Electrochemistry Crash Course for Engineers [1st ed. 2021] 3030615618, 9783030615611

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Slobodan Petrovic

Electrochemistry Crash Course for Engineers

Electrochemistry Crash Course for Engineers

Slobodan Petrovic

Electrochemistry Crash Course for Engineers

Slobodan Petrovic Oregon Institute of Technology Happy Valley, OR, USA

ISBN 978-3-030-61561-1 ISBN 978-3-030-61562-8 https://doi.org/10.1007/978-3-030-61562-8

(eBook)

# The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover Illustration credit: Kevin Hudson This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The field of renewable energy is extremely diverse and multidisciplinary. The individual renewable energy technologies are enabled by many other technologies and areas of science. One of the most critical enabling areas is electrochemistry, the interfacial science that studies the intersection between chemistry and electricity. Knowledge of electrochemistry is necessary to understand and design energy storage systems, batteries, fuel cells, electrochemical supercapacitors, and hydrogen technologies. Electrochemical principles are also important for understanding mechanisms in solar photovoltaic devices. Additionally, corrosion and electrochemical sensing control systems play an important role in all aspects of integrated system design. Electrochemistry is one of the most important sciences in our present-day economy. It provides a basis for significant processes such as those in primary and secondary batteries and fuel cells; the production of chlorine and caustic soda; electrowinning of metals, electroplating, electromachining; the study and prevention of corrosion; and numerous types of sensors and electroanalysis. In the USA, the electrochemical technologies contribute with 1.6% of all manufacturing and comprise roughly one third of the entire chemical industry. This makes electrochemistry a very significant area of science intersecting with technology! The goal of this book is to provide the theoretical foundation and to teach the principles of electrochemistry, but it will ultimately present the behavior of electrochemical systems from a practical point of view. The approach will, therefore, not involve details of the microscopic phenomena nor derivations of critical laws and formulas. Instead, the focus will be to provide skills to evaluate and design electrochemical systems and to test the behavior of electrodes to be used in those systems. The fundamental areas covered are basic electrode behavior, thermodynamics, electrode kinetics, and transport phenomena. An attempt is made to explain these concepts and illuminate them sufficiently for the subsequent determination of the behavior of electrochemical systems. In the second part of the book, practical electrochemical systems will be evaluated: industrial electrolytic processes, galvanic cells, analytic applications, and corrosion. The fascination with electrochemical systems is in the complexity of phenomena that influence them and the exhilaration of mastering one of the most difficult fields of study in all of science. v

vi

Preface

This book is intended for renewable energy engineering students, but it can provide an introduction into electrochemistry for students from other disciplines as well. A background in calculus and the completion of a second-year college chemistry course with a lab component is expected. Happy Valley, OR

Slobodan Petrovic

Acknowledgements

My thanks to Laura Polk for her assistance with getting this book to the publisher on time and to Justin Ringle for his help.

vii

Contents

History of Electrochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Basic Electrochemistry Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrochemical Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cathode and Anode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electronic and Ionic Conductivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrolyte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltaic and Electrolytic Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . .

3 3 3 4 5 5 6 8

Electrode Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electroneutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metal in Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electroneutrality and Salt Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Electrical Double Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measuring Electrode Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Potential Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 11 11 15 16 19 24

Effect of Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nernst Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Concentration on Cell EMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . Significance of the Nernst Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability of Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27 27 28 29 29

Electrochemical Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System and Surroundings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reaction Spontaneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Second Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . Gibbs Free Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gibbs Energy and Chemical Change . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31 31 31 32 33 34 34 36 37 38

. . . . . . . . . .

ix

x

Contents

Standard Gibbs Free Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Free Energy and Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature Effect on Equilibrium Constant . . . . . . . . . . . . . . . . . . . . . . Gibbs Energy and Cell Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cell Voltage and Equilibrium Constant . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of Electrochemical Thermodynamics . . . . . . . . . . . . . . . . . . . .

. . . . . .

40 43 44 45 46 47

Electrochemical Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Rate of Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Faraday’s Laws of Electrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49 49 50

Mass Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fick’s Law of Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nernst Diffusion Layer Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reaction Rate Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

53 53 55 58

Overpotential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Activation Overpotential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resistive Overvoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Transport Overvoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combining Overvoltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59 60 62 62 63

Industrial Electrochemical Processes . . . . . . . . . . . . . . . . . . . . . . . . . . Chlorakali Electrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molten Salt Electrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aqueous Metal Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metal Purification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Electrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Separation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

65 65 67 69 70 71 75

Galvanic Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77 77 80

Analytical Electrochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Potentiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ion-selective Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pH Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrochemical Gas Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85 85 87 89 91

. . . . .

Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oxygen Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrochemical Corrosion Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corrosion Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . .

. 93 . 94 . 96 . 99 . 101

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

History of Electrochemistry

Electrochemical phenomena were first observed by Alessandro Volta in 1793 when he demonstrated that electricity can be produced from two dissimilar metals electrically connected with a moistened paper between them. This was the first, simple battery (Fig. 1). The Volta battery was used a few years later as a source of electricity to decompose water into hydrogen and oxygen. This milestone in chemistry illuminated the discovery that hydrogen and oxygen atoms are associated with positive and negative electrical charges that are responsible for the bonding forces between them. Berzelius, a Swedish scientist, proposed in 1812 that all atoms are electrified, for example, hydrogen and metals are positive and nonmetals are negative. When electricity is applied to two electrodes immersed in a solution it provides energy to break up the attraction forces and form ions. The word ion comes from the Greek word for “traveler”. The Berzelius view was ultimately replaced by the Lewis theory of bonding through shared electrons, but it represents an important progress milestone in understanding chemical bonding. The use of newly discovered electrochemical principles continued to attract new ideas and Humphrey Davey showed that elemental sodium can be produced by the electrolysis of sodium hydroxide melt. Davey’s former assistant Michael Faraday made significant contributions to understanding electrochemical processes by establishing the relationship between the amount of electrical charge passed through the solution and the quantity of substance reacted or produced. These are known as Faraday’s Laws of Electrolysis. This new way of “seeing” things led James Clerk Maxwell to consider the existence of “molecule of electricity”, which was the first notion of the electron. The concept was not accepted, however, until the end of the nineteenth century. In 1837, Sir William Grove demonstrated the first fuel cell using platinum electrodes immersed in sulfuric acid. He observed at that time the phenomena, such as three-phase boundary and current density, that are still very much elusive and critical to the understanding of electrochemistry. Grove also correctly observed the overpotential, i.e., losses that occur in electrochemical cells by recognizing that # The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_1

1

2

History of Electrochemistry

Fig. 1 Model and schematic representation of the Volta battery Paper moisturized with NaCl solution Cu Zn

more single fuel cells had to be connected in a stack to be able to produce the voltage necessary to perform the electrolysis of water. The history of electrochemistry in the nineteenth century would not be complete without mentioning these pioneers: Johann Ritter (1776–1810) who made the first dry cell battery in 1802 and established the connection between galvanism and chemical reactivity; John Frederic Daniell (1790–1845) who made a battery consisting of copper and zinc electrodes in copper sulfate solution and created the first successful commercial power supply for telegraphs; Edmund Becquerel (1820–1891) who invented a solar cell using an electrochemical system, and his father Antoine Becquerel (1788–1878) who observed the constant current phenomenon when platinum electrodes were immersed in acid. The biggest contributors to the advancement of the electrochemical science in the first part of the twentieth century were Walther Nernst (1864–1941) for his theory of electromotive forces of voltaic cells, Frederick Cottrell (1877–1948) for his work on the diffusion effects in electrochemical systems, and Jaroslav Heyrovský (1890–1967) for his inventions of mercury electrode and polarography. The field of electrochemistry in the second part of the twentieth century was influenced by many prominent scientists, such as by Rudolph Marcus (Caltech), Ernest Yeager (Case Western University), John Bockris (Texas A&M), and Allen Bard (University of Texas at Austin). Finally, the Nobel Prize for Chemistry was awarded to John B. Goodenough, M. Stanley Whittingham and Akira Yoshino for the development of lithium-ion batteries.

Basic Electrochemistry Concepts

Definition Electrochemistry is an interfacial science between chemistry and electricity. It studies the phenomena and processes that occur when chemical processes produce electricity or when electricity causes chemical reactions to occur. Electrochemical devices and processes are widespread in everyday life and in modern science and technology. From batteries and fuel cells to corrosion protection, production of chlorine, or winning of metals, electrochemistry is one of the most important branches of science. On a microscopic level, electrochemistry is the study of reactions in which ions cross the interface between a solid (a metal electrode) and a solution or electrolyte. These reactions are influenced by the potential differences between the electrode and the solution; and they are fundamentally thermodynamically and kinetically controlled.

Electrochemical Cell An electrochemical cell consists of two electrically conductive electrodes immersed or in contact with an electrolyte (Fig. 2 in the chapter “Electrode Potential”). The electrodes are electronic conductors or semiconductors, i.e., they conduct electrons. Since electrons cannot conduct charge in solutions or salts, the charge must be carried between electrodes by charged atoms or molecules called ions. Electrolyte contains ions which engage in heterogeneous reactions on electrode surfaces that result in the transfer of electrons to or from the conductive electrodes. Neutral atoms or molecules can also react on electrodes where they will be converted into ions or formed from ions while losing or gaining electrons. An electrochemical cell is shown in Fig. 1. It depicts two electrodes immersed in solution while positive and negative ions carry charge in the electrolyte. The electrons are shown to move through the external circuit; they enter the electrode # The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_2

3

4 Fig. 1 Schematic of an electrochemical cell

Basic Electrochemistry Concepts

R

E

e-

mV/mA

e-

+ -

at which reduction occurs and leave the electrode at which oxidation takes place. The symbols in the external circuit depict three modes of operation (not used at the same time): the voltage symbol indicates electrolytic cell affecting changes in the solution and producing chemicals, galvanic cell producing power and indicated by the resistance, or electroanalytical cell measuring current and voltage. One of the unique characteristics of electrochemical reactions is that charge transfer occurs at the interface between the solid electrode and liquid electrolyte. The complexity of this process and interrelation between electrical and chemical effects is what makes electrochemistry a fascinating multidisciplinary science responsible for processes such as those in batteries, fuel cells, solar cells, electrolysis, numerous sensors, corrosion, and many more.

Cathode and Anode The electrode at which electrons enter from the outside circuit and are reactants in the reaction is called the cathode. Reduction takes place on the cathode. Some cathodic reactions shown here are the reduction of oxygen gas that takes place in a fuel cell and chlorine gas: O2 þ 4e þ 4Hþ ! 2H2 O

ð1Þ

Cl2 þ 2e ! 2Cl

ð2Þ

The electrode from which electrons leave is called the anode. Oxidation takes place on the anode and electrons are the reaction products. Some common anode reactions are the production of chlorine gas and oxidation of hydrogen that takes place in a fuel cell: 2Cl ! Cl2 þ 2e

ð3Þ

Electrolyte

5

2H2 ! 4Hþ þ 4e

ð4Þ

Perhaps the simplest memory technique is that in the oxidation/anode relationship both terms begin with a vowel, o/a; whereas in the reduction/cathode relationship both begin with a consonant, r/c.

Electronic and Ionic Conductivities Electronic conductivity is the movement of electrons in a metallic conductor. Ionic conductivity is the movement of ions through an electrolyte. Electrons conduct electricity in solid conductors, but cannot exist in solutions and very rapidly react with positive ions. Ions, on the other hand, conduct electricity in solutions, but cannot conduct electricity through solid conductors. Figure 2 shows an illustration of metallic conductor immersed in electrolyte. In a solid crystal such as NaCl, the forces that keep ions together are very powerful. Consequently, very large amounts of energy are needed to break down the crystal lattice. In cases where a crystal, such as NaCl, is mixed into a solvent (such as water), the attractive forces that hold the crystal together are reduced. The ionic attraction becomes much weaker and NaCl dissolves readily in water to produce freely moving Na+ and Cl ions. An electrical field can be applied to a solution by inserting two electronic conductors (for example, metals, carbon materials, or semiconductors) and applying a potential difference between them. These electronic conductors are called electrodes. When ions formed in the electrolyte solution are exposed to the electric field between two electrodes, they experience a force, creating motion and the transport of charge. This is the flow of ionic current through electrolyte solution.

Electrolyte Electrolyte is an ionically conductive medium, i.e., it contains ions that conduct electrical charge. It is usually a liquid solution, but it can also be a solid, a molten substance, or a polymer. Fig. 2 Metal-solution interface illustration. Electrons are shown in red between metal atoms

Metal

Solution +

+ + +

+ +

6

Basic Electrochemistry Concepts

Liquid electrolytes are most commonly aqueous (i.e., water) solutions of acids, bases, or salts. Due to the process called solvation, these compounds dissociate into ions. For example: NaClðsÞ ! Naþ ðaqÞ þ Cl ðaqÞ

ð5Þ

Occasionally, gases such as carbon dioxide or sulfur dioxide dissolve in water to produce a solution, which contains hydronium (H3O+), carbonate, and sulfate ions. Electrolyte can also be formed by melting a salt without dissolving it in water. At a certain temperature, i.e., melting point, the salt melts and dissociates into ions. An example of a molten salt electrolyte is Na2CO3 which melts at 650  C and is used in molten carbonate fuel cells: Na2 CO3 ! 2Naþ þ CO3 2

ð6Þ

An electrolyte can also be a solid substance. These are typically ceramic structures that contain ions capable of moving through the structure under the effects of concentration gradients and electrical fields. An example of a solid electrolyte is ZrO2 used in solid oxide fuel cells oxygen sensors. Zirconium oxide, usually doped with yttrium, becomes conductive at 800  C and conducts O2 ions. A polymer can also be an electrolyte if its structure is modified to enable the conduction of ions. An example of a polymer electrolyte is a membrane (brand name Nafion) used in polymer electrolyte membrane (PEM) fuel cells. This polymer electrolyte is capable of conducting hydrogen ions (H+), also called protons, when the basic polymer structure of Teflon or polytetrafluoroethylene (PTFE) is reformulated to include a branched HSO3 groups. The ionic conductivity, σ, of electrolyte depends on the temperature and is usually expressed in S/cm. In electrochemical devices, such as batteries, fuel cells, or electrolysis cells, it is always desirable for the electrolyte to have high ionic conductivity since the reactions proceed faster and with less voltage drop (leading to reduced power) due to electrolyte resistance. At the same time, the electronic conductivity of electrolyte must be very low to prevent an electrical short or leakage current. Besides being water-based or aqueous, liquid electrochemical systems can also be organic. This means that the solvent is not water and the electrolyte is formed by dissolving special salts in organic solvent to obtain ionic conductivity. Some examples of organic solvents used in electrochemical cells are methanol, ethanol, glycol, formamide, acetonitrile, diethyl ether, tetrahydrofuran, etc. The examples of salts used in organic electrolytes are NaCl, LiBF4, and HClO4.

Electrodes Electrodes can be classified based on the material of which they are made of. Various conducting and semi-conducting elements have been used as electrodes: solid metals (Pt, Au, Ag, etc.), liquid metals (Hg, amalgam), metal oxides (MoO2, MnO2, CoO2,

Electrodes Fig. 3 Sketches of disk and disk-ring electrodes. Only electrodes are depicted, not the rotator apparatus

7

Disk electrode

Disk-ring electrode

etc.), carbons (graphite, diamond, graphene, etc.), and semiconductors (ITO, Si, etc.). Electrode geometry varies and can be any of the following: flag, disk, cylinder, wire, mesh, thin layer, finely dispersed layer, liquid electrode, micro and ultra-micro electrodes, and many others. A micro or ultra-micro electrode is an electrode with dimensions of micrometers and it is used in voltammetry (i.e., analytical applications). The use of these electrodes enables measurements in poorly conductive solutions because very low currents are involved. In addition, these electrodes exhibit a very small voltage drop and small distortion of the electrode-solution interface. A rotating disk electrode (RDE) is a special type of electrode used for the characterization of the mass transport and concentration effects in electrochemical systems. The rotating disk electrode is made by sealing a metal wire in a cylindrical polymer body (e.g., Teflon) in such a way that only a cross-section of the wire is exposed to the solution. By rotating the polymer cylinder electrode special hydrodynamic conditions are created that help study the effects of mass transport of reactants and ions from the bulk solution to the electrode. Another variation of a rotating disk electrode is with an additional ring around the disk. This is appropriately called a rotating disk-ring electrode and is used for investigations of reaction mechanisms and intermediate species in electrode processes. Sketches of disk and disk-ring electrodes are shown in Fig. 3. An alternative classification of electrodes is by the function they perform in an electrochemical cell. The simplest electrochemical cell has only two electrodes and the configuration is called a 2-electrode system (or arrangement). This configuration is typically used in the industrial electrochemical process and galvanic cells, e.g., electrolysis, batteries, and fuel cells. The electrodes in these cells are usually called anode and cathode or positive and negative. In experiments using a potentiostat/galvanostat, a 2-electrode configuration best enables examination of the primary reaction of interest and the electrodes are called working electrode and counter electrode. In these cells, the reaction on the counter electrode simply serves the purpose of completing the electrochemical cell. In electroanalytical chemistry and in basic electrode process characterization, the often-used configuration or arrangement involves one or more additional electrodes compared to the basic 2-electrodes system. The challenge in electroanalytical experiments and electrochemical characterization is to accurately measure the potential of the electrode of interest or of both electrodes. If the potential of the electrode

8

Basic Electrochemistry Concepts

Fig. 4 Electrochemical cell with 3-electrode configuration

WE CE

RE

of interest (i.e., working electrode) is measured against the counter electrode it may not be accurate because the counter electrode potential is not fixed and may change during the reaction or experiment. In other words, the measurement of the voltage of a cell will be accurate, but the individual potential values (on a standardized scale) will not be measurable. For this reason, a third electrode is introduced that has a fixed potential and does not change with the reaction because it does not participate in the reaction, i.e., the current does not flow through this electrode, but between the working and counter electrodes. While the electrochemical reaction proceeds between the working and counter electrode, the individual potentials are recorded (using a voltmeter or a potentiostat) versus the reference electrode. In experiments where the potential of the working electrode is deliberately changed or controlled, such as those experiments conducted with a potentiostat, the potential of the working electrode is accurately controlled by measuring its potential versus the reference electrode and adjusting appropriately. A simple electrochemical cell made of glass with working, counter, and reference electrodes is shown in Fig. 4. These additional electrodes are called reference or sense electrodes. Hence, the electrochemical systems may be 2, 3, 4, or 5-electrode systems. The purpose of a reference electrode, in addition to an anode and cathode, is to precisely measure and control the potential of one or both electrodes of interest, i.e., anode and cathode. If more than one reference electrode is used, the additional electrodes are called sense electrodes and they are used to accurately measure the potentials of the working and counter electrodes. The sense electrodes are also positioned very close to the working and counter electrodes; they are “sensing” to minimize the potential distortion due to uneven electrolyte concentrations and changing electrical field. A 5-electrode cell configuration is shown schematically in Fig. 5.

Voltaic and Electrolytic Cells Voltaic (also called galvanic) cells are electrochemical cells that produce electricity from the reactions on the electrodes. The electrochemical system releases energy in this process. The anode is the negative electrode at which oxidation occurs. The

Voltaic and Electrolytic Cells

9

Fig. 5 Schematics of electrochemical cell with 5-electrode configuration

POWER SUPPLY

LOAD

e-

e-

Galvanic cell

e-

e-

Electrolytic cell

Fig. 6 Block diagrams of two cell types

cathode is the positive electrode at which reduction occurs. Examples of voltaic cells are batteries and fuel cells. Electrolytic cells use electricity from external sources to cause chemical reactions and produce desired chemicals. The electrochemical system consumes energy in the process. During the electrolytic processes, the anode is the positive electrode where oxidation occurs, while the cathode is the negative electrode at which reduction occurs. Examples of electrolytic reactions are the electrolysis of water to produce hydrogen and oxygen, the production of chlorine, the electrowinning of metals, electroplating, and many others. Block diagrams of two cell types are shown in Fig. 6. The two types of electrochemical cells are compared in Table 1. A rechargeable battery is a special electrochemical cell—it is a voltaic (or galvanic) cell during discharge and electrolytic cell during charge.

10

Basic Electrochemistry Concepts

Table 1 Comparison of galvanic and electrolytic cells Characteristic Energy Gibbs Free Energy (ΔG) Reaction spontaneity Standard cell voltage Negative pole Positive pole Electron flow

Voltaic cells Produces energy 0 Nonspontaneous Negative Cathode/reduction Anode/oxidation Positive to negative

Electrode Potential

Electroneutrality One of the basic phenomena in nature is the preservation of electroneutrality, the tendency to discourage and oppose any processes that lead to an excess of positive or negative charge. Since each atom consists of a positively charged nucleus surrounded by negatively charged electrons, in a neutral atom, the positive and negative charges exactly balance each other. If a piece of metal, zinc, for example, is immersed in water (Fig. 1) the ionization initially creates positively charged ions, Zn2+ which go into solution, while the same number of electrons remain in the metal (Eq. 1). This process stops because of the opposing force that attracts the positive ions back to the metal bar containing negatively charged electrons. ZnðsÞ ! Zn2þ þ 2e

ð1Þ

At the same time, the positive charge buildup in the solution similarly contributes to the prevention of further ionization by repelling additional positive ions from forming at the surface. At the point of equilibrium, when no more ionization is occurring, the resulting solution still contains a very low concentration of Zn2+ (~1010 M) that cannot be detected by ordinary chemical means.

Metal in Solution If a metal bar is immersed in a water solution the atoms on the surface react with water molecules and ionize producing positively charged ions on the surface and equal number of negatively charged electrons inside the bar (Fig. 1). Each metal reaches certain level of ionization and number of positive ions on the surface before the ionization process stops. At that point, the electrons in the bar prevent further # The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_3

11

12

Electrode Potential

Fig. 1 Metal bar in water

+ + +

- -- - - -

+ + + + + +

Fig. 2 Illustration of lithium ionization in water

+ + + + +++ + + + + + ionization by repelling additional electrons that could form and by attracting the positively charged ions. The ionization or oxidation of metal stops because of the tendency to preserve electroneutrality, which is a simple consequence of the thermodynamic work required to pull apart opposite charges. The additional work increases the free energy change of the process and makes it less spontaneous. There is only one way that the oxidation can continue—the electrons from the metal bar must be withdrawn, which in turn would allow further ionization to occur. When electrons are withdrawn, the electroneutrality of the electrode is compromised and more ionization has to occur to restore electroneutrality to the two phases. Platinum and gold ionize to a small extent, copper ionizes with some difficulty, iron ionizes fairly easily and zinc very easily, while lithium ionizes dangerously easily and loses mass, quickly becoming completely dissolved in solution (Fig. 2). Using the Periodic Table of Elements to compare ionization energy reveals a decrease down a group because of the increase in atomic radius. Group I elements have low ionization energies because the loss of an electron forms a stable electron octet. Ionization energy increases from left to right in a period as the atomic radius decreases because electrons are closer to the nucleus and the nucleus is more positively charged. When two different electrodes are immersed in an electrolyte solution and connected with an electrical conductor (a wire) the electrons will flow from one electrode to the next creating an electrical current, as well as voltage (Fig. 3). The

Metal in Solution

13

Fig. 3 Depiction of an electrochemical cell with zinc and copper electrodes immersed in an electrolyte solution

1.10 V

e-

e-

Zinc

Fig. 4 Silver and cadmium in an electrolyte solution. Positive ions are shown as + sign and electrons inside the electrodes as  sign

Copper

e-

+

-

e-

Ag

+ +

+ + +

- -- - - -

+ + + + + + Cd

question why the electrons flow between two dissimilar metals is answered further in the text. If two dissimilar metals, this time silver and cadmium, for example, are immersed in a solution, some atoms are ionized forming positively charged ions and negatively charged electrons (Fig. 4). The positively charged ions remain adsorbed at the surface while electrons remain in the bar. Silver ionizes to a very small degree because of its high ionization energy. Cadmium, on the other hand, ionizes more easily and more positively charged ions form at the surface while the same number of electrons remains in the metal bar. When the two electrodes are connected with a wire, the electrons flow from the electrode with more electrons or higher electron pressure (the cadmium electrode) to the electrode with less electrons (the silver electrode) based on the basic tendency for overall electroneutrality. The electron flow from a more ionized element to a less ionized element stops very quickly when the number of electrons in one electrode is the same as in another. As some electrons leave the cadmium bar further ionization counteracts the loss of neutrality and more cadmium atoms are ionized into positively charged ions and electrons. The electrons reaching the silver bar disrupt the electroneutrality of the silver/solution system and some silver ions on the surface recombine with the excess electrons—the silver is reduced. The electron flow from cadmium to silver proceeds until the two electrodes are at the same potential, i.e., the number of electrons in

14

Electrode Potential

Fig. 5 Cadmium and silver electrodes in a solution of H+ ions. The cadmium electrode is corroding while positively charged ions leave into the electrolyte (or water). Protons, H+, react on the silver electrode and generate hydrogen gas, H2, which bubbles off the electrode

cadmium and silver is the same or the electron pressure is the same. After the process stops there are more ionized atoms on the surface of the cadmium bar and less on the surface of the silver bar. The flow of electrons from cadmium to silver can proceed only if electrons reaching the silver bar can be used in some other reaction. The obvious reaction that can occur in aqueous solutions of low pH (acidic solutions) is the reduction of protons (Eq. 2). 2Hþ þ 2e ! H2ðgÞ

E 0 red ¼ 0 V

ð2Þ

This reaction proceeds with the evolution of gaseous hydrogen from the silver electrode. More electrons are withdrawn from the cadmium bar, which keeps oxidizing (Eq. 3). Cd2þ ! Cd0 þ 2e

E0 red ¼ 0:40 V

ð3Þ

Because the ionization is proceeding with ease the cadmium bar cannot attract positively charged ions, which leave the surface and go into solution, so the cadmium corrodes (Fig. 5). The process of the ionization of metals in water solutions can also be demonstrated on one electrode only. If a metal strip, for example, zinc, is immersed in a solution of copper sulfate instead of pure water the zinc metal quickly becomes covered with a black coating of finely divided metallic copper. The reaction is a simple oxidation-reduction process, a transfer of two electrons from the zinc to the copper (Eq. 1 and 4): Cu2þ þ 2e ! CuðsÞ

ð4Þ

This experiment is shown in Fig. 6. The dissolution of the more negative metal (zinc, aluminum, etc.) is no longer inhibited by a buildup of negative charge in it because the electrons from the bar are used to reduce the more positive element, such as copper or silver, present in the form of ions in the solution. The electroneutrality is preserved because for each Zn-ion that goes into the solution, one Cu-ion is removed (Eq. 5).

Electroneutrality and Salt Bridge

15

Zn

CuSO4

+ +

++ +

CuSO4

+

+

= Zn2+

Fig. 6 Metal immersed in a solution containing ions of a more positive metal, e.g., Zn in solution of CuSO4

ZnðsÞ þ Cu2þ ! Zn2þ þ CuðsÞ

ð5Þ

Electroneutrality and Salt Bridge The electroneutrality rule applies to a system of one electrode immersed in a solution or two electrodes immersed in a solution and it refers to the distribution of positive and negative charge and the way the charge is balanced. For example, ionization in a metal bar is hindered by the negative charge in the bar, which attracts positively charged ions from the solution back to the surface of the electrode. In addition, the reduction of the electron pressure (number of electrons in a bar) encourages further ionization. The solution reacts in the same way; it is neutral although it contains positively and negatively charged ions. For example, sulfuric acid dissociates in water as strong acid into cations, positively charged protons (H+) and anions, resulting in a negatively charged sulfate group SO42. If protons react (Fig. 5) by being reduced on a cathode in a reaction with electrons that means that positive charge is withdrawn from the solution and must be counteracted either by adding some other positive charge to the solution or by withdrawing negative charge from it. In other words, the solution must remain overall electroneutral! In the above example (Fig. 5) the loss of positive charge from the proton removal (by evolution of gaseous hydrogen) is balanced by the addition of the positive charge from the other electrode (in this case Cd2+ from the iron bar). So far, we have only looked at the situations where both electrodes are in the same solution, but it is possible to form an electrochemical cell, measure voltage, and

16

Electrode Potential

Zn(S)  Zn2+ + 2e-

e-

e-

Oxidation (anode)

Cu2+ + 2e-  Cu(S) Reduction (cathode)

Na2SO4

Cu

Zn

CuSO4

ZnSO4 Zn2+

Zn2+

Cu2+

Cu2+

Fig. 7 Electrochemical cell with a salt bridge

preserve electroneutrality using two different solutions connected with a tube called a salt bridge. The concept is demonstrated for the case of zinc and copper in Fig. 7. In this example, the system consists of two electrodes in two different solutions, connected with a tube containing a salt. As zinc gets oxidized (note that it is shown in this example on the left side of the diagram) more positive charge (Zn2+) is released into the solution and must be balanced by the migration of the SO42 from the salt bridge into the compartment on the left. At the same time, Cu2+ reacts in the reduction reaction with electrons that are arriving into the copper bar and the positive charge is removed from the solution in the beaker on the right. This condition is balanced by the migration of the SO42 ions into the salt bridge. The electroneutrality of the solutions in both beakers is preserved and encourages further flow of electrons from zinc to copper. This electrochemical cell is operational and since the process is spontaneous, it produces electricity and can power a load. This type of electrochemical cell is called a galvanic cell. The salt bridge itself contains a gel or a porous medium that prevents leakage of the salt solution into the beakers but allows the slower process of diffusion to balance the charge.

The Electrical Double Layer When a metal is immersed in a solution it undergoes ionization, which results in the formation of a positive charge adsorbed at the surface (in the case of moderate ionization), for example, Zn2+, Fe2+, or Al3+. The complete cell, comprised of electrode and solution, is electrically neutral, but it contains positive and negative ions and electrons inside the bar. The adsorbed layer of cations on the surface (i.e., positive ions) attracts nearby negative ions from the solution, which move towards the bar’s surface and form a so-called diffuse mobile layer. There is an electrostatic attraction between the layer of positive charge on the electrode surface and negatively charged diffuse mobile layer, which is concurrently repelled by the electrons in the bar. The layer of positive charge adsorbed at the metal surface is called a fixed

The Electrical Double Layer

17

Ionization + + e-

Solution in vicinity of electrode 1-10 nm

Electrons in metal

+ + + + + + + + +

- - + + - + - - + + - + -

Bulk solution + + - - - + + + +

- - +

+

Inside of a metal Fixed layer

Water molecules Diffuse mobile layer

Fig. 8 Formation of an electrical double layer in solution

layer. The two layers, one positive and one negative, are called the electrical double layer in a solution (Fig. 8). The electrode is depicted on an atomic level, i.e., individual atoms and the interstitial spaces between the atoms available for electron conduction are shown. In the case of a metal electrode immersed in solution and undergoing ionization the number of electrons in the bar is increased by the same amount as the number of positively charged ions formed, whether attached to the surface or in the solution. The ionization process also illustrated in the upper left part of Fig. 8 generates positively charged ions that form a fixed layer and electrons that remain in the metal electrode. On the solution side, it is important to distinguish a thin layer next to the electrode surface and the bulk electrolyte solution. The composition of the layer next to the surface, which is about 1–10 nanometers thick, responds to the positive charge on the electrode through diffusion of negatively charged ions close to the electrode, creating a mobile layer. This negatively charged layer of ions also includes some positive ions as well and water molecules (not explicitly shown in Fig. 8). The inner side of the mobile layer (towards the bar) contains predominantly negative ions that are attracted and balanced by the fixed layer of positive ions on the bar’s surface. The ion composition of the diffuse or mobile layer then becomes gradually more neutral until it changes into a completely random ion combination in the bulk solution. The fixed and diffuse layers are sometimes referred to as Inner and Outer Helmholtz layers. If a solution is pure water the double layer is formed by the orientation of water dipoles towards the surface (Fig. 9). If the solution contains dissolved ions (acid, base, or salt solution) some of the anions will loosely bond to the metal, creating a negative inner layer, which is compensated by an excess of cations in the outer layer and the bulk of solution.

18

Electrode Potential

Fig. 9 Formation of a double layer on a metal electrode in water

+

+ + + + + + + +

+ +

+

e-

e-

1-10 nm

1-10 nm

+ + + + + + + + +

-

-

+

+ -

Diffuse mobile layer

+ + + + + + + + +

-

-

+

+ -

Diffuse mobile layer

Fig. 10 Movement of the electrical double layer during the oxidation reaction (left) and reduction (right)

The diffuse mobile layer is not always at the same distance from the metal surface (Fig. 10). It moves closer or further away from the surface depending on the amount of the negative charge in the metal, i.e., number of electrons or electron pressure in the metal bar. When the metal electrode is the anode and an oxidation reaction takes place the electrons are withdrawn from the metal. As a result of less negative charge in the metal, the repulsion forces that keep the negatively charged diffuse mobile layer at a distance are now weaker and allow the mobile layer to move closer to the bar. If, on the other hand, the metal bar receives electrons in a reduction reaction and the amount of negative charge is increasing, the diffuse mobile layer will be repelled further from the surface. The electrical double layer is analogous to a capacitor with one fixed and one mobile plate and the distance between plates varies depending on whether an oxidation or reduction reaction takes place. The electrical double layer for the metal immersed in a solution is less than 10 nm thick. A large voltage drop forms over this small distance and the electrical fields across the double layer are on the order of 108 V/m. The drop in electrical potential from the electrode surface to the bulk of solution has four characteristic points (Fig. 11): potential at the electrode surface, inner and outer potentials (not shown in the figure), and Galvani potential difference in the bulk electrolyte solution.

Measuring Electrode Potential

Electrical potential, V

Diffuse mobile layer 1-10 nm

19

Bulk electrolyte solution Electrode potential, V

Galvani potential difference

Distance from electrode surface Fig. 11 Conceptual dependence of the electrical potential with the distance from the electrode surface

Measuring Electrode Potential The potential difference between the metal electrode and the solution (or the interfacial potential difference) is not directly observable as the potential of the solution cannot be measured without introducing another electrode. The only way is to connect the electrode of interest to another electrode, thereby forming an electrochemical cell. The second electrode is chosen because its potential is known, i.e., it serves as a reference. When the cell is assembled in this way, the potential difference is measured between the two electrodes by connecting them to the leads of a voltmeter. By visualizing this system, it becomes clear that the voltmeter measures the sum of two potential differences: the potential difference between the first electrode and the solution and the potential difference between the second electrode and the solution. For example, if zinc and copper electrodes are immersed in a solution, the following reactions occur: Oxidation : ZnðsÞ ! Zn2þ ðaqÞ þ 2e

ð6Þ

Reduction : Cuþ ðaqÞ þ 2e ! CuðsÞ

ð7Þ

Overall : ZnðsÞ þ 2Cuþ ðaqÞ ! Zn2þ ðaqÞ þ 2CuðsÞ

ð8Þ

If the electrodes are connected to the leads of a voltmeter, the voltage of 1.1 V is measured, which is the voltage difference between copper and zinc in a particular solution (Fig. 12). However, this experiment only provides information about the voltage difference between the two electrode potentials and not the absolute potential of the electrodes. To assign potential values (i.e., interfacial electrode potential versus a solution) for

20

Electrode Potential

Fig. 12 Voltage difference measurement for zinccopper cell

1.10 V

e-

e-

Zinc

Copper

electrode materials, metals, for example, a relative scale of potentials must be established. By convention, the electrode potentials are compared with the reaction of hydrogen reduction: 2Hþ þ 2e ! H2

ð9Þ

This reaction is assigned by convention value of 0 (zero) volts. All other electrode potentials are more positive or more negative than this reaction. The meaning of this relative scale is to create ranking of the affinity for the reduction of elements and compare it with that of hydrogen. The scale is called a table of Standard Reduction Potentials and lists the reduction reaction and the corresponding voltage (Table 1). The word “standard” refers to conditions of activity (concentration or pressure) of unity and temperature of 25  C. The reaction potential or electrode potential for metal immersed in solution is affected by the concentration of species in solution and by the temperature and, therefore, it will be different at conditions other than activity or concentration of 1 and temperature of 25  C. Under those conditions, it will be necessary to apply the Nernst equation to arrive at the correct electrode potential. This table is an essential tool and a starting point in analyzing and designing electrochemical reactions and systems. Any two reactions or electrodes can theoretically be paired to determine if the electrochemical cell would be functional and what voltage would it produce (galvanic cell), or what voltage would be necessary to force a certain reaction (electrolytic cell). While this is a fundamental starting point it must be understood that practical voltages always differ from the values predicted by the table of Standard Reduction Potentials. When analyzing the table, it is first observed that each of the reactions listed is a half-cell reaction and cannot take place without being coupled to another reaction. Furthermore, any electrode at which a reduction half-reaction shows a greater tendency to occur than hydrogen reduction from H+ (1 M) to H2 (g, 1 atm) has a positive potential. Any electrode at which a reduction half-reaction shows a lesser tendency to occur than hydrogen reduction has a negative value. When two electrodes, for example, mercury (Hg) and magnesium (Mg), are immersed in a

Measuring Electrode Potential Table 1 Standard Reduction Potentials (in V) for selected reaction. Compiled from a variety of sources

F2 + 2e ! 2F Co3+ + e ! Co2+ PbO2 + 4H+ + SO42 + 2e ! PbSO4(s) + 2H2O MnO4 + 8H+ + 5e ! Mn2+ + 4H2O PbO2 + 4H+ + 2e ! Pb2+ + 2H2O Cl2 + 2e ! 2Cl Cr2O72 + 14H+ + 6e ! 2Cr3+ + 7H2O O2 + 4H+ + 4e ! 2H2O Br2 + 2e ! 2Br NO3 + 4H+ + 3e ! NO + 2H2O Hg2+ + 2e ! Hg Ag+ + e ! Ag Fe3+ + e ! Fe2+ I2 + 2e ! 2I Cu+ + e ! Cu O2 + 2H2O + 4e ! 4OH Fe(CN)63 + e ! Fe(CN)64 Cu2+ + 2e ! Cu Cu2+ + e ! Cu+ Sn4+ + 2e ! Sn2+ 2H+ + 2e ! H2 Fe3+ + 3e ! Fe Pb2+ + 2e ! Pb Sn2+ + 2e ! Sn Ni2+ + 2e ! Ni Co2+ + 2e ! Co PbSO4 + 2e ! Pb + SO42 PbI2 + 2e ! Pb + 2I Cr3+ + e ! Cr2+ Cd2+ + 2e ! Cd Fe2+ + 2e ! Fe Cr3+ + 3e ! Cr Zn2+ + 2e ! Zn 2H2O + 2e ! H2(g) + 2OH V2+ + 2e ! V Mn2+ + 2e ! Mn Al3+ + 3e ! Al Mg2+ + 2e ! Mg Na+ + e ! Na Ca2+ + 2e ! Ca K+ + e ! K Li+ + e ! Li

21

+2.87 +1.80 +1.69 +1.49 +1.46 +1.36 +1.33 +1.23 +1.07 +0.96 +0.85 +0.80 +0.77 +0.54 +0.52 +0.40 +0.36 +0.34 +0.15 +0.15 0.00 0.04 0.13 0.14 0.25 0.29 0.359 0.365 0.40 0.40 0.41 0.74 0.76 0.83 1.18 1.18 1.66 2.37 2.71 2.76 2.92 3.04

22

Electrode Potential

solution and electrically connected, the Hg electrode will have a greater tendency to be reduced evidenced by a more positive standard reduction potential. There are two reactions in the table for hydrogen reduction and two for oxygen reduction, representing different pH values, i.e., one set of reactions is in acidic solutions at pH of 1 and the second set in alkaline solutions at pH of 14. For example, reduction reaction for hydrogen at pH of 1 has the standard reduction potentials of 0 V, while at pH of 14 it is 0.83 V. The later also has a different reaction equation (Eq. 10), which should be compared with the Eq. 9. 2H2 O þ 2e ! H2ðgÞ þ 2OH

E 0 ¼ 0:83 V

ð10Þ

The oxygen reduction reaction in alkaline solutions, at a pH of 14 is shown in Eq. 11. Compare it with the oxygen reduction reaction in the acidic medium with a pH of 1 (Eq. 12). O2 þ 2H2 O þ 4e ! 4OH O2 þ 4Hþ þ 4e ! 2H2 O

E 0 ¼ þ0:40 V E0 ¼ þ1:23 V

ð11Þ ð12Þ

It is important to understand that the cell voltage for the hydrogen-oxygen reaction remains the same at 1.23 V, although the individual half-cell potential values change in the table of Standard Reduction potentials depending on the pH of the solution. In other words, the theoretical voltage for water electrolysis to generate hydrogen and oxygen gas is always 1.23 V (at standard conditions of concentration/pressure and temperature) regardless of the nature of the solution and its pH. Similarly, for the reaction in the H2–O2 fuel cell (a galvanic cell producing power), the theoretical voltage is always 1.23 V, regardless of the electrolyte pH. Practical voltages, however, are always different; they are higher for the electrolysis reactions and lower for the fuel cell reactions. Using the table of Standard Reduction Potentials, the theoretical cell voltage for any paired reactions can be calculated. These reactions are called redox reactions in chemistry because one of the species undergoes reduction and the other one oxidation, i.e., one half-cell reaction is reduction and the other one is oxidation. When coupling or pairing two elements (i.e., reactions) the cell voltage will be determined by the following procedure: 1. Write reduction half-equations and their standard reduction potentials (E0 from the table). 2. Determine, by consulting the table, which of the two half-cell reduction potentials is more positive. 3. The half-cell reaction with the more positive standard reduction potential becomes the reduction half-cell reaction, E0red. The half-cell reaction equation proceeds in the forward direction. 4. The half-cell reaction with the less positive standard reduction potential is now the oxidation half-cell reaction, E0ox. The half-cell reaction equation proceeds in the reverse direction, i.e., oxidation, not reduction.

Measuring Electrode Potential

23

5. The cell (or overall) reaction voltage, E0cell is calculated as: E0cell ¼ E0red  E0ox. Example 1 What is the standard cell voltage for an electrochemical cell comprised of a silver electrode and a cadmium electrode immersed in electrolyte and connected electrically with an external wire. 1. The half-cell reactions (from the table) are: (a) Ag+ + e ! Ag E0 ¼ +0.80 V (b) Cd2+ + 2e ! Cd E0 ¼ 0.40 V 2. The half-cell reduction reaction for silver is more positive, therefore, reduction will occur on the silver electrode and oxidation on the cadmium electrode: (a) Ag+ + e ! Ag Ox. (b) Cd ! Cd2+ + 2e Red. (the reaction is reversed from the table) 3. E0cell ¼ E0red  E0ox ¼ +0.80 V  (0.40 V) ¼ 1.2 V. The standard cell voltage for this redox couple is 1.2 V. The positive value of the cell voltage means that the reaction is spontaneous. We will see later that it is possible to predetermine which half-cell reaction will be the reduction and which the oxidation, even if the table of Standard Reduction Potentials suggests the opposite. In those cases, the reaction is still possible, but it requires the input of external power, for example, from a power supply. The overall cell voltage will be negative in that case. These reactions are called electrolytic reactions and they are nonspontaneous. Remember that spontaneous reactions occur in galvanic or voltaic cells and the calculated cell voltage for these reactions is positive. Example 2 Chlorine is the basic raw material for the preparation of a range of important products including chlorinated bleaches, pesticides, and polymers. It is prepared by the electrolysis of aqueous NaCl in an alkaline solution (note the standard reduction potential for hydrogen reduction in alkaline medium). What is the cell voltage for the electrolysis of NaCl? 1. The half-cell reactions (from the table) are: (a) Cl2 + 2e ! 2Cl E0 ¼ +1.36 V (b) 2H2O + 2e ! H2(g) + 2OH E0 ¼ 0.83 V 2. The half-cell reaction for chlorine reduction is more positive, but the requirement for this industrial process is the production of chlorine, therefore the reaction for chlorine is reversed from the table: (a) 2H2O + 2e ! H2(g) + 2OH Red. (b) 2Cl ! Cl2 + 2e Ox. 3. E0cell ¼ E0red  E0ox ¼ 0.83 V  (+1.36 V) ¼ 2.19 V. The standard cell voltage for this reaction is negative and consequently the external input of power is necessary for this reaction. This is an example of the industrial electrochemical process for the production of chemicals.

24

Electrode Potential

Potential Scale The table of Standard Reduction Potentials enables determination of the position of an electrode reaction relative to a hydrogen reduction reaction and those of other elements. However, the practical potential measurement requires a known reference electrode to determine the unknown potential of the electrode of interest. Using a metallic electrode for this purpose is possible, but not a good option because metallic electrodes do not always have a stable and fixed potential due to the nature of these species in solution and their concentration. A better way is to have a reference electrode with a fixed and predictable potential, stable in any solution. The obvious choice for a reference electrode is to build an electrode that should exhibit zero volts—the half-cell reaction for hydrogen reduction. This is called the standard hydrogen electrode (SHE) and involves equilibrium between H3O+ ions from a solution at unit activity and H2 molecules from gaseous state at 1 atm (Eq. 13). 2Hþ ða¼1Þ þ 2e ! H2ðg,1atmÞ

Pt=H2 ðg, 1 atmÞ=Hþ ð1 MÞ E 0 ¼ 0 V

ð13Þ

By international agreement, SHE measures the tendency for a reduction process to occur. The value of SHE potential is arbitrarily set to zero. The SHE is constructed using a platinized platinum electrode immersed in an acidic solution and pure hydrogen gas bubbled through it. The standard conditions are applied: the concentration of both the reduced and oxidized forms is maintained at unity; the pressure of the hydrogen gas is one bar and the activity of hydrogen ions in the solution is one. The activity of hydrogen ions is also known as their effective concentration, which is equal to the formal concentration times the activity coefficient. Platinum is used as the electrode because of its inertness, ability to catalyze proton reduction, good reaction reproducibility, and high exchange current density for proton reduction. The platinum electrode is platinized, i.e., covered with a thin, rough layer of deposited platinum with a high active surface area for improved reaction kinetics. The schematic of this electrode is shown in Fig. 13.

Fig. 13 Schematics of the standard hydrogen electrode

Pt wire 1 atm H2(g)

1 M H+(aq)

H2 gas bubbles Pt electrode

Potential Scale

25

Saturated calomel reference electrode

Ag/AgCl reference electrode

AgCl coated Ag wire Hg/HgCl paste (calomel)

AgCl saturated solution

KCl saturated solution Porous frit

Porous frit

Fig. 14 Schematics of the saturated calomel and silver/silver chloride reference electrodes

The Standard Hydrogen Electrode (SHE) is difficult to construct in practice for routine measurements. It is much more convenient to use specially made reference electrodes with fixed potential and reproducible manufacturing. These electrodes are unaffected by the solution properties or concentration because they comprise an internal solution of fixed composition and concentration that does not directly mix with the electrolyte solution. The internal solution in the reference electrodes is in contact with the external solution through a porous medium such as ceramic or glass frit that allows formation of the contact potential but does not allow free mixing of two solutions. This enables repeatable measurements of electrode potential versus the reference electrode. The two most commonly used reference electrodes, saturated calomel electrode (SCE) and silver/silver chloride (Ag/AgCl), are shown in Fig. 14. The saturated calomel electrode is made of mercury chloride paste, also called calomel (Hg2Cl2) deposited on a metal wire and immersed in saturated KCl solution. The porous frit separates the internal solution from the external solution. The following reaction occurs in the saturated calomel electrode: Hg2 Cl2 þ 2e ! Hg þ 2Cl

E 0 ¼ þ0:268 V

ð14Þ

The standard reduction potential for this half-cell reaction is given for a 1 M KCL solution, while the practically saturated calomel electrode contains saturated KCl and, therefore, has a different standard reduction potential of +0.241 V. The silver/silver chloride reference electrode is made of silver chloride (AgCl) coated silver wire immersed in a saturated KCl solution and separated from the external solution with a glass frit. The half-cell reaction and the standard reduction potential for the silver/silver chloride reference electrode are: AgClðsÞ þ e ! AgðsÞ þ Cl 

E0 ¼ þ0:222

ð15Þ

26

Electrode Potential

Ag/AgCl (0.197 V) SCE (0.241 V)

-2V

-1V

0V

1V

2V

SHE

Fig. 15 Voltage scale representation with SHE, SCE, and Ag/AgCl electrodes

Because saturated KCl is used the actual standard reduction potential for the silver/silver chloride electrode is +0.197 V. In practice, the voltage is measured versus a reference electrode, e.g., SCE or Ag/AgCl, but it is a common practice to report it versus SHE. Hence, a visualization of a voltage scale with three reference voltages, SHE, SCE, and Ag/AgCl, is useful in the conversion of the expressed value of voltage (Fig. 15). Example 3 The voltage of an electrode reaction was measured against SCE to be 0.30 V. What reduction reaction is this? E 0 ðvs:SHEÞ ¼ þ0:24 þ 0:30 ¼ 0:54 V The reaction is iodine reduction (see table of Standard Reduction Potentials). Example 4 The voltage of an electrode reaction was measured against Ag/AgCl reference electrode to be –3.000 V. What reaction/electrode is this? Using voltage scale visualization, it can be established that the voltage of the reaction is: 0.197 V (Ag/AgCl)  3.000 V ¼ 2.803 V vs. SHE. Using the table of the Standard Reduction Potentials the electrode is identified as Ca.

Effect of Concentration

Nernst Equation In the previous section, the electrochemical potentials were analyzed under standard conditions of unit activity, which means that the effective concentration is 1 M or for gases the effective pressure (known as fugacity) is 1 atm; and the temperature of the reaction is 25
C. These conditions are unrealistic for practical purposes and serve simply as a reference point, i.e., conditions under which the potentials of various reactions on electrodes in solutions can be compared. Using standard reduction potential concept as a starting point the actual, practical cell potential can be predicted more accurately using the Nernst equation, which takes into account the effect of reactant and product concentrations in solution or effective pressure and temperature. The Nernst equation connects the standard reduction potential of an electrochemical cell and the reaction quotient in the following way: E ¼ E0 

RT ln Q nF

ð1Þ

In this equation, R is the universal gas constant that relates units of energy to temperature (8.314 J K1 mol1 or 0.082 L atm K1 mol1); and F is the Faraday constant indicating the amount of electrical charge per mol of electrons (96,485 C mol1). The Nernst equation is commonly simplified using a base 10 logarithm instead of a natural base logarithm, replacing values for R and F, and using 25
C for the temperature, which results in the following expression: E ¼ E0 

0:059 log Q n

ð2Þ

For a reaction of the general form: aA + bB $ cC + dD, the equation becomes:

# The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_4

27

28

Effect of Concentration

E ¼ E0 

½C c ½Dd 0:059 log n ½Aa ½Bb

ð3Þ

By examining this equation, one can conclude that the cell voltage is reduced from the standard cell voltage if the reduction quotient is larger than 1, i.e., if the reaction is shifted towards products. Conversely, the cell voltage increases if the reaction quotient is less than one, i.e., if the reaction is shifted towards reactants. The cell voltage assumes a value to favor a shift towards reaction equilibrium. This principle applies equally to voltaic and electrolytic processes. A voltaic cell voltage decreases as the reaction proceeds if products are not removed or reactants resupplied; and an electrolytic process voltage increases as the products are removed. Example 1 A hydrogen-oxygen fuel cell, H2 + ½ O2 ! H2O, has deviated from unit activity as the pressure of both hydrogen and oxygen has been reduced to one fifth. What is the cell voltage under those activity conditions if the standard cell voltage is 1.23 V? E ¼ E0 

½H2 O 0:059 0:059 1 log log ¼ 1:23  ¼ 0:20 V 1=2 n n ½0:2½0:21=2 ½pH2 ½pO2 

Example 2 A Zn/Cu cell and reaction Zn(s) + Cu2+ ! Zn2+ + Cu(s), cell notation: (Zn(s) | Zn2+(aq, .001 M) || Cu2+(aq) | Cu(s)) considered previously has Zn2+ concentration reduced from 1 M to 0.001 M. The cell voltage will be:  2þ  Zn 0:059 0:059 0:001 0   ¼ 1:10  log log ¼ 1:19 V E¼E  n 2 ½ 1 Cu2þ

Effect of Concentration on Cell EMF The standard cell potential or the Electromotive Force is the maximum potential difference between two electrodes in solution. The Nernst equation can be used to calculate EMF for any electrode pair depending on the concentration or pressure of reactants and products. It can also be used to design a cell that has the same electrode material for both anode and cathode and the EMF or cell voltage is created solely based on the difference in concentrations. This can be done in a rather simple way whereby the two cell compartments although having the same electrode material are filled with different concentrations of reactants. Based on the Le Chatelier’s principle, which is also the basis for the Nernst equation, the cell with two different concentrations of the same reactant shifts its equilibrium towards equalizing the concentrations in the two compartments.

Stability of Water

29

Example 3 Two nickel electrodes are immersed in a solution, one in 1.00 M Ni2 + (aq) and the other in 1.00  103 M Ni2+(aq). A cell with two nickel electrodes with the same concentration of Ni2+ in solution would generate a cell voltage of zero, but with different solution concentrations the cell voltage would be:  2þ  Nidilute ½0:001 0:059 0:059 0 ¼0 E¼E  log  2þ log ¼ þ0:0885 V n 2 ½ 1 Niconcent The concentrated solution has to reduce the amount of Ni2+(aq) (to Ni(s)), so must be the cathode, while the diluted solution tends to increase the concentration of Ni2+(aq) and is therefore an anode. This is called a concentration cell.

Significance of the Nernst Equation By observing the Nernst equation, we can see that half-cell potential changes by 59 mV per tenfold change in the concentration for one-electron reactions. For two-electron processes, the variation will be 29.5 mV per decade (Fig. 1).

Stability of Water It can be seen from examining the table of Standard Reduction Potentials that water reacts with both stronger oxidizing agents and stronger reducing agents. For example, in the presence of Cl2, a stronger oxidizing agent, chlorine has a stronger tendency to get reduced to Cl, which forces water to get oxidized to H+. The reduction reaction for hydrogen can be written either as:

Fig. 1 Electrode potential change with concentration for 1- and 2-electron processes

Potential, V (vs. SHE)

0.3 0.4

Slope = 0.059/2

0.5 0.6 Slope = 0.059

0.7 0.8

0

-2

-4 log [Cu2+]

-6

-8

30

Effect of Concentration

Potential, V (vs. SHE)

+1.5

2H2O  O2 + 4H++ 4e-

+1.0 +0.5 Region of thermodynamic stability of water

0 -0.5

2H+ + 2e-  H2

-1.0 0

2

4

6

8

10

12

14

pH Fig. 2 Reaction voltage for water solutions as a function of pH

2Hþ þ 2e ! H2ðgÞ

ð4Þ

or, in neutral or alkaline solutions as: 2H2 O þ 2e ! H2ðgÞ þ 2OH

ð5Þ

These two reactions are equivalent and follow the same Nernst equation which, at 25
C and unit H2 partial pressure, reduce to: ½p  0:059 0:059 1 0:059 log H2 log þ 2 ¼  f2 log ½Hþ g þ ¼ 0 n 2 2 ½H  ð6Þ ½H  þ ¼ 0:059 log ½H  ¼ 0:059 pH

E ¼ E0 

Similarly, the oxidation of water H2 O ! O2 ðgÞ þ 4 Hþ þ 2e

ð7Þ

is governed by the Nernst equation (Eq. 8) ½Hþ  ½pO2  RT 0:059 4 ¼ E0O2=  ln log ½Hþ  ½pO2  H2O 1 nF 4 4

E O2=H2O ¼ E 0O2=

H2O



The graphical representation of water stability is shown in Fig. 2.

ð8Þ

Electrochemical Thermodynamics

Introduction It is a common misconception that thermodynamics is an obscure and irrelevant branch of science, with no practical importance and overburdened with ambiguity. The truth, however, is that thermodynamics enables one to predict the equilibrium composition of a system from the properties of its components. Simply put, from thermodynamics we can anticipate if a chemical reaction will occur and to what extent. For example, thermodynamics will help us predict if hydrogen and oxygen will react in a fuel cell and produce power at a certain temperature or if NaCl and H2O will react spontaneously to produce chlorine gas and hydrogen. All this can be done without doing any experiments, simply through scientific reasoning. Without the foundations established by thermodynamics and concepts derived from it (e.g., electrode potentials) electrochemistry would be largely reduced to empiricism: gathering and categorizing of experimental data. Thermodynamic assessment is powerful because it connects the equilibrium constant K and the equilibrium quotient Q with the cell voltage. The changes in voltage and associated changes in current depend on the thermodynamic characteristic of the system or composition of the reactants and products. The system undergoes a change in composition until it reaches the equilibrium or until Q ¼ K.

System and Surroundings Every reaction in electrochemistry (as well as in chemistry) takes place in a very small portion of the universe, the system of interest, while everything else around it is considered the surroundings. In most cases, only the electrodes and the electrolyte constitutes a system; and the container or cell is considered the surroundings. A closed system means that it can exchange energy with the surroundings, but not the matter. # The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_5

31

32

Electrochemical Thermodynamics

A fuel cell, on the other hand, is an open system. When hydrogen and oxygen react in a fuel cell to form water energy is produced (Eq. 1). It is not created from nothing but liberated from the energy states in the reactants. This open system not only exchanges the energy with the environment by producing electrical current, but it also exchanges matter with the environment, through the input of reactant gases supplied to the fuel cell and the removal of product water. 2H2ðgÞ þ O2ðgÞ ! 2H2 OðlÞ þ energy

ð1Þ

An example of a closed system, on the other hand, is a sealed primary battery, or Leclanche Cell: 2MnO2 þ Zn þ 2NH4 Cl ! 2MnOOH þ ZnðNH3 Þ2 Cl2

ð2Þ

The system, in this case, includes only zinc, manganese dioxide, and ammonium chloride, while everything else is the surroundings. Although the chemicals react and change, the system does not lose or gain mass and it undergoes no exchange of matter with its surroundings, only energy.

First Law of Thermodynamics Energy is conserved. This is a simple, universal truth known as the First Law of Thermodynamics. Energy lost by a system must be gained by the environment, and vice versa. Since energy can neither be created nor destroyed, only converted from one form to another, the total energy of the universe is constant. The internal energy of a system is defined as the sum of the kinetic and potential energy of all components or reactants. In the case of hydrogen and oxygen reacting in a fuel cell (i.e., electrochemical system) the internal energy includes the motions of H2 and O2 molecules, their rotations and vibrations, as well as the energies of the nuclei of each atom. If a system performs work or there is a reaction, the internal energy of the systems changes. Since it is generally impossible to know the actual value of internal energy it is the change in internal energy, ΔE, that is of importance and it is simply: ΔE ¼ E final  Einitial

ð3Þ

Thermodynamic properties such as ΔE must also have a sign indicating the direction in which a change occurs. A positive value of ΔE means that Efinal > Einitial and the system has gained energy from the environment, e.g., the water electrolysis reaction. A negative value of ΔE means that Efinal < Einitial and the system has lost energy to the surroundings, e.g., the fuel cell reaction. The internal energy of a system changes as energy, in the form of heat or electricity, is added or removed from the system or if any work is done. When a system undergoes any chemical change there is a change in internal energy. The first

Enthalpy

33

law of thermodynamics describes how work and heat are related to system’s internal energy. ΔE ¼ q þ w

ð4Þ

When heat is applied from the surroundings to the system, q is positive and when work is done on the system by the surroundings, w is positive.

Enthalpy The thermodynamic function called enthalpy, H, is a measure of heat flow in a chemical reaction at constant pressure when no work is performed. Enthalpy is expressed by the internal energy plus the product of the pressure and volume of the system: H ¼ E þ PV

ð5Þ

If a change in the system occurs at a constant pressure, the change in enthalpy is given as the change in internal energy plus the product of the pressure (constant) and change in volume: ΔH ¼ ΔðE þ PV Þ ¼ ΔE þ PΔV

ð6Þ

The product of constant pressure and change in volume is in fact the work, so after a few substitutions: ΔH ¼ ΔE þ PΔV ¼ qp þ w  w ¼ qp

ð7Þ

The subscript “p” indicates that the reaction takes place at a constant pressure. This means that the change in enthalpy is equal to heat gained or lost at constant pressure. Enthalpy is a more useful function than internal energy because heat, q, can be measured and because most reactions take place at constant pressure (not true for some electrochemical reactions, but we still use enthalpy as a useful function to conceptually establish relationships in electrochemistry). The sign of this thermodynamic function is equally important. When ΔH is positive, the system has gained heat from the surroundings and the process is endothermic. When ΔH is negative, the system has released heat to the surroundings and the process is exothermic. Enthalpy is a “state function”, i.e., it depends only on the initial and final states of the system, not on the pathway of the change or intermediate states. Thermodynamic functions that are state functions are expressed using capital letters. The confusion may arise when examining Eq. 7 in which enthalpy, a state function, equals q, a non-state function. The equation’s irregularity is allowed because heat, q, is used at constant pressure.

34

Electrochemical Thermodynamics

Reaction Spontaneity Spontaneous processes in nature occur in one direction without any external action or driving force. We all know from experience that ice melts to water above 0  C and that water freezes below 0  C or that iron rusts (i.e., corrodes) in reaction with oxygen: 4Fe þ 3O2 ! 2Fe2 O3

ð8Þ

We also know from experience that some processes would not be spontaneous (Fig. 1). We know that hydrogen and oxygen react spontaneously in a fuel cell to produce energy. It is also experiential understanding that the processes that are spontaneous in one direction are nonspontaneous in the opposite direction, e.g., iron oxide will not spontaneously change to pure iron. However, the reverse or nonspontaneous processes are not impossible; they can occur if an outside force acts on the system, as in the case of voltage being applied to electrolyze water and decompose it to hydrogen and oxygen—the reverse of a fuel cell reaction. Experience alone cannot predict everything as there is only so much we can directly experience. Considering any number of different reactions and all possible conditions in which those reactions occur, such as concentration and temperature leads to the conclusion that it is impossible to address everything using experience. In those cases, the application of the laws of thermodynamics can lead to predictions about system behavior. To test your experience regarding process spontaneity you should examine the following reactions and predict if they are spontaneous: the reaction of NaOH and HCl, the electrolysis of liquid water, the melting of an ice cube, and a methanol reaction with oxygen.

Entropy Entropy (S) was first described by German physicist Rudolph Clausius in the nineteenth century. He defined it as the ratio of heat delivered and the temperature at which it is delivered:

Fig. 1 A nonspontaneous process

Entropy

35

S ¼ q=T

ð9Þ

This entropy is called thermal entropy, Sth, since the heat content q is proportional to the product of entropy and the temperature, and has the dimension of energy: q ¼ Sth T

ð10Þ

Entropy can be determined if the heat of the reaction is known. Entropy is one of the most misunderstood fundamental concepts of physical science. It is often represented, too narrowly, as a measure of system disorder— when in fact it is a measure of heat content distribution among the reactants and products. The distribution of heat depends on how many potential, quantized energy states the reactants and products have. (Note that the term “quantize” refers to the fact that not all energy states in an atom or a molecule are allowed.) These states on the molecular level are related to the kinetic energy of the molecules and their motion: translational, vibrational, and rotational. There is also a different type of entropy that comes not from the vibratory motion of the fundamental particles (as in heat entropy), but from the disorder in the arrangement of particles of a material. The best way to think about it is to consider regularity of the internal structure of a material. When that regularity changes, the entropy changes as well. One example of this type of entropy, called configurational or structural entropy, is a degree of order in a crystal. When this order changes, the entropy changes as well. Ludwig Boltzmann described molecular motions using a concept of microstates, W—the “snapshots” of the position of atoms in time. Using this concept the entropy is expressed as: S ¼ k ln W

ð11Þ

where k is the Boltzmann constant, 1.38  1023 J/K (k ¼ R/N, i.e., gas constant over Avogadro number). The implications of the Boltzmann theory are that more particles mean more states and more entropy. Higher temperature results in more energy states and more entropy, so does less structure (e.g., gas vs. solid). The number of microstates and, therefore, the entropy tend to increase with increases in temperature, volume (gases), and the number of independently moving molecules. Entropy increases with the freedom of motion of molecules. For example, entropy increases during the aggregate change from solid to liquid to gas (S(g) > S(l) > S(s)) as well as in dissolution processes. In general, entropy increases when gases are formed from liquids and solids, when liquids or solutions are formed from solids, when the number of gas molecules increases, and when the number of moles increases. Using these rules, qualitative predictions can be made about the entropy changes in chemical reactions. For example, in water decomposition to hydrogen and oxygen (Eq. 12), three moles of gas are formed from two moles of liquid and entropy clearly increases.

36

Electrochemical Thermodynamics

2H2 OðlÞ ! 2H2 þ O2

ð12Þ

Note that the reverse reaction is a fuel cell reaction and the entropy decreases. In chlor-alkali electrolysis, one of the most important industrial electrochemical processes (Eq. 13), two moles of liquid and two moles of gas are formed from four moles of liquid and entropy increases.  2Cl ðaqÞ þ 2H2 OðlÞ ! 2OHðaqÞ þ H2ðgÞ þ Cl2ðgÞ

ð13Þ

In the reaction between carbon monoxide and water, important in hydrogen production and known in the petrochemical industry and as water-gas shift reaction (Eq. 14), two moles of gas react, and two moles of gas are formed. In this case, the change in entropy cannot be predicted. COðgÞ þ H2 OðgÞ ! CO2ðgÞ þ H2ðgÞ

ð14Þ

Exercise: Predict entropy change for the following reactions: • 2NH4NO3(s) ! 2 N2(g) + 4H2O(g) + O2(g) • 2SO2(g) + O2(g) ! 2SO3(g) • C12H22O11(aq) ! C12H22O11(s) Entropy is an extensive quantity, which means that it is proportional to the quantity of matter in a system and dependent on the available, quantized energy levels that can contain thermal energy. This intuitively makes sense because, for example, 200 g of hydrogen have twice the entropy of 100 g at the same temperature.

The Second Law of Thermodynamics Thermodynamics attempts to explain fundamental processes in nature, but some of its principles are often incomplete or difficult to understand. Recalling the First Law of Thermodynamics, it should be clear that energy is always conserved. However, the First Law does not explain everything and, in particular, it does not deal with the direction of the processes, a critical observation with the implications for everything we experience in our world. For example, if the First Law was applied to a fuel cell reaction between hydrogen and oxygen, energy is produced by converting the chemical energy of the fuel to electricity in a spontaneous process. But, the First Law does not say anything about the spontaneity of the reverse reaction—the electrolysis of water to produce hydrogen and oxygen. We know from observation and experience that the electrolysis reaction, decomposition of water to hydrogen and oxygen, cannot occur spontaneously without an input of energy from the

Gibbs Free Energy

37

surroundings. From this example, you can see that the First law is not enough and we need additional explanations for processes in nature. The Second Law of Thermodynamics states that certain processes do not take place or have never been observed to take place, even though they may not violate the first law (ΔE ¼ q + w). Once a spontaneous process has occurred and, as a result, thermal energy has been distributed as entropy increases, the process cannot be reversed (or undone) without further distribution of heat and further increase of entropy. This means, for example, that heat will not flow spontaneously from a colder body to a warmer body. The Second Law refers only to spontaneous processes in nature. Therefore, a reverse process (for example, heat flowing from a colder body to a warmer one) is possible, just not spontaneous. Deriving such processes would require external energy, which results in increased entropy. Other implications of the Second Law are that heat energy cannot be completely transformed into mechanical work and that a perpetual-motion machine could, therefore not be built. All spontaneous processes produce an increase in the entropy of the universe, which only increases and never decreases. When evaluating a single system, it is possible that the entropy of that system decreases (e.g., fuel cell reaction—Eq. 15). 2H2 þ O2 ! 2H2 O þ energy

ð15Þ

This system, a fuel cell, not only exchanges energy with the environment by producing electrical current, but it also exchanges matter with the environment as the gases are supplied to the fuel cell and product water is removed. Therefore, the system is not isolated from the surroundings, so the heat and the entropy of the surroundings increase, causing the overall entropy of the system plus its surroundings, i.e., the entropy of the universe, to increase: ΔSuniverse ¼ ΔSsystem þ ΔSsurroundings > 0

ð16Þ

Similarly, when water freezes, there is a flow of heat (the heat of fusion) into the surroundings and ΔSsurr increases. At temperatures below the freezing point of water, this increase is larger than the decrease in the entropy of the water itself; the entropy of the universe (ΔSuniverse) exceeds zero and the process is spontaneous. It should be understood that the spontaneity of all such processes will depend on the temperature.

Gibbs Free Energy The most useful thermodynamic function for the evaluation of electrochemical systems, as well as most other reactions, is free energy. Free energy provides a criterion for predicting the direction of chemical or electrochemical reactions and the composition of the system at equilibrium. Free energy is most often expressed using Gibbs Function and is, therefore, called Gibbs Free Energy.

38

Electrochemical Thermodynamics

J. Willard Gibbs (1839–1903) was an American scientist. He is considered the father of modern thermodynamics. The term Gibbs Free Energy requires immediate clarifications to prevent confusion about the subsequent concepts and in fact it is better to use Gibbs Energy. The word “free” is not very helpful and would more accurately mean that energy can be freed from the system to do useful work (e.g., “removing” electricity or obtaining electrical work by moving electrical charge through a potential difference). Another problem is that Gibbs Free Energy or Gibbs Energy is not really energy since it is not conserved, which would violate the First Law of Thermodynamics. There are systems where the decrease in Gibbs Energy is not followed or accompanied by an energy increase in the surroundings. Note, however, that G has the units of energy, e.g., kJ/mol. The most unclear aspect of Gibbs Energy comes from the realization that it is not connected to anything real in a physical world. Unlike enthalpy or entropy that can be related to physical states of atoms or molecules, Gibbs Energy has no more meaning than being a useful construct to make calculations easier and improve understanding of changes in chemical reactions. Gibbs Energy is defined as: G ¼ H  TS

ð17Þ

All functions in this equation are state functions, i.e., they depend on the initial and final state, not the pathway between them. So, for a chemical or electrochemical reaction the change in Gibbs Energy becomes: ΔG ¼ ΔH  TΔS

ð18Þ

This is a very important relationship in thermodynamics and an essential concept in predicting the spontaneity of electrochemical reactions. If examined carefully the formula reveals more than is obvious at the first glance. It connects heat distribution between the universe, the system, and the surroundings. The enthalpy change of the reaction, ΔH, is defined as the flow of heat into the system from the surroundings, or vice versa, when the reaction is carried out at constant pressure. If the right side of the equation shows heat distributed between the system and the surroundings then the left side, Gibbs Energy (ΔG) is a measure of the heat change in the universe.

Gibbs Energy and Chemical Change ΔG determines the direction and extent of chemical change, however, a single calculation is valid only if temperature and pressure are constant. More importantly, Gibbs Energy determines if a given chemical change is thermodynamically possible. The direction of a reaction depends on the sign of ΔG, if it is negative (i.e., the free

Gibbs Energy and Chemical Change

39

energy of reactants is greater than that of products) the reaction will proceed in the forward direction, as written. If Gibbs Energy is positive, the reaction will not proceed spontaneously in the direction written. If Gibbs Energy is zero, the process is at equilibrium and no change occurs. It now becomes clear that for all spontaneous processes, Gibbs Energy decreases, while the entropy of the universe increases. When water freezes, H2O(liquid) ! H2O(S), entropy decreases below the freezing point because of the more ordered structure. But the heat of fusion is released to the surroundings and leads to an increase in entropy. In turn, the entropy of the universe increases. So, Gibbs Energy for this reaction is negative and the reaction proceeds spontaneously. By examining the equation for Gibbs Energy, it is obvious that it depends on the temperature at which the process takes place mainly because of the TΔS, but also as a result the gradual increase of H and S with temperature. The sign of the entropy change determines if the reaction is more or less spontaneous with an increase in temperature. Additionally, the sign of ΔH can also be positive or negative. This means that there are four possibilities for the influence that temperature can have on the spontaneity of a process. If ΔH is negative and ΔS positive the ΔG is always negative and spontaneous at all temperatures. If both ΔH and ΔS are negative, the ΔG is negative at low temperatures and switches to positive at a characteristic temperature when the product TΔS exceeds the value of ΔH. The most common examples for this type of system are the freezing of water to ice and the fuel cell reactions. If both ΔH and ΔS are positive the ΔG is positive at low temperatures and negative at high temperatures, so the reaction is nonspontaneous at low temperatures and spontaneous at high temperatures when TΔS exceeds the value of ΔH. Finally, if ΔH is positive and ΔS is negative for a reaction, ΔG is always positive, and the reaction is nonspontaneous at all temperatures. Example 1 At approximately what temperature in Kelvin does the fuel cell reaction 2H2 (g) + O2(g) ! 2H2O(g) change from spontaneous to nonspontaneous? (ΔH (H2O) ¼ 241.8 kJ/mol, ΔS (above reaction) ¼ 90.8 J/mol; assume that both ΔH and ΔS are temperature independent). ΔG ¼ ΔH  TΔS T ¼ (ΔH  ΔG)/ΔS and since ΔG ¼ 0 T ¼ 2663 K Example 2 Calculate ΔG at 298 K for the reaction: 2NO(g) + O2(g) ! 2NO2(g) at 298.15 K. ΔH ¼ 114.1 kJ/mol, ΔS ¼ 146.4 J mol1 K1. ΔG ¼ 114.1 kJ/mol – {298 K  (0.1464 kJ K1)} ¼ 70.5 kJ

40

Electrochemical Thermodynamics

Standard Gibbs Free Energy Gibbs Energy for a reaction can be calculated if the Gibbs energies of individual components are known. Gibbs Energy calculated in this way is called Standard Gibbs (Free) Energy. The standard conditions are a concentration of 1 M or pressure of 1 atm and a temperature of 25  C (298 K), while the nonstandard conditions include all practical conditions when the activity (i.e., concentration or pressure) is not unity and/or the temperature is not 298 K. Each individual component of the Gibbs Energy can be calculated using the standard enthalpies of formation and the standard entropies of formation. 



ΔG f ¼ ΔH f  TΔS f



ð19Þ

The free energy change of formation of a substance from the elements in their most stable forms (in standard states) can be obtained from the thermodynamic tables (see Table 1). Note from the table that all pure elements have zero standard enthalpy of formation and zero standard Gibbs Energy of formation, but all elements and compounds have entropy. Note as well that the values for ΔHf are given in kJ/mol while the values for ΔSf are in J/mol because of much smaller ΔSf values for all substances. When ΔGf values for all reactants and products are known, the standard Gibbs Energy for a reaction can be calculated using the formula (Eq. 20): 

ΔG ¼ ΣΔG f



ðproductsÞ

 ΣΔG f



ðreactantsÞ

ð20Þ

This is a simple, but essential formula to predict the direction of an electrochemical reaction and the energy involved. As stated earlier in the text, thermodynamic functions have zero value for pure elements. The sign of ΔG indicates the direction of the reaction, if the sign is negative the reaction proceeds spontaneously in the forward direction and is exothermic. If the sign is positive, the reaction needs an input of external energy to proceed in the forward direction, i.e., it is spontaneous in the reverse direction. Example 3 Calculate the Gibbs Energy change for reaction CH3OH + 3/ 2O2 ! CO2 + 2H2O. ΔG (CH3OH) ¼ 166.6 kJ/mol, ΔG (CO2) ¼ 394.4 kJ/ mol, ΔG (H2O) ¼ 237.1 kJ/mol. 

ΔG ¼ ½2  ð237:1Þ þ ð394:4Þ  ð166:6Þ ¼ 474:2  394:4 þ 166:6 ¼ 702 kJ=mol: Note that oxygen is a pure substance and has ΔG value of zero. The reverse direction CO2 + 2H2O ! CH3OH + 3/2O2 will result in the following calculation of ΔG :

Standard Gibbs Free Energy

41

Table 1 Selected thermodynamic values at 298.15 K (From “CRC Handbook of Chemistry and Physics,” 1st Student Edition (1988) Species Aluminum Aqueous Solutions

Bromine Carbon

Chlorine Copper Fluorine Hydrogen

Iron Lead Lithium Magnesium Mercury Nickel Nitrogen Oxygen Phosphorus Potassium Silicon Silver Sodium Sulfur Zinc

Chemical formula/ symbol Al(s) Al2O3(s) Cl(aq)

ΔHf (kJ/mol) 0 1675.7 167.16

S (J/Kmol) 28.3 50.92 56.5

ΔGf (kJ/mol) 0 1582.3 131.26

H+(aq) OH(aq) Br2(g) C(s, graphite) CH4 (g, methane) CH3OH(l, methanol) C2H5OH(l, ethanol) CO(g) CO2(g) Cl2(g) HCl(aq) Cu(s) F2(g) H2(g) H+(g) H2O(l) H2O(g) H2O2(l) Fe(s) Pb(s) Li(s) Mg(s) Hg(l) HgCl2(s) Ni(s) N2(g) HNO3(aq) O2(g) H3PO4(s) KOH(aq) Si(s) SiO2(s, quartz) Ag(s) AgCl(s) NaCl(aq) NaOH(aq) S(g) H2SO4(aq) Zn(s)

0 229.94 30.907 0 74.81 238.66 277.69 110.525 393.509 0 167.159 0 0 0 1536.202 285.83 241.818 187.78 0 0 0 0 0 224.3 0 0 207.36 0 1279 482.37 0 910.94 0 127.068 407.27 470.114 278.805 909.27 0

0 10.54 245.463 5.74 186.264 126.8 160.7 197.674 213.74 223.066 56.5 33.15 202.78 130.684

0 157.3 3.11 0 50.72 166.27 174.78 137.168 394.359 0 131.228 0 0 0

69.91 188.825 109.6 27.78 64.81 29.12 32.68 29.87 146 29.87 191.61 146.4 205.138 110.5 91.6 18.83 41.84 42.55 96.2 115.5 48.1 167.821 20.1 41.63

237.129 228.572 120.35 0 0 0 0 0 178.6 0 0 111.25 0 1119.1 440.5 0 856.64 0 109.789 393.133 419.15 238.25 744.53 0

42

Electrochemical Thermodynamics 

ΔG ¼ ð166:6Þ  ½2  ð237:1Þ þ ð394:4Þ ¼ þ702 kJ=mol: The positive sign indicates that the reaction in this direction does not proceed spontaneously and would require external energy input. Example 4 Calculate Gibbs energy change for the reaction that takes place in a fuel cell 2H2(g) + O2(g) ! 2H2O(l). From Table 1 of the thermodynamic values, we find that ΔG (H2O) for the formation of liquid water is 237.129 kJ/mol. Using three significant figures we calculate: 

ΔG ¼ 2  ð237Þ ¼ 474 kJ=mol: This is the maximum electrical work the system can perform. Note that this is the value of ΔG for the reaction between hydrogen and oxygen calculated per mole of oxygen—the value per mole of hydrogen would be one half (237 kJ/mol), but the chemical equation would have to be written per mole of hydrogen. The ΔG values for hydrogen and oxygen are zero because these are pure elements. Additional understanding of the relationships between Gibbs Energy and enthalpy, as well as entropy can be gained by extending the last example to include calculations of the heat released from a fuel cell in addition to electricity and comparing it with the heat that would be released in the direct combustion of hydrogen with oxygen. Example 5 The heat released in a direct combustion reaction H2(g) + 1/2O2 (g) ! 2H2O(l) is (per one mol of hydrogen): 

ΔH ¼ ΔH



f ðproductsÞ

 ΔH



f ðreactantsÞ


¼ 285:83 kJ mol1  0

¼ 286 kJ mol1 ðthree significant figuresÞ The heat released in a fuel cell reaction is the difference between the enthalpy of the reaction and the Gibbs Energy of the reaction, which is equal to TΔS . From Table 1 we first look up the values of reactants and products; and calculate the change in entropy: 

ΔS ¼ S



f ðproductsÞ

S



f ðreactantsÞ

¼ 164 JK1 mol1 :Entropy decreases!

Then, ΔH – ΔG ¼ TΔS ¼ (298 K)  (164 JK1 mol1) ¼ 48,900 J mol1 ¼ 48.9 kJ mol1 Additional useful information can be extracted from the last example. The fuel cell reaction generates less energy overall compared to direct combustion, but it is in the form of electricity, the most useful form of energy. The thermal energy from direct combustion, on the other hand, would require the use of a very inefficient heat

Free Energy and Equilibrium

43

engine, and more than half of that energy would be distributed to the surroundings and wasted.

Free Energy and Equilibrium It has previously been shown that the cell voltage in an electrochemical cell is dependent on the reaction mixture composition and is governed by the Nernst equation. The reaction quotient determines how the second term in the Nernst equation affects the standard cell voltage depending on the ratio between the concentrations of reactants and products. It is implied in the Nernst equation that the electrochemical reactions depend on the composition of the system and that the cell voltage changes during the reaction because of the reaction quotient change. The system only becomes stable once the reaction equilibrium is reached and there is no change in composition. Note that the reaction quotient at this point is not 1. Similar starting observations are used when examining the changes in Gibbs Energy during a reaction. The calculations and tabulated thermodynamic function values examined so far were valid for standard conditions only and obviously neglecting the effects of the system composition. Gibbs Energy will decrease in a spontaneous reaction. At the beginning, there are only reactants and no products and that becomes the driving force for the reaction. As the reaction proceeds, there is more and more product and less reactants which lowers the driving force for the reaction. The entropy at that point changes and, in turn, Gibbs Energy changes. At a certain point, the reaction system reaches the state of chemical equilibrium, where the relative concentrations of reactants and products are expressed by the equilibrium constant. Considering a simple reaction: aA þ bB⟺cC þ dD

ð21Þ

and assuming that the standard free energies of the products are less than that of the reactants, ΔG for the reaction is negative and the reaction proceeds to the right. When all reactants are transformed into products, the equilibrium constant becomes infinity. It is obvious that Gibbs Energy cannot be completely defined using the standard conditions, ΔG . Practical reactions never happen under standard conditions and it is, therefore, necessary to define Gibbs Energy under all conditions. Because all reactions always proceed towards equilibrium, it is intuitive that the reaction quotient (the ratio between the concentrations of the products and reactants) determines the direction and extent of the reaction and, therefore, Gibbs Energy. Completing the above reasoning helps arrive at the expression for Gibbs Energy: 

ΔG ¼ ΔG þ RT ln Q

ð22Þ

As the reaction proceeds and approaches equilibrium, ΔG decreases and finally reaches zero at the point of equilibrium, where:

44

Electrochemical Thermodynamics



ΔG ¼ RT ln K eq

ð23Þ

The equilibrium constant, Keq, is only one case of the reaction quotient and it is a misconception to assume that its value is 1. Instead, the equilibrium denotes the state of the reaction when there is no more overall change, although the reaction still takes place on the microscopic level at the same rate in both directions. Gibbs Energy for an equilibrium constant of 1 is zero. Values of reaction constants above 1 indicate that the equilibrium ratio is shifted towards products and since the reaction proceeds in the forward direction Gibbs Energy is negative. For example, a reaction constant of 1035 corresponds to a highly negative Gibbs Energy of 200 kJ/mol. The higher the equilibrium constant and the more negative ΔG, the more readily the reaction proceeds. A very small reaction constant, e.g., 1036, means that the reaction is shifted towards reactants (i.e., it barely proceeds), therefore, it will not spontaneously proceed in the forward direction and ΔG is positive. Example 6 Determine the equilibrium constant from the standard free energy change for a reaction at 298.15 K: Mg(OH)2(s) + 2H+(aq) ⇆ Mg2+(aq) + 2H2O(l) 



ΔG ¼ 2ΔG



    H2 OðlÞ þ ΔG ½Mg2þ ðaqÞ  ΔiG MgðOHÞ2 ðsÞ

¼ 2ð237:1 kJ=molÞ þ ð454:8 kJ=molÞ  ð833:5 kJ=molÞ ¼ 95:5 kJ=mol 

ΔG ¼ RT ln K eq ¼ 95:5 kJ=mol ¼ 95:5  103 J=mol   3 J  95:5  10 ΔG mol ln Keq ¼ ¼ ¼ 38:5 J RT 8:3145  298:15 K mol  K Keq ¼ e38:5 ¼ 5  1016 ∘

This reaction proceeds readily and spontaneously in the forward direction as indicated by the high equilibrium constant and negative Gibbs Energy.

Temperature Effect on Equilibrium Constant Temperature has an effect on the direction and extent of the reaction based on the sign of ΔS . To express the temperature dependence the reaction (Eq. 24) can be differentiated with respect to the temperature. The result is an expression that shows how the change in Gibbs Energy with temperature is affected by the sign and extent of entropy.

Gibbs Energy and Cell Potential

45





ΔG ¼ ΔH  TΔS



ð24Þ


 d ΔG =dT ¼ ΔS

ð25Þ

It is often important to determine the equilibrium constant at a given temperature if it is known at another temperature. By combining Eqs. 19 and 34, we obtain: 



RT ln K eq ¼ ΔG ¼ ΔH  TΔS



ð26Þ

And dividing by RT: 

ln K eq ¼

ΔH ΔS þ RT R



ð27Þ

Further derivation combines the expressions in Eq. 27 for two temperatures:    K ΔH 1 1 ln 2 ¼  ð28Þ K1 R T1 T2 This is known as the van’t Hoff equation.

Gibbs Energy and Cell Potential It has previously been demonstrated that a potential difference between two electrodes in an electrochemical cell is a measure of the tendency of a reaction to occur. If the cell potential is more positive the reaction has a larger tendency to proceed in the forward direction. It was also established that the standard free energy change signifies the tendency of a process to occur. Hence, ΔG and E measure the same thing and are related in a simple way: 

ΔG ¼ n F E



ð29Þ

This is the most important relation in electrochemistry (in addition to the Nernst equation and Faradays Laws). It presents a method to calculate cell voltage from a known value for Gibbs Energy or vice versa. From before, a criterion for spontaneous change is: ΔG < 0. If ΔG < 0, then Ecell > 0 (Ecell must be positive if ΔG is negative). If Ecell is positive, a reaction occurs spontaneously in the forward direction while if Ecell is negative, the reaction occurs spontaneously in the reverse direction. If a cell reaction is reversed, Ecell changes sign. Example 7 Calculate cell voltage for a hydrogen fuel cell operating at 200  C if ΔG ¼ 220.4 kJ.

46

Electrochemical Thermodynamics

E ¼ ΔG=nF ¼ ð220400 JÞ=ð2  96485 CÞ ¼ 1:14 V Example 8 Calculate cell voltage for an alkaline 2MnO2 + Zn ! ZnO + Mn2O3 if ΔG ¼ 277 kJ/mol.

primary

battery


E ¼  2:77  105 =2  96485 ¼ 1:44 V

Cell Voltage and Equilibrium Constant The relationships between Gibbs Energy and cell voltage; and between Gibbs Energy and equilibrium have been shown. The last connection to establish is between the cell voltage and equilibrium from Eqs. 29 and 34: 

ΔG ¼ RT ln K eq ¼ n F E 

Ecell ¼



cell

RT ln K eq nF

ð30Þ ð31Þ

Recall that R ¼ 8.3145 J mol1 K1; n ¼ number of electrons; T ¼ 298.15 K; F ¼ 96,485 C/mol; and the reaction becomes: 

E cell ¼

0:0257 ln K eq n

ð32Þ

and by changing to base-10 logarithm: 

E cell ¼

0:0592 log K eq n

ð33Þ

Example 9 What is the value of the equilibrium constant, Keq, for the reactions: Cu(s) + 2Fe3+(aq) ! Cu2+ + 2Fe2+(aq)? Oxidation: Cu(s) ! Cu2+(aq) + 2e E (Cu2+/Cu) ¼ 0.34 V Reduction: 2Fe3+(aq) + 2e ! Fe2+(aq) E (Fe3+/Fe2+) ¼ 0.77 V Overall: Cu(s) + 2Fe3+(aq) ! Cu2+(aq) + 2Fe2+(aq) E (cell) ¼ E red  E ox ¼ 0.77–0.34 ¼ +0.43 V 0:0257 2  0:43 ln K eq ! ln K eq ¼ ¼ 34:2 2 0:0257 ¼ 7:1  1014

Ecell ¼ 0:43 V ¼ K eq ¼ e34:2

We see from the positive value of the cell voltage and from the equilibrium constant that this reaction is spontaneous and has a moderate tendency to occur.

Summary of Electrochemical Thermodynamics

47

Looking further into the relationship between the Nernst equation and the equilibrium constant, it can be seen that the cell voltage is zero (Ecell ¼ 0) at equilibrium when Q ¼ Keq. Further derivation leads to: 0 ¼ E0 

0:0592 log K eq n

and log K eq ¼

nE 0 0:059

ð34Þ

Summary of Electrochemical Thermodynamics Cell voltage, Gibbs Energy, and equilibrium constant are all connected through thermodynamic functions that enable prediction of the reaction direction and its tendency to occur. The summary of those relationships is shown here: 

ΔG ¼ RT ln K eq 

Ecell ¼ 

RT ln K eq nF

ΔG ¼ n F E



ð34Þ ð35Þ ð36Þ

Electrochemical Kinetics

s Thermodynamics, as seen from the previous chapter, must be considered a fundamental discipline because it unmistakably predicts the direction of a reaction and the composition at equilibrium. It, furthermore, uses only the standard free energies of the reactants and products from the thermodynamic tables, so it is possible to arrive at the answer purely theoretically and without actually performing the reaction. The thermodynamic function being considered is often vaguely defined as free energy. It is simply a way of describing and quantifying a rearranging or dispersion of thermal energy in the system in relation to the thermal energy in the world. The chemical reaction takes place spontaneously if it moves to a maximum thermal energy dispersion, which is expressed as more negative free energy. When it reaches the minimum the system is at equilibrium and no further change occurs. But thermodynamics has no element of time involved and cannot, therefore, include the prediction of how fast a reaction may occur. In other words, just because the reaction seems possible based on thermodynamic predictions, it does not mean at all that it will happen at a measurable rate. The discipline of kinetics studies how fast the reactions occur, but it has no ability to theoretically predict the rate of reaction, which must be determined experimentally for every reaction.

The Rate of Reaction The rate of a chemical reaction is the change in concentration of reactants and products as a function of time. The rate of reaction can be expressed either as the rate of disappearance of reactant or the rate of appearance of product. For a simple reaction A + B ! C the rate can be expressed as:

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49

50

Electrochemical Kinetics

rate ¼ 

ΔA ΔB ΔC ¼ ¼þ Δt Δt Δt

ð1Þ

ΔA (or B or C) means concentration difference between the starting and ending measurement points during the specified time, for example, [A1]–[A2]. The “minus” sign in front of reactants A and B indicates that the concentration is decreasing (since the reactants are being consumed) while the “plus” sign in front of the product C indicates that the concentration is increasing. However, the sign only indicates if the substance is being consumed or created—the actual rate cannot be negative. Consider a reaction in which the coefficients are different, for example, A + 3B ! 2D. It is evident from a simple observation that the concentration of reactant [B] decreases three times as fast as the concentration of reactant [A]. For clarity and convenience each concentration change is divided by the stoichiometric coefficient: rate ¼ 

ΔA ΔB ΔD ¼ ¼þ Δt 3Δt 2Δt

ð2Þ

Example 1 We can consider a fuel cell reaction 2H2 + O2 ! 2H2O and express the rate of reaction as: rate ¼ 

Δ½H2  Δ½O2  Δ½H2 O ¼ ¼þ 2Δt Δt 2Δt

Example 2 For a direct methanol fuel cell reaction CH3OH + 3/2O2 ! CO2 + 2H2O, the rate of reaction can be expressed as: rate ¼ 

Δ½CH3 OH 2Δ½O2  Δ½CO2  Δ½H2 O ¼ ¼þ ¼þ 2Δt 3Δt Δt 2Δt

Faraday’s Laws of Electrolysis The two laws of electrolysis were formulated in 1832 by Michael Faraday. There are several versions of these laws, with one presented here: 1. The mass of a substances formed at an electrode during electrolysis or consumed in a galvanic cell is directly proportional to the quantity of electricity involved in the reaction. 2. The mass of a substance altered, produced or consumed, at an electrode is directly proportional to its equivalent weight. The quantity of electricity is measured in coulombs (C). One mole of electric charge (96,500 coulombs), when it passes through a cell, discharges half a mole of a divalent metal ion, such as Cu2+.

Faraday’s Laws of Electrolysis

51

The equivalent weight of a substance is the molar mass, divided by the number of electrons required to oxidize or reduce each unit of a substance. For example, one mole of Al3+ corresponds to three equivalents and requires three faradays of charge to deposit it as metallic aluminum. Faraday’s Law can be expressed mathematically as:

 Q M w¼  ð3Þ F n In this equation, w is the mass of a substance in grams, Q is the charge passed through the system (¼ I  t), F is the Faraday constant (96,485 C), M is the molecular weight, and n is the number of electrons in the reaction. The equivalent weight, M/n, is the mass of a substance converted into the electrochemical reaction. The ratio w/M is the number of mols and sometimes the expression takes this form: m¼

m Q ¼ M nF

m ¼ number of mols

ð4Þ

or mnF ¼ It

ð5Þ

This is a critical equation to remember! Example 3 Let us consider again the direct methanol fuel cell reaction: CH3OH + 3/2O2 ! CO2 + 2H2O and calculate the consumption rate of methanol for a certain power generation. First, the expression for Faraday’s Law from Eq. 5 can be rearranged by dividing both sides by time to express consumption or m/t. Next, the current will be expressed as power/voltage (P/E).   m I P mols ¼ ¼ t nF nFE s and the mols are changed to mL/h using the molecular weight of methanol and its density. 32 g=mol

CH3 OH

Consumption

¼

0:8 g=mL

6  96485C=mol h i P mL ¼ 0:25  E h



h i P½W  P mL ¼ 7  105 E s E ½V 

Mass Transport

The reactant concentration on the electrode surface is dependent on the mass transport of reactants from the bulk solution. There are three forms of mass transport as depicted in Table 1 in the chapter “Galvanic Cells.” Diffusion is the movement of species as a result of the concentration gradient and it takes place whenever a chemical change takes place at the electrode surface. When the reaction consumes reactant at the electrode surface and lowers its concentration it initiates diffusion from the bulk that equalizes the concentration. Convection is the movement of species as a result of the velocity gradient and is a result of mechanical forces. Natural convection occurs because of small differences in solution density as a result of local temperature variations, while forced convection is induced by electrolyte or electrode movement. Migration is the movement of charged species as a result of a potential gradient. It is the passage of ionic charge through the electrolyte and it is driven by electrostatic forces. In practice, migration does not make a significant contribution to mass transport.

Fick’s Law of Diffusion To understand mass transport in electrochemical cells, it is first necessary to review the Fick’s Laws of Diffusion. Fick’s first law describes the flux or the rate of flow of any property or quantity per unit area on a selected plane (Fig. 1). The property can be mass or fluid, such as water or solution. It can also be a form of energy such as sunlight or heat. Flux is expressed in units of quantity per time per area. Fick’s first law states that the flux is proportional to the change of concentration over position or length (Eq. 1).

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53

Mass Transport

Concentration, c

54

Flux = −D

dc dx

O

e-

R

Distance, x

Fig. 1 Fick’s law of diffusion depiction

Flux ¼ D

∂C ∂x

ð1Þ

D in the equation is the diffusion coefficient. It has units of [length2 time1], for example, [m2/s]. Fick’s Law of Diffusion may be applied to the reaction: O + ne- ! R. At any instant, a flux balance must exist in order to satisfy the law of conservation of mass at the electrode surface (where x ¼ 0), so the reactant loss flux must be equal to the product formation flux. From Faraday’s Law, it is understood that m/t, the change in the number of mols of substance over time, equals current, I/nF. By combining the two laws, the following equation is obtained: DOX

∂C OX i ∂CR ¼ ¼ DR nF ∂x ∂x

ð2Þ

After rearranging, the current density, i or j, can be expressed as (Eq. 3): j ¼ nFDOX

∂C OX ∂x

ð3Þ

In the case of steady-state conditions, the concentration profiles to and from the electrode surface are linear (Fig. 2). It can be taken from the figure that the concentration of reactants decreases linearly from the bulk of the solution to the electrode surface and that the concentration of products linearly decreases from the electrode surface to the bulk solution. However, the diagram shows only a portion of the electrolyte solution in the immediate vicinity of the electrode. The concentration profiles in practice are generally following those shown in Fig. 3. Electrode or cell current can be expressed as total current, I (e.g., in A), but it is more often given as current density, i or j. Current density is the total current per surface area (e.g., A/cm2). Current density more accurately describes the extent of the reaction or the quality of the electrode catalyst.

Nernst Diffusion Layer Model

55

Fig. 2 Concentration profiles of reactants “o” and products “r” to and from the electrode surface

Surface

−D

Ox

j nF

dc dx

Reactant supply

ne-

Product removal

Electron supply

Red

Electrode

Electrolyte

D

dc dx

x=0

Cox Concentration, c

Fig. 3 Concentration profiles (conceptually presented) in a practical system

Cred

Distance, x

The situation changes in the case of convective diffusion, i.e., diffusion caused by external forces or some means of natural convection. External forces include, for example, electrolyte pumped through the cell, stirring by air, gases produced at the electrodes, mechanical agitation, or moving electrode (e.g., rotating, vibrating). Natural convection includes changing density or temperature differences in the electrolyte, which can produce complex velocity and concentration profiles near the electrode surface.

Nernst Diffusion Layer Model To evaluate the concentration profile further it is useful to assume that the electrolyte layer near the surface of the electrode may be divided into two zones: close to the surface, where it is assumed that there is a completely stagnant layer, δN, of thickness such that diffusion is the only mode of mass transport; and outside of this layer, (at x  δN), where strong convection occurs. This is called the Nernst diffusion layer concept and it is shown in Fig. 4.

56

Mass Transport

x = δN

Concentration, c

Diffusion

Diffusion

Nernst diffusion Layer thickness Reactant concentration in bulk solution

C0

Distance, x Fig. 4 Nernst diffusion layer and concentration profile

At open circuit (current, I ¼ 0 A), the concentration of reactants on the electrode surface is the same as in the bulk electrolyte, C0, as no net transformation of electroactive species occurs, for example, oxidation or reduction or “o” to “r” (see Fig. 2). If the current in the cell is raised to some value I, reactant “o” is converted to product “r” and the reactant concentration must decrease near the electrode surface. This decrease in reactant concentration is more pronounced if the current further increases, i.e., the higher the rate of reaction, the larger the drop in reactant concentration on the electrode surface. In reality, there is no such demarcation between pure diffusion and pure convection at the distance from the electrode surface, x ¼ δN, rather a gradual transition occurs (Fig. 5). At some high current, the concentration of the reactant at the surface falls to zero indicating that the reaction cannot take place at a rate or current higher than this value. This is called the limiting current, IL. For a particular reaction, controlled solely by mass transport, the current density increases as a function of potential until reaching a steady-state value—this is the maximum possible current (under given conditions), i.e., limiting current density (Fig. 6). The Nernst diffusion layer model can be further developed to express the limiting current density. The expression in Eq. 2 can be rearranged to describe the change in the concentration from the bulk solution to the electrode surface (Eq. 4) and to also include the Nernst diffusion layer thickness, δN, which replaces the distance, x. Note the change in sign because the concentration is not decreasing, but rather the difference in concentration between the bulk solution and electrode surface is used. “j” is the current density. j ¼ nFDOX

C 0  ðC 0 Þx¼0 δN

ð4Þ

Nernst Diffusion Layer Model

57

Concentration, c

C0 I=0 I1 I2 I3

x = δN

Distance, x Fig. 5 Depiction of the gradual change in concentration between convection and diffusion zones Fig. 6 Current density as a function of electrode potential

Current, I

IL

0 Voltage, E

At the limiting current density, the concentration of reactant at the surface, (C0)x¼0, is zero, hence: jLim ¼

nFDC 0 δN

ð5Þ

The limiting current is the product of the limiting current density and the surface area: I lim ¼ i  A

ð6Þ

Therefore, from Eqs. 5 and 6, the following expression is derived for limiting current:

58

Mass Transport

I Lim ¼

AnFDC 0 δN

ð7Þ

A practical question for many electrochemical processes is how to increase the reaction rate and limiting current. From Eq. 7, the limiting current can be increased by increasing the active electrode area, A; increasing the diffusion coefficient, D0, (by, for example, elevating the temperature); increasing the reactant concentration, c0; or by decreasing the Nernst diffusion layer thickness, δN, (by enhancing relative electrode/electrolyte movement).

Reaction Rate Constant It is usually not possible to directly measure δN experimentally, so Eq. 7 is simplified to: I Lim ¼ AnFk m C 0

ð8Þ

where Km is: km ¼

D δN

ð9Þ

km is the rate constant for mass transport and is known as the mass transport coefficient (units: m s1). It is measurable by experimentation and can also be expressed (from Eq. 8) as: km ¼

jL nFC 0

ð10Þ

It is important to relate km to the electrolyte flow conditions, so: k m / νa

ð11Þ

In Eq. 11, ν is a characteristic velocity (e.g., the linear velocity of the electrolyte or the rotation speed of a rotating electrode). The velocity exponent (0.3 < a < 1) depends on the electrode geometry and the flow regime (e.g., laminar or turbulent flow). The expression for limiting current becomes: I L ¼ KAC 0 νa

ð12Þ

In Eq. 12, K is a constant, which depends on the electrode geometry, the electrolyte conditions, and the flow conditions.

Overpotential

Overpotential or overvoltage is often a misunderstood term in electrochemistry. It relates to losses that occur in practical electrochemical systems; it is the difference between the voltage we would expect from a cell operating ideally and the actual voltage. η ¼ E  E NO LOSS

ð1Þ

There are several commonly used names for this voltage difference besides overpotential (or overvoltage): polarization, irreversibility, voltage drop, or losses. The causes of overpotential (the term used throughout this text) are: slow charge transfer (i.e., the change from electrons carrying charge to ions), resistance losses, and mass transport losses. The prefix “over” suggests that the actual voltage is higher than the ideal or thermodynamic voltage, but in fact the losses can also result in lower voltages. The overvoltage term was first coined to describe the voltage increase in electrolytic processes and it historically remained in use also for galvanic processes despite the fact that the voltage is actually lower than theoretical for those processes. The overvoltage concept is graphically depicted in Fig. 1 for currentcontrolled processes. The analysis of graphs shows that there are three regions of overpotential: at low, medium, and high current densities. These regions correspond to losses due to charge transfer, resistance, and mass transport. Charge transfer (or sometimes called activation) overpotential refers to the part of the cell voltage that is “lost” to maintain the required rate of reaction on the electrodes. Resistive (or sometimes called ohmic) overpotential is due to electronic and ionic conduction. Mass transport (or sometimes called concentration) overpotential is evident at high current densities and refers to losses as a result of mass transport limitations.

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59

60

Overpotential

Galvanic Cell

Electrolytic Cell

Cell Voltage/V

Cell Voltage/V

“NO LOSS” VOLTAGE

“NO LOSS” VOLTAGE

Current density/mAcm-2

Current density/mAcm-2

Fig. 1 Overpotential concept in electrochemical systems. The curve shapes in the graphs are not from an actual experiment, but are average or typical values and should be considered conceptual

Activation Overpotential The activation component of the overvoltage (or loss) takes place at low current densities as a result of a slow transfer of charge to or from the electrode in electrochemical reactions. To achieve the required current, a portion of the cell voltage is consumed to “drive” the reaction (maintain it at a certain rate)—this is called activation overvoltage (i.e., overpotential) or voltage loss. Overpotential is typically used to describe the behavior of one electrode while the term overvoltage is used for the complete cell and includes overpotential from each electrode as well as losses in the electrolyte and other components. Activation overpotential is described by the empirical relationship known as the Tafel equation (Eq. 2):   i η ¼ A ln ð2Þ i0 In this equation, A is the constant that is higher for slower reactions, i is the current density at any point, and i0 is another constant called “exchange current density”. If an electrochemical system had only activation or charge transfer losses, the cell voltage would be: E ¼ E0  A ln

  i i0

ð3Þ

The Tafel equation and activation overvoltage are graphically shown in Fig. 2.

Activation Overpotential

61

Fig. 2 Graphical representation of activation overvoltage. The values in the graph are not from an actual experiment but are average or typical and should be considered conceptual

Overvoltage/V

0.6

SLOW REACTION

0.5 0.4 FAST REACTION

0.3 0.2 0.1 0 0

1

2

3

4

5

Log current density/mAcm-2 Table 1 Exchange current density for selected metals for hydrogen evolution reaction. Compiled from a variety of sources

Metal Pb Zn Ag Ni Pt Pd

I0 (acm2) 2.5  1013 3  1011 4  107 6  106 5  104 4  103

By analyzing the figure, we see that there is a first part of the curves where the system behaves according to the Tafel equation, i.e., logarithmically and there is a second, linear portion of the curves. In the first part of the graph, overvoltage slowly increases as the current increases for fast reactions (this part is extended), while the overvoltage increases much faster for slow charge transfer reactions. Extrapolation of the linear portion of the graph to the log of current density axis gives the property of an electrochemical system known as the exchange current density. This constant describes the catalytic properties of the electrode or the activity of an electrode for a certain reaction, i.e., if the exchange current density is high, the electrode is more active. Exchange current densities depend on the material properties and the nature of the reaction, i.e., they are reaction-specific. Their values are very small as shown in Table 1. Both the anode and cathode contribute to cell overvoltage, so Eq. 3 becomes:     i i E ¼ E 0  Aa ln  Ac ln ð4Þ i0 ðaÞ i0 ðcÞ Activation overvoltage can be reduced by increasing the cell temperature, increasing the “true” surface area of electrodes (increasing electrode roughness), increasing concentration or pressure, and through the use of more efficient catalysts.

62

Overpotential

Resistive Overvoltage The losses or overvoltage due to the electrical resistance of the electrodes and the resistance of the flow of ions in the electrolyte are generally called resistive or Ohmic overvoltage. The term Ohmic is used because the voltage loss, in this case, obeys the Ohms Law and the size of the voltage drop is simply proportional to the current: η ¼ iR

ð5Þ

To be consistent with the other equations for voltage loss, the equation is expressed in terms of not only current density but also in terms of resistance corresponding to the surface area, e.g., 1 cm2. This is called area-specific resistance and is represented with the letter “r”. Eq. 5 then becomes: η ¼ ir

ð6Þ

Area-specific resistance is typically given in Ωcm2. It is obvious from the equations that voltage drop is higher for higher currents and that the change is linear. In most electrochemical systems, the largest component of the resistive overvoltage is the resistance to ionic charge transfer in electrolyte. Other methods to reduce resistive overvoltage include the use of highly conductive electrodes, good interconnects, and minimizing the thickness of electrolyte.

Mass Transport Overvoltage The overvoltage component dominant at high current densities is the mass transport overvoltage or sometimes called concentration overvoltage. This voltage loss eventually terminates the operation of an electrochemical system either because of complete voltage loss in the case of galvanic cells or a very high voltage required for electrolytic cells. As previously discussed in the chapter on mass transport, as the rate of reaction increases and the current increases, the concentration at the electrode surface is further reduced. Eventually, a point is reached where the concentration through the Nernst diffusion layer cannot be further increased to support the reaction and the limiting current density is reached, beyond which the current cannot increase for a given system (Fig. 6 in the chapter “Mass Transport”). If this current or current density is reached and exceeded, the voltage loss is so large that the cell ceases to operate. This is seen in Fig. 3 as a sharp voltage decrease for galvanic processes and increase for electrolytic processes. Mass transport or concentration overpotential is expressed using the following equation obtained by combining the Nernst equation and the expression for limiting current:

Combining Overvoltages

63

Theoretical cell voltage

Electrical potential

Activation (i.e., charge transfer) voltage loss

Resistance (i.e., Ohmic) voltage loss

Mass transport (i.e., concentration) voltage loss

Current density Fig. 3 Conceptual dependence of electrochemical system voltage with current. This is the general or typical shape of the curve and not based on any particular experiment

ηconc ¼

  RT i 1 nF iLim

The above equation sometimes takes the following form:   i ηconc ¼ B 1  iLim

ð7Þ

ð8Þ

For purely mass transport or concentration-controlled processes, the current dependence on voltage is shown in Fig. 6 in the chapter “Mass Transport.”

Combining Overvoltages Each voltage loss mechanism is dominant in a certain current range. However, they all affect system behavior in a mixed or combined mode for all current densities. Hence, the overall system behavior and the curve describing it is somewhat different from the profiles shown so far for individual overvoltage losses. The typical behavior in a “mixed” mode is shown in Fig. 3. The expression for the cell voltage for a “mixed” control regime and all three cell overvoltage types contributing to the overall behavior is shown in Eq. 9.     i i E ¼ E 0  A ln  ir þ B ln 1  ð9Þ i0 iLim Note that the expression in Eq. 9 indicates the sign of each term that leads to lowering the “no loss” voltage and is therefore valid for a galvanic process. In electrolytic processes, the signs of the voltage loss (or overvoltage) terms will be

64

Overpotential

reversed and the overall voltage increases. To avoid confusion, overvoltage is often determined separately (Eq. 10) and the actual cell voltage is subsequently calculated according to Eq. 11, where overvoltage is added to “no loss” voltage for electrolytic cells and subtracted for galvanic cells.     i i ΔE ¼ η ¼ A ln þ ir  B ln 1  ð10Þ i0 iLim E ¼ E0  η

ð11Þ

Industrial Electrochemical Processes

Industrial electrochemical processes require external energy to produce useful chemicals and are, therefore, classified as electrolytic processes. They involve both inorganic and organic substances as well as gases. The most important processes are: chloralkali electrolysis, electrolytic refining of aluminum, water electrolysis, preparation of various chemicals, purification methods, and separation methods.

Chlorakali Electrolysis Chlorine is the basic raw material for the preparation of a range of important products including chlorinated bleaches, pesticides, and polymers. It is almost exclusively prepared by the electrolysis of aqueous NaCl, according to the following reactions: Anode : 2Cl
! Cl2 þ 2e


ð1Þ

Cathode : 2H2 O þ 2e
! H2 þ 2OH


ð2Þ

Overall : 2NaCl þ 2H2 O ! Cl2 þ H2 þ 2NaOH


ð3Þ

The standard cell voltage and Gibbs Free Energy change for this reaction are: E0 cell ¼ E0 red
E0 ox ¼
0:83
ð1:36Þ ¼
2:19 V

ð4Þ

ΔG ¼
nFE 0 ¼
2  96500  ð
2:19Þ ¼ 422 kJ

ð5Þ

It can be seen from Eq. 3 that three useful chemicals are produced in this process: chlorine, hydrogen, and sodium hydroxide, while the reactants are only inexpensive sodium chloride solution (commonly called brine) and water. Schematics of the chloralkali electrolysis process is shown in Fig. 1. There are three versions of the electrolysis process: diaphragm, amalgam, and membrane. The diaphragm process uses expanded titanium covered with RuO2 as # The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_9

65

66

Industrial Electrochemical Processes

Power Source

Cl2(g)

H2(g)

Cathode compartment NaCl (aq)

Anode compartment

NaCl (aq) + NaOH (aq) Cathode deposited on diaphragm

Fig. 1 Schematic of the chloralkali electrolysis process

the anode and steel as the cathode. A synthetic plastic or asbestos diaphragm surrounds the cathode and prevents OH
transport. The level of liquid in the cathode compartment is lower than in the cell and hydrostatic pressure continually forces NaCl electrolyte into the cathode region, preventing OH
escape. A typical cell operates at 80–95  C, with 6 M NaCl and constant current density of 250 mA/cm2 and voltage of about 3.5 V. The practical voltage is much higher than the theoretical or ideal voltage of around 2.2 V because the high hydroxide ion concentration in the cathode compartment lowers the thermodynamic potential for H2 evolution below
0.9 V and because the formation of bubbles at both electrodes causes high resistance in the electrolyte. Example 1 What is the cell voltage for a chloralkali electrolysis of 3 M NaCl if the products are 3 M NaOH, Cl2 at 2 atm, and H2 at 1 atm? E0 cell ¼ E0 red
E0 ox ¼
0:83
ð1:36Þ ¼
2:19 V   C products ½32  2  1 0:059 0:059 0 log log E¼E
¼
2:20 V ¼
2:186
n 2 ½C reactants  ½32 The most popular of the three electrolysis processes is the membrane process. In this process, an ion-exchange membrane is used as the cell separator. The membrane conducts Na+ ions, it is impermeable to Cl
and OH
ions, it must be stable for long periods of time in a very aggressive medium, and it must have high transport selectivity, low electrical resistance, and mechanical robustness. The schematics of the membrane process are shown in Fig. 2.

Molten Salt Electrolysis

67

Cl2

+

NaOH + H2

-

Membrane 2Na+ 2Cl-  Cl2 + 2eCl-

NaCl

2H2O + 2e-  2OH- + H2 OH-

H2 O

Fig. 2 Schematic representation of the processes in a membrane cell

In the membrane process, the anode is a so-called DSA type electrode (dimensionally stable anode) and the cathode is a Raney nickel electrode, with very high activity. Cell current density and voltage are 3–4 kA/m2 and 3–3.2 V, respectively. The voltage and, therefore, the energy consumption is 10–20% lower than in the diaphragm cell. The membrane thickness is 0.1–0.2 mm, it has low permeability for Ca2+ and Mg2+, and it is impermeable to chlorine or hydroxyl ions. The remaining challenge for chloralkali electrolysis processes is the reduction of high energy consumption due to high cell voltages. Example 2 How much electric energy in kWh per day is required to produce 1 metric ton (1000 kg) of chlorine from brine, assuming the cells operate at 3.0 V and assuming 100% efficiency? Electrical energy ¼ I  t  V ¼ ðmnFÞ  V 
 ¼ 1  106 g=71 g  2  96485 C  3 V ¼ 8:2  106 kJ ¼ 2:3  103 kWh:

Molten Salt Electrolysis Many metals cannot be deposited from aqueous solutions because their reduction potentials are more negative than the hydrogen reduction reaction and hydrogen evolution takes place first. However, aqueous solutions are not the only electrolytes and ion conductivity, and thus, electrochemical processes can be accomplished using molten salts. Because salts are not molten (therefore not conductive) at room temperature, these processes must be conducted at higher temperatures. Molten salt processes are the basis for the extraction of metals from their ores. The most important are aluminum extractions (>16 million tons per year

68

Industrial Electrochemical Processes

worldwide), magnesium extraction (0.25 million tons per year), and sodium extraction on a large scale. Other metals like Li, Be, B, Ti, Nb, and Ta are also extracted on a smaller scale. Unlike Mg or Na, which can be obtained from relatively low-temperature molten salts or hydroxides, the main source of Al is in the ore bauxite, Al2O3, whose melting point is very high, 2050  C. This temperature is too high for practical electrolysis because of extreme material challenges and large energy loss through thermal radiation. The process, however, can be accomplished at lower temperatures by using a material that forms a eutectic mixture with Al2O3 and lowers its melting point. The right substance was found in cryolite, Na3AlF6 (a mixture of NaF and AlF3), which forms a eutectic mixture with 12–22.5% Al2O3 that melts at 935  C. The practical electrolytic process was developed in 1886, independently by Charles Hall and Paul Herault, and is now called the Hall-Herault process. It is impossible to write the exact electrode reactions because the species present in the electrolyte are not fully defined. The equations below give approximate reactions. Anode : 3C þ 3O2 ! 3CO2 þ 6e


ð6Þ

Cathode : Al3þ þ 3e
! Al

ð7Þ

Overall : 2Al2 O3 þ 3C ! 4Al þ 3CO2

ð8Þ

The three-valent aluminum, Al(III), in Eq. 7 is a complex oxyfluoride ion that results from the mixture with cryolite, while the oxygen in Eq. 6 originates from Al2O3. Because the equations in molten salt reactions cannot be balanced using the same method as in aqueous solutions, the reactions (Eqs. 6–8) are only the approximation of the actual, much more complex processes. The main anode reaction is actually an evolution of the intermediate oxygen, which immediately reacts with carbon to form CO and CO2. The anode material is carbon or, more accurately, a mixture of pitch and coal. The anode is consumed in the reaction. The cell voltage in the Hall-Herault process is approximately 4.2 V, which is much higher than the theoretical value of 1.7 V. The current densities at the anode are 6.5–8 kA/m2 and 3–3.5 kA/m2 at the cathode. Common total currents are about 100,000 A for large facilities and, consequently, electricity consumption is a critical issue. Aluminum refining is the largest consumer of industrial electricity, accounting for about 5% of all electricity generated in North America. The process is shown in Fig. 3. The aluminum extraction process is a complex process and numerous issues must be properly controlled. For example, fluorine gas is generated as a by-product in the anodic reaction and it must be efficiently removed, which is a very expensive process. Also, aluminum from the cryolite process contains approximately 0.1% Fe and 0.1% Si, and sometimes must be further purified using another electrochemical process.

Aqueous Metal Extraction

69

Fig. 3 Schematic representation of Hall-Herault aluminum extraction process

Aluminum extraction plants are extremely large and are usually built near large power plants (for example, hydroelectric power plants) to ensure electrical energy availability at low transmission losses.

Aqueous Metal Extraction Metals whose deposition potential is negative with respect to the normal hydrogen potential can be deposited from acid solutions only if they show a large overpotential for hydrogen evolution. Recall that overpotential depends on many factors, including the activity of the electrode material for a specific reaction and the nature of the catalyst. In this case, it is desirable that the overpotential is large. If the high overpotential condition for hydrogen reduction is met, the following metals can be extracted electrochemically: Pb, Zn, Ni, Co, Cd, Cr, Sn, and Mn. Metal ores typically react in the air to form oxides, which are then dissolved in aqueous sulfuric acid. From this solution, the metal is then electrochemically deposited at the cathode and oxygen is simultaneously evolved from the anode. General equation for any metal, Me, is shown in Eqs. 9–12. Since the reactions apply to any metal electrowinning, MeOx represents any metal oxide, H+ represents the acid, and stoichiometric coefficients are shown as x. Dissolution : MeOx þ 2xHþ ! Me2xþ þ xH2 O

ð9Þ

Anode : xH2 O ! ½O2 þ 2xHþ þ 2xe


ð10Þ

Cathode : Me2xþ þ 2xe
! MeðsÞ

ð11Þ

Overall : MeOx ! Me þ ½O2

ð12Þ

The most important electrowinning process is the production of Zn. In one example of this process, the cells used are open, lead or plastic-lined concrete troughs 3 m  1 m  1.5 m deep, in which the pure aluminum sheet cathodes and lead anodes are suspended from current collectors. The cells are filled with a solution

70

Industrial Electrochemical Processes

of 95 g/L zinc sulfate and 40 g/L concentrated sulfuric acid. The application of a cell voltage of 3.5–4 V leads to zinc deposition with a practical current density of 0.5–1 kA/m2 and simultaneous evolution of oxygen at the anode (vented into the atmosphere). The deposition is continued until zinc is reduced in concentration to 35 g/L and the acid has increased in concentration to 135 g/L. Sulfuric acid is then regenerated and reused. Despite the requirement for high hydrogen reduction overpotential, some hydrogen evolution is always observed in practice, lowering the process efficiency, but on the other hand contributing to improved mass transport through the generation of gas bubbles. If a source of hydrogen is available, the cell voltage can be substantially reduced by replacing the anodic oxygen oxidation, which generates oxygen, with the hydrogen oxidation reaction, in which hydrogen gas is a reactant.

Metal Purification Electrolytic metal purification refers to refining an impure metal by removing the impurities while preserving the original composition. For example, if a copper anode and a copper cathode are immersed in an acidified (added acid for conductivity) copper sulfate solution and a voltage is applied, copper dissolves at the anode and deposits at the cathode (Fig. 4). The process requires a voltage of only 0.1–0.2 V for current densities of 0.1–0.3 kA/m2. At this low voltage, the energy consumption is very low (i.e., 250 kWh/ton Cu) and the process is very economical. Only those impurities in copper with potentials more negative than the working potential of the anode, roughly +0.5 V, will dissolve as ions (Fe, Ni, Co, Zn, and As). More noble metals (Ag, Au, and Pt) remain behind in finely divided metallic form and collect under the anode as “anode sludge”. A schematic representation of the process is shown in Fig. 5. Processes similar to copper plating have been developed for the purification of Ni, Co, Ag, Au, Pb, and Zn. Fig. 4 Schematic of the copper purification electrolytic cell

POWER SUPPLY

e-

Pure metal cathode

e-

Impure metall anode

Water Electrolysis

71

Fig. 5 Schematic representation of the voltagecurrent graph in copper purification

Example 3 An object to be plated with copper is placed in a solution of CuSO4. To which electrode of a direct current power supply should the object be connected? What mass of copper will be deposited if a current of 0.22 A flows through the cell for 8 h? The object should be connected to the cathode. It ¼ mnF

m ¼ ð0:22 A  8 h  3600 s=hÞ : ð2  96485 CÞ ¼ 0:033 mols of Cu Mass of copper ¼ 0:033 mols  63 g=mol ¼ 2 g

Water Electrolysis Water electrolysis is one of the most important future technologies and a critical link for the implementation of renewable energy technologies. Hydrogen can be produced from water electrolysis by using renewable power, such as solar or wind, stored, and used in fuel cells at the time of demand. Water electrolysis is performed using highly conductive, porous electrodes that are inert in the voltage range required for electrolysis or have high overpotential for hydrogen and oxygen evolution. The overall reaction describes the decomposition of water with external electrical energy to gaseous hydrogen and oxygen: H2 O þ electrical energy ! H2 þ ½O2

ð13Þ

Water is a poor ionic conductor and needs a conductive electrolyte for technically acceptable cell voltages. An electrolyte can be acidic or alkaline. In alkaline medium, the two reactions at the electrodes are: Cathode : 2H2 O þ 2e
! H2 þ 2OH


ð14Þ

Anode : 2OH
! ½O2 þ H2 O þ 2e


ð15Þ

Net reaction : H2 O ! H2 þ ½O2

ð16Þ

The reactions in acidic medium are:

72

Industrial Electrochemical Processes

Fig. 6 Schematic representation of water electrolysis

Table 1 Dependence of the Gibbs Free energy on temperature T/ C ΔG/kJ mol
1

25 237

80 228

100 225

200 220

400 210

600 200

800 189

1000 177

Cathode : 2H3 Oþ þ 2e
! 2H2 O þ H2

ð17Þ

Anode : 3H2 O ! 2H3 Oþ þ ½O2 þ 2e


ð18Þ

Net reaction : H2 O ! H2 þ ½O2

E 0 ¼ 1:23 V

ð19Þ

A schematic representation of the water electrolysis cell at low temperature, with illustrations of gas evolution on both electrodes, is shown in Fig. 6. The overall reaction requires less energy at a higher temperature because of the reduction in Gibbs Free Energy with increased temperature. The reduction in Gibbs Free Energy with temperature increase is shown in Table 1. There are three main types of practical electrolyzers: alkaline, high-temperature, and solid polymer electrolyte electrolyzers. The main advantage of the alkaline water electrolysis is in the fast reaction rates for the anodic oxygen evolution and the use of inexpensive Ni-based, non-noble metal catalysts. Typical alkaline electrolysis uses 25% KOH as electrolyte at 80  C. Electrodes are porous to ensure more surface area. The largest process losses occur in the diaphragm, which was previously made of asbestos and presently made of synthetic polymers. The operating voltage is typically 1.7–1.9 V, the current density is 1 kA/m2, and the hydrogen production rate is 4.3 kWh/Nm3. There are two configurations used in alkaline water electrolyzers: monopolar electrode configuration and bipolar configuration. In the monopolar electrolyzer design, the cathodes and anodes are alternatively suspended in a tank filled with a 20–30% solution of potassium hydroxide in water (see Fig. 7). The bipolar design, often called the filter-press, has alternating layers of electrodes and separation diaphragms that are clamped together. The cells are connected in series and this results in higher stack voltage. The advantages of bipolar

Water Electrolysis

73

Fig. 7 Monopolar alkaline electrolyzer design

Fig. 8 Bipolar alkaline electrolyzer configuration

H2 O2 H2 O2 H2 O2 H2 O2 Insulator

Diaphragms

-

- + - + - + - +

+

n x 2V

design are reduced stack footprint, higher current densities, and product hydrogen being delivered at higher pressure. The bipolar electrolyzer configuration is shown in Fig. 8. The most commonly used technology at present is based on electrolyzers containing proton conducting membranes, also called polymer electrolyte membranes (PEM). In these electrolyzers, water reacts on the anode producing oxygen gas and protons, H+-ions. Protons are then conducted from the anode side to the cathode side, where they are reduced to generate hydrogen gas. The polymer membrane not only serves as an ionically conductive medium but also as the structural support for the electrodes and a separator for gases. The electrodes in PEM electrolyzers contain noble metal and noble metal oxide catalysts typically on a carbon support, e.g., Pt/C (1 mg/cm2) and (IrO2 or RuO2) on carbon support. The cross-section of the membrane-electrode assembly, which is the central structure of a PEM electrolyzer, is shown in Fig. 9. In a membrane-electrode assembly, two electrodes deposited on either side of the membrane form an intimate bond with the membrane through extension of the

74

Industrial Electrochemical Processes

Fig. 9 Cross-section of a membrane-electrode assembly (MEA) in PEM electrolyzers

O2

H+

H2

H2O

Anode

Cathode Membrane

membrane material in a thin layer that encapsulates catalyst particles and provides a large surface area available for reaction. When the necessary voltage in excess of the thermodynamic voltage of 1.23 V is applied, the electrons flow into the cathode at which hydrogen gas is generated in the reduction of protons. At the same time, oxygen is evolved from water on the anode releasing protons and electrons. Both electrodes are porous to allow for the formation and removal of gases formed at the interface of the electrode catalyst and the membrane. The Solid Polymer Electrolyte membrane was originally developed for fuel cell applications as part of the Gemini space program. The main polymer chain or backbone of this polymer is the Teflon (PTFE) structure. It has durability, as it is inert in many different environments, and also H+-conducting properties through the addition of side chains that terminate in SO3
2 groups, providing sites for the attachment of H+-ions and their propagation through the membrane. PEM electrolyzers are usually configured in a serial connection and bipolar design, shown in Fig. 10. The yellow blocks in the figure represent conductive material that connects the anode of one cell with the cathode of the next. Hydrogen and oxygen gases are collected on opposite sides of the electrolyzer. The cost of electrolytic hydrogen is still too prohibitive at present to make it a wide-spread, industrially important method for hydrogen production. The majority of the cost (i.e., ~70%) is due to the cost of electricity, except in cases where there is an excess of electricity available (e.g., from hydroelectric power plants, solar PV, or wind-generated electricity). The challenge remains at present for water electrolysis processes to develop more efficient electrolysis steps and electrolyzer components to make hydrogen production from water electrolysis more economically attractive.

Separation Methods

75

Fig. 10 Cross-section of a bipolar PEM electrolyzer

O2

e-

O2

H2

H+

e-

H2

H+

O2

e-

H2

H+

Separation Methods Electrolytic methods can be used for water purification and the removal of toxic and dangerous inorganic or organic chemicals from solutions or sludges. The application of voltage either directly oxidizes the organic chemical or produces an intermediate chemical that then reacts with the targeted impurity. An example of direct electrolytic impurity oxidation is the removal of cyanide ions from an alkaline solution (Eq. 20): 2CN
þ 8OH
! 2CO2 þ N2 þ 4H2 O þ 10e


ð20Þ

Indirect electrochemical oxidation involves, for example, a generation of the powerful oxidizing agent hypochlorite (ClO
), which then reacts with cyanide (Eq. 21): 2CN
þ 5ClO
þ H2 O ! N2 þ 2CO2 þ 5Cl
þ 2OH


ð21Þ

The electrodes in this method are a graphite or titanium anode immersed in contaminated water. Common organic impurities, such as phenols, mercaptans, napthenates, aldehydes, nitriles, amines, and dyes can be removed using this electrolytic process. Electrodialysis is the separation of low-molecular weight material from solution through a selective membrane. If the material to be separated is ionic, then the process can usually be accelerated by an electric field and can even take place against the concentration gradient. The main application for electrodialysis is the purification of salt water to produce drinking water. Electrolytic separation is also used in nuclear reprocessing for the purification of used fuel.

Galvanic Cells

Electrochemical devices that produce electricity in spontaneous reactions when their electrodes are connected through a load are called galvanic cells. They include batteries and fuel cells. The difference between batteries and fuel cells is that batteries can deliver a limited and predetermined amount of electricity based on the finite quantity of reactants in their enclosed casing, while fuel cells operate as long as reactants (fuel and oxidant) are supplied from external sources. Some fuel cells operate with one electrode (i.e., cathode) which utilizes oxygen from air and only has fuel for the anode supplied. Sometimes the distinction between batteries and fuel cells is defined as the ability of certain batteries to be recharged by applying voltage to the cell and reversing the battery reaction (i.e., rechargeable batteries). Fuel cells are usually not considered “rechargeable”, although so-called reversible fuel cells can operate in the reverse mode as electrolyzers. There are other electrochemical devices that clearly combine principles of both batteries and fuel cells; they are called the flow batteries. They are batteries because of their recharging capability but are more similar to fuel cells because the fuel or reactants are supplied from the outside in a continuous fashion. Metal-air batteries are devices that combine one traditional battery type electrode (i.e., a metal anode) with the second electrode, the cathode, that operates on oxygen from air just like the majority of fuel cell cathodes.

Batteries From electronic devices to electrical cars and large stationary applications, batteries provide power in every segment of modern life. They represent one of the most important energy storage technologies and firmly hold numerous application markets based on size and convenience. Batteries are used for applications that require power from kW (and below) to several MW and operate for lengths of time measured in hours. # The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_10

77

78

Galvanic Cells

Table 1 Battery characteristics for selected rechargeable batteries. Data shown is not for any particular battery system, but average data sampled for a variety of batteries Battery characteristic Nominal cell voltagea, V Self-discharge, %/month Cycle life, # of cycles a

Lead-acid 2.0 5 300–500

Ni-Cd 1.2 20 800–1500

Ni-metal hydride 1.2 30 ~500

Li-Ion 3.7 3–5 300–3000b

Manufacturer’s rated cell voltage at a certain rate of discharge, i.e., discharge current Different Li-ion chemistries

b

Batteries are usually classified as primary and secondary (or rechargeable) batteries. The main characteristic of primary batteries is that once they are used and completely discharged the reactions cannot be reversed and these batteries cannot be recharged. Secondary or rechargeable batteries are based on reversible reactions. After being discharged these galvanic cells can be turned into electrolytic cells and recharged. The most important rechargeable batteries are lead-acid, nickel-based batteries, and lithium ion batteries. Lithium ion batteries are made with lithium anodes and a variety of cathode materials, popularly called “chemistries”. Each battery chemistry is effectively a different battery system. Batteries are characterized by the following most important performance attributes: energy density (Wh/kg) or sometimes called specific energy, power density (W/kg), cell voltage, cycle life (number of cycles), self-discharge, and voltage efficiency. Energy density is the most important battery comparison criteria. It defines how much energy a battery is capable of storing and delivering per its unit weight (or sometimes unit volume). This is a particularly important characteristic for portable and automotive applications, but less so for stationary applications. The more energy stored in a battery per unit weight the better a battery is. Beginning with the first commercial applications of batteries, the demands of applications have driven the research to produce batteries with higher energy density. Progress in energy density for rechargeable batteries has been steady for more than a century and each new battery system technology chronologically developed has had higher energy density. The development of new systems was necessary for each new generation because of the higher demands for better functionality, particularly energy density. Power density (in W/kg), sometimes called specific power, is a very different property than energy density. It refers to power that a battery can deliver in the form of instantaneous current. In most cases, if a battery has high energy density, it does not have high power density and vice versa. To understand this, it is necessary to envision the construction and microscopic properties of battery electrodes. The main property of an electrode required for high power density is the high surface area of the porous, active battery material in contact with the electrolyte. More active material in general means higher energy density.

Batteries

79

Battery voltage varies for different batteries, as shown in Table 1 for selected rechargeable battery systems. Average self-discharge rates and battery cycle life are also included for these systems. Self-discharge is a process in which battery reactions occur spontaneously even in the absence of a load connected to the battery terminals. It is an important characteristic of battery systems, but it only refers to immediately available battery capacity after a period of storage. It is typically not an irreversible capacity loss and, therefore, the battery capacity is fully restored after the next charge cycle. Cycle life for batteries is expressed not in time, but in number of cycles that a battery can deliver before the capacity drops to some arbitrary value, typically 80% of the original (or nominal) capacity. The cycle life for all batteries strongly depends on the conditions of discharge, such as discharge current, end of discharge voltage, and temperature. Table 1 reveals that Ni-Cd batteries have excellent cycle life. These battery systems were superior in this category until the invention of the Li-Ion battery chemistry with a Li-FePO4 cathode, which shows promise for cycle life close to 3000. The ability of a battery to store energy has been traditionally expressed in capacity (Ah) and not in terms of energy. The historical reason for this is that lead-acid batteries were the only commercial battery system for a long time, and it was intuitive to compare batteries based on Ah capacity at a fixed voltage of 12 V (voltage of the most common lead-acid battery with 6 cells). However, to accurately compare battery systems, it is necessary to take into account the cell voltage as well (see Table 1). Theoretical capacity is determined by the amount of active material in the cell through the connection between the equivalent weight and capacity in Ah: 1 gram
equivalent of material ¼ 96, 485 C or 26:8 Ah

ð1Þ

1 gram-equivalent is the atomic or molecular weight of the active material in grams divided by the number of electrons involved in the reaction. Example 1 Calculate the theoretical capacity of an electrochemical cell: Zn þ Cl2 ! ZnCl2 : The first step is to calculate the equivalent weight of zinc and chlorine gas from the atomic weights: Zn (eq. weight) ¼ 65g:2 ¼ 32.5 g; Cl2 (eq. weight) ¼ 71:2 ¼ 35.5 g. If an equivalent weight of zinc and chlorine material, react in a spontaneous reaction it will produce 26.8 Ah. This means 0.82 Ah/g for Zn and 0.76 Ah/g for chlorine. For ZnCl2 it is 0.394 Ah/g. To obtain specific energy we multiply 0.394 Ah/g with 2.12 V (standard cell voltage) and obtain 0.835 Wh/g.

80

Galvanic Cells

Table 2 Battery characteristics and reactions System Lead-acid Nickel Cadmium Nickel Metal Hyd. Li-Ion

Anode Pb Cd

Cathode PbO2 Ni

Electrol. H2SO4 KOH

MH

Ni

KOH

Cell reaction Pb + PbO2 + 2H2SO4 $ 2PbSO4 + 2H2O Cd + 2NiOOH + 2H2O$ Cd(OH)2 + 2Ni (OH)2 MH + NiOOH$ M + Ni(OH)2

Li

MOy

LiPF6

xLi + MOy $ LiMOy

The actual specific energy is much lower, only about 50–75% of the theoretical specific energy, due to the weight of other components and losses in electrochemical reactions similar to other electrochemical systems such as slow charge transfer, resistance, and mass transport. Despite their ubiquitous presence in today’s life and billions US$ market, batteries are not a mature technology. Because of the persistent search for better batteries and inevitable changes to battery “chemistries”, the technology is going through continuous changes, where each new development represents a new technology. The most important rechargeable batteries, along with their electrodes and cell reactions are shown in Table 2.

Fuel Cells A fuel cell is another type of electrochemical device based on a continuous supply of reactants (fuel and oxidant) to produce power. Fuel reacts on the anode and is oxidized, while the oxidant is reduced on the cathode. In most fuel cells, the reactants are gaseous, for example, hydrogen gas and oxygen gas, but they can be liquid as well, e.g., methanol as fuel or hydrogen peroxide as an oxidant. The most common fuel cell uses hydrogen and oxygen. Since hydrogen has the highest energy density of all substances (33 kWh/kg), three times higher than gasoline, a system comprised of a fuel cell and hydrogen storage is considered an ideal energy storage and conversion device. The basic equations for the electrode and overall fuel cell reactions in both the acidic and alkaline aqueous electrolyte have been shown previously: Acidic electrolyte

Alkaline electrolyte:

H2 ! 2Hþ þ 2e


ð2Þ

½O2 þ 2Hþ þ 2e
! H2 O

ð3Þ

H2 þ ½O2 ! H2 O

ð4Þ

Fuel Cells

81

Table 3 Fuel cell classification based on the temperature of operation and type of electrolyte. Also listed are ionic charge carriers Fuel cell system Alkaline (AFC) Polymer electrolyte (PEMFC) Phosphoric acid (PAFC) Molten carbonate (MCFC) Solid oxide (SOFC)

Temperature range 60–90  C 50–80  C

Electrolyte 35–53% KOH Polymer membrane H3PO4 (conc.) LICO3/Na2CO3 ZrO2/Yt2O3

160–200  C 620–660  C 800–1000  C

Ionic charge curlers OH
H+ H+ CO3
2 O
2

LOAD

eOXIDANT

FUEL AFC

H2

OH-

O2

80°C 80°C

PEMFC

H2

H+

O2

PAFC

H2

H+

O2

MCFC

H2/CH4

CO3-2

SOFC

H2/CH4

O2-

O2/CO2 O2

PRODUCTS

180°C - 220°C 650°C 800°C - 1000°C PRODUCTS

Anode

Cathode Electrolyte

Fig. 1 Cross-section of a fuel cell with temperatures of operation and ionic charge carriers for five fuel cell types

H2 þ 2OH
! 2H2 O þ 2e


ð5Þ

½O2 þ 2e
þ H2 O ! 2OH


ð6Þ

H2 þ ½O2 ! H2 O

ð7Þ

The temperature of operation and the type of electrolyte are the critically important fuel cell factors used to establish fuel cell classification (Table 3). The reactions for these five fuel cell types and ionic charge carriers are also shown in Fig. 1. It is important to understand that different ionic charge carriers transfer charge between electrodes in the electrolyte depending on the type of electrolyte.

82

Galvanic Cells

Because different electrolytes become conductive at different temperatures, the corresponding fuel cells must operate above those temperatures. Efficiency of fuel cells is an often misunderstood and misquoted category. The simplest definition of efficiency is based on the ratio of practical cell voltage and thermodynamic or standard cell voltage (Eq. 8). E  100% E0

η¼

ð8Þ

Fuel cell efficiency is often quoted as the maximum possible, purely thermodynamic (i.e., theoretical) efficiency or the ratio between the Gibbs Free Energy change and enthalpy change. This efficiency only shows how much energy can be obtained from an electrochemical, fuel cell reaction compared to thermal reaction in heat engines if there were no kinetic limitations (Eq. 9). ηmax ¼

ΔG f  100% ΔH f

ð9Þ

Another component of efficiency is the fuel efficiency, which is the ratio of fuel that reacted in a fuel cell and total fuel that entered the cell (Eq. 10). μfuel ¼

Qreacted  100% Qin

ð10Þ

The overall efficiency is the product of the fuel efficiency and practical voltage efficiency (Eq. 11). ηtotal ¼ μfuel 

E  100% E0

ð11Þ

Fuel cell efficiency can be examined in comparison with the efficiencies of some other, traditional energy conversion processes. For example, it is well known that the efficiency of wind-driven generators is 0.58  kinetic energy of the fluid, the so-called Betz coefficient. In heat engines, the maximum possible efficiency is based on Carnot efficiency and is equal to (T1
T2)/T1, where T1 is the maximum temperature of the heat engine and T2 is the temperature at which the heated fluid is released. Fuel cell efficiency has no such limitations, but it cannot be automatically assumed that it is higher than for wind generators or heat engines. As discussed in the chapter on Thermodynamics, the fuel cell reaction has negative entropy and, therefore, Gibbs Energy change for a fuel cell reaction decreases with temperature. This means that the fuel cell efficiency, a ratio between the maximum energy that can be extracted and its enthalpy decreases with temperature. Example 2 Determine the theoretical efficiency limit for a CH3OH/O2 Fuel Cell: E ff: ¼ ΔG f =ΔH f ¼
702:0=
726:9 kJ=mol  100% ¼ 97%

83

Fig. 2 Conceptual fuel cell voltage trend as a function of current

Cell Voltage

Fuel Cells

Current Density Example 3 What is the theoretical cell voltage for a hydrogen fuel cell operating at 200  C if Gibbs Energy at that temperature is ΔG ¼
220.4 kJ/mol? E ¼ 220400 kJ=mol : ð2  96485 CÞ ¼ 1:14 V: Operational fuel cell voltage is affected by kinetic limitations, i.e., losses, and is much different than a “no loss” voltage. As in the case of all other electrochemical systems, fuel cells have three main sources of voltage loss: activation (or charge transfer), resistive (or ohmic), and mass transport (or concentration) losses. The higher the current or current density drawn from a fuel cell the larger are the voltage losses (Fig. 2).

Analytical Electrochemistry

Besides galvanic cells (i.e., batteries, fuel cells) and electrolytic processes, electrochemistry is pervasive in many other spheres of life and technology. It is the basis for a wide range of test methods and sensors; it is also used in industries from health care to automotive. In these applications usually very little current flows through a cell, unlike in galvanic and electrolytic cells. The electrode voltage and current are used to determine properties or identify species and very little current is required for that purpose. Therefore, the electrodes are typically small, and emphasis is placed on their properties relative to a particular application and on the method of voltage or current perturbation.

Potentiometry The potentiometric method is based on the voltage measurement on an indicator electrode to establish chemical information, identify unknown substances, and determine their concentrations. Various indicator electrodes have been designed that respond selectively to specific analytes. (Analyte is the substance or component that is of interest in the chemical analysis.) There are two possible cell configurations, single cell (Fig. 1) with reference electrode and two half-cells connected via salt bridge. The opposite electrode is a reference with known potential (e.g., Saturated Calomel Electrode or Silver Chloride electrode). If a reference electrode is used, the salt bridge preventing the mixing of solutions does not need to be external because the reference electrode comprises a porous membrane at its tip. By measuring the potential of the indicator electrode, the identity of the analyte can be determined. The indicator electrode is designed to specifically respond to analyte or analytes of interest. This configuration enables accurate determination of the concentration of the analyte in the solution by direct measurement of the cell potential. # The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_11

85

86

Analytical Electrochemistry V Voltmeter

Reference electrode

Indicator electrode

Analyte

Porous membrane

Fig. 1 Schematic representation of the potentiometric cell

Cell voltage

Fig. 2 Potentiometric titration curve

Volume of titrant

The presence of other ions in addition to those targeted for analysis can interfere with the measurement. In those cases, an additional step is needed to accurately determine the concentration of the analyte. This step is accomplished by graduate addition of another reactant and is called potentiometric titration. The added reactant or titrant creates a redox reaction and forces a change in the analyte (or titrant) concentration, which is monitored by the voltage change. If the voltage is recorded versus the volume of the titrant, the steep change in voltage reveals the point at which the analyte has been completely reacted and the voltage is, from that point, controlled by the concentration of the titrant. A typical potentiometric titration curve is shown in Fig. 2. An example of a potentiometric titration is the determination of the concentration of Fe3+-ions by titrating the analyte with a strong oxidizing agent such as cerium ions, Ce4+. The cell configuration (Eq. 1) includes a platinum indicator electrode and SCE reference electrode. PtðsÞ j Fe2þ , Fe3þ j SCE ðreference electrodeÞ

ð1Þ

Ion-selective Electrodes

87

The two vertical lines in the equation indicate separation between two half-cell compartments in the case when mixing of the two half-cell solutions is necessary. The separation can be in the form of a salt bridge, diaphragm, membrane between compartments, or in the case shown, a membrane on the tip of the reference electrode. Initially, the solution contains only Fe2+. When Ce4+ is added, the Fe2+-ions are oxidized to Fe3+ and the cell voltage is determined from the concentration of Fe2+ions. Fe2þ þ Ce4þ ! Fe3þ þ Ce3þ

ð2Þ

The cell potential is monitored as the Fe3+-ion concentration increases in controlled amounts. Once the first drop of ceric ion titrant has been added, the potential of the left cell is controlled by the ratio of oxidized and reduced iron according to the basic cell voltage expression from standard reduction potentials and the Nernst equation:
2þ ! Fe 0:059 Ecell ¼ 0:771  log
3þ   0:197 V ð3Þ 1 Fe Note that the Ce4+/Ce3+ redox couple is not included in the Nernst equation because the indicator electrode is not sensitive to these ions. In this equation, the concentration of Fe2+ is shown as products because the Pt indicator electrode (with Fe2+/Fe3+) reaction is the cathode when measured against the reference electrode. Platinum is the most common metal indicator electrode because it is inert and does not participate in many chemical reactions. It is, therefore, simply used to transfer electrons for the species from the solution (e.g., Fe2+/Fe3+ example from above). Other indicator electrodes include gold and carbon. Metal electrodes, such as Ag, Cu, Zn, Cd, and Hg, can be used to detect their aqueous ions. However, in general, most metallic electrodes are not useable because they are not inert, or their required ion equilibrium is not easily established.

Ion-selective Electrodes A special case of the indicator electrodes are the ion-selective electrodes specifically designed to be sensitive to only one ionic species. The electroanalysis based on ion-selective electrodes is one of the most important and convenient techniques for measuring ion concentration in solution. Some of the applications of ion-selective electrodes are: • • • •

Pollution Monitoring: CN, F, S, Cl, NO3, etc., in effluents, natural waters. Agriculture: NO3, Cl, NH4, K, Ca, I, CN in soils, plant material, fertilizers. Food Processing: NO3, NO2 in meat preservatives. Salt content of meat, fish, dairy products, fruit juices, brewing solutions.

88

Analytical Electrochemistry

Fig. 3 Representation of a cross-section of ion-selective membrane

Inner solution M+ L-

M+

LL-

L-

M+ L-

LL-

L-

M+ + M+ M+ M+ M M+ M+ Outer solution

• • • • • • • • •

F in drinking water and other drinks. Ca in dairy products and beer. K in fruit juices and winemaking. Detergent Manufacture: Ca, Ba, F for studying effects on water quality. Paper Manufacture: S and Cl in pulping and recovery-cycle liquors. Explosives: F, Cl, NO3 in explosive materials and combustion products. Electroplating: F and Cl in etching baths; S in anodizing baths. Biomedical Laboratories: Ca, K, Cl in body fluids (blood, plasma, serum). F in skeletal and dental studies.

The principle of ion-selective electrodes is different from the indicator electrodes or reference electrodes and does not involve a redox reaction. Instead, at its tip, the electrode contains a thin membrane specially formulated to detect only one type of ion and allow its penetration. The membrane is complex; it is made of a polymer material that contains a ligand (i.e., ion bonded to central atom), which specifically and tightly binds only the analyte of interest. For example, if the electrode is sensitive to potassium ions, K+, the membrane contains a ligand, L, that specifically binds K+. Since other ions cannot cross the membrane a concentration difference that is established across the membrane is only due to K+ and it depends on its concentration in the analyte solution. Behind the membrane, the electrode also contains an inner solution, containing a fixed concentration of the ions of interest. The ions of interest in the analyte are attracted to negative sites inside the membrane and they diffuse into the membrane based on the concentration difference between the outer and inner solutions. A cross-section of the general ion-selective electrode composition is shown in Fig. 3, where M is any metal, e.g., K, Na, Ca, etc. This discussion and representation refer to cation sensitive membranes, while the anion sensitive membranes contain reverse charge signs for ions in the analyte and for the sites in the membrane. Electrode potential in ion-selective membranes is determined by the potential difference between the inner and outer membranes, E ¼ Eouter – Einner, where Einner is a constant and Eouter depends on the concentration of M+ in analyte solution. The potential can be defined using the Nernst equation:

pH Electrodes

89

E ¼ E cons: þ

0:059 log ½M þ  n

ð4Þ

There are two general types of ion-selective membranes, crystalline and noncrystalline. Examples of crystalline membranes are LaF, selective to F ions or AgS, selective to Ag+ and S2 ions. Noncrystalline membranes are, for example, glasssilicate membranes for H+ or Na+ or immobilized liquid-liquid in a PVC matrix for Ca2+ and NO 3.

pH Electrodes pH electrodes are a special type of ion-selective electrodes made to detect the concentration of H+-ions in solution. Some of the extensive applications of pH electrode measurements include the monitoring of salts, acids, or bases; the control of bath composition in electroplating; the monitoring of water quality in rivers and reservoirs; the collection of numerous measurements in chemical, petrochemical, and paper and textile industries; the control of pH during the treatment of drinking water, i.e., acidic or alkaline effluents; and measuring of pH for various medical uses. The most commonly used type of pH electrode uses glass as a membrane and is appropriately called a glass electrode. The glass membrane is composed of SiO2 with the addition of N+ to bind oxygen when the membrane is immersed in water (Fig. 4). The configuration of a pH electrode with glass membrane is shown in Fig. 5. This is a typical configuration that involves an internal and external reference electrode. In the particular case shown in the figure, the internal reference electrode is Ag/AgCl and the external is SCE. These two reference electrodes have fixed potentials, so the pH will be determined based on the additional potential component, the potential difference across the glass membrane, i.e., junction potential, caused by a difference in H+-concentration on two sides of the membrane: E ¼ ðERE1  E RE2 Þ  0:059 pH

Fig. 4 Representation of the glass membrane cross-section

ð5Þ

Glass membrane

H+ -O H+ + External H -O H solution H+ + -O

O - H+ Internal O+ H O solution

90

Analytical Electrochemistry

Internal reference solution

External reference electrode SCE Analyte solution

[H+]

Glass membrane

[H+], [Cl-], AgCl(sat’d) Ag

E1 – E2

Fig. 5 Configuration of the pH electrode with glass membrane Fig. 6 Voltage vs. pH plot for buffer solutions

250 200 150 Standard buffers

E (mV)

100 50 0

4

5

6

7

–50

pH

–100

Calibration line

8

9

10

11

–150 –200

A pH electrode should be calibrated with two or more standard buffers before use. A plot of voltage versus pH should yield a straight line (Fig. 6) and the pH for an unknown solution should fall within a range for standard buffers. Errors in pH measurements come from poor standards, junction potential drift, and false response at very low [H+] due to Na+ interference and at high [H+] values due to glass saturation. Proper procedure and care of pH electrodes include enough equalization time for a measurement (up to a couple of minutes), enough hydration time for the membrane (dry membrane does not operate properly), temperature correction if necessary, and proper electrode cleaning between measurements. If proper procedure and care are used, the pH measurements using a glass electrode are accurate to +/ 0.02 pH units. Modern pH sensors are based on solid-state devices and include base construction of the transistors (Fig. 7). The membrane or the ion-selective material is deposited in the gate area of the transistor and exposed to analyte solution. Potential is measured versus the reference electrode as in the case of glass pH electrodes. These pH sensors, called ion-selective-field-effect-transistors, ISFETs, can be made very small and can measure the pH of small volume solutions (i.e., drop size).

Electrochemical Gas Sensors

91

Fig. 7 Schematic representation of the crosssection of ISFET

Reference electrode

Solution

Ion selective gate

SiO2 n+ Source

n+ P-Si

Drain

ISFET

Electrochemical Gas Sensors One of the largest applications of electrochemical sensors is in the gas analysis. Gas concentration in solutions or partial pressure in gas phase can be determined using electrochemical techniques. Partial pressure of gases in a mixture can also be determined by dissolution, as gas solubility is related to partial pressure. The detection can be accomplished potentiometrically by measuring the voltage of a cell. When gas is dissolved in solution the equilibrium potential is established at the electrode, which is proportional to the logarithm of pressure. For example, SO2 concentration can be determined by dissolving the analyzed gas in bromine water: SO2 þ 2 H2 O þ Br2 ! 4Hþ þ SO4 2 þ 2Br

ð6Þ

The reaction can be monitored by measuring the concentration of the Br2/Br couple or the change in pH. Another example is the detection of CO2, which diffuses from a gas mixture through a porous membrane forming HCO3 and H+: CO2 þ H2 O ! HCO3  þ Hþ

ð7Þ

H+ is then detected using a glass electrode. The same principle can be used for the detection of other gases: NH3, SO2, NO2, H2S, and HCN. Oxygen partial pressure can be measured using a cell that is fabricated from an oxide ion conductor with porous Pt electrodes on both sides. Standard pressure is maintained on one side and oxygen partial pressure, on the other side, is determined from the Nernst equation. To achieve conductivity of the ceramic oxygen ion conductor such as ZrO2, the cell operates at 800  C. The reaction in the sensor and the potential difference is based on the fact that oxygen concentration is higher on one side of the ceramic membrane. The system is driven towards equalization of the oxygen partial pressures and the reaction taking place on the side with higher partial pressure is the reduction of oxygen gas:

92

Analytical Electrochemistry

pO1 2

Ion conductor

Internal electrode

External electrode

pO2 2 Fig. 8 Schematic of a Lambda sensor

O2 þ 4e ! 2O2

ð8Þ

Oxygen ions then diffuse through the membrane and the reverse reaction, reduction, takes place on the other side of the membrane. The basic configuration is shown in Fig. 8. An oxygen gas sensor, also called Lambda Sensor, is used to monitor oxygen partial pressure in molten steel and in the exhaust gas of the internal combustion engine. A different type of sensors is based on the amperometric principle of measuring current at applied voltage. The method can be used for determining traces of gases based on the oxidation or reduction of electroactive species, which are generated by the dissolution of gases. Construction relies on a thin layer of electrolyte to ensure the rapid transport of dissolved gas to the electrode surface. The magnitude of oxidation or reduction current is determined by the partial pressure of the gas in the gas stream and the effective thickness of the Nernst diffusion layer. The expression for current takes a form of limiting current density: jlim ¼

nFDKpgas δN

ð9Þ

In this equation, K is the Henry’s constant (in mol/L atm) and it is used to quantify the gas solubility. (Note that there are different forms of Henry’s constant). Comparison with Eq. 7 in the chapter “Mass Transport” reveals that the partial pressure of gas is used instead of concentration. A frequently used method for dissolved oxygen determination is called Clark cell. It uses silver electrodes and an oxygen-permeable membrane.

Corrosion

Corrosion is an undesirable, spontaneous process that results in material degradation upon exposure to the environment. Corrosion is a spontaneous process because it leads to metal returning to a more stable state, the same state as in metal ores. While the corroding materials can be polymers, ceramics, or composites, the term corrosion usually refers to metals. There are many different types of corrosion: uniform, galvanic, pitting, crevice, intergranular, hydrogen damage, cracking, microbial, erosion, etc. Of all these types, the most important by far is the electrochemical corrosion of metals, in which the oxidation process M ! M+ + e is enabled by the presence of a suitable electron acceptor, known as a depolarizer. A depolarizing cathodic reaction usually involves oxygen reduction or hydrogen evolution. Corrosion can occur readily on a single piece of metal, but it also progresses if two metals are in contact and connected with an electrolyte film. This is called dissimilar metal corrosion. The metal that has a more positive standard reduction potential and is more noble undergoes cathodic reaction, while the more electronegative metal becomes an anode and gets oxidized. Corrosion usually starts at a location where metal is affected by stress (e.g., bend, weld, or paint damage). It is generally understood that corrosion can take place even if a metal is not directly immersed in an electrolyte, in air for example, but the actual mechanism, in that case, is less understood. The main condition for any electrochemical process, including corrosion to occur is the existence of electrolyte. For corrosion in the atmosphere, the electrolyte film is created on the surface of metal from the humidity in the environment. The ionic conductivity is established from dissolved ions of impurities on the surface or from the reaction of CO2 or SO2 from air. A specific example is the corrosion of cars that very commonly starts from salt on the road. As the corrosion progresses, metal dissolution into the electrolyte film takes place and electrons migrate to the location of the depolarizing cathodic reaction. For the most common cathodic reaction oxygen is the depolarizer and the reaction product is a mixture of hydrous metal oxides (called rust in the case of iron). Once corrosion starts, the rate of reaction can actually increase. This happens because the product of # The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8_12

93

94

Corrosion

the initial cathodic reduction reaction of oxygen is hydroxyl ions, OH (O2 + 2H2O + 4e ! 4OH); an increase in the pH of the electrolyte film can often compromise the protective oxide or paint on the metal surface, allowing oxygen-free access, and permitting the corrosion reaction to proceed unhindered.

Mixed Potential Understanding the corrosion of metal requires a modified view of an electrode in solution and the requirement for two electrodes. When a metal corrodes, both anodic and cathodic processes take place simultaneously, on the same surface of the metal and in the vicinity of each other. Because anodic and cathodic currents are equal, but opposite in sign, the total current from the sample is zero—no net current flows in or out of the sample. The two currents are equal at a certain potential, called rest potential. It is also called mixed potential because it is between anodic and cathodic potential. Even at rest potential, conversion of reactants to products is taking place at an electrode. The anodic half-reaction is always metal oxidation and the cathodic half-cell current is due to the reduction of H+ to H2 (acid) or O2 reduction to H2O (in basic electrolyte). For example, corrosion of zinc in acidic solution takes place according to the following reactions: Anodic : Zn ! Zn2þ þ 2e

ð1Þ

Cathodic : 2Hþ þ 2e ! H2 ðgasÞ

ð2Þ

Overall : Zn þ 2Hþ ! Zn2þ þ H2 ðgasÞ

ð3Þ

Graphical representation of the mixed potential is shown in Fig. 55. There is no net current to or from the sample, so ian ¼ icat in the figure, but both anodic and cathodic reactions proceed, and the zinc sample corrodes. The value of the current density is a measure of the rate of corrosion. This is a critically important property that determines how fast a sample corrodes. It is also called corrosion current density, icorr. By further analyzing the graph in Fig. 1, it can be concluded that corrosion potential must be between the standard potentials for the anodic and cathodic reactions. The cathodic reaction and, therefore, the overall corrosion reaction rate is dependent on the pH of the solution. Figure 2 shows a general comparison between hydrogen reduction reactions at pH of 1 (green line) and 14 (red line). By further examining the example of zinc corrosion, it is evident that zinc does not corrode in alkaline solutions if the cathodic reaction is hydrogen reduction because the standard reduction potential for hydrogen reduction at a pH of 14 is 0.83 V and is more negative than the standard reduction potential for zinc (0.76 V). In other words, zinc would be reduced in an alkaline solution (Fig. 3).

Mixed Potential

Current density, i/A

+

95

Zn  Zn2+ + 2e-

ian

Ecor

icat

Electrode potential, E/V 2H+ + 2e-  H2

-

+ 2H2O + 2e-  H2 + 2OHE0 = -0.83 V

Current density, i/A

Fig. 1 Mixed potential for a metal in solution

E0 = 0 V

Electrode potential, E/V 2H+ + 2e-  H2

Fig. 2 Current versus voltage for hydrogen reaction in acidic and alkaline solutions

It can be concluded from the graph that zinc would corrode if the depolarizing reaction was more positive, such as if electrically connected with a more noble metal, i.e., metal with a more positive standard reduction potential. In that case, the curve (i.e., line) for more noble metals would be shifted to the right, towards more positive potentials, thereby, making corrosion possible. As a result, the presence of

Corrosion

+ 2H2O + 2e-  H2 + 2OH-

Current density, i/A

96

E0 = -0.83 V Zn2+ + 2e-  Zn Electrode potential, E/V E0 (Zn) = -0.76 V

Fig. 3 Current-potential diagram for zinc in alkaline solution

small amounts or impurities of copper, for example, makes zinc corrode in alkaline solutions.

Oxygen Corrosion The other highly likely cathodic reaction is oxygen reduction. Oxygen from air is present in most environments and its solubility in aqueous solutions makes it a very probable cathodic reaction. It can be observed from the table of Standard Reduction Potentials that oxygen reduction, in both acidic and alkaline solutions, occurs at much more positive potentials than hydrogen reduction. Using the current-voltage relationship, it can be seen that the corrosion currents are theoretically much higher in the case of oxygen reduction because of the larger difference in standard potentials (Fig. 4). The analysis so far has taken into account only the standard conditions, so the Nernst equation should be used to determine the exact position of reaction potentials and properly estimate the corrosion current. In addition, the overpotential for certain reactions can play a significant role. For example, while corrosion of zinc is possible in neutral solutions, with hydrogen reduction as the cathodic reaction, it does not proceed at any significant rate because of the high overpotential for H+/H2 reaction (i.e., the current/voltage curve in the diagram is shifted to the left). As a result of this overpotential, zinc is stable in neutral solutions. The diagrams in Figs. 2–4 show current as a linear function of voltage for simplicity. However, the actual profile of a current-voltage relationship includes all three influencing factors (activation, resistance, and mass transport) and is more

97

Current density, i/A

Oxygen Corrosion

Zn2+ + 2e-  Zn

O2 + 4H+ + 4e- ---> 2H2O E0 = 0.40 V

E0 (Zn) = -0.76 V

Electrode potential, E/V

E0 = 1.23 V O2 + 2H2O +

4e-

--->

4OH-

Fig. 4 Current-voltage diagram for zinc corrosion in the presence of oxygen. The red curve and reaction is in acidic medium and green is in alkaline medium

Current density, i/A

+

Cu  Cu2+ + 2e-

Fe  Fe2+ + 2e-

ian

Ecor

Electrode potential, E/V

icat

O2 + 2H2O + 4e- ---> 4OH-

2H2O + 2e-  H2 + 2OH-

Fig. 5 Potential diagram for corrosion of iron and copper in alkaline solutions

properly shown in Fig. 5 for the case of iron corrosion in the presence of oxygen. The following observations can be made from the graph: • Copper will not corrode if the cathodic reaction is hydrogen reduction because the standard reduction potential for copper is more positive than that for hydrogen.

98

Corrosion

Fig. 6 Iron corrosion in the presence of oxygen

Water droplet Fe2O3 O2

Fe2+

Fe  Fe2+ + 2e-

O2 + 2H2O + 4e- ---> 4OHor O2 +

4H+

+ 4e- ---> 2H2O

• Copper might corrode in the presence of oxygen due to slightly more negative voltage, but the corrosion current would be very small. In addition, as a result of overvoltage, the reaction would likely not take place at all. • Iron will not corrode with hydrogen reduction as the cathodic reaction since its voltage is more positive. • Iron will corrode in the presence of oxygen at a significant corrosion rate. This is the most important form of iron corrosion. • In solutions of different pH values, the thermodynamic potential for oxygen reduction is: E ¼ 1.23  0.059 pH. • The mixed potential for iron corrosion is in the region where oxygen reduction is mass transport controlled (flat portion of the red curve) and each oxygen molecule arriving at the iron surface will be immediately reduced and this rate, which determines the corrosion current icorr. Corrosion of iron is conceptually presented in Fig. 6. It is evident from the figure that water is necessary for corrosion to take place as a medium for the transport of ions, which then react with products of oxygen reduction (water or hydroxyl ions) to form rust, Fe2O3. The reactions for the iron corrosion in the presence of oxygen are summarized in the following equations. Oxidation Fe ! Fe2þ þ 2e

ð4Þ

Reduction O2 þ 4Hþ þ 4e ! 2H2 O ðacidic solutionÞ

ð5Þ

O2 þ 2H2 O þ 4e ! 4OH ðalkaline solutionÞ

ð6Þ

Overal 2Fe þ O2 þ 4Hþ ! 2Fe2þ þ 2H2 O ðacidic solutionÞ

ð7Þ

Overall 2Fe þ O2 þ 2H2 O ! 2Fe2þ þ 4OH ðalkaline solutionÞ

ð8Þ

Electrochemical Corrosion Theory

99

O2

Passive

Potential

H2O Fe2O3 Corrosive Fe2+ Fe3O4 Fe

Stable

pH Fig. 7 Pourbaix diagram for iron in aqueous solutions

The products of the reactions shown in Eqs. 7 and 8 are hydrous mixtures of iron oxides, commonly known as rust. Stability of metals, in particular iron in aqueous solutions in the presence of oxygen is sometimes presented in the form of voltage–pH diagrams, called Pourbaix diagrams. These diagrams show the effect of potential changing from a corrosive (or active) region to a passive region. Under certain conditions of potential and pH, some metals form protective films, i.e., they passivate. A Pourbaix diagram for iron is shown in Fig. 7.

Electrochemical Corrosion Theory Two separate processes occur during the corrosion of metals. The anodic oxidation reaction of metal must be accompanied by a depolarizing cathodic reaction, such as hydrogen reduction or oxygen reduction. The standard reduction potential for an oxygen reduction reaction is more positive and this reaction does, therefore, produce faster corrosion rates. This reaction occurs more frequently since oxygen from air is usually present in the environments where a metal is corroding. Each half-reaction, metal corrosion, and oxygen reduction proceeds with the same limitations as discussed in the chapters on electrode kinetics and mass transport. The first region of voltage-current behavior is controlled by the logarithmic type of dependence based on the Tafel equation, the second pseudo-linear region follows Ohm’s Law due to resistive losses, and the third is characterized by mass transport control at higher currents. Mixed control may be observed for many corrosion reactions. Overpotential also plays a significant role in altering the potential for the cathodic reactions. Since this is a very special case of electrochemical

100

Corrosion

Pit

Oxide layer Water droplet

O2

Fe2+

Fe2O3

O2 + 2H2O + 4e- ---> 4OHor Fe  Fe2+ + 2e-

O2 + 4H+ + 4e- ---> 2H2O

Fig. 8 Diagram of pitting corrosion

processes, where a spontaneous reaction is not desired, the overpotential works in favor of minimizing corrosion. Depending on these reactions and their rates, corrosion products form on the surface of corroding metal. In many cases, these are oxides or hydroxides of the corroding metal and they are beneficial for preventing further corrosion by protecting the underlying metal. Since a coating forms on the metal, the main cathodic reactant, oxygen is prevented from reaching the metal and causing further corrosion unless the coating (i.e., oxide or hydroxide) is porous and enables oxygen diffusion. Because diffusion is encouraged at higher temperatures the protective nature of these coating or passivation layers is less effective in slowing down the corrosion at higher temperatures. Sometimes, even in the presence of passivating layers, a narrow channel or pit can develop in the metal and pitting type corrosion can occur. The inside of these pits is deprived of oxygen and passivation layers of oxide cannot form, while the cathodic reaction still takes place elsewhere on the metal. This causes corrosion in the pit to propagate fast and deep into the metal (Fig. 8). Any electrochemical reaction can be divided into two or more oxidation and reduction reactions. In a corroding system, oxidation of the metal (corrosion) and reduction of some species in solution are taking place at the same rate and the net measurable current is zero. iMEAS ¼ iRED  iOX ¼ 0

ð9Þ

When a metal or alloy is placed in contact with a solution, the metal assumes a potential that is dependent upon the metal and the nature of the solution. This “open circuit” potential when no external potential is applied to the cell is referred to as the corrosion potential, ECORR. The oxidation and reduction currents at the corrosion potential are equal and nonzero. Only the total or net current is measurable and that current is zero.

Corrosion Protection

101

Overpotential, η/V

0.2

0

-0.2 100nA

1μA

10μA

100μA

1mA

log i Fig. 9 Corrosion current determination from the potential-current diagram

The mechanism of corrosion is very complex and the corrosion rate measurement is based on the determination of the oxidation current at the corrosion potential. The corrosion current and corresponding overpotentials for half-reactions are given by Tafel-type Equations: 10 for the reduction half-cell reaction and 11 for the oxidation half-cell reaction. The evaluation is called the Stern-Geary Treatment. η ¼ βcat log η ¼ βox log

ired i0

iox i0

ð10Þ ð11Þ

The principle of measuring the corrosion current involves disturbing the system by an externally applied potential, which changes the anodic and cathodic reaction rates. The voltage sweep is first done in one direction, then the other, e.g., first in the anodic direction, then in the cathodic direction. The resultant corrosion current is found by graphical analysis of the two branches of the plot (Fig. 9). The electrochemical cell is comprised of a working electrode (i.e., the electrode of interest), counter electrode, and reference electrode.

Corrosion Protection Designing corrosion protection methods is based on the fact that there are two halfreaction in corrosion and preventing either one can be used in stopping corrosion. The most commonly used method for protecting metal from corroding is to apply a

102 Fig. 10 Schematic diagram of noble metal coating failure

Corrosion

Fe

Cu

Coating damage

Fe

Fe2+

2e-

Cu

O2 + 2H2O

4OH-

Fe

protective coating, such as paint. This method can never be applied perfectly, leaving points of defect in places where there is damage to the coating. Metals susceptible to corrosion can be protected by deposition of a thin film of less susceptible metal, e.g., silver, copper, and nickel plating of iron. The metals used for coating have more positive reduction potentials, thereby, reducing or eliminating the probability of corrosion. The coating must always be intact and pinhole-free, otherwise the underlying metal would undergo a very fast corrosion reaction in the exposed area (Fig. 10). If iron is coated with tin, for example, even the slightest damage in tin coating would make iron exposed and dissimilar metal corrosion would take place. Because of that tin cans corrode rapidly in air. Coating can also be less noble. Such coatings undergo oxidation and, therefore, prevent oxidation of the protected metal. An example is the protection of iron with zinc coating, a process called galvanizing. Zinc exhibits a more negative reduction potential than iron and will be oxidized first while protecting iron. The coating of less noble metal does not have to be perfect as an imperfection in coating does not change the fact that the more electronegative element, the coating, oxidizes first. The damage to such coating will not affect the metal to be protected as the oxidation reaction will still take place on the protective coating metal, e.g., zinc (Fig. 10). The cathodic reduction of oxygen takes place on the exposed area of iron. In this corrosion protection method, the less noble metal is called a sacrificial anode. The most commonly used sacrificial anodes in industrial corrosion protection are zinc and magnesium (Fig. 11).

Corrosion Protection

103

Fig. 11 Corrosion coating of a less noble metal

Fe

Zn Zn2+ Zn

2e-

O2

O2 + 2H2O

4OHZn Fe

Fig. 12 Cathodic corrosion protection

Zn2þ ðaqÞ þ 2e ! ZnðsÞ

E

Fe2þ ðaqÞ þ 2e ! FeðsÞ

E



red

¼ 0:76 V

ð12Þ

red

¼ 0:44 V

ð13Þ



Besides coatings for corrosion protection, an electrical method can be used to apply negative voltage to the metal and prevent anodic reaction (M ! M+ + e). This method is known as cathodic protection. An external power supply is used to apply cathodic protection. The method is very commonly used to protect oil pipelines and other buried structures (Fig. 12). An alternative method is to connect a more active (i.e., more negative) piece of metal to the structure that needs to be protected, making it therefore a dissimilar

104 Fig. 13 Depiction of a sacrificial anode concept

Corrosion

Structure to be protected, e.g., a ship, material: Fe

More electronegative element, e.g., Zn as sacrificial anode

metal corrosion (Fig. 13). The more negative or more active metal is the sacrificial anode, typically zinc or aluminum. Other methods for corrosion protection and prevention include anodization (increasing the thickness of the oxide coating using constant anodic current), organic coatings, anodic inhibitors, and cathodic inhibitors.

Index

A Alkaline electrolysis, 72 Alkaline water electrolyzers, 72 Anode, 4, 5, 7, 8 Anodic oxidation reaction, 99 Aqueous metal extraction, 69, 70 B Batteries cycle life, 79 primary, 78 secondary/rechargeable batteries, 78, 79 store characteristics and reactions, 80 theoretical capacity, 79 store energy, 79 Batteries vs. fuel cells, 77 Bipolar electrode configuration, 72 Boltzmann theory, 35 C Cadmium charged ions, 13 flow of electrons, 14 ionization, 13, 14 and silver, 13, 14 Cathode, 4, 7–9 Cathodic protection, 103 Cell current, 54 Cell potential, 45 Cell voltage, 4, 7, 8 Chemical equilibrium, 43 Chemical reactivity, 2 Chloralkali electrolysis process, 65, 66 Chlorine, 23 Clark cell, 92

Convection, 53 Corrosion alkaline solution, 96 anodic half-reaction, 94 cathodic reaction, 94 copper, 97 definition, 93 hydrogen, 98 ionic conductivity, 93 iron, 97 oxygen, 96 stress, 93 Corrosion current, 101 Corrosion potential, 100 Corrosion protection methods, 101, 102 Cottrell, Frederick, 2 Crystalline membranes, 89 D Diaphragm process, 65 Diffusion, 53 Dissimilar metal corrosion, 93 DSA type electrode, 67 E Electrical double layer, 16–18 Electrochemical cell characteristics, 4 electrical and chemical effects, 4 electrically conductive electrodes, 3 electrodes, 3 electrons, 3 galvanic and electrolytic cells, 10 ions, 3 neutral atoms/molecules, 3 organic solvents, 6

# The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Petrovic, Electrochemistry Crash Course for Engineers, https://doi.org/10.1007/978-3-030-61562-8

105

106 Electrochemical cell (cont.) schematic, 4 with 3-electrode configuration, 8 with 5-electrode configuration, 8, 9 with zinc and copper electrodes, 13 Electrochemical phenomena, 1 Electrochemistry cathode and anode, 4, 5 definition, 3 devices and processes, 3 electrical field, 5 electrochemical cell, 3, 4 electrodes (see Electrodes) electrolyte, 5, 6 electrolytic cells, 9 electronic conductivity, 5 interfacial science, 3 ionic conductivity, 5 microscopic level, 3 voltaic, 8 Electrode interface, 19 Electrode potential electrical double layer, 16–18 electroneutrality, 11, 15, 16 measuring potential, 19, 20 metal in solution, 11–14 potential scale, 24 salt bridge, 16 SCE, 25 SHE, 24, 25 table of standard reduction potentials, 20–23 Electrodes, 54 cadmium and silver, 14 carbons, 7 cathode, 4 conduct electrons, 3 counter electrode, 7 disk and disk-ring, 7 electrochemical cell, 3, 7 electrolyte, 3, 12 electrons, 3 geometry, 7 liquid metals, 6 metal oxides, 6 micro/ultra-micro, 7 RDE, 7 reference/sense electrodes, 8 semiconductors, 7 solid metals, 6 voltaic cells, 8 working electrode, 7, 8 zinc and copper, 13 Electrodialysis, 75

Index Electrolysis, 50 Electrolyte, 3 description, 5 gases, 6 ionic conductivity, 6 liquid, 6 polymer, 6 solid substance, 6 temperature, 6 Electrolytic cells, 9, 10 Electrolytic separation, 75 Electromotive Force (EMF), 28 Electroneutrality, 11–16 Electronic conductivity, 5, 6 Energy density, 78 Enthalpy, 33 Entropy, 34–36 Equilibrium constant, 43, 44, 46 External forces, 55 F Faraday’s Law, 51 Faraday’s Laws of Electrolysis, 1 Fick’s Laws of Diffusion, 53, 54 Flow batteries, 77 Fuel cell, 80 acidic, 80 alkaline, 80 classification, 81 efficiency, 82 ionic charge, 81 voltage trend, 83 G Galvanic cell, 4, 7–10, 77 Galvanism, 2 Galvanizing, 102 Gas sensors, 91 Gibbs Energy, 37, 39, 42, 43, 46 Glass electrode, 89, 90 Grove, William, 1 H Hall-Herault process, 68, 69 Heyrovský, Jaroslav, 2 History of electrochemistry Becquerel, Edmund, 2 Berzelius, 1 Cottrell, Frederick, 2 electrochemical principles, 1

Index Faraday’s Laws of Electrolysis, 1 Grove, William, 1 molecule of electricity, 1 Nernst, Walther, 2 Ritter, Johann, 2 Volta battery, 1, 2 Volta, Alessandro, 1 Hydrogen-oxygen fuel cell, 28 I Indicator electrode, 85 Industrial electrochemical processes, 65 Internal energy, 32 Ionic conductivity, 5, 6 Ions, 3 Ion-selective electrodes, 87, 88 ion-selective-field-effect-transistors (ISFET), 90, 91 Iron corrosion, 98 L Lambda sensor, 92 Le Chatelier’s principle, 28 Liquid electrolytes, 6 Lithium ionization in water, 12 M Mass transport, 53, 58 Measuring electrode potential, 19, 20 Membrane-electrode assembly (MEA), 74 Membrane process, 66, 67 Metal-air batteries, 77 Metal bar in water, 11, 12 Metal purification, 70, 71 Metal-solution interface, 5 Migration, 53 Mixed potential, 94 Molecular motions, 35 Molten salt processes, 67 Monopolar electrode configuration, 72 N Nernst diffusion layer concept, 55–57 Nernst equation, 27–29, 47, 87 Nernst, Walther, 2 Noncrystalline membranes, 89 Nonspontaneous process, 34

107 O Overpotential, 59 Overvoltage, 59 activation component, 60 Oxygen gas sensor, see Lambda sensor P pH electrodes, 89 Pitting corrosion, 100 Platinum, 12, 24 Platinum electrode, 1, 24 Polymer electrolyte, 6 Polymer electrolyte membranes (PEM), 73–75 Potentiometric method, 85 Potentiometric titration, 86 Pourbaix diagram, 99 Power density, 78 R Rate of a chemical reaction, 49 Rechargeable batteries, 78, 79 Rest potential, 94 Reversible fuel cells, 77 Ritter, Johann, 2 Rotating disk electrode (RDE), 7 S Sacrificial anode, 102, 104 Salt bridge, 16 Saturated calomel electrode (SCE), 25 Secific energy, 78 Self-discharge, 79 Silver and cadmium, 13, 14 electron flow, 13 electroneutrality, 13 ionization energy, 13 and saturated calomel, 25 Solid Polymer Electrolyte membrane, 74 Spontaneous processes, 34 Standard Gibbs (Free) Energy, 40 Standard hydrogen electrode (SHE), 24–26 Standard reduction potentials, 22, 29 Stern-Geary Treatment, 101 T Table of standard reduction potentials, 20–26 Tafel equation, 99 Thermodynamic assessment, 31

108 Thermodynamic assessment (cont.) closed system, 32 First Law, 32 open system, 32 properties, 32 Second Law, 36, 37 surroundings, 32 Thermodynamics, 49 V Volta, Alessandro, 1 Volta battery, 1, 2

Index Voltage vs. pH plot, 90 Voltaic cells, 8 W Water electrolysis, 71, 72 Water stability, 30 Z Zinc, 11