 atoms cm−3 (Young et al. 2014 and references therein). The main source of Cl atoms is the photolysis (eqs. (5.186) and (5.187); also see Table 5.35) of nitryl chloride (ClNO2 ) and nitroxyl chloride (ClNO), which are formed at night by reactions of N2 O5 and N2 O3 on particles containing chloride (eqs. (5.422), (5.423), and (5.440)). On the next day, sunlight breaks ClNO2 down into Cl radicals and nitrogen dioxide (NO2 ). The Cl radicals can then attack the GHG methane (CH4 ) and VOCs, and subsequently gained peroxy radicals turn the NO 󴀗󴀰 NO2 cycle to the formation of ozone (O3 ). Whereas this formation pathway was detected already in 1989 (Finlayson-Pitts et al. 1989, Behnke et al. 1997), confirmation of its atmospheric role did not occur until 2008, when Osthoff et al. (2008) observed high ClNO2 concentrations in coastal regions and ship plumes, places where chloride from sea salt meets pollution, and highlighted by Glasow (2010). If other continental regions also act as sources of ClNO2 , then the cycling of nitrogen oxides and Cl through this compound is of global relevance. In recent years, many measurements of ClNO2 have been carried out (Wang et al. 2017 and references therein).

436 | 5 Substances and chemical reactions in the climate system

Tab. 5.35: Photodissociation of inorganic halogen compounds in the troposphere. HOCl ClO OClO ClOO Cl2 O Cl2 O2 ClNO ClNO2 Cl2 O7 ClO4 ClONO2 Cl2

→ → → → → → → → → → → →

OH + Cl Cl + O ClO + O Cl + O2 and ClO + O Cl + ClO and Cl2 + O 2 ClO Cl + NO Cl + NO2 ClO4 + ClO3 ClO2 + O2 ClO + NO2 2 Cl

HBr Br2 HI

→ → →

H + Br 2 Br H+I

} } } } } } } } } } } } } also for Br and I } } } } } } } } } } } } } }

The photolysis of halogenated organic compounds in the troposphere (i.e., at wavelengths > 300 nm) is insignificant. The only possible decomposition pathway is by OH attack, but at relatively slow rates leading to lifetimes of about 2 years for CH3 Cl. Nevertheless, according to Fabian et al. (1996), less than 10% of the amount of methyl chloride emitted reaches stratosphere. The OH oxidation pathway (k CH3 Cl = 3.6 ⋅ 10−14 cm3 molecule−1 s−1 and k CH3 F = 2.1 ⋅ 10−14 cm3 molecule−1 s−1 ) is given by OH

O2

NO

(−H2 O)

(−NO2 )

(−NO2 )

CH3 Cl 󳨀󳨀󳨀󳨀󳨀→ CH2 Cl 󳨀󳨀󳨀󳨀󳨀→→ O2 CH2 Cl 󳨀󳨀󳨀󳨀󳨀→ HCHO + Cl .

(5.443)

Methyl halides with ≥ 3 halogens react too slowly (k < 10−16 cm3 molecule−1 s−1 ) to cause measurable decomposition in the troposphere. Other photolytic pathways are listed in Table 5.35; they always break down halogen compounds into halogen atoms and monoxides. Therefore, “storage” in aerosol particles and interfacial formation or the release of halogen compounds is important for atmospheric transportation and gaining reactive halogens. Cl atoms (and other halogens with decreasing rates from F over Cl to Br; no reactions with I are described) react similarly to OH (e.g., in the oxidation of VOCs) (Cai and Griffin 2006) with HY compounds abstracting an H atom and gaining HX (X = Cl, Br, I): CH4 + F → CH3 + HF CH4 + Cl → CH3 + HCl HCHO + Cl → HCO + HCl HCHO + Br → HCO + HBr

k 5.444 = 6.3 ⋅ 10−11 cm3 molecule−1 s−1 , −13

k 5.445 = 1.0 ⋅ 10

−11

k 5.446 = 7.2 ⋅ 10

−12

k 5.447 = 1.1 ⋅ 10

(5.444)

3

−1 −1

,

(5.445)

3

−1 −1

,

(5.446)

3

−1 −1

.

(5.447)

cm molecule s cm molecule s cm molecule s

5.7 Halogens (Cl, Br, F, and I) |

437

Whereas the role of halogens in the depletion of stratospheric ozone has been studied for several decades, the role of halogens in tropospheric O3 reactions in marine and polar environments has only been studied in the past 20 years. In competition to the above mentioned reactions, halogen atoms (F, Cl, Br, and I) react with ozone, k 5.448 = 1.2 ⋅ 10−11 cm3 molecule−1 s−1 : Cl + O3 → ClO + O2 .

(5.448a)

Simonaites and Heicklen (1975) suggested an additional pathway to ClO3 , which was adopted by Catling et al. (2010) as a likely first step in the formation of stratospheric perchloric acid (HOClO3 ) (k 5.449 < 1 ⋅ 1031 [M] cm3 molecule−1 s−1 ): Cl + O3 + M → ClO3 + M , Cl + O2 → ClOO

followed by ClOO + NO → ClO + NO2 .

(5.448b) (5.449)

Halogen atoms also react with HO2 to give HCl (or HBr), k 5.433 = 3.5 ⋅ 10−11 cm3 molecule−1 s−1 : Cl + HO2 → HCl + O2 ,

(5.450a)

Cl + HO2 → ClO + OH .

(5.450b)

However, the main sink of Cl atoms is via reaction with methane (eq. (5.445)). The radical chlorine monoxide undergoes many reactions. ClO can either photodissociate (Table 5.35) to Cl atoms or react with O3 (as with BrO and IO), k 5.451 < 1.5 ⋅ 10−17 cm3 molecule−1 s−1 , k IO < 10−15 cm3 molecule−1 s−1 : ClO + O3 → ClOO + O2 ,

(5.451a)

ClO + O3 → OClO + O2 .

(5.451b)

All halogen monoxides (ClO, BrO, and IO) react with NOx : ClO + NO → Cl + NO2 M

ClO + NO2 󳨀→ ClONO2

k 5.452 = 1.7 ⋅ 10−11 cm3 molecule−1 s−1 ,

(5.452)

k 5.453 = 7 ⋅ 10−11 cm3 molecule−1 s−1 .

(5.453)

The reaction with HO2 yields hypohalogenic acids (HOCl, HOBr, and HOI; structure: H–O–X), k 5.454 = 6.9 ⋅ 10−12 cm3 molecule−1 s−1 : ClO + HO2 → HOCl + OH ,

(5.454a)

ClO + HO2 → HCl + O3 .

(5.454b)

With hydroxyl it reacts according to ClO + OH → Cl + HO2 (90%) ,

(5.455a)

ClO + OH → HCl + O2 (10%) ,

(5.455b)

ClO + OH → ClOOH .

(5.455c)

438 | 5 Substances and chemical reactions in the climate system

Clorine monoxide reacts with itself to yield a dimer and several products: ClO + ClO → Cl2 O2 (O=Cl–Cl=O) ,

(5.456a)

ClO + ClO → OClO + Cl ,

(5.456b)

ClO + ClO → Cl2 + O2 ,

(5.456c)

ClO + ClO → ClOO + Cl .

(5.456d)

It is produced from the reaction between hypochlorous acid and hydroxyl: HOCl + OH → ClO + H2 O .

(5.457)

The fate of OClO (chlorine dioxide) and ClOO (chloroperoxo radical) is mainly photolysis (Table 5.35). Another pathway of OClO is important for the formation of chlorine trioxide (Wayne et al. 1995): OClO + O3 → ClO3 + O2 , OClO + O + M → ClO3 + M .

(5.458) (5.459)

Chlorine trioxide generates perchloric acid M

ClO3 + OH 󳨀→ HOClO3

k 5.451 < 6.7 ⋅ 1013 cm3 molecule−1 s−1

(5.460a)

and turns back with OH into chlorine dioxide: ClO3 + OH → OClO + HO2 .

(5.460b)

However, textbook knowledge says that ClO3 dimerizes almost to C2 O6 , which can be regarded as chlorylperchlorate ClO2 ⊕ ClO4 ⊖ . It likely decays photolytically to chlorine dioxide ClO2 (not ClOO) and ClO4 radical. The atmospheric formation of perchlorate is accepted, but the photochemical pathway remains speculative. Chlorine oxides are readily generated from chlorine inputs to the atmosphere (eq. (5.448)) and reaction pathways that include O3 can produce perchloric acid (HClO4 ). Thus far, it is likely that different chlorine radicals and oxides interact with the condensed phase and undergo aqueous chemical conversions, ultimately to perchlorate (Chapter 5.7.4). Mixtures of chlorine and ozone in contact with water generate as final products perchlorate ClO−4 and Cl− , as found by Allmand and Spinks (1929). Perchloric acid exists as a gas in air and is a stable end product of atmospheric chemistry in the condensed phase due to its resistance to photolysis (Simonaitis and Heicklen 1975): O3

O3

O3

(−O2 )

(−O2 )

(−O2 )

OH

Cl 󳨀󳨀󳨀󳨀→ ClO 󳨀󳨀󳨀󳨀→ OClO 󳨀󳨀󳨀󳨀→ ClO3 󳨀󳨀→ HOClO3 . Perchloric acid was characterized by Simonaites and Heicklen (1975) as a sink for “missing chlorine” in the budget of reactive stratospheric chlorine (in Chapter 5.7.1

5.7 Halogens (Cl, Br, F, and I) | 439

NaCl(s)

RCl

degassing

Cl2

hν (-R)

hν

OH (-H2O)

Cl

HCl RH (-R) NO (-NO2)

HO2 (-O2) O3 (-O2)

hν

ClONO2

NO2

O3 (-O2)

hν HO2 (-O2)

HOOCl

ClO

hν hν

ClO2

hν

HO2 (-O2)

HOCl

Fig. 5.39: Simplified scheme of gas-phase chlorine chemistry.

we mentioned that perchlorate is found in certain arid places on Earth, dry deposited and accumulated over geological periods of time). Martin et al. (1979) also proposed a heterogeneous pathway: H2 SO4

ClO 󳨀󳨀󳨀󳨀󳨀→ HClO4 + HCl + products .

(5.461)

In reaction (5.455c) peroxohypochlorous acid (ClOOH) is generated and was proposed to be relatively stable (Lee and Rendell 1993). The reaction is too slow in the troposphere but could be of interest in the stratosphere (in solution we will encounter ClOOH in what follows). Figure 5.39 shows a simplified tropospheric chlorine chemistry (those of bromine and iodine are similar). Chlorine chemistry is too slow for ozone depletion in the troposphere, but bromine and, in particular, iodine – combined with heterogeneous chemistry (see below) – lead to ozone depletion in marine environments by the following catalytic cycles (termed bromine explosion) (Barrie and Platt 1995, Platt and Mortgaat 1999, Wennberg 1999). Intense plumes of bromine monoxide (BrO) – up to 50 ppt – are regularly observed over sea ice during polar spring by satellite, and several studies have shown that the plumes are often of tropospheric origin and occur in conjunction with widespread ozone depletion.⁶² It is concluded that weather conditions associ62 Reactive bromine plays a key role in oxidizing gaseous elemental mercury to reactive gaseous mercury compounds (Simpson et al. 2007). This increases deposition of mercury in snow and ice, which is harmful to the environment. Bromine explosion events therefore not only cause ozone depletion events but also atmospheric mercury depletion events during polar spring.

440 | 5 Substances and chemical reactions in the climate system

ated with the polar cyclone favored the bromine activation cycle and blowing snow production to form Br2 from Br− in a condensed-phase substrate (Chapter 5.7.4), which is released to the atmosphere (Blechschmidt et al. 2016 and references therein). The gas-phase molecular bromine is photolyzed in the presence of sunlight and oxidized subsequently by ozone to form BrO. The latter then reacts with HO2 to form HOBr, which is eventually removed from the atmosphere by wet scavenging. The exact chemical reaction cycle and the substrate from which bromine is initially released to the gas phase remain unclear: Br2 + hν → 2Br ,

(5.462) −12

Br + O3 → BrO + O2

k 5.463 = 1.2 ⋅ 10

3

−1 −1

cm molecule s

BrO + HO2 → HOBr + O2 , +

,

(5.463) (5.464)

−

HOBr + [H + Br ]s/aq → Br2 + H2 O .

(5.465)

The net budget of this sequence results in the oxidation of particulate bromide and its transformation to gaseous bromine atoms, which turn into BrO, causing ozone depletion according to 2 O3 → 3 O2 : hν+2 O3 +HO2 +H+

(Br− )aq + BrO 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ 2 BrO .

(5.466)

(−3 O2 −H2 O)

Hence, effectively, one BrO molecule is converted into two BrO molecules by the oxidation of bromide from a suitable surface. The “catalytic” ozone depletion cycle follows, which results in the net process 2 O3 → 3 O2 : Br + O3 → BrO + O2 ,

(5.463)

BrO + O3 → Br + 2 O2 , BrO + BrO → 2 Br + O2

(5.467) −12

k 5.468 = 2.7 ⋅ 10

3

−1 −1

cm molecule s

.

(5.468)

It is worth noting that the bromine explosion mechanism only occurs on sea salt with pH < 6.5, requiring acidification by strong acids such as HNO3 and H2 SO4 . With respect to iodine chemistry, the major source of iodine is macroalgae in seawater, which release organoiodine compounds that produce atomic iodine after photolysis in air. What follows is a list of some of the main reactions: I + O3 → IO + O2 , IO + hν → I + O

(5.469)

with subsequent

O + O3 → O3 ,

(5.470)

IO + IO → I2 + O2 ,

(5.471a)

IO + IO → 2 I + O2 , IO + IO → I + IO2 IO + IO → I2 O2 I2 + OH → HOI + I IO + ClO → ICI + O2

(5.471b) −11

k 5.471c = 3.8 ⋅ 10

−11

k 5.471d = 9.9 ⋅ 10

−10

k 5.472 = 2.1 ⋅ 10

−12

k 5.473 = 2.4 ⋅ 10

3

−1 −1

,

(5.471c)

3

−1 −1

,

(5.471d)

cm molecule s

cm molecule s 3

−1 −1

,

(5.472)

3

−1 −1

.

(5.473)

cm molecule s cm molecule s

5.7 Halogens (Cl, Br, F, and I) | 441

5.7.4 Aqueous and interfacial chemistry As already discussed, the surface of sea salt provides an interface for many heterogeneous reactions. We introduced HCl release (eq. (5.415)) and especially the reactions of N2 O5 (eq. (5.184)) and NO2 (eq. (5.185)) with particulate NaCl and subsequent release of reactive ClNO2 and ClNO, which are rapidly photolyzed (eqs. (5.187) and (5.186)), yielding an important source of Cl radicals (it also happens principally with bromine and iodine): NOy

hν

(−NaNO3 )

(−NOx )

NaCl(s) 󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ ClNO x (g) 󳨀󳨀󳨀󳨀󳨀→ Cl(g) .

(5.474)

Another pathway for releasing reactive chlorine from the aqueous phase is the oxidation of HCl (or chloride) in solution by H2 O2 , as described in older literature; here, we present the following speculative scheme of multiphase chemical production of atomic Cl from dissolved HCl (its oxidation by H2 O2 is described in Gmelin 1927)⁶³: H O

H+ +Cl−

degassing

2 2 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀→ [HCl 󳨀󳨀󳨀󳨀→ HOCl 󳨀 ← 󳨀󳨀 Cl2 ]

H2 O

hν

RH

󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ Cl2 (g) 󳨀󳨀→ Cl(+Cl) 󳨀󳨀→ HCl (+R) . aqueous

(5.475) Assuming photocatalytic H2 O2 formation in liquid films (eq. (5.96)), the foregoing scheme would represent another radical source via the aqueous phase without consumption of gas-phase-produced oxidants and a recycling between HCl and atomic Cl. This scheme would also support the findings of increasing chlorination together with (which, as we know, contains TiO2 ) desert dust deposition in oceans. O−2 as a precursor of H2 O2 has recently been measured directly at ocean water surfaces (Heller and Crott 2010). It seems that the aqueous particulate (namely sea-salt-containing) phase is a source of reactive halogen compounds, summarized in what follows. Key reactions are HX + H2 O2 gaining X2 (X = Cl and Br), already shown by Connick (1947): NO+ + Cl− → ClNO ,

(5.235)

NO+2

+ Cl → ClNO2 ,

(5.476)

HCl + H2 O2 → HOCl + H2 O ,

(5.477)

−

−

+

HOCl + Cl + H → Cl2 + H2 O , HBr + H2 O2 → HOBr + H2 O ,

(5.478) (5.479)

−

+

(5.480)

−

+

(5.481)

HOBr + Br + H → Br2 + H2 O , HOBr + Cl + H → BrCl + H2 O .

63 This reaction chain presents an indirect oxidation of organic compounds in the gas and aqueous phases through hydrogen peroxide where reactive chlorine cycles; note that in the first step of Cl− + H2 O2 , an OH radical is likely generated from H2 O−2 (eq. (5.101)).

442 | 5 Substances and chemical reactions in the climate system

Reactions (5.477) and (5.478) can be described by two different mechanisms: Cl− + H2 O2 󴀘󴀯 Cl− − [HO⊕ − ⊖ OH] → HOCl + OH− , H2 O

Cl

Cl− + H2 O2 → Cl + H2 O−2 󳨀→ Cl2 + OH + OH− 󳨀󳨀󳨀→ HOCl + Cl− + OH + H2 O . Bromine chloride (BrCl) is in the following equilibria, hence generating bromine: BrCl + Br− 󴀘󴀯 Br2 Cl− , −

−

Br2 Cl 󴀘󴀯 Br2 + Cl .

(5.482) (5.483)

The important reactions (5.478), (5.480), and (5.481) proceed likely via an internal shift from covalent to ionic bonding; the short-lived radical cation Cl+ undergoes several reactions in solution (see subsequent discussion). The following scheme also explains why the formation of Cl2 proceeds only in acid solution, whereas in alkaline solution hypochlorite is obtained: H+ +Cl−

HOCl 󴀘󴀯 [HO⊖ ] − [Cl⊕ ] 󳨀 󳨀󳨀󳨀󳨀󳨀→ Cl2 ,

(5.484)

(−H2 O)

OH−

HOCl 󴀘󴀯 [HO⊖ ] − [Cl⊕ ] 󳨀󳨀󳨀→ [HO⊖ Cl⊕ –OH− ] → H2 O + − OCl .

(5.485)

The aqueous chlorine chemistry was studied for a long time because of its strong oxidizing properties, and chlorine was used as a cleansing and disinfecting agent already in the nineteenth century. Chlorination is an ancient process used to treat drinking water as well as wastewater (Deborde and Gunten 2008, Stefan 2018). In aqueous solution, hypochlorous acid HOCl (and HOBr and HOI) is produced by Cl2 hydrolysis (inverse reaction in foregoing scheme in eq. (5.478)): k 5.486 = 0.4 cm3 molecule−1 s−1 : Cl2 + H2 O → HOCl + H+ + Cl−

K5.486a = 5.1 ⋅ 10−4 L mol−1 .

(5.486a)

This reaction can be explained by the characteristics of chlorine and a similar reaction such as between NO+ and Cl− (eq. (5.235)): OH−

Cl2 = [Cl⊖ –Cl⊕ ] 󴀘󴀯 Cl− + Cl+ 󳨀󳨀󳨀󳨀󳨀−→ HOCl . (−Cl )

(5.486b)

The acid and its salts are unstable (reactions (5.487), (5.489), and (5.492)); HOCl is a very weak acid (pKa = 7.5, pKHOBr = 7.7, and pKHOI = 10.6) and so is almost unprotolyzed in solution; this explains why pH < 6.5 is needed for reactions of unprotolyzed HOCl and HOBr in solution. Because dichloroxide is regarded as the anhydride, the following equilibrium holds: 2 HOCl 󴀘󴀯 Cl2 O + H2 O

K5.487 = 8.7 ⋅ 10−3 L mol−1 .

(5.487)

HOCl is a strong oxidizing agent (EHOCl/Cl− = 1.49 V, pH = 0) in acid but not in alkaline solution. Hence, oxidation proceeds only from HOCl or its protonized form HOClH+

5.7 Halogens (Cl, Br, F, and I) | 443

with the direct transfer of Cl (chlorination); similar are the reactions of HOBr and HOI. The adduct HOClH+ explains its decay into H2 O and Cl+ (compare this mechanism with reaction HNO2 + H+ in eq. (5.217)): Cl−

HOCl + H+ 󴀘󴀯 ([H+ ][HO⊖ ] − [Cl⊕ ]) 󳨀󳨀󳨀󳨀󳨀→ Cl+ 󳨀󳨀→ Cl2 . (−H2 O)

(5.488)

HOCl disproportionates (eq. (5.489)) into chloride (Cl− ) and chlorite (ClO−2 ), and afterwards chlorate (ClO−3 ) is gained (eq. (5.490)). Finally, a singlet oxygen radical can be generated (eq. (5.78)) that can oxidize organic compounds (the biocidal application of hypochlorite is based on this property); therefore, solutions containing hydrogen peroxide and reactive chlorine have a high oxidizing capacity: HOCl + ClO− → [HO⊖ –Cl⊕ –⊖ OCl] → HO–Cl=O + Cl− → ClO−2 + HCl , HOCl +

ClO−2

−

→

ClO−3 −

+ HCl ,

(5.490)

ClO + H2 O2 → Cl + H2 O + O2 , 1

−

(5.489)

+

(5.491a) 1

HOCl + H2 O2 → Cl + H2 O + H + O2 .

(5.78)

Equation (5.491a) denotes a complex process whose mechanism is unknown. In acid solution, HOCl decays according to (see the earlier intermediate structure HO⊖ –⊕ Cl) HOCl → OH + Cl , −

+

HOCl 󴀗󴀰 OH + Cl

(5.492a) or

+

+

HOCl + H 󴀗󴀰 H2 O + Cl

pK = 3 to 4 .

(5.492b)

Solutions containing chlorine and hydrogen peroxide also generate peroxohypochlorous acid HOOCl, which decays gaining singlet dioxygen (Holleman-Wiberg 2007): Cl2 + H2 O2 → HOOCl + Cl− + H+ , −

+

HOOCl → Cl + O2 + H . 1

(5.493) (5.494a)

Recently, a reaction between hypochlorite and hydrogen peroxide (see also eq. (5.78)) was proposed in alkaline solution (Castagna et al. 2008) as a mode of electron transfer where the OCl radical can couple together with OH to form peroxohypochlorous acid (ClOOH), which decomposes with a yield of singlet dioxygen: ClO− + H2 O2 → ClO + OH + OH− , ClO + OH → HOOCl , −

(5.495) −

HOOCl + OH → O2 + H2 O + Cl . 1

(5.491b) (5.494b)

However, this pathway of chemical singlet dioxygen formation from MO2 molecules (such as in the reaction between hypochlorite and hydrogen peroxide), where O2 is eliminated with simultaneous conservation of its total spin has long been known (Holleman-Wiberg 2007; oxygen formation in this reaction was known as early as 1847, see Gmelin 1927). The net reaction of the sequence (5.493)–(5.495) is given by aqueous solution

Cl2 + H2 O2 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀→ 2 HCl + 1 O2 .

444 | 5 Substances and chemical reactions in the climate system It is known that Cl− has a high affinity for the scavenging of reactive species (such as NO3 in reaction (5.198)) and possibly OH: Cl− + OH → [Cl− –OH] → Cl + OH− .

(5.496)

If so, it is also likely that OH reacts with chlorite (ClO−2 ) and chlorate (ClO−3 ): ClO−x + OH → [HO–ClO−x ] → OH− + ClOx

(5.497)

O2

ClO−x + OH → [HO–ClO−x ] 󳨀󳨀󳨀󳨀󳨀→ OClO−x

(5.498)

(−HO2 )

Reaction (5.499) – cf. discussion of eq. (5.477) – corresponds to the mechanism in the reaction between sulfite and H2 O2 (eq. (5.310)) i.e., an electron transfer to hydrogen peroxide that decays into hydroxyl radical and hydroxide ion. We cannot exclude the possibility that, analogously to sulfur chemistry, H2 O2 , O3 , and OH play a role in oxidizing chlorite to perchlorate (ClO−4 ); the following reactions are speculative: Cl− + H2 O2 → Cl + H2 O−2 → Cl + OH + OH− , −

−

(5.499)

−

Cl + O3 → [Cl –OOO] → ClO + O2 , −

−

ClO + O3 → O=Cl–O ClO−2 ClO−3

+ O3 → + O3 →

(ClO−2 )

(5.500)

+ O2 ,

(5.501)

−

[ O–Cl(=O)–OOO] → ClO−3 [− OCl(=O)2 ] + O2 , [− O–Cl(=O)2 –OOO] → ClO−4 [− OCl(=O)3 ] + O2 .

(5.502) (5.503)

Perchloric acid (HOClO3 ) is the strongest known acid (pKa ≈ −8); chloric acid (HOClO2 ) is very strong (pKa = −2.7), and chlorous acid (HOClO) is strong (pKa = 2.0); under natural conditions they exist fully dissociated as anions. Chlorate can dimerize, giving dichlorate: − − 2 ClO−3 → Cl2 O2− 6 [ O(O=)Cl–O–Cl(=O)2 O ] .

(5.504)

In summarizing aqueous chlorine chemistry, we obtain a chain of a nucleophilic ozone oxidizing pathway simply explaining the final formation of stable perchlorate; alternatively, a mechanism of electron transfer to H2 O2 is possible: O3

O3

O3

O3

(−O2 )

(−O2 )

(−O2 )

(−O2 )

Cl− 󳨀󳨀󳨀󳨀→ ClO− 󳨀󳨀󳨀󳨀→ ClO−2 󳨀󳨀󳨀󳨀→ ClO−3 󳨀󳨀󳨀󳨀→ ClO−4 , H2 O2

ClO−x (x = 1, 2, 3) 󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀󳨀−→ ClO−x+1 . (−OH−OH )

In aqueous solutions of reactive chlorine compounds such as dichloric acids, the intermediate product peroxochloric acid (HOOCl(=O)2 ) as well as peroxochlorous acid (HOOCl=O) and their individual derivatives and anions (peroxochlorate − OOCl(=O)2 and unknown peroxochlorite − OOCl=O) were detected (Wannowius and Kaiser 2007). Peroxochlorite dimerizes (not to be confused with dichlorate in eq. (5.504)): −

−

− OOCl=O + − OOCl=O → Cl2 O2− 6 [ O–O–Cl–O–Cl(=O)–O–O ] ,

−

−

OOCl(=O)2 + OClO →

Cl2 O2− 6

.

(5.505) (5.506)

5.7 Halogens (Cl, Br, F, and I) | 445

The dimer (it is formally reduced Cl2 O6 – dichlorine hexoxide⁶⁴: ClO−2 –ClO−4 ) decays in an intermolecular redox process into peroxochlorite and chlorate (5.507a) or chlorite and perchlorate (5.507b): − − Cl2 O2− 6 → OOClO + ClO3 , −

Cl2 O2− 6

→ OClO

+ ClO−4

(5.507a)

.

(5.507b)

Little is known about the reactions of chlorine oxides with water. The only anhydrides Cl2 O and Cl2 O7 react to form hypochlorous and perchloric acid, respectively. In older literature the reaction of chlorine dioxide to chloric and perchloric acid is described (disproportionation): ClO2 + ClO2 + H2 O → HClO3 + HClO4 .

(5.508)

The following pathway also is likely: water

ClO3 (g) → C2 O6 (g) 󳨀󳨀󳨀󳨀→ ClO+2 + ClO−4 , ClO+2

−

+ Cl → Cl2 + O2 .

(5.509) (5.510)

In alkaline solution chlorine dioxide combines with chlorite and chlorate, likely via a dimer: OH−

OH−

OClO + OClO → OClOCl(=O)2 󳨀󳨀󳨀→ OClOH(󳨀󳨀󳨀󳨀󳨀→ ClO−2 ) + ClO−3 . −(H2 O)

(5.511)

Chlorate (ClO−3 ) is relative stable; it decays slowly (especially when heating) into chloride and perchlorate (ClO−4 )⁶⁵: 4 ClO−3 → Cl− + 3 ClO−4 .

(5.512)

The electrochemical chain (values given in V as electrode potential) for pH = 0 and pH = 14 is as follows: +1.189

+1.214

+1.645

+1.611

ClO−4 󳨀󳨀󳨀󳨀󳨀→ ClO−3 󳨀󳨀󳨀󳨀󳨀→ HClO2 󳨀󳨀󳨀󳨀󳨀→ HOCl 󳨀󳨀󳨀󳨀󳨀→ +0.36

+0.33

+0.62

+0.326

ClO−4 󳨀󳨀󳨀󳨀→ ClO−3 󳨀󳨀󳨀󳨀→ ClO−2 󳨀󳨀󳨀󳨀→ ClO− 󳨀󳨀󳨀󳨀󳨀→

1 +1.358 Cl2 (g) 󳨀󳨀󳨀󳨀󳨀→ Cl− 2

1 +1.358 Cl2 (g) 󳨀󳨀󳨀󳨀󳨀→ Cl− 2

In summarizing, there occurs a stepwise oxidation from chloride to perchlorate. This chain explains how from chloride aerosol perchlorate can be generated and is present

64 It is the relatively stable dimer of chlorine trioxide ClO3 that does not exist in unimolecular form in air. C2 O6 was formely chloryl perchlorate [ClO+2 ][ClO−4 ]. The dianion is [ClO−2 ][ClO−4 ], an adduct between chlorate and perchlorate. 65 In the human body, perchlorate inhibits the uptake of iodide by the thyroid and thus may lower the amount of thyroid hormone in the body. Insufficient levels of this hormone can cause permanent neurological damage in children.

446 | 5 Substances and chemical reactions in the climate system

in many rain and snow samples (Dasgupta et al. 2005)⁶⁶; note thate oxidation is also likely with dissolved O3 instead of HOCl (see above): H2 O2

±H+

HOCl

HOCl

HOCl (?)

(−H2 O)

(−H2 O)

(−H2 O)

HCl 󳨀󳨀󳨀󳨀󳨀→ HOCl ←󳨀󳨀→ − OCl 󳨀󳨀󳨀󳨀󳨀→ ClO−2 󳨀󳨀󳨀󳨀󳨀→ ClO−3 󳨀󳨀󳨀󳨀󳨀󳨀→ ClO−4 (−H2 O)

In technical applications for purposes of desinfection, solutions of chlorine or hypochlorite are used, gaining reactive species: H2 O

󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀→ HOCl → OH + Cl . Cl2 󳨀 ← 󳨀󳨀 + − H +Cl

Sodium hypochlorite is a cheap and powerful oxidizing agent widely used in household bleaches. Typical household bleach may contain between 1 and 5% NaOCl under alkaline conditions to maintain hypochlorite stability. Hypochlorite exhibits useful actions such as decolorization of soil/stains, breaking of soil matrix, and killing of microorganisms. While it is clear that these actions are due to the oxidative properties of hypochlorite, precise mechanisms are still the subject of debate (many of the previously listed reactions may be realistic, but not all are proved). Much of the confusion arises because of the relatively complex aqueous chemistry of chlorine. The precise speciation of hypochlorite solution depends on pH. It may contain ClO− , HOCl, Cl2 (aq), and Cl2 O(aq), as well as low levels of chlorites and chlorates. All these species are strong oxidants, so establishing the nature of active oxidizing species and their mode of attack under any given set of conditions is difficult. HOCl, ClO− , and Cl2 O are considered the main oxidizing species. HOCl predominates in solution between pH 4 and 7.5, below which Cl2 gas evolution becomes dominant. Hypochlorite ion is the main solution species above pH 7.5. Chlorite and chlorate are less effective oxidizing agents and, so their levels should be low in hypochlorite solutions. This is done by ensuring that hypochlorite solutions are maintained at high pH because the rate of their formation is low at high alkalinities. The ClO− ion oxidizes chromophores in colored materials and is itself reduced to chloride and hydroxide ions. The chlorine cation (Cl+ ), principially existing in aqueous solution of chlorine and hypochlorous acid (cf. eq. (5.492b)), is a short-lived radical, combining with Cl− (the equilibrium lies on the left site; cf. also with eq. (5.484) and (5.486b)) Cl2 󴀘󴀯 Cl+ + Cl−

or

HOCl + H+ 󴀘󴀯 H2 OCl+ 󴀘󴀯 H2 O + Cl+ .

(5.513)

It has been reported that HOCl and Cl+ (see also eq. (5.525)) can react with amino groups (which provide important biomolecules); it is clear that this process is life damaging: HOCl + R–NH2 → R–NHCl + H2 O or

Cl+ + R–NH2 → R–NHCl + H+ .

(5.514)

66 Perchlorate is found everywhere in nature (Gmelin 1927), in precipitation (< 0.1 μg L−1 ), in soils (< 10 μg kg−1 ), in groundwater (0.01 to > 100 μg L−1 ), and in drinkling water and food (Go and Coates 2006).

5.7 Halogens (Cl, Br, F, and I) |

447

Chlorine radicals are also produced in solution from chloride by other radicals (X) such as nitrate (NO3 ), sulfate (SO−4 ), and hydroxyl (OH), with k ≈ 107 . . . 108 cm3 −1 molecule−1 s (see eqs. (5.198) and (5.328)): Cl− + X → Cl + X− .

(5.515)

The process, which includes OH, is also described as being in equilibrium: K5.516 = 0.7 and K4.517 = 1.6 ⋅ 107 : Cl− + OH 󴀘󴀯 ClOH− , −

+

ClOH + H 󴀘󴀯 Cl + H2 O .

(5.516) (5.517)

Chloride and chlorine atoms form an adduct, the chlorine radical being in equilibrium: K5.518 = 1.9 ⋅ 105 . Therefore, all reactions proceed from Cl−2 : Cl + Cl− 󴀘󴀯 Cl−2 .

(5.518)

In Table 5.19 we list two reactions where Cl−2 oxidizes sulfite: HSO−3

Cl−2 󳨀󳨀󳨀󳨀󳨀−→ Cl 󳨀󳨀󳨀󳨀󳨀󳨀→ Cl− . (−Cl )

(−HSO3 )

(5.519)

The presence of peroxides leads to radical termination: k 5.520 = 1.3 ⋅ 1010 cm3 molecule−1 s−1 (cf. with mechanism in eq. (5.26) likely via protonated oxygen HO+2 ): Cl−2 + HO2 → 2 Cl− + H+ + O2 .

(5.520)

The dichlorine radical Cl−2 decays in water and gives the hydroxyl radical (k 5.521 = 6 cm3 molecule−1 s−1 ), explaining the oxidative capacity of water chlorination for the removal of organic substances (this reaction proceeds likely via H2 O+ , cf. eq. (5.76)): Cl−2 + H2 O → 2 Cl− + H+ + OH .

(5.521)

However, it should be mentioned that chlorination also leads to harmful chlorinated organic substances. Atomic chlorine (Cl) is important in the oxidation of hydrocarbons (eq. (5.522)) but can also be added to R radicals, forming unwanted organic halides (eq. (5.523)): Cl + RH → HCl + R , 󸀠

Cl + R → R –CH2 Cl .

(5.522) (5.523)

Reaction eqs. (5.521)–(5.526) show the principal mechanism of unwanted byproduct formation in water treatment by chlorination. Hence, in the case of water pollution by organic compounds (e.g., in swimming pools, wastewaters), it is likely that halogenated organic compounds are gained. Moreover, toxic chloramines are produced. The following species have been found in swimming pools: chloroform (CHCl3 ), carbon tetrachloride (CCl4 ), dichloromethane (CH2 Cl2 ), trichloroethylene (CCl2 CHCl), bromoform (CHBr3 ), and tetrachloroethylene (CCl2 CCl2 ). Moreover, the condensed atmospheric phase (wetted aerosol particles and cloud droplets) are likely the place

448 | 5 Substances and chemical reactions in the climate system

of formation of a huge variety of halogenated semi-VOCs that can be transported over long distances and could have as of yet largely unknown impacts on health. Hypochlorous acid reacts directly with organic nucleophilic compounds (X = O, N, S) or via the intermediate formation of the chlorine cation Cl+ (HOCl → OH− + Cl+ ) (Gallard and Gunten 2002, Hanna et al. 1991). These reactions might also explain the formation of halogenated organic compounds in soils from macromolecular organic material such as humic acids, where the volatile fraction (e.g., chloroform) is emitted into the air. All olefinic hydrocarbons and aromatic compounds add Cl and OH from HOCl (e.g., reaction eq. (5.526)): HOCl + RX− → OH− + RXCl , +

+

(5.524)

Cl + RXH → RXCl + H ,

(5.525)

HOCl + CH3 CH=CHCH3 → CH3 CH(Cl)–CH(OH)CH3 .

(5.526)

Figure 5.40 summarizes aqueous-phase chlorine chemistry (that of bromine is similar), and Figure 5.41 shows the multiphase chemistry of iodine. In contrast to the other halogens, iodine forms polymeric oxides that can provide effective CCNs in the marine environment (O’Dowd et al. 2002a, O’Dowd and de Leeuw 2007). RXCl RX

Cl+ Cl-

Cl2

Cl2O

(-OH-) H2O

HOCl

H2O H2O2

HOOCl

1

(-HCl)

O2

(-OH)

Cl2-

Cl-

Cl

RX

RXCl

e-

Cl-

H+

HCl

Fig. 5.40: Simplified scheme of aqueous-phase chlorine chemistry; dotted line – multistep process.

5.8 Metals and metalloids

I2

| 449

I2O2 gas phase hν

hν

RI

hν

HI

IO (-O2) IO

O3 (-O2)

I

HO2 (-OH)

HO2(-O2) hν

InO2n

IO

HO2 (-O2)

HOI

hν (-I)

n IO2

I, Br, Cl

IO2

hν

I-

HOI O3 (-O2)

(-I2)

HIO3

H+

Br- (Cl-) (-Br2, Cl2)

IBr (ICl)

H+

aqueous phase IO-

IO3-

Fig. 5.41: Simplified scheme of multiphase iodine chemistry (NOx chemistry not included).

5.8 Metals and metalloids So far, we have discussed the chemistry of almost all volatile compounds from nonmetals such as hydrogen, oxygen, nitrogen, sulfur, carbon, phosphorus, and halogens (novel gases as permanent constituents of the atmosphere play no role in environmental chemistry). Nonmetals form a large group of anions, such as hydroxides, nitrates, sulfates, carbonates, phosphates, and halides. Metal hydrides and oxides convert instantly in aqueous solution to hydroxides; hydrides, which were likely present in the early history of Earth, generated additional molecular hydrogen. Some nonmetal hydrides can act as acids (H2 S, HCl, HBr) and others act as bases (NH3, PH4 ), whereas H2 O is defined to be neutral and CH4 is insoluble. PH3 is of minor importance. Of the metalloids (which have properties between metals and nonmetals), boron (B) and silicon (Si) are of crucial natural importance, as borate (BO−3) in seawater (buffer capacity) and silicate (SiO4− 4 ) in rocks. Metals provide equivalent cations to form with different anions salts and minerals. Recommended books for the aqueous chemistry of metals are those by Schweitzer and Pesterfield (2010) and Mason (2013).

5.8.1 General remarks Seawater contains all elements. The most abundant metals and metalloids are as follows (concentrations in ppm): sodium (10.8), boron (1–4), magnesium (1.3), calcium

450 | 5 Substances and chemical reactions in the climate system

(0.44), potassium (0.40), lithium (0.17), strontium (0.008), and silicon (0.003). The chemical composition of the oceans is a result of rock dissolution (salts and minerals) and scavenging of atmospheric constituents (nonmetals) in Earth’s early evolution. In the crust remain significant amounts of calcium, sodium, magnesium, and potassium (together 12%). Three main elements (apart from oxygen) compose the crust: silicon (27.7%), aluminum (8.1%), and iron (5.0%), which are essential constituents of minerals. Going deeper into the Earth, in the mantle we see a depletion of aluminum, sodium, and potassium, whereas silicon and iron remain, but magnesium increases. Finally, the Earth’s core contains iron (89%), nickel (6%), and sulfur (4%). Volcanoes emit dust composed of many metals: Cd, Hg, Ni, Pb, Zn, Ca, Sb, As, and Cr; volcanoes contribute 40–50% Cd to global emissions and 20–40% Hg. Based on global emissions estimates, the emission of heavy metals amounts to 2–50 kt yr−1 . Volcanic eruptions are important sources of elements in the atmosphere, almost globally distributed and deposited. Soils serve as the interface between the atmosphere and the crust, which is thus rich in many elements. Consequently, soil dust is an important source of metals (and all elements) in the atmosphere, distributed over larges areas. Hence, metals and metalloids are ubiquitous in the environment. Vital (life-essential) elements⁶⁷ occurring in many but not all organisms are metals such as Li, Be, Na, Mg, K, Ca, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo, Sb, and Sr, nonmetals such as O, H, C, N, S, P, Se, and halogens (F, Br, Cl, and I), and the metalloids B, Si, and As. Those likely without any vital functions are (in increasing order) Al, Ti, Ga, Ge, Rb, Y, Zr, Nb, Ru, Os, Pd, Ag, Cd, In, Sb, Te, Cs, La, Hf, Ta, W, Re, Pt, Au, Hg, Tl, Bi, and all radioactive elements. Some of these are nontoxic (Al, Zr, Ru, Pd, Ag⁶⁸, Re, Pt, Au, La, and Bi), others are of low toxicity (e.g., Bi and Os) or highly toxic (Hg and W). Some of the trace elements, being essential, such as arsenic, selenium, and chromium, are toxic and can even cause cancer. The toxicity of an element often depends on its chemical form (e.g., only Cr(V) is carcinogenic). Every element has three possible levels of dietary intake: deficient, optimum, and toxic in order of increasing dosage. For humans, all elements exceeding toxicologically relevant limits (which are, however, very hard to determine and heatedly debated among experts) can present reproductive dangers and even suspected cancerogenic and teratogenic properties. In the human body, trace elements (Rb, Sr, Al, Ba, B, Li, V, and others) are present in very small amounts, ranging from a few grams to a few milligrams, but are not required for growth or good health. Examples are rubidium (Rb) and strontium (Sr), whose chemistry is similar to that of the elements immediately above them

67 There is no scientific consensus about which elements are essential for life; the issue is the subject of ongoing scientific investigation. Some trace elements can replace known elements in their life-essential function, e.g., tin (Sn). Organisms do not need all elements, and some elements are essential only to plants, microorganisms, or primitive animals. 68 Only to humans; very toxic for microorganism.

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in the periodic table (potassium and calcium, respectively, which are essential elements). In the aqueous-phase chemistry of oxygen and sulfur, we have emphasized the importance of redox processes and oxidation states of TMIs such as iron, copper, and manganese. We have mentioned the role of semiconductor metal oxides (Ti, Zn, Fe, Cu, Sn, and others), which were recognized in photosensitized electron transfers to important gas molecules such as O2 , O3 , NO, NO2 , CO, and CO2 . Elements with an impact on biogeochemical redox processes are (in order of increasing atomic number) Se, Fe, Mn, Co, Cu, Cr, Hg, Tc, As, Sb, U, and Pu; some of them are only anthropogenically released (Hg, Tc, U, Pu). The basic elements in soil dust and rainwater are Na, K, Ca, and Mg. Nevertheless, in minor and trace concentrations all stable elements can be detected such as (in decreasing concentrations) Fe, Zn, Mn, Cu, Ti, Pb, Ni, Sb, V, Cr, Sb, Hg, and Th. They are called crystal elements and are thus found in dust emissions from coal-fired power plants, soil dust, and sea salt. There are “typical” metals, which can be associated with different sources (however, it can vary): – soil dust: Ti, Fe and Ni, – combustion of fossil fuels (strong enrichment comparing to geogenic sources): Sb, Pb, Zn, Cu, Hg, V, – vehicles (especially tires and brakes): Fe, Cu, Sb, Zn, and – flue ash (coal-fired burners): Fe, Ti, Mn, Zn, V, Cu, Cr, Ni. Tables 5.36 and 5.37 show some metal concentrations in rain and cloud water and atmospheric dust. Rainwater and cloud water concentrations (from different regions in Germany) are very similar. The derived atmospheric particulate residual matter from cloud water at Mount Brocken (Table 5.36) is not very different from the dust concentration found at a Berlin tower (Table 5.37), indicating the large-scale and widely homogeneous distribution of metals. Interesting is the comparison of “atmospheric” metals with those in seawater; in seawater, Fe, Mn, Cu, and Pb are depleted, whereas V and Ni are enriched relative to the metals in the atmosphere. Fe, Mn, Cu, and Pb are predominantly anthropogenically emitted by the combustion of fossil fuels. Potentially toxic metals are now normally far below thresholds given by the WHO for water, air, and food. However, in the early period of industrialization, when there was no knowledge about toxicology and no pollution control, serious damage to health due to pollution events (catastrophes) and long-term impact by high concentrations in the working environment were reported. Doubtless, the air of settlements and towns was extremely polluted in the past. Heavy metals have been found in Greenland ice cores dating back to the Roman Empire, demonstrating that metallurgical operations on an immense scale took place in that era.

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Tab. 5.36: Trace metals in rain (near Frankfurt/M, Germany, Möller et al., unpubl.) and cloud water (Mount Brocken, Germany, Plessow et al. 2001); in μg L−1 (long-term measurements). Residual is c(aq) ⋅ LWC, representing the CCN composition (ng m−3 ) at Mount Brocken. Seawater composition is in ppb (ng L−1 ) for comparison. Metal

Seawater (ng L−1 )

Rain water (μg L−1 )

Cloud water a

Residual (ng m−3 )

Fe Zn Pb Mn Cu Ti V Ni Sb Cr Co

3.4 5 0.03 0.4 0.9 1 1.9 6.6 0.33 0.2 0.4

79.6 13.2 2.3 5.4 3.4 2.4 0.3 1.3 1.0 0.2 0.1

134 37.2 11.0 7.8 5.7 2.3 1.8 1.0 0.36 0.3 0.08

31 8.5 2.5 1.8 1.3 0.5 0.4 0.2 0.08 0.07 0.02

Additionally, we found (not listed here) Sr and Ba in the range 2–3 mg L−1 , As, Mo, Cd, Sn, and Ba in the range 0.3–0.4 mg L−1 , Li, Be, Ga, Ge, Rb, Y, Zr, Nb, Cs, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ti, Bi, Th, and U < 0.1, but almost < 0.1 mg L−1 .

a

Tab. 5.37: Atmospheric trace metal concentrations (in ng m−3 ) in Berlin and environs (Germany); average from 1-year (2001–2002) measurements in PM10 . Metal

Street, heavy traffic

Rural background

Tower, 300 m

Fe Pb Ni Cd As

680 (±263) 16.3 (±9.6) 1.9 (±1.1) 0.35 (±0.20) 1.6 (±2.0)

150 (±130) 8.0 (±5.5) 1.3 (±0.5) 0.29 (±0.16) 1.2 (±1.2)

100 (±61) 8.0 (±4.7) 1.7 (±1.5) 0.27 (±0.15) 1.3 (±1.2)

Many metals form complexes, highly dependent on pH, soluble and insoluble minerals, and so vary in their availability for life (essential or not) and redox processes. The interested reader is referred to the specialized literature. Most of the scientific literature is on iron, the fourth most abundant element on Earth. In the following sections, only the main features of some environmentally important metals are presented.

5.8.2 Alkali and alkaline earth metals: Na, K, Mg, and Ca Of the alkali metals (group 1 of the periodic table of the elements), Li, Na, K, Rb, Cs, and Fr, only sodium (Na) and potassium (K) are distributed in soils, the crust, and water at significant levels. As mentioned, Li is found in seawater in high concentrations.

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Alkali metals form monovalent cations and salts, which are all soluble. In water, their oxides and hydroxides provide the strongest bases. Ca, Mg, Na, and K are the main metals in atmospheric samples (rain, clouds, dust), together accounting for almost 100% of metallic composition; therefore, we call all other metals trace metals. Sodium is deposited from oceans in huge pools as rock salt (halite) and potassium as sylvine (which is an important fertilizer). The main mineral of rare Li is spudomen LiAl[Si2 O6 ]. Of the alkaline earth metallic cations (Be, Mg, Ca, Sr, Ba, and Ra) – together with Na and K – Ca and Mg are the main metallic cations (99%) in atmospheric samples such as rain, clouds, and dust (another important cation is ammonium NH+4 ). Sr and Ba are found in relatively high concentrations in seawater. The main mineral is calcite CaCO3, forming large rocky mountains worldwide, and furthermore dolomite, MgCa(CO3 )2 , and magnetite MgCO3 . Many silicates contain Mg and Ca (remember that Mg is abundant in Earth’s mantle). Gypsum is a soft sulfate mineral composed of CaSO4 ⋅ 2 H2 O and is used as a building material (it is the final and commercial product of flue-gas desulfurization). In contrast to the alkali metals, carbonates of all earth-alkali metals are difficultly soluble; fluorides of Ca, Ba, and Sr are insoluble. The hydroxides of Ca and Mg (and other metals of group 2) are relative difficultly soluble. Much more soluble is Ca(HCO3 )2 , which is important for washout processes in carbonate mountains and forming limestone caves: CaCO3 + H2 O + CO2 → Ca(HCO3 )2 .

(5.527)

The “equilibrium” between more easily soluble bicarbonate and shell-forming insoluble CaCO3 is essential in seawater for many organisms (biomineralization). Ca and Mg are extremely important life-essential elements for plants and animals (including humans).

5.8.3 Iron: Fe Iron is in the first row of the transition metals together with Ti, V, Cr, Mn, Co, and Ni. Iron is almost bound together with silicates; the dark colors of primary rocks and the red brown color of soils are due to Fe compounds, such as hematite Fe2 O3 . Other important minerals are magnetite (Fe3 O4 ) and pyrite (FeS2 ). Other metals of this group (Ti, V, Cr, Ni) form minerals together with Fe (which explains why all this metals are found approximately in accordance with their abundance with Fe): ilmenite (FeTiO3 ), chromite (FeCr2 O4 ), pendlandite ((Ni,Fe)9 S8 ). Manganese is found almost exclusively as pyrolusite MnO2 and manganese nodules on the sea floor. All the aforementioned metals occur as positively bi- and trivalent: M2+ and M3+ . The change in the oxidation state in redox processes is likely the most important chemical property of Fe and Mn (as well as Cu: Cu+ /Cu2+ ) as presented in Chapter 5.2.5. Iron forms poorly defined oxides FeO, F3 O4 (FeO ⋅ Fe2 O3 ), and Fe2 O3 ; furthermore, it

454 | 5 Substances and chemical reactions in the climate system

forms hydroxides, the white unstable Fe(OH)2 , and the black Fe(OH)3 and FeO(OH), all of which are insoluble (Table 3.3). We discussed in Chapter 4.5.3 the rusting of iron and in Chapter 5.2.5.3 its redox properties, providing electron transfers (the biological important Fenton reaction; see eq. (5.97)). The iron complexes undergo oxidative additions and reductive eliminations. Most important are [FeII (CN)6 ]4− , [FeIII (CN)6 ]3− , [FeII (C2 O4 )3 ]4− , [FeII (H2 O)6 ]2+ , and [Fe0 (CO)5 ]. Iron oxalate complexes, often found in surface waters, can easily be photolyzed gaining peroxo radicals (eq. (5.82)). The ferric/ferrous pair (Fe3+ /Fe2+ ) – because of the significant iron concentration compared to other transition metals – is the most important redox pair in natural waters. Besides its function of carrying out important electron transfer processes in living organisms, iron holds and transfers oxygen in hemoglobin (the red pigment in blood) and myoglobin (a protein found in the muscle cells of animals). Other iron porphyrin proteins (e.g., cytochrome) and iron-sulfur proteins are responsible for electron transfers in complex biochemical processes such as nitrogen and carbon dioxide fixation, photosynthesis, and respiration. The ion [FeIII (H2 O)6 ]3+ is stable only at pH < 0 (not found under environmental conditions) and transfers in a pH range of 0–2 to yellow-brown [Fe(H2 O)5 (OH)]2+ and [Fe(H2 O)4 (OH)2 ]+ : ±H+

±H+

2+ 󳨀󳨀 + 󳨀󳨀 󳨀→ [FeIII (H2 O)6 ]3+ 󳨀 ← 󳨀󳨀 [Fe(H2 O)5 (OH)] 󳨀 ←󳨀→ 󳨀󳨀 [Fe(H2 O)4 (OH)2 ] .

(5.528)

The solution becomes colloidal and, shifting the aqueous solution, more alkaline, amorphous red brown Fe2 O3 ⋅ (H2 O)x is deposited. These processes can be seen in lakes created from former mining areas, which were very acidic initially. In the early Earth, all metals were in a lower oxidation state, such as Fe2+ . With the evolution of oxygen (Volume 2), FeO oxidized to Fe2 O3 (depending on the modification, the color is between red brown and black). The relationship between oxidant availability and iron mobility during weathering is the primary tool for estimating oxygen levels. In most soils, H2 CO3 is the most important weathering acid. If oxygen is supplied much more rapidly to a weathering horizon than carbon dioxide is consumed, then essentially Fe2+ in the weathering horizon will be oxidized to Fe3+ and retained as a component of ferric oxides and oxohydroxides.

5.8.4 Mercury: Hg Mercury (Hg) is one of the few elements (Be and Cd are the others) that is not essential for organisms. It is the only metal that is liquid at room temperature.⁶⁹ In nature it occurs almost exclusively (it is rarely found in elemental form as small droplets) as sulfide, such as cinnabar HgS.

69 Gallium (Ga) and caesium (Cs) melt at 30 °C and 28.5 °C, respectively.

5.8 Metals and metalloids |

455

Tab. 5.38: Global source fluxes of mercury (Mg Hg yr−1 ). Data from Pirrone et al. (2010). Source

Emission

Natural sources Ocean Soils Biomass burning Vegetation Lakes Others Volcanic activities Subtotal

2682 546 673 918 96 200 90 5207

Anthropogenic sources Fossil-fired power stations Gold mining Noniron metallurgy Cement production Waste disposal Caustic soda production Others Subtotal

810 400 310 232 187 163 218 2320

Hg is very toxic, but its toxicity depends on the chemical form of bonding; methylmercury (and other organic Hg compounds) is the most toxic form of Hg. Methylmercury⁷⁰ is formed from inorganic mercury by the action of anaerobic organisms that live in aquatic systems, bioaccumulated and transferred via the food chain. The only natural sources of Hg are volcanoes, fumaroles, and hot springs. Due to the geochemical global distribution over the Earth’s history, Hg became a constituent of soils (soil dust emission) and as (the main source at present but with low specific emission) oceanic emission of volatile organic Hg (Table 5.38). Surface seawater contains globally around 6 ng L−1 Hg. Today, natural and anthropogenic sources are hard to separate because human activities have led to a global Hg redistribution. There is no doubt that coal combustion is the largest anthropogenic source, and power plants (or burners) without gas treatments are the largest single emitters of Hg. The Hg content of coal amounts to 0.02–1.0 ppm, that of flue ash 0.62 ppm, and the emission factor

70 Methylmercury is an ion, CH3 Hg+ , i.e., it exists as (mostly) chloride, nitrate, and so forth (e.g., CH3 HgCl). It forms crystalline solids and is not volatile (in many publications methylmercury – often written MeHg – is described incorrectly as a molecular compound). Dimethylmercury (CH3 HgCH3 ) is a highly toxic liquid. Both compounds are enriched at seawater surfaces and easy photolyzed to CH3 Cl and Hg(0), where Hg escapes into air due to its large vapor pressure (aqueous-phase Hg concentration is larger than in air).

456 | 5 Substances and chemical reactions in the climate system amounts to 0.04–0.3 g Hg t−1 coal (all global averages).⁷¹ In coal, Hg represents a mineralic bond as Hg(II), likely as HgS. During combustion, Hg is quantitatively released, first in gaseous, elemental form. However, during processing in a power plant (including gas treatment), it converts into particulate and bonded mercury Hg(II). Mercury exists in four different forms in the environment: – elemental (also gaseous): Hg(0) – particulate (soluble and insoluble): Hg(p)⁷² – oxidized (almost exclusively as chloride): Hg(I)⁷³ and Hg(II) – organic (almost exclusively as CH3 Hg+ ): Hg(org) In power plant chemistry, the following reactions are taken into account: HgS(coal) + O2 → Hg(0) + SO2 ,

(5.529)

2 Hg(0) + O2 󴀘󴀯 2 HgO(s) ,

(5.530)

HgO(s) + 2 HCl(g) → HgCl2 (g) + H2 O(g) , Hg(0) + Cl + M 󴀘󴀯 HgCl(g) + M , Cl2 + M 󴀘󴀯 2 Cl + M , HgCl(g) + HCl → HgCl2 + H .

(5.531) (5.532) (5.533) (5.534)

HgO is decomposed into the elements only at temperatures greater than 500 °C. Mercury chloride can exist at high temperatures. Hg(0) passes the power plant and is emitted quantitatively; hence, the more gaseous HgCl2 /HgCl is produced, the more efficiently it is removed by scrubbing. We see that the chloride content of coal is important for Hg speciation. Particulate HgO forms after decreasing the flue gas temperature below 500 °C. Together with HgCl2 it is adsorbed on flue ash particles. Globally, we may assume that Hg emissions are divided into about 50% Hg(0) and 50% Hg(II). Hg(0) is relatively rapidly (residence time of about a month) oxidized to Hg(II) by OH (k = 9 ⋅ 1014 cm3 molecule−1 s−1 ) and O3 (k = 3 ⋅ 1020 cm3 molecule−1 s−1 ); the mechanism is not known, but HgO is assumed to be a product: Hg(0) + OX(OH, O3 ) → HgO + products .

(5.535)

The rate of oxidation of elemental mercury is fundamental to atmospheric mercury chemistry because the oxidized mercury compounds (such as HgO and HgCl2 ) are more soluble (and so are readily scavenged by clouds), less volatile (and therefore 71 For west German power stations, fired with hard coal, the mean Hg content averages 0.04 (0.18– 0.48) ppm and in flue ash 0.23 (0.4–1.9) ppm. 72 All forms of bonding are possible, but the most likely is Hg(II). 73 Monovalent mercury arises always from two atoms: Hg2 X2 (dimer Hg2+ 2 ). In contrast to HgCl2 (sublimate), Hg2 Cl2 (calomel) is difficultly soluble (by contrast, HgNO3 is easily soluble). Sublimate finds wide applications in medicine, a good example illustrating that it is the amount that makes a substance poisonous.

5.8 Metals and metalloids | 457

more rapidly scavenged by particulates), and have a higher deposition velocity. HgO is easily soluble, can be scavenged by wetted aerosol particles, clouds, and rain, and dissociates to Hg2+ . Under most atmospheric conditions, chloride concentrations in the aqueous phase are sufficiently high to drive recomplexation to HgCl2 . Oxidized mercury can also be reduced to elemental mercury in atmospheric droplets, limiting the overall rate of oxidation and deposition: O−2

O−2

(−O2 )

(−O2 )

Hg2+ 󳨀󳨀󳨀󳨀→ Hg+ 󳨀󳨀󳨀󳨀→ Hg(0) .

(5.536)

However, the intermediate Hg+ can also be rapidly back oxidized. Mercury dichloride has a large Henry’s law constant (H = 1.4 ⋅ 106 M atm−1 ) and escapes from droplets. In air, it is rapidly photolyzed to Hg(0) and chlorine. Hence, a dynamic equilibrium Hg(0) 󴀘󴀯 Hg(II) is established; about 90% of total Hg is in the form of Hg(0) in the lower troposphere. Only in the upper troposphere (where there are no or only insignificant clouds) is Hg(0) more in oxidized form. In aqueous solution, several reactions have been studied: oxidation of Hg(0) with OH and HOCl/− OCl, reduction of Hg(II) with S(IV) and HO2 , and photoreduction of Hg(OH)2 (Lin and Pehkonen 1998, 1999 and references therein); see also Liu et al. (2012) for chemistry and toxicology.

5.8.5 Cadmium: Cd To the so-called zinc group (subgroup 2 or group 12 of the periodic table of the elements) belong zinc (Zn), cadmium (Cd), and mercury (Hg). In contrast to Hg and Cd, Zn is essential for all living organisms – biologically speaking, it is the most important after Fe. From Table 5.36 we see that Zn follows Fe in terms of atmospheric abundance; it is a commonly encountered element in the Earth’s crust, soil, and water. Global cycling is due to soil dust, volcanic emissions, and anthropogenic particulate emissions (mining, metallurgical operations, use of commercial products containing zinc⁷⁴). Cadmium mainly occurs in Earth’s crust in association with zinc ores. The average content is generally between 0.1 and 0.5 μg g−1 , although much higher levels can also be found in sedimentary rock and marine phosphates and phosphorites. Ambient air Cd concentrations have generally been estimated to range from 0.1 to 5 ng m−3 in rural areas, 2.0 to 15 ng m−3 in urban areas, and 15 to 150 ng m−3 in industrialized areas (Cheng et al. 2014 and references therein). Volcanic activity for as much as 820 Mt per year (Nriagu 1989). Cadmium emissions may be considered as arising either from point sources such as large manufacturing or production facilities or from diffuse sources such as may occur from the use 74 When collecting rainwater near a tower or container of galvanized metallic construction, you will always detect increased Zn in solution!

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and disposal of products by many consumers over large areas. The combustion of coal and oil are major sources of atmospheric cadmium pollution. Emissions from point sources have been stringently regulated since the 1970s, and cadmium emissions from point sources have decreased dramatically. The vast majority of cadmium emissions, approximately 80% to 90%, presently comes from soils, where cadmium is largely bound to nonexchangeable fractions, for example, clays, manganese, and iron oxides. For this reason, its mobility and transfer to animal and human food chains is limited. Cadmium exerts toxic effects on the kidney, the skeletal system, and the respiratory system and is classified as a human carcinogen.⁷⁵

5.8.6 Lead: Pb Lead is one of four metals (the others being Cd, Hg, and As) that have the most damaging effects on human health. Lead as an element was already known to ancient civilized peoples in 3000 BC and was used in many everyday objects. Therefore, lead poisoning is as old as its use. The downfall of the Romans is often attributed to their use of Pb in tableware and water pipes; each year they produced around 60,000 t. However, lead poisoning is a chronic disease due to the small uptake of Pb by organisms at high doses. Lead pipes were still in use after the World War II. Native lead is rare in nature. Currently lead is usually found in ores with zinc, silver, and copper and is extracted together with these metals; the main lead mineral is galena (PbS). Native lead is still used in daily life and industry. However, the environmental problem arose from tetraethyl lead (Pb(C2 H5 )4 ) in gasoline to achieve higher octane ratings. In the burning of gasoline in an engine, Pb is released and combines rapidly with oxygen to form PbO and PbO2 . These particles provide surface to terminate the radical chain reaction. To avoid Pb deposits in the engine, organochalogens were added to gasoline. Therefore, volatile PbCl2 and PbBr2 were released into the air, which were soon deposited on particles (at that time almost exclusively sulfate); PbSO4 is insoluble in water. Due to the application of lead in gasoline (first use in 1923), an unnatural lead cycle has emerged. The phase-out of Pb in gasoline ultimately resulted from two factors: the ability of refiners to produce gasoline with a higher octane rating and the widespread use of catalytic converters, which are incompatible with the use of lead.

75 Itai-itai disease was the name given to the mass cadmium poisoning of Toyama Prefecture, Japan, starting around 1912. Mining companies in the mountains released cadmium into rivers. The causes of the poisoning were not well understood and, up to 1946, it was thought to be simply a regional disease or a type of bacterial infection. Medical tests started to be conducted in the 1940s and 1950s in search of the cause of the disease. In 1968, the Ministry of Health and Welfare issued a statement about the symptoms of itai-itai disease caused by cadmium poisoning.

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5.8.7 Arsenic: As The metalloid arsenic is essential for humans and is found in all tissues at levels up to 0.008%. Biologically it serves as an inhibitor affecting free SH groups of certain enzymes. Elemental As and insoluble compounds (such as sulfides) are not toxic but As3+ in soluble substances such as As2 O3 and AsH3 is toxic. Arsenic is among the volatile pollutants such as Cd, Pb, and Hg emitted from coals combustion. Arsenic is most commonly found in groundwater in many regions of the world; it is of natural origin and is released from sediments into groundwater. The WHO standard is 10 ppb, but studies suggest that significant increases in cancer mortality appear only at levels above 150 ppb. Generally, the main forms of As under oxic condi3− tions are H3 AsO4 (pH 2), H2 ASO−4 (pH 2–7), H2 ASO2− 4 (pH 7–11), and ASO4 (pH 11). Under reducing conditions, H3 AsO4 is predominant at pH 2–9.

5.8.8 Silicon (Si) and aluminum (Al) Silicon and aluminum are the main constituents (apart from oxygen) of all rocks (alumosilicates) in the form of SiO2 and Al2 O3 . Silicon is essential for life, though aluminum is not. Diatoms (a major group of unicellular algae, and among the most common types of phytoplankton) are enclosed within a cell wall made of silica (hydrated SiO2 ). The cycle of Si weathering is described in Chapter 3.2.2.3, Volume 2. Both elements are widely used in human activities and are nontoxic. However, chronic silicosis, an occupational lung disease (pneumoconiosis) resulting from long-term exposure (10 years or more) to relatively low concentrations of silica dust (SiO2 ) and usually appearing 10–30 years after first exposure, occurs. Pulmonary complications of silicosis include chronic bronchitis and airflow limitation, the same symptoms caused by smoking and asbestosis. This effect is not toxicological but “simply” the result of deposition of material in the lung that cannot be removed by a natural self-cleansing mechanism. The material is not quartz sand such as is found in the Sahara Desert (no Tuareg – a Berber people inhabiting the Sahara – have been known to get silicosis even from breathing the huge amounts of sand corns they do over the course of their lifetimes), which is largely made up of spherical and polished particles. During mining, mineral dust particles with crystalline surfaces and broken, sharp edges are formed, which are fixed and accumulated in lung tissue. Cigarette tar and asbestos fibers are deposited in the same way, accumulating over decades before the lung can no longer fully function. Moreover, inflammations are caused by the additional adsorption of toxic substances, and finally lung cancer develops. These particles are unknown in nature; evolution created very effective strategies for protection only against natural soil dust (all animals and humans live on sandy surfaces) (see also Chapter 4.5.4 in Volume 2).

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When analyzing atmospheric PM (Tables 3.8, 3.9 and 5.37), normally the watersoluble fraction is only determined, and in the case of metals, an acidic fusion is necessary. The residual of the total sum of analyzed compounds to the total weighted PM, insoluble SiO2 (only under fusion with hydrofluoric acid transfers into aqueous solution) amounts to about one-third, that is, 5–10 μg m−3 . Aluminum is not an essential element for either plants or animals but common in all soils and waters. As Al exists almost exclusively in insoluble compounds, available excess Al3+ can occur due to acidification. It can reduce the availability of phosphorus and sulfur to plants due to the formation of insoluble phosphates (AlPO4 ) and sulfates (Al2 (SO4 )3 ). The amount of soluble Al increases dramatically in nearly all soils as the soil pH drops below pH 5.0. In soils, Al occurs as hydroxides Al(OH)3 and AlO(OH), which are (in contrast to acidic silicates) amphoteric. In addition, aluminates, several hydroxyaluminates such as [Al n (OH) m ], and oxoaluminates [AlO m ] are found. From hydroxide, free Al3+ forms under acidic conditions (eq. (5.537)), and aluminates form under alkaline conditions (eq. (5.539)): Al(OH)3 + 3 H+ 󴀘󴀯 Al3+ + 3 H2 O , −

Al(OH)3 + OH 󴀘󴀯

Al(OH)−4

(5.537)

.

(5.538)

The amphoteric character of Al is evident in 2+ + Al (H2 O)3+ 6 󴀘󴀯 Al(OH) (H2 O)5 + H

Al(OH) (H2 O)2+ 5

󴀘󴀯

Al(OH)2 (H2 O)+4

+

+H

pH 3–7 ,

(5.539)

pH 4–8 .

(5.540)

6 Biogeochemistry and global cycling We stated earlier that the climate system can be described (and widely quantified through measurements) by the natural energy system, the hydrological cycle, the carbon cycle, and other biogeochemical cycles. Hence biogeochemistry combines scientific disciplines (chemistry, physics, geology, and biology) to study the climate system as a whole. The evolution and (under human influence) changing biosphere is described in Volume 2, whereas in the following sections some fundamentals of water and biogeochemical cycling as well natural sources are characterized.

6.1 The hydrosphere and the global water cycle Water is the most abundant compound in the climate system (Table 6.1). It is the only substance that can exist simultaneously in the Earth’s climate system in all three states of matter: gaseous (vapor), liquid (natural waters), and solid (ice and snow). As discussed in great detail in Volume 2 (Chapters 3.1 and 3.2), water, together with hydrocarbons, is among the most abundant compounds in space and was delivered to the early Earth through asteroids and other celestial bodies. The term “water” is used in two senses. First, pure water is a chemical substance, and we call the discipline that studies it water chemistry (or chemistry of water), which deals with the chemical and physical properties of water as molecules, liquid, and ice. Second, natural water is a solution; the discipline that studies it is referred to as hydrochemistry (sometimes hydrological chemistry), chemical hydrology, and aquatic chemistry. Water in nature is always a solution, mostly a diluted system, and in equilibrium or nonequilibrium but in exchange with the surrounding medium, solids (soils, sediments, rocks, vegetation) and gases (atmospheric and soil air). The fundamentals of these physical and chemical processes were described in more detail in Chapter 3.4. The aim of this section is to present the key features of water in the climate system, along with its distribution and cycling. The unique chemical and physical properties of water mean that it plays the key role in the climate system as: – solvent (for compounds essential for life, but also pollutants, dissolved and nondissolved), – chemical agent (for photosynthesis in plants and photochemical oxidant production in air), – reaction medium (aqueous-phase chemistry), – transport medium (in the geosphere, for example, oceanic circulation, rivers, clouds, and in the biosphere in plants, animals, and humans), – energy carrier (latent heat: evaporation and condensation; potential energy in currents and falling waters), and – geological force (weathering, ice erosion, volcanic eruptions). https://doi.org/10.1515/9783110561265-006

462 | 6 Biogeochemistry and global cycling Tab. 6.1: Global water reservoirs (1018 g) and fluxes (1018 g yr−1 ) on Earth; adapted from A: Berner and Berner (1987), B: Berner and Berner (2012), C: Schlesinger (1997), D: Trenberth et al. (2007). Reservoirs

A

B

C

D

Oceans Ice caps and glaciers Groundwater Lakes Rivers Soil moisture Permafrost Atmosphere total Biosphere (plants)

1,370,000 29,000 9,500 125 1.7 65 – 13 0.6

1,400,000 43,400 15,300 125 1.7 65 – 15.5 2

1,350,000 33,000 15,300 – – 122 – 13 –

1,335,040 26,350 15,300 }

178 122 22 12.7 –

Total Fluxes Evaporation ocean Precipitation ocean Evaporation land Precipitation land Atmospheric transport a River runoff a

423 386 73 110 37 37

434 398 71 107 36 36

425 385 71 111 40 40

413 373 73 113 40 40

From marine to continental atmosphere (equal to river runoff).

Natural water is an aqueous solution of gases, ions, and molecules, but it also contains undissolved, suspended, or colloidal inorganic particles of different sizes and chemical compositions and biogenic living or dead matter such as cells, plants, and animals, for example, sometimes termed hydrosol. Water occurs in the climate system in different forms: – liquid bulk water (natural waters): in rivers, lakes, wetlands, oceans, and groundwater (held in aquifers), – humidity (soil water): adsorbed onto soil particles, – liquid droplet water: in clouds, fog, and rain, but also as dew on surfaces, – ice-particulate water in the atmosphere: snow, hail, grains, – water vapor (humidity) in the atmosphere (one gaseous component among many other gases of air), – hydrates: chemically bonding water molecules onto minerals, – clathrate hydrates: crystalline water-based solids physically resembling ice, inside of which small nonpolar gas molecules are trapped (existing under high pressure in the deep ocean floor), and – bulk ice: snow cover, glaciers, icebergs. Water and the hydrosphere are practically synonymous, but not completely. The hydrosphere is the total sum of water on Earth, except for that portion in the atmosphere.

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The hydrosphere combines all water underground, as well as all freshwater in streams, rivers, and lakes, saltwater in seas and oceans, and frozen water in icebergs, glaciers, and other forms of ice.

6.1.1 The hydrological cycle and the climate system In ancient Greek, άτμις (atmis: water vapors) denotes the transfer of water (by evaporation) from telluric form (hydrosphere) into άηρ (aer), the water vapor of the atmosphere and its return as precipitation to the Earth, (with water) one of the two lower elements. We know from Herodotus that in the fifth century BC this theory was known and accepted and described by Hippocrates (for more details see Volume 2, Chapter 2.1.2). The water or hydrological cycle is the continuous circulation of water throughout the Earth and between its systems. At various stages, water moves through the atmosphere, the biosphere, and the geosphere, in each case performing functions essential to the survival of the planet and its life forms. Thus, over time, water evaporates from the oceans, then falls as precipitation, is absorbed by the land, and, after some period of time, makes its way back to the oceans to begin the cycle again. The total amount of water on Earth has not changed in many billions of years, though the distribution of water has changed. Compared with other biogeochemical cycles, water provides the largest turnover of material on Earth (Figure 6.3). The long-term mean values for hydrological reservoirs and fluxes (as depicted in Table 6.1 and Figure 6.1) are uncertain. Various versions have been published, and tracing some of the references indicates a cascade whereby one source cites another that in turn cites another, making the original value rather uncertain (Trenberth et al. 2007); many of these values in turn come from Baumgartner and Reichel (1975). Trenberth et al. (2007) used values from the Global Precipitation Climatology Project (GPCP) from 1988 to 2004, which results in an annual mean global precipitation of (489.9 ± 2.9) ⋅ 103 km3 , separated into a global mean ocean precipitation (372.8 ± 2.7) ⋅ 103 km3 and (112.6 ± 1.4) ⋅ 103 km3 over land. The water cycle is driven by processes that force the movement of water from one reservoir to another. Evaporation from the oceans and land is the primary source of atmospheric water vapor (Figure 6.2). Water vapor is transported, often over long distances (which characterizes the type of air masses), and eventually condenses into cloud droplets, which in turn develop into precipitation. Globally, there is as much water precipitated as is evaporated, but over land precipitation exceeds evaporation, and over oceans evaporation exceeds precipitation (Figure 6.2). The excess precipitation over land equals the flow of surface and groundwater from continents to the oceans. Flowing water also erodes, transports, and deposits sediments in rivers, lakes, and oceans, affecting the quality of water.

464 | 6 Biogeochemistry and global cycling

Fig. 6.1: Water reservoirs and the hydrological cycle (reservoir concentrations in 1018 g, fluxes in 1018 g yr−1 ). Data from Table 6.1.

This natural cycling of water is now perturbed by human activities. Together with changing vegetation patterns due to land-use management (Chapter 4.2.4 in Volume 2), these factors complicate the prediction of the consequences of climate change on the global water cycle. The global water cycle includes subcycles, such as cloud processing (condensation onto CCNs and evaporation forming new CCNs), the plant water cycle (assimilation and transpiration), and the human water cycle (water processing for drinking and processing as well as wastewater) (Figure 6.2). As water cycles through the climate system, it interacts intensively with other biogeochemical cycles, notably the cycles of carbon, nitrogen, and other nutrients. These linkages directly affect water quality and the availability of potable water and industrial water supplies. It is estimated that 70– 80% of worldwide water use is for irrigation in agriculture, while 15–20% of worldwide water use is industrial. The remainder of worldwide water use is for household purposes (drinking, bathing, cooking, sanitation, and gardening). The feedback between the water and carbon cycles (Chapter 3.2.2.6 and also Figure 3.11 in Volume 2) is not only given by water in its essential role in sustaining all forms of life. Observational evidence indicates that transpiration rates of plants are high at the same time as CO2 fixing by plants, so CO2 flux from the atmosphere to the plant canopy is large. When an environment is humid, plants grow more rapidly, draw more CO2 from the atmosphere, and release more water to the atmosphere. Seasonal to interannual variability in the global water cycle is largely determined by ocean and land processes and their impact on the atmosphere. The prediction of

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465

Fig. 6.2: The global water cycle; (reservoir concentrations in 1018 g, fluxes in 103 km3 yr−1 ). Data from Table 6.1.

this variability relies on the persistence of surface conditions that tend to provide the atmosphere with consistent anomalies in fluxes over periods of weeks or months or even years. The timescale of “memory” in the atmosphere is fairly short, but, due to the atmosphere’s connection to the land and ocean, each of which is characterized by a much longer memory, the climate system becomes complex in time and space; for example, the atmospheric residence time of trace substances is not constant but a function of time and space. Current dynamic climate models on regional and global scales demonstrate a limited ability to predict precipitation on timescales beyond a few days. It is obvious that a better understanding of the variability would have important consequences for agricultural and water resource management. The El Niño and La Niña cycles are the most obvious examples of a coupled phenomenon that produces significant seasonal to interannual variability.

466 | 6 Biogeochemistry and global cycling

As mentioned in Chapter 3.4.4, water has an important influence on atmospheric circulation and plays a key role in the maintenance of the climate system as a moderator of the Earth’s energy cycle. Water cools its surroundings as liquid and ice are converted into water vapor. On average, this latent cooling is balanced by the latent heat released when vapor is condensed into clouds. Water is a very effective means of storing and transporting energy in the atmosphere. In general, latent heat is the principal source of energy that drives cyclogenesis and sustains weather systems, such as the convective cells that generate tornadoes and tropical storms that evolve into hurricanes. The different types of clouds in the atmosphere are linked to the climate system by a multitude of dynamic and thermodynamic processes, including numerous feedback mechanisms. In the present-day climate, on average, clouds cool our planet, and the net cloud radiative forcing at the top of the atmosphere is about −20 W m−2 . One of the most interesting questions concerning clouds is how they will respond to changes in climate. A slight change in cloud amount or a shift in the vertical distribution of clouds might have a considerable impact on the energy budget of the Earth. The IPCC states clearly that cloud processes and related feedbacks are among the physical processes leading to large uncertainties in the prediction of future climate. The main reason for this is that many microphysical and dynamic processes controlling the life cycle and radiative properties of clouds are not adequately incorporated into global climate models. The interaction of aerosols and clouds and the resulting radiative forcing (indirect and semidirect aerosol effect) is one of the major fields of active cloud research at present. Therefore, the hydrological cycle is not only a cycle of water; it is a cycle of energy as well.

6.1.2 Soil water and groundwater: Chemical weathering Water falling to the surface of continents in any form of precipitation, upon striking the surface, undergoes major modifications both in mode of transport and chemical composition. Infiltration is the flow of water from the ground surface into the ground. Once having infiltrated the ground, the water becomes soil moisture or groundwater. In the cryosphere, precipitated snow undergoes transformation into ice layers. Drilling of so-called ice cores gives us insights into the chemical composition of the paleoatmosphere. Ice cores have been taken from many locations around the world, especially in Greenland and Antarctica. In January 1998, the collaborative ice-drilling project between Russia, the United States, and France at the Russian Vostok station in East Antarctica yielded the deepest ice core ever recovered, reaching a depth of 3623 m. Preliminary data indicate the Vostok ice-core record extends through four climate cycles, with ice slightly older than 400,000 years. This data set contains ice-core chemistry, timescale, isotope, and temperature data analyzed by several investigators. Dome F in Antarctica, also known as Dome Fuji, is another example of well-described

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Tab. 6.2: Typical residence times of water found in various reservoirs; after Pidwirny (2006). Reservoir

Average residence time

Glaciers Seasonal snow cover Soil moisture Groundwater: shallow Groundwater: deep Lakes Rivers

20 to 100 years 2 to 6 months 1 to 2 months 100 to 200 years 10,000 years 50 to 100 years 2 to 6 months

ice cores; recently a depth of 3035 m was reached, and according to preliminary dating, it reaches back 720,000 years ago. However, the processes of laying down snow and its conversion into ice are complicated, and air is slowly exchanged by molecular diffusion through pore spaces in firn. Thermal diffusion causes isotope fractionation in firn when there is rapid temperature variation, creating isotope differences that are captured in bubbles when ice is created at the base of firn. Firn is partially compacted névé,¹ a type of snow left over from past seasons, and recrystallized into a substance denser than névé. It is ice that is at an intermediate stage between snow and glacial ice. In the biosphere, rain that is not lost back to the atmosphere by evaporation from the ground or from trees may pass deep underground, only to emerge at a much later date (Table 6.2) in a river or lake. Water coming into contact with rocks (and derived soils) reacts with primary minerals contained in them. The minerals dissolve to varying extents, and some of the dissolved constituents react with one another to form new, secondary minerals. Dissolution is mainly controlled by the water acidity provided from plant mineralization (humic acids), atmospheric carbonic acid, and “acid rain.” The overall process is known as chemical weathering (Berner and Berner 2012).

6.1.3 Surface water: Rivers and lakes Rivers and other forms of surface water actually account for a relatively small portion of the planet’s water supply, but they loom large in the human imagination as the result of their impact on our lives. The first human civilizations developed along rivers in Egypt, Mesopotamia, India, and China, and today many great cities lie alongside rivers. Rivers provide us with a means of transportation and recreation, with hydroelectric power, and even – after the water has been treated – with water for drinking and bathing. River waters typically begin with precipitation, whether in the form of

1 Young, granular type of snow that has been partially melted, refrozen, and compacted. This type of snow is associated with glacier formation through the process of nivation.

468 | 6 Biogeochemistry and global cycling Tab. 6.3: Composition of average river water and seawater (mg L−1 ); data from Langmuir (1997). Substance

River water

Seawater

Seawater to river water

Ratio

River water

Seawater

HCO−3 Ca2+ SO2− 4 Cl− Na+ Mg2+ K+

58.6 15.0 10.6 7.8 6.3 4.1 2.3

146 412 2,707 19,383 10,764 1,243 105

2.5 27 255 2,485 1,794 303 39

Ca/HCO3 Ca/SO4 Na/Cl Na/Mg Na/K – –

0.26 1.4 0.77 1.46 2.22 – –

2.8 0.15 0.55 8.66 102.5 – –

rainwater or melting snow. They also are fed by groundwater exuding from bedrock to the surface. As we have already noted, however, a river is really the sum of its tributaries, and so hydrologists speak of river systems rather than single rivers. Finally, rivers discharge into an ocean, a lake, or a desert basin. The chemical composition of river water is significantly different from that of seawater (Table 6.3). At first approximation, seawater is mainly a solution of Na+ and Cl− , whereas river water is a solution of Ca2+ and HCO−3 . Interestingly the Na/Cl ratio is the only one that is relatively similar for rivers and oceans, suggesting that both components are within a global cycle from sea spray through cloud transportation to continents and precipitation. Carbonate is approximately in equilibrium with atmospheric CO2 , and the concentration difference between river water and seawater is determined by the pH. Ions transported by rivers are the most important source of most elements in the ocean. Rivers collect dissolved matter from precipitation, weathering, and pollution. Their chemical composition shows large seasonal and interannual variations as well as great differences among the continents, reflecting the processes of the sources (Table 6.4). Tab. 6.4: Chemical composition of various rivers (mg L−1 ); data from Livingstone (1963) and Holland (1984).

North America South America Europe Asia Africa Australia World

HCO−3

SO2− 4

Cl−

NO−3

Mg2+

Na+

K+

Fe

SiO2

68 31 95 79 43 32 58.1

20 4.8 24 8.4 13.5 2.6 11.2

8 4.9 6.9 8.7 12.1 10 7.8

1 0.7 3.7 0.7 0.8 0.05 1

6 1.5 5.6 5.6 3.8 2.7 4.1

9 4 5.4 9.3 11 2.9 6.3

1.4 2 1.7 – – 1.4 2.3

0.16 1.4 0.8 0.01 1.3 0.3 0.67

9 11.9 7.5 11.7 23.2 3.9 13.1

6.1 The hydrosphere and the global water cycle | 469

6.1.4 The oceans The chemical composition of the oceans defines the impact of the other geochemical reservoirs on the oceanic reservoir, leading to the addition of elements to, or removal from, seawater (Elderfeld 2006). The ocean is the global disposal center of chemicals. In Volume 2, Chapter 3.2, the evolution of the ocean is discussed in connection with the interaction of degassing from the Earth’s surface and atmospheric deposition. Comparison of the amount of material supplied to the oceans by rivers with the amount in the ocean reveals that most of the elements were replaced many times. Thus, chemical reactions occurring in the ocean balance river input by sediment removal. The main input and removal fluxes for seawater ions can be roughly estimated from the averages of river composition and the global runoff value (36–40)⋅1018 g yr−1 . Sillén (1967) first constructed a simplified multicomponent equilibrium model based on nine components: HCl, H2 O, and CO2 , which represent acid volatiles from inside the Earth, and KOH, CaO, SiO2 , NaOH, MgO, and Al(OH)3 , which correspond to the bases of the rocks. To close the global mineral cycle, a reverse weathering in the sea (eq. (6.1)) was proposed by Mackenzie and Garrels (1966): Clay mineral + HCO−3 + H4 SiO4 + cation → cation-rich silicate + CO2 + H2 O .

(6.1)

However, most of the sedimentary mass is of detrital origin. Nutrient elements (Si, P, V, N, and trace metals) are removed in the ocean as biological debris to sediments. The main sink of substances is by hydrothermal reactions (volcanic activity) at locations of seafloor spreading and circulation through the ocean crust. Volcanic activities in the oceans are extensive and produce submarine lava flows that are unstable in seawater. The high temperature (200–400 °C) is not only important for basalt-seawater reactions but also triggers circulation. Subduction (Chapters 3.2.1.1, Volume 2) transfers seawater and its constituents back to the magma. Because of the large volume of seawater, almost all ions are conservative, meaning they do not change their concentrations over geological periods. As a result of sea salt emissions from oceans (Chapter 6.3.3.2) huge amounts of NaCl go to global cycling; Cl− even undergoes important chemical reactions in the climate system (Chapter 5.7) despite the fact that they do not affect chloride concentrations in any reservoir due to the high chloride pool concentrations. However, Na+ is involved in rock weathering (it is a major constituent of silicate minerals), cation exchange, and possibly volcanicseawater reactions and reverse weathering. Seawater, compared with all other natural waters, is remarkably constant in composition. However, all elements involved in biological turnover (oxygen and carbon being the most important) may have variations (and possibly trends), again due to changing key parameters of the climate system, of which temperature is the most important. Concerning the global climate, the oceans have two essential functions: – They are the largest pool of carbon (almost in the form of HCO−3 ) in the climate system (Table 6.12) and the only ultimate sink of atmospheric CO2 (burial in sed-

470 | 6 Biogeochemistry and global cycling

–

iments, Sabine et al. 2004); temperature change results in solubility change as well as changes in circulation and, hence, total fluxes. Global oceanic circulation is closely interlinked with atmospheric circulation; hence, oceans transport energy and material and exchange them with the atmosphere. Change in one reservoir results in change in the other, but on different timescales.

Wind-driven circulation occurs in the surface layer (50–300 m), creating a number of current rings, or gyres, that flow clockwise in the Northern Hemisphere and counterclockwise in the Southern Hemisphere. The circulation pattern is a result of complicated interactions of wind and water, but other factors are also involved, such as the Earth’s rotation and friction. Coastal upwelling is a special case of surface circulation that has an important effect on biological productivity in the ocean. Below a few hundred meters, oceanic circulation is a result of gradients in density due to differences in temperature and salinity. In contrast to freshwater lakes, where the density maximum is at 4 °C, the deep ocean is vertically stratified into various water masses, with the densest water at the bottom and the lightest at the top. All density-related stratification owes its origin to conditions at the surface: temperature differences due to the radiation budget, salinity due to evaporation (increase in salinity) and precipitation (decrease in salinity), and ice formation (dissolved ions remain in liquid water) and melting (temperature and salinity are interlinked properties). As a result of deep stratification, deep circulation is much more horizontal than vertical. Diffuse upwelling is very slow (about 1 m yr−1 ) and the residence times of deep water are on the order of hundreds, or even thousands, of years. For further reading, see Berner and Berner (2012), Bigg (2003), Lehr and Keeley (2005), and Follows and Oguz (2007).

6.1.5 Atmospheric waters (hydrometeors): Chemical composition Atmospheric water includes physical water in all aggregate states, i.e., as gaseous, liquid (in droplet form), and solid (ice particles) (Figure 6.3). The historic term “atmospheric waters” has the meaning of hydrometeors in current terminology, i.e., meteoric water (Chapter 2.4, Volume 2). For historical reasons, dew was considered to belong to these “waters,” but that was before Wells (1814) stated that dew was not from water drops falling from heaven. The phenomena fog and clouds, precipitation (rain, snow, hail), and dew were well described as early as antiquity. A phenomenological understanding of physical (but not chemical) processes associated with hydrometeors was complete only by the late nineteenth century. Today we understand the physics and chemistry in the chain aerosol–cloud–precipitation and in relation to the climate relatively well. However, it seems that because of the huge complexity a mathematical description (i.e., parameterization for chemistry and climate modeling) is under ongoing development.

6.1 The hydrosphere and the global water cycle | 471

evaporation

gaseous precursors

(< 0 °C)

gas-to-particle conversion

nucleation

cloud, fog, mist

CCN

rime

impaction

interception (> 0 °C) dry deposition

emission

condensation

precipitation

mountain surface

evaporation

water vapor

(< 0 °C)

condensation

frost

(> 0 °C)

dew

wet deposition ground surface

Fig. 6.3: Simplified scheme of atmospheric water forms, transfers, and removal (deposition); note that different scavenging processes are not shown in their entirety.

Clouds and precipitation are not only an atmospheric link in the global water cycle but also an important reservoir for chemical processing and the transportation of trace substances. Naturally, clouds are far above the surface (with the exception of fog) and thus not easy to study even at present. Precipitation (rain, snow, hail), however, has always been easy to observe by human senses (seeing, touching, smelling, and tasting) and to collect for volume estimation and analysis. Precipitation was probably long considered a climatic precondition for survival by early humans, but, with extreme events, it could also be catastrophic for housing as well as farming. The mixing of air and water with pollutants (accurately referred to in old terminology as “foreign bodies”) was known since Aristotle; the role of precipitation in cleansing the surroundings was wonderfully described by John Evelyn (Volume 2, Chapter 2.5.3). Only a very small percentage of all the water in the climate system is actually present in the atmosphere. Most atmospheric water is in the vapor phase; the liquid water content (LWC) of clouds is only on the order of 1 g m−3 , the cloud ice water content (IWC) still less, down to 0.0001 g m−3 . But clouds play a huge role in the climate system, whereas precipitation closes the cycle for water and also for substances dissolved in it (wet deposition). Some of the processes (droplet formation, transfer processes, deposition, and chemistry) were described in previous sections; the aim of this section is to describe the chemical composition.

472 | 6 Biogeochemistry and global cycling

6.1.5.1 Clouds The fact that cloud droplets form only on preexisting aerosol particles determines the initial chemical composition of cloud water: in maritime air masses sea salt (NaCl) is dominant, whereas in continental air masses ammonium sulfate dominates (Chapter 3.6.4). Nitrate and calcium originate from both anthropgenic pollution sources (gaseous NO x and dust) and natural sources such as vegetation and soils. After droplet formation, uptake of gases modifies the chemical composition of cloud water. Generally, all elements can be found in cloud water (Table 5.36). Tab. 6.5: Chemical composition of cloud water at different sites around the world (μeq L−1 ); A – altitude a.s.l. in meters. NO−3

Site /area

A

Cl−

Mount Rigi (Switzerland) a Seeboden (Switzerland) a Mount Wilson (LA, USA) b Whiteface Mountain (USA) c Whiteface Mountain (USA) d Mount Brocken m (1960/62) Mount Brocken e (1993/95) Mount Brocken f (1996/02) Soviet Union g Soviet Union n Soviet Union o Kleiner Feldberg h Åreskutan (Sweden) i Åreskutan (Sweden) j Åreskutan (Sweden) k Mount Norikura (Japan) l

1620 1030 750 1483 1483 1142 1142 1142 – – – 826 1250 1250 1250 3026

53 490 300 77 440 380 190 1486 859 – 73 410 31 110 140 206 224 775 73 236 213 92 235 176 48 7 128 178 2 12 59 13 185 242 779 409 5 9 32 19 68 700 0.8 2 6 118 55 531

a

SO2− Na+ 4 34 20 241 – 11 296 303 279 35 104 30 107 6 33 < 0.4 96

NH+4

K+

660 920 580 157 89 711 72 96 61 35 105 1543 10 – 1 183

8 46 15 88 21 139 – – 20 17 87 220 6 57 4 38 18 45 44 20 15 50 22 56 < 0.8 0.7 6 22 < 0.8 0.3 74 –

Ca2+

Mg2+ H+ 12 23 21 5 90 1184 – 32 6 280 – 8 22 103 22 61 45 8 74 5 37 0.8 – 316 0.8 35 12 4 < 0.2 13 – 160

Winter 1990 to spring 1991 (Collett et al. 1993). 120 samples between 1982 and 1983 (Waldman et al. 1985). c 1986–1988 (Mohnen and Vong 1993). d 28 samples from stratus clouds, 1976 (Castillo et al. 1983). e 3476 samples, 1993–1995. f 8086 samples, 1996–2002. g 655 samples from aircraft between 1960 and 1970 (Petrenchuk 1979). h 1983–1986 (Wolfgang Jaeschke, pers. commun.) i 80 samples, summer 1983/1984 (Ogren and Rodhe 1986), only sectors NE + W. j Four samples from south (polluted air) (g). k 41 samples from NW (clean air) (g). l Ten samples, 1963 (Okita 1968). m Mrose (1966), n = 18; due to the much higher concentration than that found 30 years later, it must be assumed that fog water was sampled, not cloud water (Table 6.7). n 16 aircraft samples around Leningrad (Petrenchuk and Drozdova 1966). o 46 aircraft samples NW of European territory of USSR (Petrenchuk and Drozdova 1966). b

6.1 The hydrosphere and the global water cycle |

473

The number of cloud chemical measurements is rather limited; cloud water was sampled at about 50 sites, almost always only for a short time (see Table 6.5 for selected examples).² The smallest ever measured concentrations were found at Åreskutan from northwestern (polar) air masses, likely representing North Atlantic CCN background. At this station, when southern (continental) air masses arrive, concentrations increase by more than one order of magnitude. Local pollution (e.g., at Kleiner Feldberg) is responsible for higher sulfate and nitrate levels, but also ammonium, which originates from agricultural activities. For the first time, at three different mountain sites in about the same season in 1993 in Europe, my group studied cloud chemistry using identical sampling techniques and analytical procedure, which allowed for a highly qualitative geographic cross-comparison (Table. 6.6). Despite the predominance of sea salt (NaCl) at Great Dun Fell, the general chemical composition was not very different. Note that in 1993 already large air pollution abatement projects were under way in Eastern Europe (Chapter 4.2.5, Volume 2). See further details on cloud chemical composition at Mount Brocken in Chapter 4.2.5.3, Volume 2. Cloud water sulfate at Mount Brocken is not very different from that at the five White Mountain sites (1986–1989), ranging from 176 to 489 (290 ± 124) μeq L−1 and Whiteface Mountain (1994–1999), varying between 202 and 379 (298 ± 86) μeq L−1 (Table 6.50. Very low sulfate levels were found in Northern Europe in clouds from northern directions (around 30 μeq L−1 ), whereas air masses from the south contained 700 μeq L−1 (Ogren and Rodhe 1986). In the early 1990s, cloud-water sulfate estimated from other mountains in Europe ranged between 300 and 500 μeq L−1 (Tables 6.5 and 6.6). Tab. 6.6: Chemical composition of cloud water at three different sites in Europe (LWC weighted, μeq L−1 , LWC in mg m−3 ) (Acker et al. 1999b). Site

Altitude

LWC

Cl−

NO−3

SO2− 4

Na+

NH+4

Ca2+

Mg2+

H+

pH

Great Dun Fell a Mount Brocken b Mount Srenica c

847 1142 1362

146 258 323

238 41 46

238 260 502

472 280 447

246 33 58

306 408 471

37 39 88

67 16 29

321 90 354

3.49 4.05 3.45

a

Central England, 4 cloud events, 30 samples (May 1993). 8 cloud events (August–October 1993). c Krkonoše, southwest Poland, 6 cloud events, 63 samples (September/October 1993). b

2 A comprehensive review of cloud chemical studies is given in Chapter 2.4.8, Volume 2.

474 | 6 Biogeochemistry and global cycling Tab. 6.7: Chemical composition (in μeq L−1 ) of fog water in different regions of the world (arithmetic mean unless otherwise noted). Site/region NY (USA) a

Brooklyn, Nantucket Island (USA) a Kap Arkona (Rügen) b Collmberg (315 m) b Zinnwald (877 m) i Taunus c Central California d Po Valley, Northern Italy e San Joaquin Valley, California f San Joaquin Valley, Bakersfield, California g Bern-Belpmoos (Switzerland) h

Cl−

NO−3

SO2− 4

Na+

NH+4

Ca2+

Mg2+

H+

pH

28 2500 1738 583 450 642 223 174 572 47

– – 153 190 680 1540 1110 775 1425 850

312 1061 1860 3302 1960 1210 292 820 493 1160

– – 1500 – – – 139 37 316 19

– – 1653 2100 1500 – 1580 1606 750 1440

– – 750 3176 – – 84 52 74 47

– – – – – – 27 17 89 6

20 – 158 63 5 1450 479 292 1105 60

4.7 – 3.8 4.2 5.3 2.8 3.3 3.7 3.0 4.2

605

578

1300

54

1534

309

58

3

5.5

a

11 and 5 samples, resp. (Houghton 1955). 28–42 samples, around 1960 (Mrose 1966). c (Schrimpff u. a. 1983). d 1980–1982, ten samples, 150 km north of Los Angeles (Brewer et al. 1983). e November 1984 and 1985, 169 samples (Fuzzi 1988). f 1981–1983, 53 samples from 11 stations (Jacob et al. 1985). g December 1982 to January 1983, 108 samples (Jacob et al. 1984). h Median, agricultural area 515 m a.s.l., October 1983 until March 1985, 27 samples (Fuhrer 1986). i 105 samples from 35 events May–November 1987 (Zier 1992). b

6.1.5.2 Fog The chemical concentration in fog water is almost always significantly higher compared to that in cloud water (Tables 6.7 and 6.8). This is due to higher ground-based concentrations of precursors (gases and aerosol particles) and the fact that fog moves slowly and fog droplets reside longer than cloud droplets, leading to the enrichment of soluble substances. Moreover, chemical reactions are of greater importance in fog water than in cloud water, simply due to the larger residence time. Hence local pollution and emission sources are reflected by fog water chemical composition, for example, chloride and sodium close to the ocean and ammonium at agricultural sites. High acidity (pH < 3) and likely phytotoxic substances found in fog led in the early 1980s to the idea that forest damage observed at lower mountain sites could be caused by fog (or clouds). Observation of forest decline stimulated fog research in the 1980s. 6.1.5.3 Rain (precipitation) The exploration of the chemical composition of rainwater and snow is among the first activities in studying air chemistry (Chapter 2.4.6, Volume 2). It requires only relatively simple techniques (which, of course, can be continuously improved, finely by combining automatic wet-only samples with in situ analysis techniques):

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475

Tab. 6.8: Chemical composition (μmol L−1 ) of fog water in California (USA), 108 samples, December 1982–January 1983, after Jacob et al. (1984). Substance

Concentration

Substance

Concentration

TOC S(IV) Fe Pb HCHO Ni

4000 515 400 330 165 61

V Cu Mn Sum of organics Sum of inorganics Sum of metals

55 34 14 4165 3487 894

– – –

precipitation collector (e.g., funnel) and water storage container (e.g., bucket), precipitation amount sensor (simplest volume measurement of collected water in relation to collector surface), and chemical analysis of water composition.

However, many points of quality assurance and quality control (QA/QC) must be considered to obtain real values of wet deposition and chemical composition as well (see technical literature on precipitation chemistry³). Hence, wet deposition is simple to measure, but the interpretation of the chemical composition of rain and snow is not simple due to the complex dispersion and transformation processes from emission to deposition including in-cloud and below-cloud scavenging. In other words, at the point of precipitation and its sampling, long-range transportation of precursors in air, atmospheric aerosol, and clouds, as well as the complexity of physicochemical history, determines rainwater composition in precipitating clouds (in-cloud scavenging), and local processes determine the below-cloud scavenging. At remote or very clean sites, rainwater composition is almost determined by the chemical composition of cloud water. At heavily polluted sites (at present rarely encountered), the subcloud scavenging of PM and soluble gases can dominate rainwater chemical composition. Hence, rainwater chemistry was for a long time used for air pollution monitoring. With this in mind it is remarkable that on the basis of longterm monitoring in Europe approximately linear relationships with high correlation were found between emissions and concentrations of SO2 and sulfate concentrations in precipitation (cf. Chapter 4.2.5.4 in Volume 2). Looking at the trends of rainwater constituents in Europe over the last 100–150 years (Table 6.9), we can say that sulfate increased from the early nineteenth century up to 1980 by a factor of three and decreased relative to the 1980 period by a

3 In chemistry, precipitation means a precipitate, i.e., a solid deposition within a solution. Therefore, in the literature it is called almost always rainwater chemistry. Here, the term precipitation is used in its meteorological sense. The often used term “chemistry of acid rain” is not scientifically valid because acidity is already a chemical property of rainwater.

476 | 6 Biogeochemistry and global cycling

Tab. 6.9: Changing chemical composition in rainwater (European average) by factors relative to 1 (1900); for pre-1980 references see in Möller (2003). Since 2000 no more changes have been observed. Compound

∼ 1900

1900 → 1960

1960 → 1980

1980 → 2000

Nitrate Sulfate Ammonium pH a

1 1 1 1

4–6 ∼2 ∼ constant 1

6–12 ∼3 ∼ constant 1

∼ constant ≤ 0.5 ∼ 0.8 ∼ 1.2

a The pH likely remained constant (4.0–4.5) between 1860 and 1980 due to the neutralization of acidic

by alkaline compounds and increased (in other words, acidity decreased) between 1990 and 200 to about 5.0–5.5.

factor of six to the present, putting it now at about 50% of the nineteenth century value (remember that the nineteenth century was the age of coal combustion, with sulfur pollution). In contrast, nitrate increased by about one order of magnitude from 1900 – and has not dramatically abated up to the present. This reflects the twentieth century as the mobile-fuel-based engine period. It is remarkable that ammonium did not change over the 1900–1980 period (for more information and further discussion see Sutton et al. 2008). The pH (in terms of acidity) also remains about constant and only increased slightly after 1990 due to almost total SO2 abatement. To assess anthropogenic modifications to biogeochemical cycles, it is important to know the “natural” pH or background acidity (Horváth and Möller 1987). As seen in Table 6.10, rainwater chemical composition reflects the extreme city air pollution in the nineteenth century. The London values also show the high importance of NH3 emissions at that time as a result of the lack of wastewater management. As a result, the pH was not different from late-twentieth-century values. Interesting are the Beijing rainwater values, which were not significantly different from German background values but had a very high pH due to alkaline soil dust from the Gobi Desert. Later, however, pH dropped to less than 5 due to the extreme increase in SO2 emissions in China. We see that the balance between acidic and alkaline constituents determines rainwater acidity. Tab. 6.10: Historical comparison of rainwater chemical composition. Site

pH

SO2− 4

NO−3

NH+4

Cl−

mg L−1 London 1870 Beijing 1981 Seehausen 1985 a b

4.8 6.5 4.3

57.7 16.6 13.4

Sum a μeq

8.9 5.0 4.3

10.6 4.0 2.7

10.5 2.1 2.9

∆b

Reference

1014 254 229

Smith (1872) Zhao et al. (1988) Möller (2003)

L−1

1029 254 274

− + − [SO2− 4 ] + [NO3 ] + [Cl ] − [NH4 ]. 2− − − [SO4 ] + [NO3 ] + [Cl ] − [NH+4 ] − [H+ ] = missing neutralizing cations such as Ca2+ .

6.1 The hydrosphere and the global water cycle |

477

Since about the year 2000, changes in emission structure and, therefore, “chemical climate” became negligible – emission abatement completed and “energy change” (third industrial revolution) has yet to be seen. In Germany and Central Europe we have seen a relative homogeneous distribution of atmospheric constituents (in air, precipitation, and PM); temporal and spatial variations in concentrations are slight and reflect meteorological variation (“physical climate”) and no longer variations in emission patterns. Precipitation composition in Germany is no longer very different from that in Scandinavia 20 years ago (Table 6.11, last six lines). Local “pollution” (soil dust, agriculture, power plants), however, may contribute to higher concentrations; what is remarkable is the below-cloud scavenging of sulfate and calcium at Radewiese (Table 6.11) located 5 km downwind of the largest lignite-fired power station in Germany (Jänschwalde). Tab. 6.11: Chemical composition of precipitation in different regions of the world (μeq L−1 , rounded). Site

H+

Na+

K+

NH+4

Ca2+

Mg2+

Cl−

NO−3

SO2− 4

China (1981–1984) a India (1988–1996) b Cape Grim (1977–1985) c Central Australia (1980–1984) d Lancaster (NW England) e Central Bohemia (1980s) f Hungary (1980s) g Seehausen (1983–1989) o North Sweden (1983–1987) h South Sweden (1983–1987) i Seehausen (1996–2002) o Melpitz (2000) j Neuglobsow (2000) k Staudinger (2007–2008) l Peitz (2011–2012) m Radewiese (2011–2012) n

0.2 0.1 1 17 34 42 32 44 23 46 14 13 13 10 6 4

44 18 1167 4 57 7 23 33 4 24 20 8 14 14 30 31

21 8 30 1 4 3 9 6 2 2 2 1 2 3 17 7

160 40 2 3 55 62 61 85 13 36 52 44 39 44 78 52

460 56 78 2 15 30 85 59 3 10 16 13 18 18 30 483

– – 247 1 15 – 16 12 2 7 5 3 4 5 9 12

39 32 1372 8 79 – 26 63 5 30 25 8 14 14 28 20

34 18 3 4 28 51 41 45 11 36 39 31 31 36 58 41

162 36 152 4 89 116 119 150 33 67 40 35 33 31 47 469

a

Suburb of Beijing (Zhao et al. 1988). Suburb in semiarid area (Kumar et al. 2002). c Tasmania, South Pacific air (Ayers and Ivey 1988). d Katherine, annual rainfall 75–136 mm (Likens et al. 1987). e Harrison and Pio (1983). f Hradec, mean of 483 samples (Moldan et al. 1988). g Mean from six stations (Horváth and Mészáros 1983). h Mean from ten stations (Granat 1988). i Mean from 20 stations (Granat 1988). j Rural station near Leipzig, weekly wet-only samples (UBA). k Background station 60 km north of Berlin, weekly wet-only samples (UBA). l Hanau (within power station Staudinger) 25 km east of Frankfurt, n = 61 (Möller et al., unpublished). m 15 km north of Cottbus, close to Jänschwalde power station, n = 123 (Möller et al., unpublished). n 15 km northeast of Cottbus, directly under the plume of Jänschwalde power station, n = 128. o See Chapter 4.2.5.4 in Volume 2 for more details. b

478 | 6 Biogeochemistry and global cycling

6.2 Biogeochemical cycling Fundamentally, life on Earth is composed of six major elements: H, C, N, O, S, and P. These elements are the building blocks of all major biological macromolecules, including proteins, nucleic acids, lipids, and carbohydrates (Falkowski and Godfrey 2008). The production of macromolecules requires an input of energy, which is almost exclusively derived from the Sun. The character of biological energy transduction is nonequilibrium redox chemistry. Apart from energy, the production of macromolecules requires an input of a chemical substrate as the raw material, which has transportable (volatile, solvable) and transformable (oxidable, reducible, dissociable) geochemical conditions. Biological evolution gave rise to specific cells and organisms that are responsible for driving and maintaining global cycles of the six elements. Because all redox reactions are air paired (oxidation-reduction), the resulting network is a linked chemical system of the elemental cycles (Figure 6.4). For example, the reduction of carbonate, sulfate, and nitrate requires hydrogen and the oxidation of organic compounds (including carbon, sulfur and nitrogen) requires oxygen. According to the biological cycle, which is that part of the biogeochemical cycle where biomass is produced and decomposed (Figure 6.4), all volatile compounds occurring in the biochemical cycles can be released to their physical surroundings. These are as follows: – carbon: CH4 , NMVOC (nonmethane hydrocarbons), CO, CO2 ; – nitrogen: NH3 , N2 O, N2 , NO, RNH2 (organic amines); – sulfur: H2 S, COS, (CH3 )2 S (DMS), RSH (organic sulfides). As seen, sulfur and nitrogen are important elements in organic compounds. The sulfur and nitrogen cycle is inherently linked with the carbon cycle. As discussed in Volume 2 (Chapter 3.2.2.3), oxygen is closely coupled with the carbon cycle and is chemically combined with compounds of nitrogen and sulfur (and others). Other cycles, such as those of phosphorus and of trace metals, are important for the biosphere but play a minor role in the atmosphere. With a few exceptions, most of the compounds of these cycles found in the atmosphere are condensed within PM. A major part of these species is found in soil or dissolved in water. Chlorine is not among the crucial elements important for life but is the dominant part of sea salt, one of the most important natural sources, and plays an important role in atmospheric chemistry. Apart from chlorine, other halogens such as iodine and bromine have been found – despite their much lower significance as sources compared with that of chlorine – to be very important in multiphase chemical processes in the atmosphere and at interfaces. The chemical composition of the biosphere or the climate system is the result of continuous geochemical and biological processes within natural cycles. As just discussed, since the appearance of humankind, a new driving force has developed: human matter turnover as a consequence of human-caused (or anthropogenic) emissions. Therefore, today’s biogeochemical cycles are clearly no longer natural but an-

6.2 Biogeochemical cycling

| 479

Fig. 6.4: Global cycling: the global redox process.

thropogenically modified cycles. Moreover, human-induced climate change is already causing permanent changes in natural fluxes, for example, through weathering, shifting redox, and phase equilibria. As discussed in Chapter 2.2.1, climate includes not only “traditional” meteorological elements such as temperature, radiation, and humidity but also acidity and oxidation capacity, to name some of the most important parameters influencing fluxes. From a physicochemical point of view, the driving forces in transport and transformation are gradients in pressure, temperature, and concentration. Once released from anthropogenic sources into the air, substances become an inherent part of biogeochemical cycles. It is worth noting here that different sources can provide more or less specific isotopic ratios that are very useful for source-appointment studies. Overall, concerning chemical reactions in the climate system, isotopic differences in reaction rates play no role apart from geological timescales. A biogeochemical cycle comprises the sum of all transport and conversion processes that an element and its compounds can undergo in nature. The substances undergoing the biogeochemical cycle pass through several reservoirs (atmosphere, hydrosphere, pedosphere, lithosphere, and biosphere) where certain concentrations accumulate because of flux rates determined by transport and reaction. The atmospheric reservoir plays a major role because of its high dynamic in transport and reaction processes and the global linkage between the biosphere and atmosphere (Figure 6.5). A global cycle may be derived from the budget of composition of the individual reser-

480 | 6 Biogeochemistry and global cycling

emission emission

atmosphere (CO2, H2O, NH3, O2, …) deposition

respiration (dissimilation)

photosynthesis (assimilation)

feeding

animals

plants

assimilation

(living biomass) death (decomposition) fermentation

aerob bacterial oxidation (nitrification)

litter (dead biomass) abiotic conversion

aerob mineralisation

NH3/NH4+, H2S/S2-

anaerob mineralisation

anaerob respiration (denitrification)

NO3-, SO42-

organic substances microorganisms in soil and water

Fig. 6.5: Biosphere–atmosphere interaction.

voirs, with a (quasi-)steady state being considered to exist. It shows variations on different timescales and may be disturbed by catastrophic events (e.g., volcanism, collision with other celestial bodies). The largest perturbation, however, is the one that can be observed over the past hundred years, caused by humans. The scale of anthropogenic global sulfur and nitrogen fluxes is now on the same order as natural ones. Mainly sulfur and nitrogen, among many other elements, maintain and propagate life. Biological systems constantly synthesize, change, and degrade organic and inorganic chemical species. For example, nitrogen and sulfur create compounds such as amino acids, which serve as building blocks for proteins, enzymes, and genetic materials (Figure 6.6). The biological cycle includes the synthesis of living OM (plants) from inorganic compounds, which are mainly in the upper oxidized level (carbon dioxide, water, sulfate, and nitrate). During biogenic reduction to more reduced sulfur and nitrogen species, a variety of volatile S and N compounds are formed that can enter the atmosphere; in other words, they undergo a phase transfer (emission). Biological processes that lead to this reduction can be considered the driving force of atmospheric cycles. Emitted biogenic compounds return to ecosystems (mostly) in oxidized form. This interaction is a result of the biogeochemical evolution of the Earth. Thus, the enhancement of global sulfur and nitrogen fluxes since the beginning of the Industrial Revolution about 150 years ago can lead not only to new reservoir concentrations (pools) but also to changes in the parameters of physical and chemical reser-

6.2 Biogeochemical cycling |

481

plants, algae CO2

(+O2 -H2O) respiration

(+O2 -H2O) respiration

(+H2O -O2) photosynthesis, (plants, algae)

org-S

animals

org-N

org-C

biomass H2S

anaerobic dissimilatory sulfate reduction (bacteria), aerobic assimilatory sulfate reduction (bacteria, plants, algae)

NH4+ N2

SO42-

aerobic nitrification, anaerobic denitrification (bacteria)

NO3-

bacteria, algae

Fig. 6.6: Biological cycling: The role of various species.

voirs, for example, radiation, temperature, reactivities (which themselves influence internal production rates), and transfer fluxes (positive or negative feedback).⁴ These interactions are not yet well understood. It is essential to know better the natural fluxes (anthropogenic fluxes are rather well estimated) and their variations, but even more important is knowledge about the biosphere–atmosphere interaction: What processes control the environmental parameters that themselves maintain life on Earth? We can then ask another question: What is the threshold of quantitative change (of any parameter) leading to a new quality of life? Finally, we must answer (or define) what changes in air, soil, and water quality humankind will even be able to accept in the future against the background of sustainable development. With respect to the climate system (biospheric evolution), and in comparison with human activities (noospheric evolution), it is logical to look to natural processes from which substances are released into the atmosphere (Chapter 6.2). Figure 6.6 shows the principal interaction between the biosphere (here again considered in a more narrow

4 These are good reasons to terminate the beginning of the new Anthropocene epoch.

482 | 6 Biogeochemistry and global cycling

sense) and the atmosphere. Uptake of gases by assimilation occurs in plants because of photosynthesis and respiration and in animals due to respiration. Uptake of gases by sorption onto solid and aquatic surfaces of the Earth is a physicochemical process called dry deposition (Chapter 2.6.1); however, assimilative uptake is also said to belong to dry deposition. Other processes of deposition (wet deposition and sedimentation) do not depend on surface properties but must be taken into account as input flux to the biosphere. Biogenic emission (which, as mentioned earlier, accounts for a significant fraction of NEP) is basically a loss of matter from the ecosystem. Through transfer into other ecosystems via atmospheric transport and transformation, however, it could have several functions (information by pheromones, self protection, climatic regulation, and nutrient spreading).

6.2.1 Photosynthesis: Nonequilibrium redox processes In Volume 2, Chapter 2.3.1, we have a short excursus on the history of the discovery of photosynthesis. Numerous investigations were conducted in the period from 1950 to the present to identify the detailed mechanisms, intermediates, and controlling systems of photosynthesis. Gest (1993) suggested the following general definition of photosynthesis: Photosynthesis is a series of processes in which electromagnetic energy is converted to chemical energy used for biosynthesis of organic cell materials; a photosynthetic organism is one in which a major fraction of the energy required for cellular syntheses is supplied by light. Molecular oxygen and CO2 are not included in the “common denominator definition” of photosynthesis because photosynthetic bacteria do not produce O2 , and CO2 is not necessarily a required carbon source.

Here we will discuss the chemical evolution of the assimilation process. Let us understand as assimilation generally the conversion of nutrients into the fluid or solid substance of the body of an organism, by the processes of digestion and absorption. It is not the aim here to discuss biological chemistry (biochemistry) but the pathway of inorganic molecules (CO2 , H2 O, and O2 ), which are the “fundaments” of our climate and, therefore, the climate system, through the organism. It is often said that our biosphere is far from being a redox equilibrium; in other words, without photosynthesis, atmospheric oxygen would soon be depleted. Establishing a redox equilibrium requires that all redox couples (oxidants and reductants) in a natural system (such as water, the atmosphere, or within an organism) must be in equilibrium or, in other words, the rates of oxidation must be equal to the rates of reduction – the net flux of electrons is zero. This is not the case in real systems because of different timescales between chemical kinetics (single reaction rates), transport rates, and microbial catalysis. Moreover, many reactions are irreversible in a subsystem (e.g., sulfate production in the atmosphere) and products must transfer to another system (in that example, in

6.2 Biogeochemical cycling

| 483

soil having microbial anaerobic properties) to close a cycle in the sense of dynamic but not thermodynamic equilibrium (further reading: Archer and Barber 2004). Without life on Earth, probably most of the geochemical redox potentials would be in equilibrium due to the tectonic mixing of all redox couples over the entire history of the Earth. Consequently, the role of green plants is the unique “transfer” of photons (solar radiation) to electrons (and its transfer onto carrier molecules) creating electrochemical gradients and promoting synthesis and degradation. However, reduction of water represents a redox couple: positively charged hydrogen (H+ ) is reduced to “neutral” H and negatively charged oxygen (OH− ) is oxidized to “neutral” O. In what follows, eqs. (6.2)–(6.9) do not represent elemental chemical reactions but gross turnover mechanisms (called in biology metabolization). The (bio-)chemical processes consist of many steps (reaction chains) and include organic catalysts (enzymes), complex biomolecules that are carriers of reducing (H) and oxidizing (O) properties, structured reactors with specific functions (hierarchic cell organs), transport channels, and organic membranes (which are the separating plates between different “reactors”). Organisms consist of organic bonded carbon. In biological evolution, the first primitive organisms must have based their development and growth on already existing organic compounds by resynthesis. We know that the first forms of life must have existed under anaerobic conditions. Fermentation is the process of deriving energy from the oxidation of organic compounds, a very inefficient process in which the bacteria produce ethanol and carbon dioxide from fructose (and other organic material), but many other products (e.g., acids) and carbon dioxide may be produced: C6 H12 O6 → 2 CH3 CH2 OH + 2 CO2 .

(6.2)

An important achievement was the first autotrophic forms of life (methanogens and acetogens), which transfer carbon from its oxidized (inorganic) form (CO2 ) to the reduced (organic) form that results in bacterial growth (in contrast, heterotrophic organisms can use carbon only from living or dead biomass: higher plants, animals, mushrooms, and most bacteria). This process is called anoxygenic photosynthesis: 2 CO2 + 4 H2 → CH3 COOH + 2 H2 O , CO2 + 4 H2 → CH4 + 2 H2 O .

(6.3) (6.4)

Serpentinization, arc volcanism, and ridge-axis volcanism provided hydrogen (Tian et al. 2005), where the geochemical processes may involve primordial hydrocarbon and water destruction. The next step in biological evolution, the oxygenic photosynthesis, sharply increased the productivity of the biosphere. Today the first photosynthetic prokaryotes range from cyanobacterial and algal plankton to large kelp. These organisms use H2 O as an electron donor: 2 H2 O + hν → 4 H+ + 4 e− + O2 (↑) .

(6.5)

484 | 6 Biogeochemistry and global cycling

Generally, the process of photosynthesis is written CO2 + H2 O + hν → CH2 O + O2 (↑) ,

(6.6)

where CH2 O is a synonym for OM (a building block of sugar C6 H12 O6 ). The creation of a photosynthetic apparatus capable of splitting water into O2 , protons, and electrons was the pivotal innovation in the evolution of life on Earth. For the first time photosynthesis had an unlimited source of electrons and protons by using water as the reductant. By freeing photosynthesis from the availability of volatile reduced chemical substances (such as H2 S, CH4 , and H2 ), the global production of organic carbon could be enormously increased and new environments opened for photosynthesis to occur. Great progress has been made in understanding the process of photosynthesis. The biological chemistry of oxygen remains a mystery (Falkowski and Godfrey 2008). The two steps, H2 O splitting and CO2 reduction in eq. (6.6), are chemically and biologically separated (within different cell compartments): 2 H2 O → 4 H(↓) + O2 (↑) , CO2 + 4 H → CH2 O + H2 O ,

(6.7) (6.8)

The “cycle” is closed by respiration, the process of liberation of chemical energy in the oxidation of organic compounds: CH2 O + O2 → CO2 (↑) + H2 O .

(6.9)

It is remarkable that in this way a stoichiometric ratio of 1:1 between fixed carbon and released oxygen is established. Therefore, net oxygen production is possible only when the rate of reaction (6.9) is smaller than that of reaction (6.8); in other words, the OM produced must be buried and protected against oxidation. This was the first closed biogeochemical cycle. Before “inventing” photosynthesis, when fermentation was the only process for transforming OM into biomass by primitive life (eq. (6.2)), no cycle was available. OM, derived either from hydrocarbons found in carbonaceous chondrite material or (as we consider to be less probable) synthesized photochemicals in air, is finally transformed into CO2 . We assume in the modern world that photosynthesis is balanced with respiration. Reaction (6.8) is a “Fischer–Tropsch” type synthesis. This is also known from inorganic nature under conditions deep in the Earth and in the upper atmosphere, but under extreme conditions outside the climate system or, in other words, where no life exists. We can also write the formation and degradation of “biomass” in the overall reaction: reduction

󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀󳨀 󳨀→ CO2 + H2 O + NH3 + H2 S 󳨀 ← 󳨀󳨀 Cx Hy Nn S m Oo + O2 .

(6.10)

oxidation

Water oxidation in oxygenic photosynthesis is a concerted four-electron process. Thus we can ask: was there a transitional multielectron donor before water was adopted as

6.2 Biogeochemical cycling

| 485

the universal reductant for oxygenic photosynthesis? Dismukes et al. (2001) argue that bicarbonate is thermodynamically a better electron donor than water for O2 evolution: HCO−3 󴀘󴀯 OH− + CO2

(K = 2.8 ⋅ 10−7 ) .

(6.11)

This implies that the Archean period with its high concentration of dissolved bicarbonate had available a stronger reductant than water for the first inefficient attempts at the evolution of an oxygenic reaction center. Dismukes et al. (2001) hypothesize that bicarbonate (specifically: Mn-bicarbonate oligomers), not water, was the transitional electron donor that facilitated the evolution of the bacterial photosynthetic precursor of cyanobacteria. The post-Archean period was brought on by the enormous reduction of atmospheric CO2 . Although it is unclear how this transition occurred, it would have required the evolution of a stronger inorganic catalyst and a stronger photooxidant to split water efficiently. The dissociation of water (into hydrogen and oxygen), however, is only possible under natural conditions in the upper stratosphere (Chapter 5.2.7). The most appropriate process under technical conditions, created artificially, is electrolysis. Water, however, is not nonreactive and is dissociated (protolyzed) into ions (H+ + OH− ) in solution. In the lower atmosphere, H2 O is decomposed by O1 (D) into the most reactive OH radicals. At the end of myriad reactions, OH is changed back to H2 O. There is no known way to obtain free hydrogen for reducing the nutrients important to life such as COx , SOx , and NO x outside nonliving systems. Basically, the water-splitting process in higher plants and some bacteria, where coloring matter (such as chlorophyll) is able to absorb photons and transfer them (similar to a photovoltaic cell) into electrons, works very similarly to an electrolytic cell (Figure 6.7) with a cathodic (electron donor) and an anodic site (electron acceptor). Chlorophyll (like other chromophoric substances) consists of several conjugated π-electron systems containing electrons easily excitable by light absorption. For most compounds that absorb light, the excited electrons simply return to the ground energy level while transforming energy into heat (see also Chapter 4.5.3). However, if a suitable electron acceptor is nearby, the excited electron can move from the initial molecule to the acceptor. This process results in the formation of a positive charge on the initial molecule (due to the loss of an electron) and a negative charge on the acceptor and is, hence, referred to as photoinduced charge separation: M + hν 󴀗󴀰 M+ + e− .

(6.12)

The site where the separational change occurs is called the reaction center. The first step on the negative site is the formation of an aquated electron (H2 O− ) (cf. Figure 6.7): H2 O + e− → H2 O− (≡ e−aq ) .

(6.13)

The energy provided by the donor (or the electrode potential) must be equivalent to the reaction enthalpy of eq. (6.13). Consequently, the total system “proton (wavelength) –

486 | 6 Biogeochemistry and global cycling

H2O

hν

(2 H2O = O2 + 2 H) chlorophyll

e- (+ † )

2 H2O

O2

e-

2 H2O- ( = eaq-)

2 H 2 O+

2 H + 2 OH-

2 H2O

2 H+ + 2 OH 2 H2O

2 H+ + 2 O + 2 e-

adsorption layer NADP+ (ox) NADPH (red)

O2

CO2 reduction into CH2O (+ H2O) Fig. 6.7: Basic chemistry of water-splitting process.

chromophor (photon-electron-transfer) – electron (excited state or potential)” is a result of a coupled (quantum-)chemical and biological evolution. The aquated electron undergoes several reactions (Chapters 4.4.3 and 5.2.5.1). It can be transported via water molecules and special cellular substances (electron transfer) to other molecules (respectively reactive centers) to achieve reductions (6.14a), but it can also decay into atomic hydrogen and the hydroxide ion (6.14b): H2 O− + R → H2 O + R− , −

−

H2 O → H + OH .

(6.14a) (6.14b)

Reaction (6.14b) is synonymous with H+ + e− → H (in the acidity balance, the OH− from dissociated water remains). At the electropositive site of the photosystem (M+ ) occurs H2 O + M+ → H2 O+ + M , (6.15) and again, the potential difference must be equivalent to the energy for the dissociation of an electron from a water molecule. H2 O+ splits into H+ + OH (Figure 6.7). It

6.2 Biogeochemical cycling |

487

is important to consider (similarly to electrode processes) that all species are in an electrical double layer and first undergo surface processes before diffusion into the solution occurs. The highly reactive OH radical (see also Chapter 5.2.5.4) will be further oxidized to oxygen: (6.16) OH → O + H+ + e− . The freed electrons “react” back according to eq. (6.12), M+ + e− → M, closing the electron transfer chain. Subsequent to reaction (6.16) is the evolution of molecular oxygen and its release to the air. Biological evolution created the reaction system in this way so as to avoid oxygen diffusing to reducing (electronegative) sites; see later discussion on oxidative stress. As a consequence of hydrogen formation, the process represents hydrogenation and reaction eq. (6.14a) as well as eq. (6.14b), resulting in the formation of hydrogenricher molecules (RH) via H + R → RH or R− + H+ → RH. The proton (or hydrogenium ion H3 O+ ) and the aquated electron are both the chemically fundamental species. The water molecule (H2 O) is the supporter, and, because of the special structure of water (Chapter 3.4.1), both species are rapidly transferred in aqueous solution when there are gradients in the electrical potential or acidity, respectively. In both cases, changing these natural system properties (for example, by human influences due to acidification and oxidative stress) will shift or even interrupt the natural (bio-)chemical cycles. Free hydrogen is used for carbon reduction according to eq. (6.8). The process is complex (called the Calvin cycle), and the starting point is the transfer of H onto NADP+ (nicotinamide adenine dinucleotide phosphate: C21 H29 N7 O17 P3 ),⁵ which is the oxidized form of NADPH (which is the reduced form of NADP+ ): NADP+ + H 󴀘󴀯 NADPH ,

(6.17a)

or, considering the reactive center, H C

(NADP+)

H H

H C

(6.17b)

(NADPH)

The so-called photosystems I and II are connected by an electron transport chain and produce NADPH for use in the Calvin cycle (cf. Figure 6.7). Similarly to reaction (6.17),

5 The IUPAC name is [(2R,3R,4S,5S)-2-(6-aminopurin-9-yl)-5-[[[[(2S,3S,4R,5R)-5-(5-carbamoylpyridin1-yl)-3,4-dihydroxy-oxolan-2-yl]methoxy-oxido-phosphoryl]oxy-hydroxy-phosphoryl]oxymethyl]4-hydroxy-oxolan-3-yl]oxyphosphonic acid.

488 | 6 Biogeochemistry and global cycling

very few functional groups act as redox couples, for example: O

N

C

(red)

(ox)

OH H

H

N

H

(ox)

C (red)

(6.18)

Without here touching on any biological structure, it is remarkable that the base chemical reaction in the reduction of carbon dioxide (eqs. (5.361), (6.4), and (6.8)) is the inverse reaction of CO oxidation under atmospheric conditions (CO + OH → CO2 + H): CO2 + H → CO + OH .

(6.19)

OH is deactivated in this reducing medium (or, in other words, electronegative center) by adding H onto OH, or, in terms of electron transfer, by adding an electron onto OH; see also the earlier remarks on the fate of OH in an oxidizing medium. Subsequent to reaction (6.19), the formyl radical HCO, a building block of sugars, is formed: CO + H → HCO (H − C∙ = O) .

(6.20)

Similarly, an electron transfer onto CO2 led to formic acid: e−

H+

e−

H+

󳨀→ CO2 󳨀󳨀→ CO−2 󳨀󳨀→ HCO2 󳨀󳨀→ HC(O)O− 󳨀 ← 󳨀󳨀 HCOOH .

(6.21)

Figure 6.8 shows schematically the basic (elemental) chemical reactions in the biological water-splitting process and the formation of oxygen, but also several competitive pathways. Normally, there is water input and oxygen output, whereas hydrogen (in terms of reducing power) remains in the system; the redox potentials are well balanced in their ability to maintain biological productivity in the sense of plant growth. A key species in oxygen evolution is the OH radical, which has the main feature of abstracting hydrogen from organic molecules (to oxidize them and itself to turn into a water molecule), i.e., to inhibit the biological function in building up organic molecules. Any change in the biochemical system to a more electropositive state or oxidant (increase in oxygen, ozone, and hydrogen peroxide) will turn the reaction chain to the inverse of photosynthesis, ultimately back to water according to the following reactions: H + OH− → H2 O + e− , H + O2 → HO2 󴀗󴀰 O2 + e− →

H+ O−2 󳨀󳨀→

O−2

(6.22) +

+H , e−

HO2 󳨀󳨀→

H+ HO−2 󳨀󳨀→

(6.23) e−

H2 O2 󳨀󳨀→ OH + OH− ,

(6.24)

+

H

O3 + e− → O−3 󳨀󳨀→ OH + O2 .

(6.25)

6.2 Biogeochemical cycling

e

O3-

| 489

O3

H+ O

O2

OH H2O+

H2O

hν -

H2O2

H2O H

O2

HO2± e

OH

± e

O2-

± e

H2O e

H2O

H H+

e-

± e

± H+ HO2

± H+

H2O2 H+

Fig. 6.8: Photosynthesis and oxidative stress.

It is therefore assumed that under increased oxic conditions – known as oxidative stress – not only will the Calvin cycle be interrupted due to reactions such as eqs. (6.22) and (6.23), but also the potential concentration of OH will increase as a result of the reaction eqs. (6.24)–(6.25). All these findings emphasize the central role of H2 O2 in radical chains during biochemical processes; its ubiquitous presence in living cells is proved (Möller 2009a). This suggests that H2 O2 may not be only a harmful byproduct of many normal metabolic processes but can also serve the function, via the Fenton reaction (OH formation via electron transfer to H2 O2 ; see reaction (6.25), right-hand side), of attacking unwanted particles such as viruses and bacteria. The enzymatic deactivation of H2 O2 prevents damage⁶ by its transformation into oxygen: −H+

−e−

−H+

−e−

H2 O2 󳨀󳨀󳨀→ HO−2 󳨀󳨀󳨀→ HO2 󳨀󳨀󳨀→ O−2 󳨀󳨀󳨀→ O2 .

(6.26)

As already mentioned, the fundamental role of H2 O2 in environmental chemistry lies in the simple redox behavior between water and oxygen depending on available electron donors or acceptors: reduced

oxidized

H2 O ←󳨀󳨀󳨀󳨀󳨀󳨀 H2 O2 󳨀󳨀󳨀󳨀󳨀󳨀→ O2 .

6 By catalase, which has one of the highest turnover numbers of all enzymes: one molecule of catalase can convert millions of molecules of hydrogen peroxide to water and oxygen per second.

490 | 6 Biogeochemistry and global cycling

6.2.2 Primary production of carbon Although photosynthesis is fundamental to the conversion of solar radiation into stored biomass energy, its theoretically achievable efficiency is limited both by the limited wavelength range applicable to photosynthesis and the quantum requirements of the photosynthetic process. Only light in a wavelength range of 400–700 nm (photosynthetic active radiation, or PAR, also called daily incident radiation) can be utilized by plants, effectively allowing only 45% of total solar energy to be utilized for photosynthesis. Furthermore, fixation of one CO2 molecule during photosynthesis necessitates a quantum requirement of ten (or more), which results in a maximum utilization of only 25% of the PAR absorbed by the photosynthetic system. On the basis of these limitations, the theoretical maximum efficiency of solar energy conversion is approximately 11%. In practice, however, the magnitude of photosynthetic efficiency observed in the field is further decreased by factors such as poor absorption of sunlight due to its reflection, respiration requirements of photosynthesis, and the need for optimal solar radiation levels. The net result is an overall photosynthetic efficiency of 3–6% of total solar radiation. About 120 Gt of carbon is fixed from atmospheric and dissolved aquatic CO2 per annum by terrestrial plants. This is the gross primary production (GPP), the rate at which an ecosystem’s producers capture and store a given amount of chemical energy as biomass in a given length of time (Table 6.12). Some fraction of this fixed energy is used by primary producers for cellular respiration and maintenance of existing tissues. Whereas not all cells contain chloroplasts for carrying the photosynthesis, all cells contain mitochondria for oxidizing organics, i.e., the yield of free energy (respiration). The remaining fixed energy is referred to as net primary production (NPP): NPP = GPP − plant respiration .

(6.27)

NPP is the primary driver of the coupled carbon and nutrient cycles and is the primary controller of the size of carbon and organic nitrogen stores in landscapes. Aboveground NPP ranges from 35 to 2320 g m−2 a−1 (dry matter, or DM) and total NPP from 182 to 3538 g m−2 a−1 (Scurlock and Olson 2002). However, quantifying primary production at a global scale is difficult because of the range of habitats on Earth and because of the impact of weather events (availability of sunlight and water) on its variability. Direct observations of NPP are not available globally, but computer models based on remote sensing and derived from local observations were developed to represent global terrestrial NPP showing a range of 40–80 Gt C yr−1 (Cramer and Field 1999). For example, the model developed by Potter et al. (1993) estimates a global terrestrial NPP of 48 Gt C yr−1 with maximum light use efficiency (LUE) of 0.39 g C MJ−1 absorbed photosynthetically active radiation (APAR). Over 70% of terrestrial net production takes place between 30° N and 30° S latitude. It is estimated that the total (photoautotrophic) NPP of the Earth was 104.9 Gt C yr−1 . Of this, 56.4 Gt C yr−1 (53.8%) was the product of terrestrial organisms, while the remaining 48.5 Gt C yr−1 was ac-

6.2 Biogeochemical cycling

| 491

Tab. 6.12: Global estimates of GPP (after Gough 2012) and NPP in Gt C yr−1 and biomass carbon in Gt C and biome area (after Amthor et al. 1998). Biome

Forest, tropical Forest, temperate Forest, boreal Savannah, tropical Grassland, temperate Deserts Tundra Croplands Other a Total a b

GPP

NPP

Plant carbon b

Soil carbon b

Area in 1012 m2

Gough (2012)

Amthor et al. (1998)

40.8 9.9 8.3 31.3 8.5 6.4 1.6 14.8 –

16.0–23.1 4.6–9.1 2.6–4.6 14.9–19.2 3.4–7.0 0.5–3.5 0.5–1.0 4.1–8.0 –

13.7 5.0 3.2 17.7 4.4 1.4 1.0 6.3 3.0

244 92 22 6 9 7 6 3 85

123 90 135 264 295 168 121 117 542

14.8 7.5 9.0 22.5 12.5 21.0 9.5 14.8 55.4

121.7

48.0–69.0

59.0

486

2057

150.8

Ice, lakes, peatlands, human areas, extreme deserts. Assuming that phytomass is 45% C.

counted for by oceanic production (Staley and Orians 2000). For the 1997–2004 period, Werf et al. (2006) found that on average approximately 58 Gt C yr−1 was fixed by plants. The current “best guess” is 60 Gt C yr−1 (Table 5.2) (Haberl et al. 2007). Consistent data on terrestrial NPP is urgently needed to constrain model estimates of carbon fluxes and, hence, to refine our understanding of ecosystem responses to climate change. Recent climatic changes have enhanced plant growth in northern midlatitudes and high latitudes. Research findings by Ramakrishna et al. (2003) indicate that global changes in climate have eased several critical climatic constraints to plant growth, such that NPP increased by 6% (3.4 Gt C over 18 years, 1982–1999) globally. The largest increase was in tropical ecosystems. Newer estimates of global GPP using remote sensing (107 Pg C yr−1 ) is in the range of previous GPP models (Yebra et al. 2015). In contrast, for oceanic NPP there appear to be great uncertainties, but it is agreed that ocean phytoplankton is responsible for approximately half the global NPP. Oceans (especially at high latitudes) typically represent a net sink of atmospheric carbon. These regions are dominated by diatoms, which typically grow and sink faster than other phytoplankton groups and thus can represent an important carbon transfer mechanism to the deep sea. The low latitudes, conversely, represent a source of CO2 to the atmosphere. Satellite-based ocean chlorophyll records indicate that global ocean annual NPP has declined more than 6% since the early 1980s (Gregg et al. 2003). The reduction in primary production may represent a reduced sink of carbon here via the photosynthetic pathway.

492 | 6 Biogeochemistry and global cycling The fate of NPP is heterotrophic respiration (R h ) by herbivores (animals), who consume 10–20% of NPP, and respiration of decomposers (microfauna, bacteria, fungi) in soils. The largest fraction of NPP is delivered to the soil as dead OM (litter), which is decomposed by microorganisms under release of CO2 , H2 O, nutrients, and a final resistant organic product, humus. Hence, net ecosystem production (NEP) is defined as follows: NEP = NPP − consumers respiration(Rh ) . (6.28) Another part of NPP is lost to fire (biomass burning), by the emission of VOCs, and as a result of human activities (food, fuel, and shelter). Loss of NPP (1015 g C yr−1 ) has been calculated as follows: – biomass burning: ∼ 4.0 (Malingreau and Zhuang 1998) – human activities: 18.7 (Krausmann et al. 2008) – VOC emissions: 1.2 (Guenther et al. 1995) NEP ultimately represents buried carbon, a large flux at the beginning of the biosphere’s evolution but at present limited to about zero. Most of the NPP goes to litter and is eventually mineralized back to CO2 . Werf et al. (2006) estimated for the 1997– 2004 period that approximately 95% of NPP was returned back to the atmosphere via Rh , another 4% (or 2.5 Gt C yr−1 ) was emitted by biomass burning, and the remainder consisted of losses from fuel wood collection and subsequent burning. Historically, global estimates of litter production have ranged from 75 to 135 Gt C yr−1 (often cited as DM, which is not the same as carbon; Werf et al. (2006) use a DM carbon content of 45%). Steady-state pools of standing litter represent global storage of around 174 Pg C (94 and 80 Pg C in nonwoody and woody pools, respectively), whereas the pool of soil C in the top 0.3 m, which turns over on decadal timescales, comprises 300 Pg C. Several estimates from Matthews (1997) suggest values in the middle of this range, from 90 to 100 Gt C yr−1 , accounting for both aboveground and belowground litter. Aboveground litter production may be 5–10 Gt C yr−1 including mainly forest, woodland, and grassland. The global litter pool estimated by Matthews (1997) from the measurement compilation is 136 Gt C. Inclusion of the remaining ecosystems may amount to ∼ 25 Gt C, raising the total to ∼ 160 Gt C. An additional ∼ 150 Gt C is estimated for the coarse woody detritus pool. Global mean steady-state turnover times of litter estimated from the pool and production data range from 1.4 to 3.4 years; mean turnover time from the partial forest/woodland measurement compilation is ∼ 5 years, and turnover time for coarse woody detritus is ∼ 13 years. Forests⁷ cover about 30% of the Earth’s land surface and hold almost half of the world’s terrestrial carbon; if only vegetation is considered (ignoring soils), forests hold

7 The definition of a forest according to FAO (2001) is an ecosystem that is dominated by trees (defined as perennial woody plants taller than 5 m at maturity), where the tree crown (or equivalent stocking level) exceeds 10% and the area is larger than 0.5 ha. The term includes all types of forests but excludes

6.2 Biogeochemical cycling

| 493

Tab. 6.13: Global forest, after FAO (2003); C&N – Central and North, S – South (values rounded). Region

Africa Asia Europa C&N America Oceania S America World

Land area (1012 m2 )

Production a (1015 g yr−1 )

Forest, in stock Area Volume (1012 m2 ) (109 m3 )

Mass (1015 g)

Density Wood (m3 ha−1 ) fuel

Total wood

29.8 30.8 22.6 21.4 8.6 17.5

6.5 5.5 10.4 5.5 2.0 8.9

46.5 34.5 116.4 67.3 10.8 110.8

70.9 45.1 61.1 52.4 12.6 180.2

72 63 112 123 55 125

0.81 1.02 0.06 0.12 0.01 0.30

0.93 1.56 0.48 0.95 0.09 0.65

130.7

38.8

386.4

422.3

100

2.32 b

4.66

Data from FAO (2003) given in m3 yr−1 ; recalculated using the regional mass-volume ratio. Given in 1.78 ⋅ 109 m3 yr−1 by FAO (2003); using world mean mass/volume ratio yields only 1.94 ⋅ 1015 g yr−1 . This slight inconsistency may be explained by different averaging methods but reflects the uncertainty of global values, which are “masked” when using “virtually correct” statistical data given in digits down to kt yr−1 by FAO (2003). For example, the values of the world forest area are different in this table (38.8), Table 6.14 (39.8), and Table 6.12 (42.3). a

b

about 75% of the living carbon (Houghton 2005b) (Table 6.13). Per unit of area, forests hold 20 to 50 times more carbon in their vegetation than the ecosystem that generally replaces them. The aboveground living biomass was estimated by Keith et al. (2009) to be about 200 t C ha−1 for tropical and temperate forest and 60 t C ha−1 in boreal forests. The global estimate by Kindermann et al. (2008) comes to 60 t C ha−1 (Table 6.14). According to different scenarios (Nabuurs et al. 2007), forest area in industrialized regions will increase between 2000 and 2050 by about 60 to 230 million ha. At the same time, the forest area in the developing regions will decrease by about 200 to 490 million ha. As noted in Table 6.14, the ratio between aboveground carbon in vegetation and organic carbon in soils is globally 0.4–0.6, where the upper estimate represents tropical forests; in other words, about twice the carbon in living biomass is stored in the soil. Table 6.15 shows a very rough assessment of the budget of forest carbon fluxes. The estimated net flux (∼ 1 Gt C yr−1 ) suggests that the global forest is a sink for atmospheric CO2 . However, this value, based on forest inventories, is only a fraction of the sinks inferred from atmospheric data and models, estimated to be 2.1(±0.8) Pg C yr−1 , referred to the northern midlatitudes and suggesting that more than half of the northern terrestrial carbon sink is in nonforest ecosystems (Houghton 2005a). The uncertainties are large, however.

stands of trees established primarily for agricultural production and trees planted for agroforestry systems.

494 | 6 Biogeochemistry and global cycling

Tab. 6.14: Global forest biomass, after Kindermann et al. (2008). Forest area (1012 m2 ) Forest volume Mass (1015

(1011

m3 )

g)

39.8 4.7 Biomass

Carbon

Aboveground Belowground Dead Litter Soil

470 130 80 – –

234 b 62 41 23 398

Total

680 a

758

a

The total is not equal to the sum of aboveground, belowground, and dead biomass. The changes were estimated to be (in 1015 g C) 299 (1990), 288 (2000), and 282 (2005), after Denman et al. (2007). These values (in the range 230–290 Pg C) are considerably lower than other estimates: 359–536 (different estimates in IPCC 2001), 335–365 (IPCC 2007), and 422 (Nieder and Benbi 2008). Interestingly, all authors state a percentage of global forest to global land vegetation of about 80% (77–82%); Chapin et al. (2000) state that 50% are in tropical forests and the remaining 30% in other forests. Schlesinger (1997) gives 560 Pg as the global plant carbon stock, and so derived about 450 Pg in forests.

b

Tab. 6.15: Approximate global terrestrial carbon fluxes, based on forest inventories (1015 g C yr−1 or Gt yr−1 ); – release from ecosystems (harvesting and emission into atmosphere), + uptake by ecosystem (NEP minus CO2 sequestration), + emission into atmosphere (source) and − uptake from atmosphere (sink). Process

Fluxes, total

Land-use change, total Soil emission b Forest fires Wood harvesting d Woodfuel use Vegetation growth, total Forest growth

−2.0 a

Budget (net flux)

+1.3 (0.9) f

a

Fluxes, forests

−1.0 c −2.4 +3.3 c (1.7–4.1)

+1.0 +1.0 c +? e +1.4 −3.3 c (1.7–4.1)

+1.6 f −1.8

Loveland et al. (2000). Difference between total land-use change and forest fires. c Mouillot et al. (2006). d Includes wood-fuel use. e Wood products (e.g., paper, panels). f Denman et al. (2007). b

Fluxes, atmosphere

±0

6.2 Biogeochemical cycling

| 495

The global organic carbon amount in soil ranges from 1500 to 2000 Pg C (to 1 m depth) and comes in various forms, from recent plant litter to charcoal and very old humified compounds. Inorganic carbon (carbonate) amounts to 800–1000 Pg C.

6.2.3 Nitrogen cycling Even though the atmosphere is 78% nitrogen (N2 ), most biological systems are nitrogen limited on a physiological timescale because most biota are unable to use molecular nitrogen (N2 ). Two natural processes convert nonreactive N2 to reactive N: lightning and biological fixation. Reactive nitrogen is defined as any single nitrogen species with the exception of N2 and N2 O. Atmospheric NO production via lightning is based on the same thermal equilibrium (N2 + O2 ↔ 2 NO) that takes place in all anthropogenic high-temperature processes (e.g., burning) (Chapter 5.3.2). This natural source, however, is too limited to supply the quantity of reactive nitrogen in the global biological nitrogen cycle (Figure 6.9). Biological nitrogen fixation by microorganisms in soils and oceans produces organic nitrogen (as reduced N3− in the form of NH2 bonding N) in fixing organisms. This nitrogen is lost from organisms after their death as ammonium (NH+4 ) via mineralization. Nitrification is the biological oxidation of ammonium (NH+4 ) to nitrate (NO−3 ), with nitrite (NO−2 ) as an intermediate under aerobic conditions: (NH+4 → NO−2 → NO−3 ). Under oxygen-limited conditions, nitrifiers can use NO−2 as a terminal electron acceptor to avoid accumulation of potentially toxic NO−2 , whereby N2 O and NO are produced. During that process, because separate bacteria (Meiklejohn 2006) oxidize NH+4 into

N2 / N2O denitrification fixation

fixation nitrification

NHx

NOy mineralisation

assimilation

assimilation

organic N

Fig. 6.9: The biological nitrogen cycle.

496 | 6 Biogeochemistry and global cycling NO−2 and NO−2 into NO−3 , the process can lead to the temporary accumulation of NO−2 in soil and water. These bacteria are generally chemoautotrophic, requiring only CO2 , H2 O, and O2 . The nitrifying bacteria Nitrosomas, which converts NH+4 to NO−2 , is also able to reduce NO−2 . This nitrite can decompose abiotically, yielding NO or NO2 , substantially favored in acidic soils (Figures 6.10 and 6.11). The debate about whether NO is an intermediate or is produced by nitrifiers itself via NO−2 reduction remains open (Firestone and Davidson 1989). Denitrification is a microbial process promoting the growth of some bacteria in soil and water that reduces nitrate (NO−3 ) or nitrite (NO−2 ) to gaseous nitrogen oxides (almost all N2 O and NO) and molecular N2 by essentially aerobic bacteria. The general requirements for denitrification to occur are: – the presence of bacteria possessing a metabolic capacity, – the availability of suitable reductants such as organic carbon,

Fig. 6.10: The biogeochemical nitrogen cycle. A ammonia synthesis (human-caused N fixation), B oxidation of ammonia (industrial production of nitric acid), C fertilizer application, D formation of NO due to high-temperature processes, E oxidation of N2 O in stratosphere, F oxidation of NO in troposphere, G ammonia deposition and transformation into ammonium, H biogenic emission, I biogenic N fixation, K denitrification, L nitrification, M assimilation (biogenic formation of amino acids), N mineralization. RNH2 organically bonded N (e.g., amines).

6.2 Biogeochemical cycling

– –

| 497

the restriction of O2 availability, and the availability of N oxides.

Current knowledge shows that the NO flux from the soil will depend both on physical transfer processes from the site of denitrification to the atmosphere and on the relative rates of production and consumption of NO (Galbally 1989b). Field measurements show that N2 is the main product. NO2 has been found in soil emissions (Slemr and Seiler 1984). Colbourn et al. (1987) suggested that the NO2 they detected was due to the oxidation of NO either in soil air or in their chamber system. However, there are abiotic processes in soils that produce NO2 from nitrite. The accepted sequence for denitrification is demonstrated in Figure 6.10 – the inverse process corresponds to nitrification: HNO3 (nitric acid) → HNO2 (nitrous acid) → HNO (nitroxyl) . Nitroxyl exists only as an intermediate and acts as a very weak acid (pK = 11.4), with NO− being the protolytic anion from which NO is formed via electron transfer (and vice versa). HNO is the transfer point to NO (as just described) and to N2 and N2 O in parallel pathways (Figure 6.11). H2 N2 O2 (hyponitrous acid), probably produced by enzymatic dimerization of HNO, is formally acid in the form of its anhydride N2 O (see Chapter 5.3.5.2 for details). Consequently, the biological nitrogen cycle is closed, beginning and ending with N2 : N2 fixation → NH+4 nitrification → NO−3 denitrification → N2 (Figure 6.10). Each intermediate, which is produced in a biological cycle (NO, N2 O, NH3 , HNO2 , organic N species) (Figure 6.11), can escape the “biosphere” (in terms of organisms, soil, water, and plants) by physical exchange processes depending on many environmental factors. On the other hand, plants and organisms can take up these species as well as other abiotically oxidized compounds such as NO2 and HNO3 from their environment again. The bacterial processes of denitrification and nitrification are the dominant sources of N2 O and NO in most systems. Only denitrification is recognized as a significant biological consumption fate for N2 O and NO. The chemical decomposition of HNO2 (or chemical denitrification), that is, the reduction of NO−2 by chemical reductants under oxygen-limited conditions and at low pH, can also produce N2 , N2 O, and NO. Chemical denitrification generally occurs when NO−2 accumulates under oxygenlimited conditions, which may occur when nitrification rates are high, for example, after application of NH+4 -based mineral fertilizers or animal manure. This process may account for 15–20% of NO formation. Abiotic HNO2 emission from soil NO−2 because of a simple chemical acid–base equilibrium was demonstrated by Su et al. (2011). Oswald et al. (2013) showed from equilibrium calculations that ammonia-oxidizing bacteria can directly release HNO2 at higher-than-expected levels, whereas soil emissions of HNO2 and NO feature similar optimum curves. HNO2 is produced and emitted during nitrification under low soil water content (less than 40%) and may contribute up to 50% of the reactive nitrogen release from soils (Oswald et al. 2013). Emission or deposi-

498 | 6 Biogeochemistry and global cycling

Fig. 6.11: Biochemical, soil chemical, and atmospheric chemical nitrogen oxidation and reduction in biosphere (nitrification, ammonification, and denitrification). Symbols for redox processes: −e: red, +e: ox, −H: ox (≡ e + H+ ), +H: red (≡ +H+ − e), −O: red (≡ +2 H+ − H2 O), +O: ox (≡ +H2 O − 2 H); circles: gases; dotted boxes: intermediates.

tion (biosphere–atmosphere exchange) is therefore a complex function of biological, physical, and chemical parameters describing the system. In the process of ammonification, hydroxylamine (NH2 OH) is an important intermediate in two directions, denitrification directly to ammonium and the oxidation of ammonium to nitrate (nitrification). As long as nitrogen remains in its reduced form (NH+4 ), it remains in the local environment because of its affinity for soil absorption and its rapid uptake by biota. NH+4 is in equilibrium with NH3 , which can escape to the atmosphere, depending on pH, temperature, soil moisture, soil type, and atmo-

6.2 Biogeochemical cycling

| 499

spheric NH3 partial pressure. The equilibrium between emission and deposition (gas uptake) is called the compensation point; similar factors control the emission/dry deposition of NO (see also Chapter 2.6.1). In addition to being important to biological systems, reactive nitrogen also affects the chemistry of the atmosphere. At very low NO concentrations, ozone (O3 ) is destroyed by reactions with radicals (especially HO2 ), although at higher levels of NO (larger than 10 ppt), there is a net O3 production (because HO2 reacts with NO to form NO2 ). The photolysis of NO2 is the only source of photochemically produced O3 in the troposphere. Although N2 O is not viewed as a reactive form of nitrogen in the troposphere, it adsorbs IR radiation and acts as a GHG. In the stratosphere, N2 O will be oxidized to NO x and impacts O3 concentrations. NH3 is the major source of alkalinity in the atmosphere and a source of acidity in soils. A small part of atmospheric NH3 (≤ 5%) is only oxidized by OH radicals, where a main product was estimated to be N2 O (Dentener and Crutzen 1994), thus contributing around 5% to estimated global N2 O production. Deposited NH3 /NH+4 will be nitrified in soils and water to NO−3 , where two moles of H+ are formed for each mole of NH3 /NH+4 . Thus, any change in the rate of formation of reactive nitrogen (and N2 O), its global distribution, or its accumulation rate can have a fundamental impact on many environmental processes. The linkage between the biosphere and the atmosphere must be assumed to have been in equilibrium prior to the current industrial age. Nitrogen species (NO x , N2 O, N2 ) emitted from plants, soils, and water into the atmosphere that are biogenically produced in a redox cycle between nitrification and denitrification will be oxidized to nitrate and return to the biosphere. This cycle was increasingly disturbed since the beginning of the Industrial Revolution more than 100 years ago. The most important aspect in the anthropogenically modified N cycle is the worldwide increase of nitrogen fertilizer application. Without human activities, biotic fixation provides about 100 Tg N yr−1 on the continents, whereas human activities have resulted in the fixation of around an additional 170 Tg N yr−1 by fossil-fuel combustion (∼ 30 Tg N yr−1 ), fertilizer production (∼ 100 Tg N yr−1 ), and cultivation of crops (e.g., legumes, rice; about 40 Tg N yr−1 ) (Table 6.16) (Galloway et al. 1995, 2004). The oceans receive about 100 Tg N yr−1 (about 60 Tg N yr−1 by atmospheric deposition and about 40 Tg N yr−1 via rivers), which is incorporated into the oceanic nitrogen pool. The remaining approximately 230 Tg N yr−1 is either retained on continents, in water, soils, and plants or denitrified to N2 . Thus, although anthropogenic nitrogen is clearly accumulating on continents, we do not know the rates of individual processes. Galloway et al. (1995) predict the anthropogenic N fixation rate will increase by 60% (based on 1990) by the year 2020, primarily due to increased fertilizer use and fossil-fuel combustion. About two-thirds of the increase will occur in Asia, which by 2020 will account for over half the global anthropogenic N fixation. Bouwman et al. (2013) estimated the global N input to soils through fertilizers, animal manure, biological fixation, and atmospheric deposition to be 155 (1900), 345 (2000), and 408–510 (2050) Tg N yr−1 ; they estimated the soil N

500 | 6 Biogeochemistry and global cycling Tab. 6.16: Global turnover of nitrogen (Tg yr−1 ); data adapted from Galloway et al. (2004).

Fixation Terrestrial Oceanic Atmospheric Industrial Total Emission Deposition Transport to groundwater Oceanic denitrification

Natural

Anthropogenic

Total

107 86–156 5.4 a 0

32 0 36 c 100 b

139 86–156 41 100

200–250

170

270–420

63 –

50 –

– –

– –

Atmospheric burden (emission + atmospheric flux) d

113 200 48 147–454 154

a

By lightning (NO formation). Ammonia synthesis (NH3 ). c High-temperature NO formation. d Should be equal to deposition. b

budget surplus (input minus withdrawal by plants) to be 118 (1900), 202 (2000), and 275 (2050) Tg N yr−1 . In contrast to sulfur species, there are no differences in principle between natural and anthropogenic processes in the formation and release of reactive nitrogen species. Industrial nitrogen fixation (in separate steps: N2 → NH3 , N2 → NO x , NOx → NO3 ) proceeds via the same oxidation levels as biotic fixation and nitrification, either on purpose in chemical industries (ammonia synthesis, nitric acid production) or unintentionally in all high-temperature processes, specifically combustion, as a byproduct due to N2 + O2 → 2 NO.

6.2.4 Sulfur cycling Because of the versatility of the sulfur atom and its prevalence in the primordial environment, it is not surprising that sulfur evolved to serve many structural, catalytic, and regulatory roles in biology (Figure 6.12). Sulfur is life-supporting in the following processes (Toohey and Cooper 2014): – Elemental sulfur reduction to H2 S provides a source of energy in Desulfuromonas and archaea. – H2 S oxidation to elemental sulfur provides a source of energy in Beggiatoa. – H2 S or S0 oxidation to sulfate provides a source of energy in Thiobacillus and archaea.

6.2 Biogeochemical cycling

| 501

Fig. 6.12: The biogeochemical sulfur cycle. A burial (formation of sediments), B assimilation (bacterial sulfate reduction), C aerobic oxidation, D deposition, E emission, M mineralization, P plant assimilation, O oxidation.

– –

Sulfate or sulfite reduction to H2 S provides a source of oxygen for Desulfovibrio, archaea. H2 S splitting during photosynthesis provides a source of hydrogen atoms in purple and green sulfur bacteria.

In an anaerobic environment (e.g., anoxic water basins, sediments of wetlands, lakes, and coastal marine ecosystems), sulfur bacteria reduce sulfate to support respiratory metabolism, using sulfate as a terminal electron acceptor instead of molecular oxygen (dissimilatory sulfate reduction). This process is the major pathway for H2 S production globally. However, since the anaerobic environment is often not in direct contact with the atmosphere, the escape of H2 S is limited because of reoxidation in an oxic layer. Reduced sulfur provides substrates for microbial oxidation to sulfate from which certain bacteria can obtain energy. These microorganisms are present in high numbers at the oxic–anoxic interface and can completely oxidize H2 S and other reduced sulfur compounds in a layer smaller than 1 mm (Andreae and Jaeschke 1992). Consequently,

502 | 6 Biogeochemistry and global cycling

Tab. 6.17: Global turnover of sulfur. Data adapted from Andreae (1990), recalculated from mole in mass (rounded). Process

Tg S yr−1

Bacterial dissimilatory sulfate reduction Costal zone Shelf sediments Depth sediments

70 190 290

Assimilatory sulfate reduction Land plants Ocean algae Anthropogenic SO2 emissions Total biogenic gaseous sulfur emissions Total natural sulfur emission (without sea salt) a

100–200 300–600 ∼ 100 a ∼ 50 ∼ 70

Today, global anthropogenic SO2 emissions are considerable lower (Chapter 4.3.2, Volume 2).

the large amount of H2 S that is produced in coastal areas cannot usually be transferred to the atmosphere. In the biological sulfur cycle, immense amounts of sulfur are turned over: 550 Tg yr−1 in the oceanic and assimilative bacterial sulfate reduction (100–200 by land plants and 300–600 by sea algae) (Table 6.17). COS is the most abundant tropospheric sulfur gas on Earth. Most biota, however, need sulfur to synthesize organosulfur compounds (cysteine and methionine as examples of the major sulfur amino acids). In contrast to animals, which depend on organosulfur compounds in their food to supply their sulfur requirement, other biota (bacteria, fungi, algae, plants) can obtain sulfur in the aerobic environment from sulfate reduction (assimilatory sulfate reduction). Most of the reduced sulfur is fixed by intracellular assimilation processes, with only a minor fraction released as volatile gaseous compounds from living organisms. However, after the death of organisms, during microbial degradation, volatile sulfur compounds may escape to the atmosphere, mainly H2 S, but also organic sulfides such as CH3 SH, CH3 SCH3 (DMS), CH3 S2 CH3 (DMDS), and CS2 , COS. CS2 and COS in air were first detected as recently as 1976; Crutzen (1976) proposed that COS might be a source of sulfur for the stratospheric sulfate in the Junge layer in quiescent volcanic periods because of its relative abundance and long lifetime compared with other sulfur trace gases (Noholt et al. 2003). In open ocean waters, DMS is the predominant volatile sulfur compound, being formed by phytoplankton. The precursor of DMS is dimethylsulfoniopropionate (DMSP), which is produced within phytoplankton cells and is thought to have a number of important physiological functions. Comparisons of the results of three-dimensional models of the sulfur cycle globally (Langner and Rodhe 1991, Pham et al. 1995) with field observations suggest that the marine DMS emission value of 16 Tg S yr−1

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503

(given by Bates et al. 1992) is reasonable. This, however, contrasts with Andreae’s (1990) range of 19–58 Tg DMS–S yr−1 for marine emissions; see also the discussion on oceanic DMS emissions in Chapter 6.3.2.2. The uncertainty factor in the DMS emission estimate of 2 to 3 is therefore an unresolved issue. This is a serious problem because of the dominant role of DMS in the natural sulfur budget (50–80% of total natural sulfur emissions). The CLAW hypothesis (named after the authors of the paper) (Charlson et al. 1987) highlighted the important potential role in climate regulation of DMS production in the oceans (Figure 2.5). Since the hypothesis was presented, it has become increasingly apparent that a complex network of biological and physicochemical processes control DMS emissions from the oceans. However, several of the crucial biological controls on DMS production remain uncertain, representing a major hindrance to our ability to decipher whether DMS cycling could contribute to the regulation of a warming climate (Archer 2007). What, then, is the fate of DMS in the marine troposphere? The gas-phase oxidation pathways of DMS involve OH and NO3 (the last mainly in NOx -polluted air masses) as oxidants forming either dimethylsulfoxide (DMSO), methansulfonic acid (MSA), or SO2 itself. DMS oxidation by IO is known to be negligible (Andreae 1990); oxidation by Cl and BrO are interesting possibilities. DMS oxidation by OH is rapid (Chapter 5.4.2), so that a residence time equal to or less than 1 day could be assumed, which is significantly shorter than the 3 days assumed by Langner and Rodhe (1991). The lower estimate of DMS residence time, τ, is consistent with an estimate via the ratio of burden to flux (τ = M/F) using a DMS concentration average for the mixing layer (typically 1 km) of 20–100 ppt. Considering a DMS emission range of 15–58 Tg S yr−1 , the possible range of τ lies between 0.06 and 1.2 days. DMSO and MSA also have some uncertain aspects. DMSO reacts rapidly with OH, probably resulting in the formation of SO2 and MSA (Andreae 1990). Mihalopoulos et al. (1993) estimated the annual average wet de−1 position of MSA to be 0.51 μeq m−2 d , corresponding to a flux of 2 Tg S yr−1 , which is between 5% and 10% of the annual DMS emission. Ayers et al. (1986) found a molar ratio of 6% of MSA to excess sulfate in the aerosol phase in a study conducted at Cape Grim Baseline Air Pollution Station (Tasmania, Australia). Both values support the idea that most DMS is oxidized to SO2 and probably SO2− 4 . The marine S(IV) budget is negligibly enlarged as SO2 is produced from H2 S and CS2 at only 1–2 Tg S yr−1 . DMS is now believed to be the most likely natural sulfate precursor, and SO2 from fossil-fuel combustion is the dominant anthropogenic one. Could this natural DMSderived “sulfate function” be a result of the Earth’s evolution, and are there feedbacks between the climate system and the sulfur cycle (Lovelock and Margulis 1974, Charlson et al. 1987)? Has the natural functioning of the atmospheric sulfur cycle been perturbed by human activities? Temperature records supporting the hypothesis that anthropogenic sulfate aerosol influences clear-sky and cloud albedo, and thus climate, have been advanced by several investigators (see, for example, Hunter et al. 1993), who have suggested that any natural role of sulfur in climate was subsumed by anthropogenic pollution. The direct climatic effect of sulfate aerosol is due simply to re-

504 | 6 Biogeochemistry and global cycling

flection of sunlight back to space, while indirect climatic effects of sulfate result from aerosol influence on cloud albedo or extent. Sulfate aerosols contribute to cooling, either directly or indirectly through their role in cloud formation. Also, changes in the chemical composition of aerosols may either increase or decrease the number of CCNs. Changes in the concentration of the number of cloud droplets can affect not only the albedo but also the cloud lifetime and precipitation patterns. Precipitation is both an important aspect of climate and the ultimate sink for submicron particles and scavenged gaseous pollutants. Climate change and decreasing seawater pH (ocean acidification) have widely been considered as uncoupled consequences of anthropogenic CO2 perturbation. Recently, experiments in seawater enclosures showed (Hopkins et al. 2011) that concentrations of DMS were markedly lower in low-pH environments. Six et al. (2013) concluded that global DMS emissions will decrease by about 18(±3)% in 2100 compared with preindustrial times as a result of the combined effects of ocean acidification and climate change. The reduced DMS emissions induce a significant additional radiative forcing. However, Arnold et al. (2013) showed that DMS production was sensitive both to acidification and temperature and that “global change” may not result in decreased DMS, as suggested in earlier studies. Sulfur, or more precisely sulfur dioxide (SO2 ), is the oldest known pollutant. Without knowledge of the chemical species, its influence on the air quality was described several hundred years ago in European cities where it was prevalent because of coal burning (e.g., Evelyn 1661). More than 150 years ago, SO2 was first identified as the cause of forest damage in the German Erzgebirge. However, it became of huge environmental interest only in the middle of the twentieth century after the well-known London episode in 1952, where increased concentrations of SO2 and PM in the presence of fog led to an unusually high mortality rate for the particular time of year. Subsequently, the atmospheric chemistry of SO2 and global sulfur distribution was studied intensively. Since then, anthropogenic sulfur emissions (and, consequently, atmospheric SO2 concentration) have continuously decreased in Europe. Today, since the introduction of measures for the desulfurization of flue gases from all power plants, SO2 no longer plays a role as a pollutant in Europe (Chapters 4.2.2, 4.2.5.2, and 4.4.2, Volume 2). Because the only natural source of SO2 (volcanism) shows large variations and the mean annual estimate is around 10 Tg yr−1 , anthropogenic SO2 emissions currently still account for around 80% of the total global flux of SO2 , and more than 90% end up in the Northern Hemisphere (Langner and Rodhe 1991, Dignon 1992, Spiro et al. 1992). Nevertheless, 10% of the global anthropogenic sulfur emissions account for 50% of the sulfur budget of the Southern Hemisphere. Thus, even in remote areas, we must assume that the sulfur budget is markedly disturbed by human activities. Moreover, the ratio between the direct SO2 removal flux and the flux due to its longer-lived sulfates, which cover regions up to several thousands of kilometers across, still remains an imprecise estimate. Many attempts have been made to quantify the global sulfur budget, beginning with the first estimates by Eriksson (1959, 1960, and 1963) and con-

6.3 Natural sources of atmospheric substances | 505

tinuing to the most recent one by Pham et al. (1995). It is remarkable that no more updated natural sulfur emission estimates have appeared, at the time of this writing, for some 15 years. While the estimate of the ratio between natural and anthropogenic sulfur emissions was a primary goal of the first established global sulfur budgets that were established (e.g., Möller 1982, 1983, 1984a, 1984b, 1995a, 1996), in more recent estimates the question of sulfate aerosols and their precursors was the main point of interest.

6.3 Natural sources of atmospheric substances For a given subsystem such as the atmosphere, the sources of compounds to be emitted into the air are crucial, similar to a chemical reactor in the sense of one boundary condition (the others are temperature, pressure, radiation, mixing, and water⁸ in different phases). For the atmosphere as a three-dimensional reservoir, the spatial distribution of sources, together with the source strength (or, in other words, the emission flux) must be known. This topic is presented very differently in the literature. Normally, a distinction is made between natural and anthropogenic sources and emissions. This is important for the knowledge needed to assess the degree of anthropogenic changes in the climate system, but for modeling the physics and chemistry of the climate system, for example, this separation is unimportant. Moreover, in some respects it is difficult to separate “natural” from “anthropogenic” sources and emissions. Agriculture with arable and livestock farming is “natural-biological” processing but is considered among man-made sources. Similarly, biomass burning (Chapter 4.2.4.2, Volume 2) accounts for about 90%, caused by humans by unintended or intentional reasons. Budget estimations on secondary sources (Chapter 6.3.4.2) cannot distinguish between natural and artificial primary sources. Finally, through land-use and climate change, biogeochemical cycles were also changed and therefore the source of strength of many natural biotas. Nevertheless, we follow here the “classical” treatment; the main natural source categories – biological processes (plants, microorganisms, and animals), – wind-driven resuspension (sea salt and soil dust), – volcanism and lightning, and – secondary atmospheric chemical processes. are briefly described, where the typical compounds belong to the sources, and emissions are also mentioned. In Chapter 4.3, Volume 2, the compounds themselves are the focus with emissions from different sources. The literature on this subject is huge; 8 Water is the atmospheric compound with the largest flux by far and the most significant for weather, climate, and chemistry (Chapters 3.4.4 and 6.1.1).

506 | 6 Biogeochemistry and global cycling

the interested reader is referred to more specialized literature. My aim is to present a comprehensive critical overview and to provide the “best known” current emission values.

6.3.1 Source characteristics Natural sources of atmospheric components are principally divided into biogenic and abiogenic (or geogenic). They may relate to biological processes in the soil (e.g., bacteria), in vegetation (plants), in the oceans (substances produced by algae) and nonbiological processes in the Earth’s crust (volcanoes or gas/oil seepage), or in the atmosphere (lightning), but also simply in the dispersion of particles by wind–surface interactions. Geogenic or abiotic/abiogenic sources can be distinguished as physical processes (dispersed soil dust and sea spray), geochemical processes (gaseous emanations, volcanic eruptions), and atmospheric chemical processes (lightning causing nitrogen oxides). A special – so-called secondary emission – source is lightning; through physicochemical processes (electric discharges) new products are produced from ambient molecules (N2 and O2 ). All of atmospheric chemistry itself continuously produces new secondary compounds. Natural emissions often depend strongly on climate, soil, or water characteristics, thereby showing a strong temporal variation in seasonality, diurnal cycle, or both. Soils act as source as well as sink; the direction of the flux changes with the compensation point. Thus, soil biological activities (as found for COS by Conrad and Meuser 2000) may depend on ambient concentrations, stressing the necessity to measure fluxes as a function of concentration to obtain reliable source or sink data for atmospheric budgets. Thus, natural sources often have a distinctly different character than anthropogenic sources, which are comparably constant with respect to seasonality. In addition, the source strength as well as the spatial distribution of natural sources may differ substantially from year to year. An extreme example is volcanic emissions. Cultivated soils produce soil dust by wind erosion: Is that a contribution by anthropogenic or natural sources? Nonetheless, desert dust is globally the dominant source in this category. Changes in land use over hundreds or even thousands of years (e.g., deforestation) have changed the quantity and the mix of VOC emissions from soils and vegetation. Biomass burning (wildfires) is at present almost all attributed to human activity, whether intentional or not; the only natural cause is lightning strikes, which are of minor importance globally. We see that it is becoming increasingly difficult to distinguish clearly between natural and anthropogenic emissions. This book will not draw a sharp line – it is more important to understand different sources and the controlling parameters of the emissions. With our understanding that humans are part of the biosphere and have changed it in an evolutionary way into the noosphere, we have to consider the (climate) system as a whole. The only difference between natural and artificial emissions

6.3 Natural sources of atmospheric substances | 507

lies in the fact that human-caused emissions are unbalanced in nature or, in other words, are in an open-loop. As a somewhat extravagant example, we could assert that it does not matter how one reduces the concentration of chlorine in the upper troposphere, whether by cleansing volcanic plumes of chlorine (if there were such a facility) or by banning its use. The effects are always based on the sum of molecules in the atmosphere. However, some sources or substances used without anticipating any environmental problem, due to small volume or chemical virtual harmlessness, such as halogenated and resistant organic compounds, and some heavy metals, have resulted in serious problems and required countermeasures.

6.3.2 Biological processes 6.3.2.1 Continental For the atmosphere, the Earth’s surface acts as both a source and a sink for trace gases and particles. Field measurements (mostly via concentration gradients) only quantify the net flux F, i.e., emission–deposition (Matson and Harriss 1995). The so-called compensation point is reached when F = 0. Hence, to calculate individual fluxes (emission and deposition) separately, empirical relationships and models are needed. The extrapolation of local measurements to broader ecosystems or grids concerning the spatial resolution of climate models under different meteorological conditions remains a major challenge. Key to an understanding of the exchange between the surface and the atmosphere is the planetary boundary layer (PBL). This layer, with a variable thickness between several hundred meters and a few kilometers, is defined as that region of the lower troposphere that responds to surface forcing (e.g., frictional drag, heat transfer). Temperature gradients influence vertical mixing and, hence, vertical transport rates. In the case of positive T gradients (increase with height), gases accumulate near the surface, so surface emission is reduced and even halted depending on the equilibrium conditions. In the case of strong convection producing rapid mixing, surface trace gases can reach the upper troposphere in just a few hours. Meteorological conditions strongly influence near-surface concentrations of gases and particles. As shown in Figure 6.13, organisms themselves emit gases via respiration, breathing, and transpiration. Plants can emit trace substances only during respiration (together with CO2 ); it was determined that 2–3% of their photosynthetic capacity is released in the form of diverse organic substances, though significantly more under stress conditions. As discussed in Chapter 6.1.1, the emission of trace gases by plants is always in relation to the assimilation and respiration process (Kesselmeier 2001, Kesselmeier et al. 2002). In plants nitrate is reduced to nitrite in the cytoplasm, after which the nitrite is reduced to NH3 in the chloroplasts (Galbally 1989b). Consequently, plants emit NO and NH3 . Plants also take up NH3 and NO2 very rapidly. This NO2 is chemically produced by atmospheric oxidation of biogenic and anthropogenically emitted NO, either above

508 | 6 Biogeochemistry and global cycling

C1 chemistry

CO2

2H(-H2O)

H

CO

H

HCO

2H

HCHO

CH3OH

H(-H2O)

H

CH3

CH4

CO 2H

C2 chemistry

COCH3

CH3CH2OH

H

CH3CHO C3 chemistry

CH3

CH3(CO)CH3

4H(-H2O)

Cn chemistry

CH2CH3

CO+H(-H2O)

CnHm

Fig. 6.13: Simplified reaction scheme of photosynthetic formation of organic compounds. In boxes are stable substances that might be emitted. The radical intermediates may undergo several competitive reactions, especially HCO (formyl) and CH3 (methyl) depending on the ratio between reactants (H, CO, and O2 ). In oxidative environments, acids are formed from aldehydes.

Tab. 6.18: Average global annual emission of organic substances emitted from terrestrial vegetation in Tg yr−1 . – no value given (note that the RETRO values are modeling results – the two decimal places imply a false accuracy; the imprecision is very likely ±20%) . Substance

RETRO(2008) b

Lathièreet al. (2005)

Isoprene Monoterpenes Methanol d CO Acetaldehyde Formaldehyde Acetone Propene Propane i–pentane Ethane Ethene i–butane

539.07 194.66 269.72 96.01 37.44 33.76 30.26 15.66 – – 4.12 3.84 –

460 117 106 – – – 42 – – – – – –

Total a a

–

752(±16) c

Guentheret al. (1995) 506 126 – – – – – – – – – – – 1150

Jacobet al. (2002) – – – – – – 33(±9) – 12 5 – – 3.6 –

Not the sum of the listed compounds but all. Only terrestrial fluxes as computed by the MEGAN model in MOZECH. Note that the computed values simulate exactness not being true. c This error is unrealistic small. d Further estimate (in Tg yr−1 ): 100 (Galbally and Kirstine 2002). b

6.3 Natural sources of atmospheric substances |

509

the canopy or below the canopy from soil-emitted NO. In the last case, a “closed” N cycle between soil and plant occurs, resulting in a smaller ecosystem emission. The uptake of NO2 faster than that of NO through stomata can be explained by different rates of conversion into some readily metabolized forms (e.g., NO−2 ), perhaps by photolytically produced solvated electrons: NO2 + e−aq → NO−2 . Similarly, sulfur species (almost all organic sulfides) are produced by assimilatory sulfate reduction. Plants emit DMS and COS, but also take them up (Yonemura et al. 2007). The largest amount of emitted species is based on carbon itself (Table 6.18). Care should be taken when using emission values referred to as “terrestrial emission” because it is probably the sum of plant (vegetation) and soil emission. Soils containing microorganisms predominantly emit inorganic compounds (NH3 , HNO2 , NO, N2 O, N2 , H2 S, and COS) because of nutrient cycling. It is evident that plants take up gases from air in the assimilation process, but only during the daytime. In contrast, soils can absorb them during both the day and night. Animal feces are rich in nitrogen and so are used in internal cycles, but by decomposition they emit many different volatile substances. Microorganisms are distributed in soils, aquatic systems, and oceans. Most of the material turnover in ecosystems is due to microorganisms. All substances exchanged with the local environment are therefore found in the given reservoir (soil, lake, river, and ocean), dissolved, suspended, or adsorbed. Thus, physical equilibrium and transport processes determine the reservoir distribution and phase partitioning. Between surfaces (soils and waters) and their surrounding air, a permanent exchange exists where the sensitive equilibrium is influenced by the air concentration. The escape of NO from soils is driven by molecular diffusion in soil pore spaces and by advective and convective air flows through the soil due to pressure and thermal forcing. Liquid water in soil pores can drastically reduce the NO escape due to much slower diffusivities. Field studies have shown that soil water forms a substantial barrier to the escape of NO from soils; however, a simultaneous increase in N2 O was observed (Galbally 1989b). The increased formation of N2 O could be explained by increasing oxygen deficiency and, therefore, higher reduction capacity. Bodies of water (rivers and lakes) may – especially when they are polluted – provide an important source of atmospheric emissions locally, but they play no role globally. Wetlands are among the most important ecosystems on Earth; an excellent book on wetland chemistry is Reddy and DeLaune (2008). Wetlands occupy about 5–8% of the global land surface (Table 6.19) and have a global NPP of (4–9) ⋅ 1015 g C yr−1 (Mitsch and Gosselink 2007), which corresponds to approximately 10–20% of total land surface NPP (Chapter 6.1.3). Natural wetlands contribute about 20% to global CH4 emissions (115–145 Tg yr−1 ). Rice paddies are anthropogenic wetlands and emit 60−80 Tg CH4 -C yr−1 (Megonigal et al. 2004, Whalen 2005). In the 1960s it was believed that huge sulfur emissions in the form of hydrogen sulfide were emitted from wetlands (Möller 1984a), but after reevaluation it now appears they are negligible on a global scale.

510 | 6 Biogeochemistry and global cycling

Tab. 6.19: Global wetlands (from data in Mitsch and Gosselink 2007). Type

Area (106 km2 )

Polar / boreal Temperate Subtropical / tropical Rice paddies

2.4–3.5 0.7–1.0 1.9–4.8 1.3–1.5

Total

6.8–12.8

It is possible to determine the emissions of different compounds by specific animals similarly to plants, depending on biological parameters (e.g., age, status, health) and physical parameters (e.g., temperature, radiation, humidity, acidity) (Table 6.20). Animals (including humans) contribute to atmospheric emissions along different pathways: directly through breathing, transpiration, and flatulence, indirectly through the conversion of excrement. As the total biomass of animals compared with that of plants is negligible, with the exception of emissions of NH3 and CH4 , there is no global significance in these emissions. Methane production by termites was first reported by Cook (1932), who observed the evolution of a gas from a species of termite. Apart from CH4 , termites may emit large quantities of carbon dioxide and molecular hydrogen into the atmosphere. Termites inhabit many different ecological regions, but they are concentrated in tropical grasslands and forests. Studies have indicated that methane is produced in a termite’s digestive tract during the breakdown of cellulose by symbiotic microorganisms. Later studies showed large variations in the amount of CH4 produced by different species. Estimates of the contribution to the global CH4 from termites vary widely, from negligible up to 15%. Zimmermann et al. (1982) estimated global annual emissions calculated from laboratory measurements of 150 Tg methane and 5000 Tg CO2 . As much as 200 Tg molecular hydrogen may also be produced. Seiler et al. (1984) estimated the flux of CH4 and CO2 from termite nests into the atmosphere to be in the range of only 2–5 Tg. Tab. 6.20: Emission factors for wild animal and human emissions (in kilograms per animal/person and year). Species

Assumed lifeweight (kg)

CH4

NH3

Reference

Deer (red deer, reindeer) Moose Roe deer Boar Birds Large birds Humans

100 350 15

25 50 4 1.5 – – 0.1

1.1 2.2 0.2 1 0.12 0.36 0.05

Sutton et al. (1995) Crutzen et al. (1986) Scaled from red deer a Niethammer and Krapp (1986) Sutton et al. (1995) Sutton et al. (1995) Crutzen et al. (1986)

a

0.8 2.4

Use animal weights to similarly scale emissions for other species.

6.3 Natural sources of atmospheric substances | 511

Fermentation of feed in the rumen of cows, goats, sheep, and several other animals belonging to the class of animals termed ruminants is the largest source of methane, from enteric fermentation by methanogenic bacteria and protozoa. In the European Union in the late 1990s, approximately two-thirds of emitted CH4 come from enteric fermentation and one-third from livestock manure (Moss et al. 2000). The composition of the animal feed is a crucial factor in controlling the amounts of methane produced, but a sheep can produce about 30 L methane each day and a dairy cow up to about 200 L. The reason that ruminants are so important to humans is that much of the world’s biomass is rich in fiber. Ruminants can convert this into high-quality protein sources (i.e., meat and milk) for human consumption, and this benefit needs to be balanced against the concomitant production of methane. 6.3.2.2 Oceanic The ocean as a source of trace gases is between biogenic and abiotic processes; hence, we consider the ocean here in a separate subsection. Whereas the generation of sea salt particles from the surface of seawater is a purely physical process (Chapter 6.3.3.2), it was identified as a considerable global source of different nitrogen, sulfur, and carbon species (Table 6.21). These species are produced in the ocean by biological processes similar to those in soils, but photochemical processes in surface water (e.g., Zhou and Mopper 1997) also provide products that can exchange with the air. It is assumed that surface seawater is saturated or even supersaturated with these gases (e.g., CO and dimethyl sulfide). The principles regulating the flux between ocean and atmosphere are well understood (Liss and Slinn 1983). However, systematic measurements of concentrations in surface air over the oceans are lacking, as are the measurements necessary to evaluate the equilibrium partial pressure in surface water. For example, alkyl nitrates were measured (Chuck et al. 2002) in surface seawater and air from the North and South Atlantic, which indicated a (natural) flux out of the oceans. Although production processes for trace gases in seawater are often poorly known or completely unknown, in the case of these alkyl nitrates, laboratory experiments indicate that they can be formed photochemically by the reaction of alkyl radical (ROO) and NO (Dahl et al. 2003). In a number of cases, we lack even basic knowledge of how the gases are formed (and destroyed) in the surface oceans, and this is a real handicap in trying to predict how the fluxes may change under an altered climate (Liss 2007). By far the most important trace gas emission from the ocean influencing our climate is dimethyl sulfide (DMS), a gas that is biogenically produced by algae in marine waters. It is formed by cleavage of the precursor molecule dimethylsulfoniopropionate (DMSP), which acts as an osmolyte and cryoprotectant for the organisms. A small fraction (probably less than 10%) of the total DMS formed in seawater is transferred to the atmosphere across the air–sea interface. In the atmosphere, it is unstable and converted into a variety of products, some of which are particulate, making DMS a major

512 | 6 Biogeochemistry and global cycling Tab. 6.21: Global oceanic trace gas emissions (Tg yr−1 as element). Substance

Flux

Reference

N2 O

1.4–2.6 4 (1.2–6.8) 4.7 0.9–1.7

Khalil and Rasmussen (1992) Nevison et al. (1995) IPCC (2001) Rhee at al. (2009)

NH3

8–15

cf. Table 4.29

CO

47 (5–41) 23 (9–38) 6 (3–14) 5 (0–14) 9

Seiler and Crutzen (1980) Khalil and Rasmussen (1990a) Bates et al. (1995) Khalil (1999) RETRO (2008)

CH4

3.5 (3–4) 0.4 (0.2–0.6) 10 0.6–1.2

Lambert and Schmidt (1993) Bates et al. (1996) Watts (2000) Rhee at al. (2009)

Isoprene Alkanes and Alkenes

Alkanes Alkenes Acetone CH3 Cl CHCl2 CH2 Cl2 C2 HCl3 C2 Cl4 DMS

5 30 0.3–0.6 ∼1 7.6 1 (0–2) 6 (3–12) 10–27 (±50%) 0.46 0.32 0.16 0.02 0.02 35 (±20)

Guenther et al. (1995) Bonsang et al. (1988) Plass-Dülmer et al. (1995) Rudolph (1997) RETRO (2008) Williams and Koppmann (2007) Williams and Koppmann (2007) Jacob et al. (2002) Khalil et al. (1999) Khalil et al. (1999) Khalil et al. (1999) Khalil et al. (1999) Khalil et al. (1999) Möller (2003) and references therein

natural provider of fine particles over the open oceans. In this way, it plays an important role in climate as a source of cloud condensation nuclei (CCNs), as well as supplying the element sulfur to the terrestrial environment, where it is essential for plant growth. In the atmosphere, DMS is subject to oxidation by free radicals, including OH and NO3 , to yield a number of gaseous and particulate products. The major difficulty in estimating global sea–air fluxes of DMS is in interpolating measured concentrations of DMS in seawater to create seasonally resolved gridded composites (e.g., Kettle et al. 1999). Attempts to correlate DMS with variables that can be mapped globally, for example chlorophyll, have not yielded reliable relationships. Using the parameterizations of Liss and Merlivat (1986), Wanninkhof (1992), and Er-

6.3 Natural sources of atmospheric substances | 513

ickson (1993), and using published wind fields and the maps of sea-surface DMS concentrations of Kettle et al. (1999), Kettle and Andreae (2000) calculated the fluxes of DMS from the global oceans at approximately 15, 33, and 21 Tg S yr−1 , respectively. This shows that the air–sea exchange (model assumptions for the gas transfer velocity; see also Chapter 3.6.5) may be the dominant factor in controlling the emission value. Nightingale et al. (2000) reported the first estimation of the power dependence of gas transfer on molecular diffusivity in the marine environment. A gas exchange relationship that shows a dependence on wind speed intermediate between those of Liss and Merlivat (1986) and Wanninkhof (1992) is found to be optimal. Recent estimates of globally integrated DMS fluxes from ocean to atmosphere tend to the higher value given by Möller (2003) as 35 ± 20 Tg S yr−1 . Anderson et al. (2001) estimated 0.86 and 1.01 Tmol S yr−1 (about 30 Tg S yr−1 ), and Simó and Dachs (2002) have globally quantified this as 23–35 Tg S yr−1 , and Kloster (2006) and Kloster et al. (2006) simulated a global annual mean DMS emission of 28 Tg S yr−1 . The ocean’s influence on VOCs in the atmosphere is poorly understood. For example, Sinha et al. (2007) showed that compound-specific PAR and biological dependency should be used for estimating oceanic VOC emissions. They estimated the mean fluxes in a Norwegian fjord for methanol, acetone, acetaldehyde, isoprene, and DMS −1 as −0.26, 0.21, 0.23, 0.12, and 0.3 ng m−2 s , respectively. It was observed that under conditions of high biological activity and a PAR of ∼ 450 μmol photons m−2 s−1 , the ocean acted as a net source of acetone. However, if either of these criteria was not fulfilled, then the ocean acted as a net sink of acetone. This new insight into the biogeochemical cycling of acetone at the ocean–air interface has helped to resolve discrepancies from earlier studies, such as that of Jacob et al. (2002), who reported the ocean to be a net acetone source (27 Tg yr−1 ), and that of Marandino et al. (2005), who reported the ocean to be a net sink of acetone (−48 Tg yr−1 ). The ocean acted as a net source of isoprene, DMS, and acetaldehyde but a net sink of methanol. This is also supported by shipboard measurements made off Mace Head Research Station (Ireland) (Lewis et al. 2005), which demonstrated a strong inverse correlation of CH3 OH with DMS, with both species showing wind-speed dependence indicative of air–sea exchange. Marine concentrations of acetone and acetaldehyde are similar, at around 0.4–0.5 ppb. The statement of Singh et al. (2001), that large and widespread (most likely oceanic) sources must be present for oxygenated hydrocarbons, is therefore supported by these results. A large enrichment of acetone and of other carbonyl compounds (e.g., acetaldehyde) was measured by Zhou and Mopper (1997) in seawater samples of the surface microlayer of the ocean, and a sea–air flux was suggested for less soluble compounds (such as acetone and acetaldehyde). Isoprene (Chapter 4.3.9.1, Volume 2) is a gas reactive in the atmosphere that is particularly important for the formation of organic particles. It is known to be emitted from the oceans (Broadgate et al. 1997), but generally not thought to be of sufficient magnitude to lead to particle formation. However, Meskhidze and Nenes (2006) have used satellite imagery to show that over a biologically productive region of the South-

514 | 6 Biogeochemistry and global cycling

ern Ocean, CCN number density and cloudiness are enhanced compared with the less productive surrounding area. Controversially, they attribute the additional CCNs to particles formed from isoprene emitted from the biologically productive water, where it might be expected that DMS would be the more obvious precursor. This finding is of importance not only because it shows that marine trace gas emissions can have a direct effect on CCNs and cloudiness and, hence, climate, but it also reopens the question of the role of oceanic isoprene emissions on the marine atmosphere. Recent reassessment (Rhee et al. 2009) has shown global oceanic emission estimates of CH4 to be approximately ten times lower and of N2 O to be approximately three times lower than the “established” emission values used in the recent IPCC report (Denman et al. 2007). The reasons for the discrepancies are unknown, but three studies (Conrad and Seiler 1988, Bates et al. 1996, Rhee et al. 2009) indicate that the open ocean is supersaturated with respect to atmospheric CH4 at a level of ∼ 0.04, about an order of magnitude lower than the ∆CH4 value of 0.3 suggested by Ehhalt (1974) and used by others (e.g., Watts 2000 and the IPCC reports from 1995, 2001, and 2007). The much lower N2 O estimate implies (Rhee et al. 2009) that upwelling activities or the amount of dissolved N2 O in upwelling subsurface waters of the Atlantic are weaker than in the other oceans. Emissions of organohalogen (Br or I) gases (one to two carbon atoms) from the oceans can have significant effects on the oxidant chemistry of the atmosphere, and in some cases on particle formation. There is a growing database of shipboard measurements from which sea-to-air fluxes can be calculated (e.g., Chuck et al. 2005). However, in contrast to DMS, there is little understanding of how these compounds are formed, with both direct biological production and indirect photochemical formation from organic precursor being invoked, but with little knowledge of the detailed mechanisms by which these processes operate. The “best guess” emissions (Tg element yr−1 ) from the oceans are summarized here (cf. also Table 6.21 with older data): OVOC

DMS

NH3

NMVOC

N2 O

CH4

org. Cl

50 ± 20

30 ± 15

10 ± 5

7±4

1±1

1 ± 0.5

1±1

6.3.3 Geogenic processes The term geogenic excludes biological (or biogenic) processes and should reflect mainly physical processes causing atmospheric emissions. This is absolutely true for (primary) emissions due to wind blasting such as sea salt and soil dust and mainly for volcanism in all its different forms; however, (geo-)chemical processes in the magma region occur.

6.3 Natural sources of atmospheric substances |

515

6.3.3.1 Soil dust The magnitude and distribution of atmospheric dust is strongly controlled by dust emissions, which depend on the extent and type of terrestrial vegetation and land use, as well as on soil properties and meteorological conditions. Soil particles are entrained into air by wind erosion caused by strong winds over bare ground. While large sand particles quickly fall to the ground, smaller particles (less than about 10 μm) remain suspended in the air as mineral (or soil) dust aerosols. Billions of tons of mineral dust aerosols are released each year from arid and semiarid regions to the atmosphere (Tanaka 2009). Mineral dust particles are estimated to be the most common aerosols by mass (Chapter 3.6.3). Estimates of their total global source strength range from 1000 to 5000 Mt yr−1 (Duce 1995). Table 6.22 shows estimates depending on particle type and size. In recent years, the soil dust burden has been studied by modeling because of its contribution to climate (negative) forcing (Jaenicke 1993, Tegen and Fung 1995, Tegen et al. 2004, Hara et al. 2006) and to air pollution and air chemistry (Andreae and Crutzen 1997, Prospero 1999, Goudie and Middleton 2006). The chemical composition of dispersed soil varies over a wide range; Table 6.23 provides the global average of composition of the Earth’s crust. The agreement of older and modern estimates is remarkable – with the exception of estimates for sulfur and carbon. It seems that the use of this mean composition Tab. 6.22: Estimates of global particulate emissions (Penner et al. 2001; IPCC 2001 estimates). NH – Northern Hemisphere, SH – Southern Hemisphere, OM – organic matter, BC – black carbon. Type and characteristics OM

Biomass burning Fossil fuel burning Biogenic

BC

Biomass burning Fossil fuel burning

Industrial dust

NH

SH

28 28 – 2.9 6.5 –

Global

Reference

26 0.4 –

54 (45–80) 28 (10–30) 56 (0–90)

A B, C D

2.7 0.1

5.7 (5–9) 6.6 (6–8)

A B, C

–

100 (40–130)

E, F, G

Sea salt

< 1 μm 1–16 μm

23 1420

31 1870

54 (18–90) 3290 (1000–6000)

IPCC (2001) IPCC (2001)

Soil dust

< 1 μm 1–2 μm 2–20 μm total

90 240 1470 1800

17 50 282 349

110 290 1750 2150 (1000–3000)

IPCC (2001) IPCC (2001) IPCC (2001) IPCC (2001)

A: Scholes and Andreae (2000) B: Penner et al. (1993) C: Cook et al. (1999) D: Penner (1995)

E: Wolf and Hidy (1992) F: Andreae (1995) G: Gong et al. (1997)

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Tab. 6.23: Average composition of known terrestrial matter (%); – no value given. Element

Wedepohl (1995)

Mason and Moore (1982)

Clarke (1920)

O Si Al Fe Ca Na Mg K Ti H P Mn F Ba Sr S C

– 28.8 7.96 4.32 3.85 2.36 2.20 2.14 0.40 – 0.076 0.072 – – – 0.070 –

46.60 27.72 8.23 5.00 3.63 2.83 2.09 2.59 0.44 0.14 0.105 0.095 0.0625 0.0425 0.0375 0.0260 0.0200

47.33 27.74 7.85 4.50 3.47 2.46 2.24 2.46 0.46 0.22 0.12 0.08 0.10 0.08 0.02 0.12 0.19

is also not valid for large-scale deposition estimates (Table 6.24); from the data listed in Table 6.24, a mean Fe concentration in dust deposition amounts to 0.35%, in contrast to the mean lithosphere composition of around 4.5%. The sulfur content of soils varies between 0.009% and 11.5% (Ryaboshapko 1983), in contrast to the mean crust composition of between 0.03% and 0.1% (Table 6.23). There are only two estimates of the contribution of soil dust to atmospheric sulfate (T S yr−1 ): 20 (10–30) and 3–30 (Ryaboshapko 1983, Andreae 1985, 1990). A contribution of 20 Tg S yr−1 to continental sulfate is significant in comparison with the assessed continental emission, in a range between 3 and 7 Tg S yr−1 , from biogenic sources, including biomass burning. Tab. 6.24: Deposition of soil dust on oceans (Tg yr−1 ) (Duce et al. 1991). Ocean

Total deposition

Deposition of iron

Northern Pacific Southern Pacific Northern Atlantic Southern Atlantic Northern Indian Ocean

470 39 220 24 100

1.6 0.14 0.76 0.08 0.35

Total

900

3.2

6.3 Natural sources of atmospheric substances | 517

Tab. 6.25: Variation of chemical composition of soil-forming rocks (igneous, sandstone, and limestone), in percentage from date in Clarke (1920). Element

Concentration range

Al Fe Mg Ca Na

0.8–16 0.5–3.1 1–8 3–43 0.05–4

Soil-forming material such as igneous, sedimentary, and metamorphic rocks determines the chemical soil composition, which varies by more than one order of magnitude (Table 6.25). It is logical that material containing volatile elements such as C, N, and S but also halogens is concentrated in soils and is resuspended in the air by wind. The particle size is mainly in a range of 1–3 μm, but submicrometer particles are also observed. Locally, especially in urban areas where there is traffic on the streets, resuspension of soil dust by moving vehicles contributes to about one-third of the PM10 levels; this fraction is mainly between 2.5 and 10 μm (see also Chapter 3.6.3, Tables 3.8 and 3.9). 6.3.3.2 Sea salt SSA has multiple impacts (apart from other PM categories) on atmospheric properties: response to climate by optical properties (e.g., Mahowald et al. 2006), providing CCNs (e.g., Clarke et al. 2006), being a heterogeneous surface for multiphase chemical reactions, for example, SO2 oxidation (Luria and Sievering 1991), and serving as a source for reactive chlorine (e.g., Finlayson-Pitts et al. 2003), whereas gaseous HCl is the most abundant form of chlorine; see also Chapter 5.7.2. Only in the last few years has evidence been found that SSA is also occurring in the very fine fraction below 250 nm (down to 10 nm) depending on sea state (e.g., Geever et al. 2005, Clarke et al. 2006). This aerosol may be the dominant contributor to both light scattering and cloud nuclei in those regions of the marine atmosphere where wind speeds are high or other aerosol sources are weak (O’Dowd et al. 1997, Murphy et al. 1998, Quinn et al. 1998). Sea salt particles are very efficient CCNs, and therefore characterization of their surface production is of major importance for aerosol indirect effects. For example, Feingold et al. (1999) showed that at concentrations of 1 particle per liter, giant salt particles are able to significantly modify stratocumulus drizzle production and cloud albedo. A semi-empirical formulation was used by Gong et al. (1997) to relate the sizesegregated surface emission rates of SSAs to wind field and produce global monthly sea salt fluxes for eight size intervals between 0.06 and 16 mm dry diameter. SSAs are generated by various physical processes, especially the bursting of entrained air bub-

518 | 6 Biogeochemistry and global cycling

bles during whitecap formation (Blanchard 1983, Monahan et al. 1986), resulting in a strong dependence on wind speed. Sea salt particles cover a wide size range (about 0.05 μm to 10 mm diameter) and have a correspondingly wide range of atmospheric lifetimes. Thus, as for dust, it is necessary to analyze their emissions and atmospheric distribution in a size-resolved model. Several studies have quantified the flux and concentration of sea salt particles. Blanchard (1983) expressed that it is impossible to estimate the total sea salt emission more accurately than between 1000 and 10,000 Tg yr−1 ; the flux is strongly dependent on the height above sea level: at the 0–1 m level the flux is > 10,000 Tg, and at the ∼ 5000 m level the flux is < 1000 Tg. Jaenicke (1982) estimated the transport of submicrometer sea salt particles into higher atmospheric levels to be 180 Tg yr−1 . Using detailed wind-field data, Erickson and Duce (1988) estimated much higher fluxes than Blanchard. They give fluxes through a plane 15 m above the sea for dry deposition (8000–22,000 Tg yr−1 ) and wet deposition (1500–4500 Tg yr−1 ), resulting in a total flux of 10,000–30,000 Tg yr−1 . These estimates have often used empirical relations for the surface concentration, assumed a relationship between dry and wet deposition, and calculated the dry deposition. Tegen et al. (1997) found the global average burden of sea salt to be 22 mg m−2 (with a source strength of 5900 Tg yr−1 ) using a three-dimensional tracer model, whereas Takemura et al. (2000) calculated the source strength to be 3321 Tg yr−1 and the global burden to be 11 mg m−2 using a general circulation model. Both studies calculated the sea salt concentration directly from an empirical dependence on surface wind. The corresponding sulfate value is 300–800 Tg S yr−1 , of which probably a mere 10% (50 Tg yr−1 ) reaches the upper PBL. The global average mass percentage of sulfate in seawater amounts to 7.68%. Assuming no deviation in pure sea salt, this value must be multiplied by the total estimate of sea salt emissions to the atmosphere. Using a sea salt production of 1800 Tg yr−1 , a value for sea salt sulfate emission of 44 Tg S yr−1 (Eriksson 1960) was used for more than 20 years by all investigators of the global sulfur cycle (Cullis and Hirschler 1980). Higher values of the sea salt sulfate contribution, between 100 and 300 Tg S yr−1 , were published by Ryaboshapko (1983), Möller (1983, 1984a), and Várhelyi and Gravenhorst (1983). Petrenchuk (1979) estimates that the river runoff of sea salt is 300–400 Tg yr−1 . This should equal what is deposited over land (as nothing is assumed to be accumulated on land). Using yearly river data of 35.6 ⋅ 103 km3 and an average chloride concentration in rivers of 6.4–7.8 mg L−1 , Petrenchuk (1979) finds 230–280 Tg yr−1 chloride. This should be approximately the same as the chloride deposited over land from SSAs. Grini et al. (2002) model deposits of 161 Tg yr−1 sea salt over land, corresponding to 88 Tg yr−1 chloride. Given the uncertainties and assumptions in making such a comparison, the estimates compare reasonably well. Several studies in the last few years have shown that “sea salt” aerosol actually contains a substantial amount of OM, consisting both of insoluble material (e.g., biological debris, microbes) and water-soluble constituents. Organic materials and sea

6.3 Natural sources of atmospheric substances | 519

salt are present as internal mixtures, consistent with a production mechanism that involves fragmentation of organic-rich surface film layers during the bursting of air bubbles at the sea surface (Andreae et al. 2009b and references therein). 6.3.3.3 Volcanism Volcanoes emit gases, aerosols, and fine PM in modes ranging from continuous to ephemeral (Table 6.26) (cf. Chapter 3.2.1.1 in Volume 2). From 1975 to 1985, an average of 56 volcanoes erupted yearly. While some showed continuous activity, others erupted less frequently or only once, so that 158 volcanoes actually erupted over this time period. This number increases to 380 volcanoes with known eruptions in the twentieth century, 534 volcanoes with eruptions in historical times, and more than 1500 volcanoes with documented eruptions in the last 10,000 years (McClelland et al. 1989). Hence, emission estimates found in the literature always represent averages over different long periods of time. Therefore, the true annual emission for a given year is almost unknown and varies considerably from year to year. In years with large Tab. 6.26: Composition of volcanic gases; – no value given. Substance

H2 O CO2 SO2 H2 S HCl HF HBr CO COS CS2 H2 N2 CH4 Ar NH3 a

Vol-% (Symonds et al. 1988, 1994) Kilauea summit (1170 °C)

Ertá Ale d (1130 °C)

MomoTombo e (820 °C)

37.1 48.9 11.8 0.04 0.08 – – 1.51 – – 0.49 – – – –

77.2 11.3 8.34 0.68 0.42 – – 0.44 – – 1.39 – – – –

97.1 1.44 0.50 0.23 2.89 0.26 – 0.01 – – 0.70 – – – –

Mol-% (Edmonds et al. 2005) a

Vol-% (Textor et al. 2004) b

Mol-% (Seventh 2000) c

75–85 0.1–3 10–13 0.1–0.8 0.3–0.6 0.1–0.5 – 0.015–0.025 – – – – – – –

50–90 1–40 1–25 1–10 1–10 < 0.001 ? – 10−4 –10−2 10−4 –10−2 – – – – –

94–99 0.3–1.4 0.1–4.5 0.02–1.5 0.001–1.0 0.0003–0.4 0–0.0003 0–0.0018 – – 0.0001–0.4 0.003–0.07 0–0.0006 0–0.00007 0–0.00003

Kilauea Volcano, Hawaii (2004–2005). Means, based on values from Symonds et al. (1988, 1994), Cadle (1980), Chin and Davis (1993). c Based on 39 samples from 2 fumaroles at Satsuma-Iwojima and 1 at Kuju Volcano in 2000 (T : 100– 800 °C). d Ethiopia. e Nicaragua. b

520 | 6 Biogeochemistry and global cycling

Tab. 6.27: SO2 emissions of some large volcanic eruptions (Tg S). Volcano (USA) a

Roza Laki (iceland) Pinatubo (Indonesia) Agung El Chichón (Mexico) Nyamuragira (Congo) St. Helens (USA)

Year of eruption

Emission

Reference

14.7 Myr ago 1783–1784 1991 1963 1982 1994 1980

6210 b, e

Thordarson and Self (1996) Thordarson et al. (1996) Bluth et al. (1997) Self and King (1996) Bluth et al. (1997) Bluth et al. (1997) Bluth et al. (1997)

61 c 10 3.5 d 3.5 2 0.5

a

The Roza Member represents a compound pahoehoe flood basalt lava flow field, with an area of 40,300 km2 and a volume of 1300 km3 . b Over 10 years. c Over 8 month. d Over 2 days. e Additionally from lava degassing: 1410 Mt S.

volcanic eruptions, the emission could be many times higher than the average. On a short timescale, volcanic emissions play no role compared with other sources of emissions – with the exception of supervolcanic events (Table 6.27). However, because of emissions into the upper troposphere, and occasionally directly into the lower stratosphere, volcanoes play an important role in providing trace species in layers of the atmosphere where the residence times increase significantly (Graf et al. 1997, 1998). Chin and Jacob (1996) found that volcanic sulfur comprises 20–40% of the sulfate in the mid-troposphere globally and 60–80% over the North Pacific. It also accounts for a significant percentage of the sulfate burden in the upper troposphere at high latitudes. These disproportionate effects are realized even though volcanic S accounts for only 7% of the total S emitted to the atmosphere in their chemical transport model, yet it accounts for 18% of the column sulfate burden globally. Thornton et al. (1996) have shown that volcanic SO2 becomes an important CCN source in the North Pacific. A large number of global estimates of volcanic SO2 have been made, with a variation between 0.75 and 30 Tg S yr−1 ; the value with the most agreement seems to be 10 ± 5 Tg S yr−1 (Tables 6.28 and 6.29). Some recent analyses suggest that up to 40% of the global tropospheric sulfate burden may be volcanic, much of it derived from open-vent volcanoes, fumarole fields, and mild eruptions (Oppenheimer et al. 2003). This is much more than previous estimates of secondary sulfate formation suggested, about only 5% (Table 6.32). However, the values (burden and emission) are not directly comparable due to the fact that normally volcanic emissions are injected into the free troposphere where they spend much more time than in the lower troposphere. On the other hand, it is possible that SO2 emissions from ongoing degassing activities globally are significantly larger than is conventionally believed.

6.3 Natural sources of atmospheric substances | 521

Tab. 6.28: Estimates of global SO2 emissions by volcanic activities (Tg S yr−1 ). Emission

Reference

0.75 17 2 5 3.75 23.5 3 2.5 20–30 15 7.5 2 9.3 4.5 25 9.6 20 7 ≥ 6.5 3.8–5.2 10 (±5) 0.75–25 12.6

Kellog et al. (1972) Bartels (1972) Friend (1973) Stoiber and Jepsen (1973) Cadle (1975) Naughton et al. (1975) Granat et al. (1976) Cullis and Hirschler (1980) Cadle (1980) Várhelyi and Gravenhorst (1981) Berresheim and Jaeschke (1983), Berresheim (1998) Möller (1983, 1984a) Stoiber et al. (1987) Warneck (1988) Lambert et al. (1988) Spiro et al. (1992) Graf et al. (1997) Chin and Jacob (1996) Andres and Kasgnoc (1998) Halmer et al. (2002) Möller (2003) Textor et al. (2004) Diehl et al. (2007)

Tab. 6.29: Emission of volcanic gases (Tg yr−1 ); – no value given. Substance

Cadle (1975)

Textor et al. (2004) b

Halmer et al. (2002) c

H2 O a CO2 SO2 H2 S HCl HF HBr CO COS CS2

– – 3.75 – 0.75 0.038 – – – –

? 75 1.5–50 1–2.8 0.4–11 0.06–6 0.0078–0.1 – 0.006–0.1 0.007–0.096

– – 7.5–10.5 – 1.5–37.1 0.7–8.6 0.0026–0.0432 – 0–0.32 0–0.044

a

Based on a concentration ratio H2 O/Cl (Table 6.25) greater than 100, the water emission should be larger than 100–1000 Tg yr−1 . b Means, based on values from Symonds et al. (1988, 1994), Cadle (1980), Chin and Davis (1993). c Compiled on a global data set on about 360 volcanoes over the past 100 years of volcanic degassing during both explosive and quiescent volcanic events.

522 | 6 Biogeochemistry and global cycling

The historical record of volcanic activity, for example, goes back only a few thousand years, yet there are innumerable apparently extinct volcanoes that are still potentially active. Volcanic gases are globally imbalanced on certain timescales compared to biogenic processes (cf. Figure 6.4). Closure of the volcanic cycle via oceanic subduction and magma transformation is very slow, which is why we consider the issue on geological time-scales. It is clear that volcanic activity during the early history of the Earth (degassing period) was orders of magnitude higher than it is today (cf. Chapter 3.2.1.1 in Volume 2). Before subduction, volcanic gases enrich the ocean. Assuming 10 Tg yr−1 as the mean volcanic sulfur level over the last 4 Gyr, it would correspond to a mass about 3000 times larger than the sulfur dissolved in the ocean (cf. Table 5.2). Taking for HCl a volcanic emission rate of 1–10 Tg yr−1 (Table 6.29) over the same period (4 Gyr) results in only 1/3 to 1/30 of the mass of chlorine dissolved in the ocean. This simple example should only show that it makes no sense to assume constant emission fluxes and ratios between different compounds over geological epochs. Volcanoes regulate the climate through CO2 emissions (Robock 1991). Carbon dioxide emissions from volcanoes are given as 75 Tg yr−1 by Textor et al. (2004) and as 200–500 Tg yr−1 by Bickle (1994). The Mount Etna CO2 plume emission and diffuse emission combined for a total of 25 Mt yr−1 (Gerlach 1991). Volcanoes are the only net source (recall that biospheric actions provide closed cycles because emission = uptake globally) of reduced substances (mainly sulfur species) that influence the oxidation capacity of the atmosphere. The most widespread effects will be derived from dust and volcanic gases, sulfur gases being particularly important. This gas is converted into sulfuric acid aerosols in the stratosphere, and layers of aerosol can cover the global atmosphere within a few weeks to months. These remain for several years and affect atmospheric circulation, causing surface temperature to fall in many regions (Mather 2008). The effects include temporary reductions in light levels and severe and unseasonable weather (including cool summers and colder-than-normal winters). Those explosive volcanic eruptions yielding more than 450 km3 of magma were termed supereruptions (Self 2006). The record of these eruptions is incomplete; the most recent known example occurred 26,000 years ago. According to the Toba catastrophe theory, a supervolcanic event at Lake Toba, on Sumatra, 70,000 to 75,000 years ago reduced the world’s human population to 10,000 (Ambrose 1998). The eruption was about 3000 times greater than the 1980 eruption of Mount St. Helens in the USA. It is hypothesized that the Toba explosion may have reduced the average global temperature by 3–5 °C for several years. According to Robock et al. (2009), the Toba incident did not initiate an ice age, but rather exacerbated an ice age that was already under way. It is more likely that the Earth will experience a supereruption than an impact from a large meteorite greater than 1 km in diameter. Depending on where the volcano is located, the effects will be felt globally or at least by a whole hemisphere. Large ar-

6.3 Natural sources of atmospheric substances | 523

eas will be devastated by pyroclastic flow deposits, and the more widely dispersed ash falls will be laid down over continent-sized areas. The 1883 Krakatau eruption was the largest explosion ever observed. The 1815 Tambora eruption produced the “year without a summer” in 1816. The 1963 Agung eruption produced the largest stratospheric dust veil in more than 50 years in the Northern Hemisphere and inspired many modern scientific studies (Robock 2003). The subsequent 1982 El Chichón and 1991 Mount Pinatubo eruptions were extensively studied from the beginning of the eruptions; they also led to very large stratospheric aerosol clouds and climatic effects. Labitzke and McCormick (1992) found a significant increase in stratospheric temperatures at 30 and 50 mbar levels in the Northern Hemisphere to be 2.5 °C higher than the 26-year mean, with some daily zonal mean increases of almost 3 °C. They believe this warming was due to the absorption of radiation by the new aerosols produced from the June 1991 eruptions of Mount Pinatubo. The largest estimates of past emissions are from the Roza Member of the Columbia River basalt flow (in the Northwestern USA) about 15 Myr ago (Table 6.26). Over 10 years annual fluxes (Tg element yr−1 ) were assessed to be ∼ 800 (SO2 ), ∼ 200 (HF), and ∼ 100 (HCl) (Thordarson and Self 1996). Thus, the atmospheric perturbations associated with the Roza eruption may have been of the magnitude predicted for a severe “nuclear” or “volcanic” winter, but lasting up to a decade or more. The composition of volcanic gases depends on a number of factors, the most important being the composition of the magma and the depth of gas-melt segregation prior to eruption; this latter parameter, which satisfies some constraints and for which it has proven difficult to find well-defined values, yet is arguably the most critical for controlling eruptive style. Some fundamental processes for how gases evolve from magma depths in the Earth were discussed in Volume 2, Chapter 3.2.1.2. The principal components of volcanic gases are water vapor, nitrogen, and carbon dioxide (Robock 2003, Robock and Oppenheimer 2003). Among the trace gases are sulfur species, halogens (HCl, HF, HBr, iodine) (Aiuppa et al. 2005), and, in very small concentrations, H2 , CH4 , and NH3 (Table 6.26). However, there are some volcanoes where some trace gases have never been detected (Ryan et al. 2006). Sulfur (S) is a common trace element in many volcanically emitted compounds. Sulfur dioxide (SO2 ) and hydrogen sulfide (H2 S) are the primary S-containing gases emitted. Other S-containing species (COS, CS2 , S2 ) usually occur in smaller quantities. The distribution between these various species differs not only between volcanoes but also during a single volcanic episode at one volcano. The chemical composition of volcanic gases varies so widely (Table 6.29) that it makes no sense to establish global mean volcanic gas compositions. Moreover, several types of volcanoes differ considerably. Recently HNO3 emissions in the plumes of the Lascar and Villarrica volcanoes (Chile) were reported (Mather et al. 2004a); molar emission ratios (HNO3 /SO2 ) of 0.01–0.07 were found. At Masaya volcano (Nicaragua), NO and NO2 are intimately associated with volcanic aerosol, such that NOx levels reach as much as an order of magnitude above local background

524 | 6 Biogeochemistry and global cycling

(Mather et al. 2004b). Volcanic sulfate aerosol is also emitted directly from volcanic vents (e.g., Allen et al. 2002, Mather et al. 2003). Andres and Kasgnos (1998) report on a mass ratio of 0.006 for sulfate/SO2 . The only published estimate attempting to quantify NH3 emissions from a volcano appears to be that of Uematsu et al. (2004) for the Miyake-jima volcano, in the south of Japan. They measured plume concentrations of NH3 up to 5 ppb (∼ 3 g m−3 ) approximately 100 km downwind of the source and reported an emission ratio of 1 ammonia : 1 ammonium : 1 sulfate : 10 sulfur dioxide. Based on the estimate that NHx emissions were 15% of SO2 emissions, they inferred an NHx release of 340 kt NH3 –N per year for the period since 2000. This is by far the largest NH3 point source emission ever reported, being similar to the total annual NH3 emissions of the UK. Improved quantification of global volcanic NH3 and NH+4 emissions must therefore be a priority (Sutton et al. 2008). Volcanoes emit in dust many metals: Cd, Hg, Ni, Pb, Zn, Ca, Sb, As, and Cr (Nriagu and Pacyna 1988); with respect to the metals Cd and Hg, volcanoes contribute 40–50% to global emissions, and for the latter 20–40%. Based on global emission estimates (Nriagu 1989), the emission of heavy metals amounts to 2–50 kt yr−1 . The total volcanic dust emissions were estimated to be between 25 and 300 Tg yr−1 (Peterson and Junge 1971, Jonas et al. 1995, Pueschel 1995).

6.3.4 Chemical processes 6.3.4.1 Lightning Liebig (1827), with his theory of nitrogen fixing by lightning, probably stimulated interest in the importance of electric discharges for atmospheric trace gas formation. Later in the nineteenth century, the formation of ozone, hydrogen peroxide, and nitric acid in air was attributed generally to electric discharges: “. . . variations in the electrical condition of the atmosphere. . . ” (Fox 1873). The general discourse was of “ozoneproducing conditions” (quiet electric discharges of air). In the late eighteenth century, this was a fashionable subject of study, and Martinus van Marum noted in 1785 “the odor of electrical matter.” Cavendish first used electric sparks for air (chemistry) studies in 1784. Cavendish and Priestley noted in 1788 HNO3 formation in moist air under the influence of electric discharges. NO formation was suggested by Noxon (1976) and Hill (1979). Lightning (Rakov and Uman 2007, Betz et al. 2009) allows – depending on the flash energy – for molecular dissociation, similar to photochemistry. Therefore, ambient air molecules are dissociated and new molecules are subsequently produced based on air chemical conditions. Depending on the flash energy and the molecular dissociation energy, there is no other limit on the decomposition (and subsequent synthesis) of molecules in the atmosphere; as an example, CO production (Chameides 1979) and the decomposition of CFCs by lightning were reported (Cho and Rycroft 1997). But surely the most dominant

6.3 Natural sources of atmospheric substances | 525

dissociation is oxygen splitting, which sets off a chain of subsequent reactions: O2

O2 󴀘󴀯 O + O 󳨀󳨀→ O + O3 → O2 + O2 .

(6.29)

Subsequently, atomic oxygen reacts with the main constituents N2 and O2 to produce NO and O3 . O2

O + N2 → NO + N 󳨀󳨀→ NO + NO + O → NO + NO2 .

(6.30)

Ozone, however, easily decays back to O+O2 by electrical discharges and radiation (reaction (6.29)). Hence, direct ozone formation by lightning (Griffing 1977, Egorova et al. 1999) occurs on a small scaled compared to the downward transport of stratospheric ozone. Indirectly lightning contributes to ozone formation in the upper tropospheric background due to the NO produced from lightning (Hauglustaine et al. 2001) (Chapter 5.2.3.2). To a minor degree, H2 O may be destroyed under lightning, finally gaining H2 O2 (detected in rain following a thunderstorm): O + H2 O → OH + OH 󴀘󴀯 H2 O2 , O2

(6.31) HO2

H2 O → OH + H 󳨀󳨀→ OH + HO2 󳨀󳨀󳨀→ OH + H2 O2 → H2 O + HO2 .

(6.32)

The range of NO formation is cited as being between 0.3 and 230 Tg N yr−1 ; (1–30)⋅1016 molecules of NO per joule of input energy are produced (see references in Lawrence et al. 1995, Rakov and Uman 2007). The key in estimating NO production by lightning is the flash rate distribution and NO production per flash (Pickering et al. 2009). Among the various NO x sources, the contribution from lightning probably represents the largest uncertainty, but recent estimates (Table 6.30) seem to agree with a global value of 5±3 Tg N yr−1 . Interestingly, many of the recent NO estimates are based on modeling and fitting emission assumptions by comparison with observations. As an example, Labrador et al. (2005) state that 0 and 20 Tg N yr−1 production rates of NO x from lightning are too low and too high, respectively. Tab. 6.30: Recent estimates of global NO production by lightning (Tg N yr−1 ). Emission

Reference

12.2 (5–25) 5 (2–20) 2 (1–8) 0.2–22 5 7 2.8 (0.8–14) 3.5–7 1.1–6.4 5.7 6±2 5±3

Price et al. (1997) Pickering et al. (1998) Lawrence et al. (1995) Huntrieser et al. (1998) Jourdain and Hauglustaine (2001) Zhang et al. (2003) Beirle et al. (2004) Tie et al. (2004) Boersma et al. (2005) Mari et al. (2006) Martin et al. (2007) Schumann and Huntrieser (2007)

526 | 6 Biogeochemistry and global cycling

6.3.4.2 Secondary atmospheric processes We have already defined secondary sources (substances and, hence, emissions in terms of matter flux) as being chemical conversion processes in the atmosphere, but there must also be a primary source at the Earth’s surface. Therefore, we exclude the uncountable number of intermediates and products from chemical processes in the atmosphere that do not have a primary source (Chapter 5); the best known atmospheric substance without a known primary source is ozone. In some estimates of biogenic and biomass burning emissions based on plume measurements, it is often impossible to separate primary from secondary sources, which is to say that the values represent the sum. For example, Andreae and Merlot (2001) give for glyoxal a value from biomass burning of 5.9 Tg yr−1 , and Stavrakou et al. (2009b) give a similar value, 7–9 Tg yr−1 , for primary and secondary pyrogenic sources, divided into 4–6 Tg yr−1 for primary and 3 Tg yr−1 for secondary formation (Table 6.31). Tab. 6.31: Global secondary production of gaseous compounds (Tg yr−1 as elements N, C and S). HCHO – formaldehyde, CHOCHO – glyoxal, CH3 C(O)CH3 – acetone, CH3 OH – methanol. Substance

Process

Emission

Reference

NO NO

Oxidation of NH3 Oxidation of N2 O