Physical Pharmacy and Instrumental Methods of Analysis [1 ed.] 9783031367762, 9783031367779, 9789385462900

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Mymoona Akhter  M. Mumtaz Alam

Physical Pharmacy and Instrumental Methods of Analysis

Physical Pharmacy and Instrumental Methods of Analysis

Mymoona Akhter · M. Mumtaz Alam

Physical Pharmacy and Instrumental Methods of Analysis

Mymoona Akhter Department of Pharmaceutical Chemistry Jamia Hamdard New Delhi, India

M. Mumtaz Alam Department of Pharmaceutical Chemistry Jamia Hamdard New Delhi, India

ISBN 978-3-031-36776-2 ISBN 978-3-031-36777-9 (eBook) https://doi.org/10.1007/978-3-031-36777-9 Jointly published with Ane Books Pvt. Ltd. In addition to this printed edition, there is a local printed edition of this work available via Ane Books in South Asia (India, Pakistan, Sri Lanka, Bangladesh, Nepal and Bhutan) and Africa (all countries in the African subcontinent). ISBN of the Co-Publisher’s edition: 978-93-8546-290-0 © The Author(s) 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of 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 publishers, 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 publishers 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 publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

I have been teaching this subject for the last 17 years and I strongly feel that there is a gap in the suggested course and the treatment of the subject in the classroom. This book is a sincere effort to bridge this gap in terms of content, expression and language. It covers the syllabus for B.Pharma currently being taught at various pharmacy colleges in India and can also be helpful for undergraduate science courses in general. This work is a culmination of our experience in teaching the subject in its entirety to undergraduate classes. The students come with varied backgrounds and face problem in book written in formal English. The book presents the concepts in a lucid language duly supported by appropriate illustrations with examples wherever necessary. Every chapter has been written with utmost care with its application in pharmacy. Important points have been put in boxes on the side to enable the students to understand, register and revise the topics during exams. Every chapter is provided with brief learning objectives and questions that help students to evaluate their understanding of the subject matter. Chapter 1-5 deals with the basic concept of physical chemistry including ionization, solution distribution law and colligative properties. Step by step solution of each numerical has been included to help student understand the calculations. Chapter 6 is based on chemical kinetics and explains different rate equations with methods of their calculations. Examples related to determination of shelf life of a drug have been discussed, as it is an important aspect of pharmaceutical science. Chapter 7 describes the concept of catalysis and related theories. Chapter 8 and 9 are related to conductometric and potentiometric measurement. pH is an important topic in pharmacy as most of drug studies are pH sensitive. Due emphasis has been given to its concepts in chapter 2 and in chapter 9 as well especially with respect to its potentiometric determination. Types of electrodes used, construction of glass electrodes are also discussed in detail. Aquametry has been given special emphasis as this topic cannot be found in any of the textbooks or reference books. Aquametry means determination of water content in pharmaceutical substances and therefore procedures written are taken from different pharmacopoeias. It includes all the relevant methods described for

v

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Physical Pharmacy and Instrumental Methods of Analysis

in pharmacy and biological sciences. Chapter 12 and 13 deal with the concept of polarimetry and refractrometry and their methods of measurement and applications B.Pharma. It describes the basic concepts, types of chromatography besides detailed explanation of a few chromatographic techniques. I thank the almighty Allah for giving me courage and making this work possible. I express my thanks to Dr. M. Shaqiquzzamman, and my research students for their constant support and good wishes. I am also thankful to Mr. Jai Raj Kapoor, for his constant encouragement and suggestions and Ane Books Pvt Ltd for bringing out

learning. All Constructive criticism and comments from students and teachers are most welcome and shall form the base for future editions.

Authors

Contents

1. Introduction and Physical Properties of Drug Molecules 1.1 Introduction 1.2 Dimensions and Units 1.3 Electromagnetic Radiation 1.4 Atomic Spectra 1.5 Molecular Spectra 1.6 Ultraviolet and Visible Spectrophotometry 1.7 Fluorescence and Phosphorescence 1.8 Infrared Spectroscopy 2. Solution 2.2 2.3 2.4 2.5

Solvent in a Solution Types of solutions Methods of Expressing the Concentration of a Solution Factors Affecting Solubility 2.5.1 Effect of Temperature 2.5.2. Nature of Solute and Solvent 2.5.2 Effect of Pressure 2.6 Solubility Expressions Judge Yourself 3. Colligative Properties 3.1 Introduction

3.3.1 Lowering of Vapour Pressure 3.3.2 Measurement of Lowering of Vapor Pressure 3.4 Osmotic Pressure 3.4.1 Theories of Semi-Permeable Membrane

1–10 1 1 4 5 6 7 8 9 11–20 12 12 12 16 16 16 20 20 20 21–44 21

22 24 25 26 vii

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viii

3.4.2 Osmotic Pressure 3.4.3 Measurement of Osmotic Pressure 3.4.4 Effects of Osmosis 3.4.5 Reverse Osmosis and Desalination 3.5 Elevation of Boiling Point 3.5.1 Determination of Boiling Point Elevation 3.6 Depression of Freezing Point 3.6.1 Determination of Molar Mass from Depression in Freezing Point 3.6.2 Determination of Depression in Freezing Point Judge Yourself 4. The Distribution Law 4.1 Introduction 4.3 Solubilities and Distribution Law 4.4 Limitations of Distribution Law 4.5 Thermodynamic Derivation 4.6.1 When Solute Undergoes Association in any one of the Solvent 4.6.2 When Solute Undergoes Dissociation in any one of the Solvent 4.6.3 The Solute Enters into Chemical Combination with one of Solvent 4.7.1 Association of a Solute 4.7.2 Dissociation of a Solute 4.7.3 Distribution Indicators 4.7.4 Extraction with a Solvent 4.7.5 Partition Chromatography Judge Yourself

27 29 31 33 34 37 39 42 42 44 45–54 45 47 47 47

48 50 50 51 52 52 52 53 53

5. Ionization and Ionic Equilibria 55–78 5.1 Introduction 55 5.2 Arrhenious Concept [Savanti Arrhenius (Doctoral thesis in 1887)] 55 5.2.1 Role of Water 56 5.3 Bronsted–Lowery Concept 57 5.4 Lewis Electronic Concept 58

Contents

ix

5.4.1 Hydrogen Ion Concentration 5.4.2 Ionization of Water 5.5 Ionization of Acids and Bases 5.5.1 Conversion of Hydrogen Ion Concentration to pH. 5.5.2 Common Ion Effect 5.6 Buffers 5.6.1 Buffer of Weak Acid and its Salt 5.6.2 Buffer of Weak base and its Salt: NH4OH & NH4Cl 5.6.3 Buffer Capacity 5.6.4 Maximum Buffer Capacity

58 59 59 62 64 65 65 66 67 68

5.7 Hydrolysis of Salt 5.7.1 Hydrolysis Constant 5.7.2 Degree of Hydrolysis 5.7.3 Salt of Weak Base and Strong Acid 5.7.4 Salt of Weak Acid and Weak Base 5.8 Solubility Product Judge Yourself

70 71 71 73 74 75 77

6. Chemical Kinetics 6.1 Introduction 6.2 Rate and Order of Reaction 6.3 Molecularity 6.5 Units of Basic Rate Constant 6.6 Calculation of Reaction Rate 6.7 Zero Order Reaction 6.7.1 Characteristics of Zero Order Reaction 6.7.2 Example of Zero Order Reaction 6.7.3 Apparent Zero Order Kinetics 6.8 First Order Reaction 6.8.1 Examples of Order Rate Kinetics 6.9 Second Order Reaction 6.10 Methods for Determination of Order of A Reaction 6.10.1 Method of Integration (Hit and trial method) 6.10.2 Graphical method 6.10.3 Half Life Method

79–96 79 80 81 82 82 83 83 83 84 84 87 87 89 89 89 90

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x

6.11 Factors that Affect Reaction Rate 6.11.1 Concentration 6.11.2 Pressure 6.11.3 Surface Area 6.11.4 Nature of Reactants 6.11.5 Temperature 6.12 Theories of Chemical Kinetics 6.12.1 Collision Theory 6.12.2 Transition State Theory 6.13 Decomposition and Stabilization of Medicinal Agents 6.14 Summary Judge Yourself

90 90 90 90 91 92 93 93 94 95 95 96

7. Catalysis 7.1 Introduction 7.2 Types of Catalyst 7.2.1 Catalyst Poison 7.2.2 Induced Catalysis 7.2.3 Catalyst Promoter 7.2.4 Autocatalysis 7.3 Characteristics of a Catalyst 7.4 Theories of Catalysis 7.4.1 The Intermediate Compound Formation Theory 7.4.2 The Adsorption Theory 7.5 Types of Catalysis 7.5.1 Homogenous Catalysis 7.5.2 Heterogeneous Catalysis 7.5.3 Enzyme Catalysis 7.6 Catalytic Poisoning 7.7 Applications of Catalysis Judge Yourself

97–108 97 99 99 99 100 100 100 101 101 102 103 103 103 105 106 106 107

8. Electrochemistry 8.1 Introduction 8.2.1 Conductance (c) 8.2.2 Resistance 8.2.3 Conductivity

109–122 109 110 110 110

Contents

xi

8.2.4 Resistivity 8.2.5 Molar Conductance 8.2.6 Equivalent Conductance 8.3 Types of Conductors 8.4 Laws of Electric Current 8.4.1 Ohms Law 8.4.2 Faraday`s Law of Electrolysis 8.4.3 Kohlrausch’s Law 8.4.4 Electrolytic Conductance 8.4.5 Mechanism of Electrolytic Conductance 8.6 Conductivity Cell 8.6.1 Types of Conductivity Cell 8.6.2 Cell Constant 8.7 Factors Affecting Electrolytic Conductance 8.7.1 Nature of Electrolyte 8.7.2 Concentration of the Solution 8.7.3 Temperature 8.8 Applications 8.8.1 Determination of Degree of Dissociation of Weak Electrolyte 8.8.2 Basicity of Organic Acids 8.8.3 Determination of Solubility and Solubility Product of Sparingly Soluble Salt 8.8.4 Ionic Product of Water 8.8.5 Determination of Total Dissolved Solids (TDS) in Water Judge Yourself 9. Potentiometry 9.1 Introduction 9.2 Cell 9.2.1 Galvanic Cell 9.2.2 Notation 9.2.3 Conductance in Cell 9.2.4 Liquid Junction 9.3 Cell Types 9.3.1 Concentration Cell 9.3.2 Electrolytic Cell 9.3.3 Electrochemical Cell

111 111 111 111 112 112 112 113 114 115 116 116 118 119 119 119 119 119 119 120 120 121 121 122

123–156 123 124 124 125 126 126 127 127 127 127

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9.4 Reversible and Irreversible Cells 9.5 Electrode Potential 9.5.1 Calomel Electrode 9.5.2 Standard Electrode Potential 9.6 Cell Potential 9.7 Reversible Electrodes 9.7.1 Electrodes Reversible with Respect to Cation or Electrode of First Kind 9.7.2 Electrodes Reversible with Respect to Anion or Electrode of Second Kind 9.7.3 Electrodes of Third Kind 9.7.4 Oxidation Reduction Electrodes or Electrodes of Fourth Kind 9.8 Some Common Reversible Electrodes 9.8.1 Meta-Metal Ion Electrode 9.8.2 Gas Electrode 9.8.3 Ion Selective Electrodes (ISE) 9.8.4 Selectivity of Ion Selective Electrodes 9.9 Sensing Electrodes 9.9.1 Polymer Membrane Electrodes (Organic Ion Exchangers and Chelating Agents) 9.9.2 Solid State Electrodes (Insoluble Conductive Inorganic Salts) 9.9.3 Gas Sensing Electrodes 9.9.4 Glass Membrane Electrodes 9.10 Glass Electrode 9.10.1 Construction 9.10.2 Storage 9.10.3 Advantages 9.10.4 Disadvantage 9.11 Reference Electrodes 9.11.1 Primary Reference Electrode e.g. Standard Hydrogen Electrode (SHE) 9.11.2 Working 9.11.3 Secondary Reference Electrode 9.11.4 Silver/Silver Chloride Electrode 9.12 Potentiometric Titration 9.12.1 Modes of Titration

127 129 130 130 130 132 132 133 133 134 134 134 134 135 136 137 137 137 137 137 138 139 141 141 141 141 141 142 143 145 147 147

Contents

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9.12.2 Acid Base Titration 9.12.3 Oxidation Reduction Titration 9.12.4 Complexometric Titration 9.13 Summary Judge Yourself 10. Aquametry 10.1 Introduction 10.2 Chemical Methods 10.2.1 The Karl Fischer Titration Method 10.2.2 Direct Titration by Karl Fischer Reagent 10.2.3 Residual Titration using Karl Fischer Reagent 10.2.4 Coulometric Method: (Electrometric Method) 10.3 Physical Methods (Azeotropic Distillation) 10.3.1 Apparatus 10.3.2 Procedure 10.4 Gas Chromatographic Method 10.5 Conductometric Method Of Water Determination 10.6 Thermal Method 10.6.1 Loss on Drying 10.7 Summary Judge Yourself   6SHFWURÀXRULPHWU\ 11.1 Introduction 11.2 Theory 11.3 Rate of Absorption And Emission 11.4 Deactivating Factors 11.4.1 Vibrational Relaxation 11.4.2 Internal Conversion 11.4.3 External Conversion 11.4.4 Intersystem Crossing 11.5 Factor Which Effect Fluorescence and Phosphorescence 11.5.1 Transition Type in Fluorescence 11.5.3 Structure 11.5.4 Structure Rigidity 11.5.5 Temperature and Solvent Effect

148 150 152 154 155 157 157 158 158 160 161 162 166 167 167 167 169 170 170 171 172 ± 173 174 176 176 176 177 177 177 178 178 178 179 179

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xiv

11.5.6 Effect of Dissolved Oxygen 11.5.7 Concentration 11.6 Instrumentation 11.6.1 Light Source 11.6.2 Monochromator 11.6.3 Detectors 11.7 Wavelength Correction and Spectra Correction 11.8 Sample Handling 11.9 Applications 11.9.1 Direct Method 11.9.2 Indirectly by Decrease 11.10 Types of Fluorescence Assay 11.10.1 The Formation of Chemical Derivatives 11.10.2 Fluorescence Quenching Analysis 11.10.3 Kinetic Methods of Analysis Judge Yourself 12. Polarimetry 12.1 Introduction 12.2 Principle 12.3 Optical Rotation and Type of Molecules Analyzed

12.6 Molecular Rotation 12.7 Intrinsic rotation 12.8 Temperature 12.9 Instrumentation 12.10 Application Judge Yourself 13. Refractometry 13.1 Introduction 13.2 Refractometry 13.2 Laws of Refraction 13.4 Critical Angle of Refraction 13.5 Polarizability and Refractive Index 13.6 Refractive Index and Temperature

180 180 180 180 181 181 182 182 182 183 184 184 184 185 186 187 189–196 189 190 190

192 192 194 194 195 195 197 197 197 199 199 200 202

Contents

13.7 Measurement of refractive Index 13.7.1 Abbe’s Refractometers 13.9 Application 13.10 Summary Judge Yourself 14. Chromatography Techniques 14.1 Introduction 14.2.1 On the basis of Property used to Separate 14.2.2 On the basis of Stationary Phase 14.2.3 On the basis of Solvent Phase 14.2.4 On the basis of Elution (development) Method 14.3 Theory of Chromatography 14.3.1 Plate Theory 14.3.2 Rate Theory 14.4 Thin-layer Chromatography (TLC) 14.4.1 Principle of TLC 14.4.2 Advantages of TLC 14.4.3 Procedure 14.4.4 Adsorbents 14.4.5 Preparation of Chromatoplates 14.4.6 Activation of Plates 14.4.7 Solvent System 14.4.8 Application of sample 14.4.9 Development of Chromatograms 14.4.10 Location of Spots 14.4.11 Evaluation of the Chromatogram 14.4.12 Applications 14.5 Paper Chromatography 14.5.1 Principle 14.5.2 Procedure 14.5.3 Types of Paper Chromatography 14.5.4 Applications 14.6 Column Chromatography 14.6.1 Experimental Aspects of Column Chromatography 14.6.2 Column Characteristics

xv

202 203 204 204 205 207–226 207 208 208 208 208 208 208 209 210 210 210 210 211 211 212 212 212 213 213 214 214 215 215 215 215 217 217 218 219

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14.6.3 Development/Elution Technique 14.6.4 Detection of Compounds 14.6.6 Application 14.7 Gas Chromatography 14.7.1 Types of Gas Chromatography 14.7.2 Experimental Aspects of Chromatography 14.7.3 Procedure 14.7.4 Derivitisation of Sample 14.7.5 Pretreatment of Solid Support 14.7.6 Various Factors Affecting Separation Process 14.7.7 Parameters used in GC 14.7.8 Applications of Gas Chromatography Judge yourself

219 220 220 220 220 221 222 222 222 223 223 224 225

1 Introduction and Physical Properties of Drug Molecules

1.1 Introduction The name pharmaceutical analysis has been associated with the area of pharmacy that deals with the quantitative and theoretic principles of science as they apply to the practice of pharmacy. It attempts to integrate the concept of pharmacy/ pharmaceutical sciences through the development of broad principles of its own. It helps the pharmacist, the pharmacologist, and the pharmaceutical chemist in their attempt to predict the solubility, compatibility, stability, and biologic action of drug products. As a result pharmaceutical scientist is in a better position to design and develop new drugs and dosage forms and to improve upon issues related to it.

1.2 Dimensions and Units and since then the system has undergone continuous evolution and improvements till 1960, when the Eleventh Conference on Weights and Measures proposed major changes in the metric system. It proposed a new name, the International System of Units, for the revised metric system. The abbreviation SI, comes from the French words ‘Systeme International’, and is commonly accepted for the revised metric International Union of Pure and Applied Chemistry (I.U.P.A.C.) have endorsed the International System of Units. The properties of matter are usually expressed by the use of three fundamental unit and a reference standard. The core of the SI system contains seven basic units listed in Table 1.1 below. All other units are derived from these basic units. © The Author(s) 2023 M. Akhter and M. M. Alam, Physical Pharmacy and Instrumental Methods of Analysis, https://doi.org/10.1007/978-3-031-36777-9_1

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Physical Pharmacy and Instrumental Methods of Analysis

2

Table 1.1: Basic physical quantities and their units

Symbol

Physical Quantity

SI Unit

Abbreviation

Length

l

metre

m

Mass

m

kilogram

kg

Time

t

second

s

Electric current

I

ampere

A

Thermodynamic temperature

T

kelvin

K

Amount of substance (moles)

n

mole

mol

v

Table 1.2: Common Derived Units

Physical Quantity

SI unit

Area

m2

Volume

m3

Density

kg m–3

Velocity

m s–1

Acceleration

m s–2 –2

Force

–2

Pressure Energy

2

Work J

2 –1

Force constant –1

Electric conductivity

m–1

J K–1 m–1 s–1

Thermal conductivity Mean free path

m

Electric charge

C (coulomb)

Dipole moment

Cm –1

s (Hz)

Frequency Potential difference

V (volt)

Power

W (watt)

Capacitance

f (farad)

Table 1.3: Some useful constants and their values in SI and c.g.s. units

Constant Avogadro’s number Planck’s constant

Symbol

Value in SI units

Value in c.g.s. units

NA

23

6.022 × 10-23 mol–1

–1

6.022 × 10 mol –34

h

6.626 × 10

Js

k

1.3806 × 10-23 J K–1

6.626 × 10–27erg s–1 l.3806 × 10–16 erg K–1

Introduction and Physical Properties of Drug Molecules

3

8.3144 J K–1 mol–1 8.206 × l0–2 dm3 atm K–1 mol–1

1.987 cal K–1 mol–1

c

2.9979 × 108 m s–1

2.9979 × 1010cm s–1

Charge on proton

e

1.602 × 10–19 C

9.8802 × 10–1 e.s.u

Electron mass

me

9.1095 × 10–31 kg

9.1095 × l0–28 g

Gas constant

R = k NA

Speed of light

Protons mass Faraday

1.6726 × 10

mn

1.6749 × 10-27 kg

1.6749 × 10–24 g

F = eNA

9.6485 × 104 C mol–1

5.9499 × 1014 e.s.u. mol–1

a0

5.29 × 10–11 m

0 529 Å

Vacuum permittivity

= eh/2

ϵo

–24

c

9.274 × 10

–27

c

5.05 × 10

–1

JT

J T–1

8.854 × 10–12J–1 C2 m–1

4πϵo

1.11264 × 10–10 m–2

Vacuum permeability

µo

–7

Gravitational constant

G

Atmospheric pressure

P

Permittivity factor

kg

l.6726 × 10–24 g

mp

eh/2 N

–27

–1 2

C

J s2 C–2 m–1

6.672 × 10–11 1.01325 × l05

2

kg–2 –1

Properties of substances that can be observed or measured without changing the identity of the substance are called physical properties of the molecules. These are important in order to understand the properties of the substance and provide a intensive. Extensive physical properties are those properties which depend upon the amount of matter present, such as volume, length and mass whereas intensive physical properties are independent of the amount of matter present like density, boiling point, melting point, color, ductility, malleability, crystalline shape, and refractive index. A study of the physical properties of drug molecules is important for product development and is often required to a better understanding of the interrelationship between molecular structure and drug actions. Physical properties can either be additive (the total contribution of atoms or the sum of corresponding properties of individual atoms or functional groups within the molecule) or constitutive (the structural arrangement of the atoms within the molecule). For example, optical rotation, surface tension, viscosity is a constitutive property whereas mass, is an additive property. Many physical properties are constitutive and yet have some measure of additivity. Molar refraction of a compound, for example, is the sum of the refraction of the atoms and groups making up the compound. The arrangements of atoms in each group are different, however, and so the refractive index of two molecules

Physical Pharmacy and Instrumental Methods of Analysis

4

will be different; that is, the individual groups in two different molecules contribute different amounts to the overall refraction of the molecules. A sample calculation will clarify the principle of additivity and constitutively. The molar refractions of the two compounds, having exactly the same number of carbon, hydrogen, and oxygen atoms are not the same. The molar refractions of the atoms are additive, but and associating physical properties of closely related molecules with their chemical nature, it is possible to describe the spatial arrangement of drug molecules, provide evidence for the relative physical or chemical behavior of a molecule, and suggest methods for the qualitative and quantitative analysis. The associations of these properties often lead to implications about chemical nature and potential action that are important for the creation of new molecules with desired pharmacologic activity. These properties also provide the tools for drug design, development and manufacturing. It also offers the analyst a wide range of methods for analyzing the quality of drug products. This chapter describes some of the important physical properties of molecules spectroscopy. Quantities have been expressed in Standard International (SI) units.

1.3 Electromagnetic Radiation Electromagnetic energy can be characterized as a continuous waveform of radiation, the nature of which depends on the size and shape of the wave. Electromagnetic about a point in space. The radiations are characterized by as a characteristic frequency, v is related to frequency by c in which c is the speed of light, 3 × 108 m/sec. Wave number, v v

v/c

in which v the wave number (in cm–1) represents the number of wavelengths found in 1 cm of radiation in a vacuum. corresponding wave number. The wavelength becomes shorter as the corresponding radiant energy or frequency increases. According to the elementary quantum theory, a chemical species has discrete energy transitions that can occur in an atom or molecule and they can absorb radiant energy corresponding to the difference between the two energy transitions. The interaction of the wavelength of the quantized electromagnetic energy with the molecules help us to determine the molecular or atomic information from the resulting spectra.

Introduction and Physical Properties of Drug Molecules

5

Table 1.4: Electromagnetic Spectrum and associated wavelength and frequencies.

WaveOHQJWKȜ (cm) higher frequency shorter wavelength

E

10–9

gamma rays

106

10–7

X rays

104

vacuum UV

102

N E

Energy kcal/mol

10–5

near UV

10–4

visible

Y

10

infrared 10–3

lower frequency longer wavelength

Ionization

Electronic transitions

R G

Molecular effect

1, 10–2

Molecular vibrations rotational motion

(IR) 10–1

microwave

10–4

104

radio

10–6

transitions

1.4 Atomic Spectra Atomic spectra are derived from the interactions between electromagnetic radiation of certain wavelengths and the electrons in valance orbitals of an atom. These interactions produce types of spectra, absorption and emission spectra. Absorption spectra are produced if radiation of a particular wavelength is passed through a sample and the decrease in the intensity of the radiation due to electronic excitation is measured whereas emission spectra is study of radiation produced by atoms whose electrons as excited by giving large amounts of energy, which can be from a

2 2

E

Z me4

n2h2

in which Z is the atomic number or effective nuclear charge of the atom, m is the mass of the electron (9.1 × 10–31 kg), n is the principal quantum number of the orbit, e is the charge on the electron (1.602 × 10–19 coulomb or 1.519 × 10–14 m3/2 kg1/2 s–1), and h is Planck’s constant, 6.626 × 10–34 joule second. If we represent E as the energy of a photon of electromagnetic radiation and cv v, the frequency of the radiation then

Physical Pharmacy and Instrumental Methods of Analysis

6

E hcv as suggested by Planck in 1900 as the basis of the quantum theory of atomic structure. In general the difference in energy levels of the two electronic states dictates the type of transition that is observed. The difference between the two electron energy levels E2 and E1 is given by expression Z me4  1 1 − 2  2 2 2 nh  n1 n2 

2 2

E2 – E1

Where n1 and n2 are respective quantum numbers Table 5: Spectral wavelengths associated with electronic transitions used in the detection of particular elements

Element

Wavelength (nm)

Element

Wavelength (nm)

As

193.7

Li

670.8

Ca

422.7

Pb

405.8

589.0

Zn

213.9

Cu

324.8

K

766.5

Hg

253.7

Each element of the periodic table has a characteristic atomic spectrum that can be associated with its electronic transition states. Atomic spectra can be used applications in analyzing for metal ions from drug products and in the quality control of parenteral electrolyte solutions. For example, blood levels of lithium, used to treat bipolar disorder (manic-depression), can be analyzed by atomic spectroscopy to determine overdosing of lithium salts.

1.5 Molecular Spectra The absorption of electromagnetic radiation by molecules includes vibrational and rotational transitions, as well as the electronic transitions just described for atoms. These additional transitions make the spectra of molecules more complex than those of atoms. The additional transitions result from energy interactions that produce either vibrations within the molecule associated with the stretching or bending of bonds between the atoms, or the rotation of the molecule about its center of gravity. In the case of vibration, the interatomic bonds may be thought of as springs depending on their energy levels, while in rotation, the motion is similar to that of a top spinning according to its energy level. In addition, the molecule may have some kinetic energy associated with its translational (straight-line) motion in a particular direction. The energy levels associated with these various transitions differ greatly from one another. The energy associated with movement of an electron from one orbital to another (electronic transitions) is typically about 10–18 joule, while the energy involved in vibrational changes is about 10–19 to 10–20 joule depending on the atoms involved, and the energy for rotational change is about 10–21 joule. The energy

Introduction and Physical Properties of Drug Molecules

7

associated with translational change is even smaller, about 10–35 joule. The precise energies associated with these individual transitions depend on the atoms and bonds that compose the molecule. Each electronic energy state of a molecule normally has several possible vibrational states, and each of these has several rotational states. The translational states are so numerous and the energy levels between translational states so small that they are normally considered as a continuous form of energy and are not treated as quantized. The total energy of a molecule is the sum of its electronic, vibrational, rotational, and translational energies. ETotal

ele

+ Evib + Erot + Etran

The energy absorbed by a molecule may be found only at a few discrete wavelengths in the ultraviolet, visible, and infrared regions, or the absorptions may be numerous and at longer wavelengths than originally expected. The latter case, involving longer wavelength radiation, is normally found for molecules that have resonance structures, such as benzene, in which the bonds are elongated by the resonance and have lower energy transitions than would be expected otherwise. Electromagnetic energy may also be absorbed by a molecule from the microwave and radiowave regions. Low-energy transitions involve the spin of electrons in the microwave region and the spin of nuclei in the radiowave region. The study

spectroscopy are discussed in the following sections.

1.6 Ultraviolet and Visible Spectrophotometry When organic substances are exposed to light in the visible and ultraviolet regions of the spectrum, they absorb light of particular wavelengths depending on the type of electronic transition that is associated with the absorption. Such electronic transitions depend on the electron bonding within the molecule For example,

compounds contains any hetero atom like oxygen, nitrogen which, possesses a pair of nonbonding (n) electrons shows n o n o from the absorption of longer wavelengths of radiation. Ultraviolet and visible spectrophotometry is a very powerful techniques for distinguishing single double from a conjugated diene from a triene. It can also distinguish between a conjugated The types of electronic orbitals present in the ground state of the molecule dictate the region of the spectrum in which absorption can take place. The part of the molecule that is responsible for absorption in UV region are called chromophores and the part which enhanced the absorbing power of the molecule are called

Physical Pharmacy and Instrumental Methods of Analysis

8

absorbed (A) to the concentration of absorbing substance (c in g/liter) and the length of the path of radiation passing through the sample (b in cm) as abc where a is a constant known as absorptivity for a particular absolving species (in units of liter g–1 cm–1). If the units of ‘c’ are moles/liter, then the constant is termed e, the molar absorptivity (in units of liter mole–1 cm–1). The absorptivity depends on the type of molecule whose absorbance is being determined and the solvent being used, as well as on the temperature and the wavelength of light used for the analysis. The quantity A is termed the absorbance and is related to the transmittance of light (T) by Io/I Io is the intensity of the incident light beam and I is in the intensity of light after it emerges from the sample. A molecule may have more than one characteristic absorption wavelength band, and the complete spectrum in the ultraviolet and visible wavelength regions can Absorption at a particular wavelength can be used to determine quantities of a drug substance in unknown sample. Standard solutions of known but varying concentration of the drug are prepared and absorbance is recorded at one selected wavelength (typically an absorption maximum). The absorbance is plotted against sample can then be determined by interpolation from such a graph. Spectrophotometry is a useful tool for determining the rate of chemical reactions or studying chemical equilibria. The chemical species participating in the equilibria must have different absorption spectra, and one simply observes the variation in absorption at a representative wavelength for each species while the pH or other equilibrium variable is changed. If one determines the concentrations an approximate pKa for a drug. Spectrophotometry can be used to study enzyme reactions and to evaluate the effects of drugs on enzymes.

1.7 Fluorescence and Phosphorescence The phenomenon of returning the absorbed light in the form of light is called

singlet state i.e. an electron is excited to higher level but retains the spin whereas phosphorescence occurs from a triplet state. The triplet state occurs when the excited singlet electron changes spin. The triplet state usually cannot be achieved according to the quantum theory. It is usually reached through the process of intersystem crossing, in which the singlet excited converts spontaneously to a triplet

Introduction and Physical Properties of Drug Molecules

9

by a change in electron spin, with loss of energy. The triplet state is usually more stable (i.e., having a longer lifetime) than the singlet excited state. Since the lifetime of triplet state is long therefore the phenomenon of phosphorescence is a delayed –6 to 10–9 seconds after excitation whereas phosphorescence occurs between 10–4 to a second after excitation.

(a) Singlet ground state

(b) Singlet excited state

(c) Triplet excited state

Fig. 1.1

Fluorescence techniques have been very widely used in pharmaceutical industry. The large number of applications ranges from the analytical determination of trace metals in the environment to pH measurements in whole cells under physiological conditions. It is used or applied to study the fundamental physical processes of molecules; structure-function relationships and interactions of biomolecules such as proteins and nucleic acids; structures and activity within whole

immunoassay techniques. range that can be achieved. Organic compounds containing aromatic rings generally biochemical, pharmaceutical, and environmental compounds are aromatic and,

1.8 Infrared Spectroscopy The study of the interaction of electromagnetic radiation with vibrational or rotational resonances within a molecular structure is termed infrared spectroscopy. The range of IR region is from 14000 cm to 10 cm and according to the wavelength or frequency, it is divided into three regions viz. near-IR (approximately 14000–4000 cm ), mid-IR (4000–400 cm ), far-IR (400–10 cm ). Among the three regions, mid-IR is the mostly used for the study of the fundamental vibrations of molecules. The collection of IR spectra is generally carried out with the help of Fourier transform infrared (FTIR) spectrometer.

10

Physical Pharmacy and Instrumental Methods of Analysis

IR spectroscopy is involved with study of interaction of absorption of IR radiation and the changes in the vibrational or rotational resonances within a molecular structure caused by it. Its main application is for determination of functional groups in a molecules. For a compound to absorb in IR region it need to have permanent or temporary dipole moment. Two types of molecular vibrations happen 1. Stretching vibrations, of atoms along the line of bond and causes change in bond length. The bending vibrations result from change in bond angle and are also known as deformation. IR spectra are used as markers for purity of the substance by matching the spectra recorded with the spectra of pure compound.

‰‰‰

2 Solution /HDUQLQJ2EMHFWLYHV z .QRZWKHGH¿QLWLRQRIVROXELOLW\DQGLWVH[SUHVVLRQ z )DFWRUVWKDWDIIHFWVROXELOLW\ z 8QGHUVWDQGLQJRILGHDODQGQRQLGHDOVROXWLRQV z 5DRXOW¶V/DZDQGGHYLDWLRQIURPLW

2.1  Defi nition A solution may be described as a homogeneous mixture, constituting one phase only, of two or more components. When two or more chemically non-reacting substances are mixed, they form mixtures. A mixture may be heterogeneous or homogenous. A heterogeneous mixture consists of distinct phases and the observed properties are just the sum of the properties of individual phases. However, a homogenous mixture consists of a single phase which has properties that may differ drastically form those of the individual components. A homogenous mixture whose composition can be varied within certain limits is termed a true solution. centrifugal action. All solutions are characterized by (i) homogeneity, (ii) absence of settling and (iii) the molecular or ionic state of sub-division of the components. When the solution is composed of only two chemical substances, it is termed a binary solution. Similarly, it is called ternary and quaternary if it is composed of three of four components, respectively. Thus, a solution may be regarded as a single phase containing more than one component.

© The Author(s) 2023 M. Akhter and M. M. Alam, Physical Pharmacy and Instrumental Methods of Analysis, https://doi.org/10.1007/978-3-031-36777-9_2

11

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12

 6ROYHQWLQD6ROXWLRQ Every solution consists of a solvent and one or more solutes. Solvent in a solution is its constituent as that of the solution. Generally, the component present in greater amount than any or all the other components is called the solvent. For the solubility of solids in liquids, where the liquid is present in large excess over the solid, there is no ambiguity in these terms, the solid being the solute and the liquid being solvent. However, if the solution is the same as that of a component present in smaller amount, the latter is called the solvent. The distinction between solvent and solute is an arbitrary one, nothing fundamental distinguishes them. For example, in syrup (liquid solution) containing 60% sugar (a solid) and 40% water (a liquid – same aggregation as solution), water is termed as the solvent. In a solution of alcohol and water, the substance present in a larger proportion by mass is called the solvent. But between solvent and solute.

 7\SHVRIVROXWLRQV All the three states of matter (gas, liquid or solid) may behave either as solvent or solute. Depending on the state of solute or solvent, mainly there may be the following seven types of binary solutions. Solute

Solvent

Example

Gas Gas Gas Liquid Liquid Solid Solid

Gas Liquid Solid Liquid Solid Liquid Solid

Air Aerated water (CO2 + H2O) Hydrogen in palladium Alcohol in water, benzene in toluene Mercury in zinc amalgam Sugar in water, common salt in water Various alloys

The solution of liquid in gas or solid in gas is not possible because the constituents cannot form a homogenous mixture. For a given solution, the amount of the solute dissolved in a unit volume of solution (or a amount of solvent) is termed as the concentration of the solute. Solutions containing relatively high concentration of solute are called concentrated solutions while those of relatively low concentrations of solute are termed as dilute solutions.

 0HWKRGVRI([SUHVVLQJWKH&RQFHQWUDWLRQRID6ROXWLRQ The concentration of a solution can be expresses in a number of ways. (i) Mass percentage (ii) Percent by volume or Volume percentage (iii) Per cent mass by volume (iv) Strength or Concentration

6ROXWLRQ

(v) (vi) (vii) (viii) (ix) (i)

13

Parts per million (ppm) Mole fraction Molality Molarity Normality Mass percentage or per cent by mass: in grams present in 100 grams of the solution. Mass percentage = = =

Mass of solute Mass of solution

× 100

Mass of solute Mass of solute + Mass of solvent

× 100

Mass of solute Volume of solution + Density of solution

× 100

The ratio Mass of solute/Mass of solvent is termed as mass fraction. Thus, Mass percentage of solute = Mass fraction × 100 10% solution of sugar means that 10 grams of sugar is present in 100 grams of the solution, i.e., 10 grams of sugar has been dissolved in 90 grams of water. (ii) Percent by volume: mL solution. Volume of solute Per cent of solute by volume = × 100 Volume of solution (iii) Per cent mass by volume: mL of solution. Per cent of solute mass by volume =

Mass of solute Volume of solution

× 100

(iv) Strength or concentration (Grams per litre): the solute in grams present in one litre of the solution. Mass of solute in grams Concentration of solution = Volume of the solution in litres =

Mass of solute in grams Volume of the solution in mL

× 100

Concentration in grams per litre is also termed as strength of the solution. Let w g of the solute be present in V litre of solution, then Strength or concentration of the solution = w/V gL–1

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14

(v) Parts per million (ppm): When the solute is present in trace quantities, it is as the quantity of the solute in grams present in 106 grams of the solution. Mass of solute × 106 ppm = Mass of solution Atmospheric pollution in cities is expressed in ppm by volume. It refers to the volume of the pollutant in 106 untis of volume. 10 ppm of SO2 in air means 10 mL of SO2 is present in 106 mL of air. (vi) Mole fraction: Mole fraction is used when the solution is constituted by of one component to the total number of moles of the solution (i.e., all the components). For example a solution of three components A, B and C. Components A B C Mass (in grams) W1 w2 w3 Molecular mass M1 m2 m3 No. of g moles =

W1w2w3 M1m2m3

Total number of g moles = w1/m1 + w2/m2 + w3/m3 Thus, Mole fraction of A (fA) = Mole fraction of B (fB) = Mole fraction of B (fB) =

W 1M 1 W1/M1+ w2/m2 + w3/m3 w2m2 W1/M1+ w2/m2 + w3/m3 w3m3 W1/M1+ w2/m2 + w3/m3

The sum of mole fractions of a solution is equal to 1, fA + fB + fC = 1.

i.e. In a binary solution,

Mole fraction of solute + Mole fraction of solvent = 1 Let n moles of solute (A) and N moles of solvent (B) be present in a solution. n = XA Mole fraction of solute = N+n Mole fraction of solvent = Thus,

N N+n

= XB

XA + XB = 1

Mole fraction is independent of temperature of the solution.

6ROXWLRQ

15

(vii) Molality: The number of the moles of the solute present per kg of the solvent is termed as molality. It is denoted by m. Molality (m) =

Number of moles of solute Number of kilograms of the solvent

Let wA grams of the solute of molecular mass mA be present in wB grams of the solvent, then WA × 1000 Molality (m) = mA × wB For Example if one mole of a solute is dissolved in 1000 g of the solvent, the concentration of the solution is said to be one molal. Relation between mole fraction and Molality: N N and XB = XA = N+n N+n XA WA × m B n Moles of solute = = = XB N Moles of solvent mA × mB XA× 1000 XB × mB or

XA× 1000 (1 – XA)

=

wA× 1000 wB × mA

= m

=m

Molality is the most convenient method to express the concentration because it involves the mass of liquids rather than their volumes. It is also independent of the variation in temperature. Relationship between molality and solubility Molality (m) =

Solubility × 10 Molecular mass of the solute

(viii) Molarity (Molar concentration) The number of moles of the solute per litre or per dm3 of the solution is termed as molarity. Number of moles of solute Molality (m) = Number of litres of solution Molarity × number of litres of solution = Number of moles of solution Let wA g of the solute of molecular mass mA be dissolved in V litre of solution. Molarity of the solution = wA/mA×V or Molarity × mA = wA/V Strength of the solution If V is taken in mL (cm3), then Molarity of the solution = wA/mA×V × 1000

16

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The unit of molarity is mol litre or mol dm If one mole of a solute is present in one litre of solution, the concentration of the solution is said to be one molar. (ix) Normality the solute present in one litre of the solution. Gram equivalent of solute

N=

Volume in litres Thus, if one gram equivalent of a solute is dissolved in one litre of the solution, the concentration of the solution is said to be one normal or Normal (N).

 )DFWRUV$IIHFWLQJ6ROXELOLW\ Solubility is a complex thermodynamic process that takes many factors into account. There are three main factors that control solubility of a solute. 1. Temperature 2. Nature of solute or solvent 3. Pressure

 (IIHFWRI7HPSHUDWXUH Generally solubility increases with the increase in temperature and decreases with the decrease of temperature but there are some exceptions to this. For example KNO3, NH4Br show marked increase in solubility with increase in temperature, whereas NaCl show only a small increase in solubility with increase in temperature. Few substances like anhydrous sodium sulphate, and CeSO4 show decrease in solubility with rise in temperature. In general two kinds of behaviours can be followed (i) In endothermic process solubility increases with the increase in temperature and vice versa. For example: solubility of potassium nitrate increases with the increase in temperature, similarly solubility of sugar in water increases with increase in temperature. (ii) In exothermic process solubility decrease with the increase in temperature. For example: solubility of calcium oxide decreases with the increase in temperature. (iii) Gases are more soluble in cold solvent than in hot solvent. According to Le Chatelier’s principle dissolution of a solute in water is an endothermic process, i.e., heat is absorbed and cooling results when a substance passes into solution. Therefore, if temperature is increased when a solution is prepared, equilibrium should shift in that direction which produces cooling i.e. should decrease with rise in temperature in accordance with Le Chatelier’s principle.

 1DWXUHRI6ROXWHDQG6ROYHQW Solubility of a solute in a solvent purely depends on the nature of both solute and solvent. If the solute and the solvent have similar chemical characteristics,

6ROXWLRQ

17

the solubility is high and if they are dissimilar, the solubility is low. That means substances with similar intermolecular attractive forces tend to be soluble in one another. This generalization is stated as “like dissolves like.” Non polar solutes are soluble in non-polar solvents; polar or ionic solutes are soluble in polar solvents.

2.5.2.1 Solubilities of Solids in Liquids Two types of solids are known ionic solids and molecular solids. Ionic solids consists of positively and negatively charged ions bound together by lattice energy of the crystal. This lattice energy opposes the tendency of a solute to dissolve. Hence, the larger the lattice energy of the crystal of a solute, the smaller is its solubility. Hence, the force of attraction increases as we pass from uni-univalent electrolytes (NaCl) through bi-univalent electrolytes (BaCl2) to bi-bivalent electrolytes (BaSO4). In such cases the energy for solubilization is given by hydration of the ions by water in aqueous solution known as the energy of hydration. That is the ionic solids dissolve to a larger extent in a solvent having a high dielectric constant than in a solvent having a low dielectric constant. Where as in case of non-ionic solids or molecular solids which may be polar or non-polar in character. The solubility is due to polar-polar interaction between the oppositely charged ends of the molecules of the solute and the solvent.

2.5.2.2 Solutions of Liquids in Liquids In this part only binary liquid solutions, i.e., two component solutions will be discussed and both the liquids are supposed to be volatile. Raoult studied vapour pressures of a number of binary solutions of volatile liquids, such as benzene and toluene, at constant temperature and gave the following generalisation which is known as the Raoult’s law: The partial pressure of any volatile constituent of a solution at any temperature is equal to the vapour pressure of the pure constituent multiplied by the mole fraction of that constituent in the solution. Consider a binary solution is made of nA moles of a volatile liquid A and nB moles of a volatile liquid B. If pA and pB are partial pressures of the two liquid components, then, according to Raoult’s law PA = xASÛA

PB = xB SÛB

... (1) ... (2)

where xA is mole fraction of the component A given by nA /(nA + nB), xB is mole fraction of the component B given by nB/(nA + nB) and SÛA and SÛB are vapour pressures of pure constituents A and B, respectively. If the vapour behaves like an ideal gas, then, according to Dalton’s law of partial pressures, the total pressure P is given by or

P = PA + PB

... (3)

P = xASÛA + xB SÛB

... (4)

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18

Experimentally it is known that the Raoult’s law is obeyed only approximately for a number of binary solutions. It is considered highly likely that the law is obeyed perfectly only in the case of ideals solutions. Therefore a solution of two or more constituents is said to be ideal if it obeys Raoult’s law exactly at all concentrations and at all temperatures. It has been found that liquid pairs which are generally similar, form ideal solutions. The following binary mixtures obey Raoult’s law over the entire range of concentration and thus form ideal solutions. Ethylene bromide and ethylene chloride; n-hexane and n-heptane; n-butyl chloride and n-butyl bromide; benzene and toluene and carbon tetrachloride and silicon tetrachloride. The vapour pressures of an ideal binary solution of two components A and B having different mole fractions are

PAo

7RWDOY DSRXU SUHV

P 9DSRXUSUHVVXUH

A

VXUHR 3D IVROXW UWLD P=X o LRQ O S P A + UHV A X P o =X B B VX A P o UH A RI $

o

PBo

I % H R VXU V H SU WLDO o 3DU PB o = XB PB

XA = 1

0RUH)UDFWLRQ

XA = 0 XB = 1

XB = 0

)LJ

Ideal Solution. Solutions in which solvent and solute interactions are similar to solvent-solvent and solute-solute interactions are known as ideal solutions. Ideal solutions obey Raoult’s Law and during their formation there is no change in heat and volume Non Ideal Solutions. Solutions in which solvent-solute interactions are different from solvent-solvent and solute-solute interactions are known as non-ideal solutions. They do not obey Raoult’s law and their formation is accompanied by changes of heat and volume. They show considerable deviation from the ideal behaviour. Deviations are of two types - positive and negative.

Vapour pressure of ideal solutions. the partial pressure of each constituent against its mole fraction in the solution is a straight line and the total vapour pressure of the solution for any given composition is equal to the sum of the partial vapour pressures of the two constituents. Solutions which show deviation (positive or negative) from the ideal behavior in their vapour pressure are called as real or non-Ideal solutions.

6ROXWLRQ

19

9DSRXUSUHVVXUHPP+J

9DSRXUSUHVVXUHPP+J

Real solutions of type I shows small deviation from ideal behavior and the total vapour pressure remains always within the vapour of the pure constituents.

0 XA = 1

0ROH)UDFWLRQ

XB = 0

1

0 0.2 0.4 $FHWDOGHK\GH

XA = 0

1 0.8 &DUERQ GLVXOSKLGH

9DSRXUSUHVVXUHPP+J

XB = 1

0.6 0ROH )UDFWLRQ

0 0.2 $FHWRQH

0.4

0.6

0ROH )UDFWLRQ

0.8

1

&KORURIRUP

)LJ9DSRXUSUHVVXUHRIQRQLGHDOVROXWLRQVD 5HDOVROXWLRQVVKRZLQJVPDOO GHYLDWLRQVIURPLGHDOEHKDYLRXUE 3RVLWLYHGHYLDWLRQVIURPLGHDOEHKDYLRXU F 1HJDWLYHGHYLDWLRQVIURPLGHDOEHKDYLRXU7KHGRWWHGOLQHVUHSUHVHQWLGHDO EHKDYLRXU

The solutions of Type II (acetaldehyde-carbon disulphide, water-propyl alcohol and ethyl alcohol-chloroform mixtures) show large positive deviations whereas Type III solutions (acetone-chloroform, water-sulphuric acid and water nitric acid) show large negative deviations. The total vapour pressure curve rises to a maximum or dips to a minimum which is above the vapour pressure of each of the pure components respectively.

3K\VLFDO3KDUPDF\DQG,QVWUXPHQWDO0HWKRGVRI$QDO\VLV

20

 (IIHFWRI3UHVVXUH The effect of pressure is observed only in the case of gases. An increase in pressure cold drink bottles under pressure.

 6ROXELOLW\([SUHVVLRQV The solubility of a substance may be expressed in a number of ways. The Pharmacopeias and National Formulary lists the solubility of drugs as the number of milliliters of solvent in which 1 gram of solute will dissolve. 7DEOH7HUPVRI$SSUR[LPDWH6ROXELOLW\

Term

Parts of Solvent Required for 1 Part of Solute

Very soluble

Less than 1 part

Freely soluble

1 to 10 parts

Soluble

10 to 30 parts

Sparingly soluble

30 to 100 parts

Slightly soluble

100 to 1000 parts

Very slightly soluble

1000 to 10,000 parts

Practically insoluble, or insoluble

More than 10,000 parts

-XGJH HBr > H2SO4 > HCl > HNO3 In HF strong acid like HNO3 behave as base

H2NO3+ + F –

HF + HNO3

...(8)

Strength is known by conductance measurement

5.4 Lewis Electronic Concept An acid is a molecule or ion that accepts an electron pair to form a covalent bond. A base is a molecule that provides unshared pair of electron by which the base coordinates with the acid. The Lewis concept of acid and bases is too broad and can be applied to substances which don’t produce protons or hydronium ions.

+

H

H :N H H

+

Saturated acid

H .. = H : N : H ]+ .. H

Base

Cl—B

Cl

CH3

Cl

= Cl—B : O

+ :O CH3

Cl Acid

CH3

Cl

CH3

Base

5.4.1 Hydrogen Ion Concentration present in one litre of the solution. In case of pure water H3+O is 1 × 10-7 gm ion /litre Therefore; if concentration of H3+O ion in a solution is = 1.01 × 10–7 neutral < 1.01 × 10–7 acidic > 1.01 × 10–7

basic

Mineral acids are highly dissociated in solution and the concentration of H3+O ion tells us about the strength of acid or it can be said that concentration of H3+O measures the acidity of an acid. With strong acids like HCl, H3+O ion concentration is nearly equal to the total concentration of HCl in dilute solution and approximately so upto decimolar concentration. Thus in N /10 HCl the H3+O ion concentration is approximately 0.1 or 10-1. Similar theory applies to the dissociation of bases.

Ionization and Ionic Equilibria

59

5.4.2 Ionization of Water

Titratable Acidity (TA): It is a measure of the amount of acid present in a solution. It is expressed as grams/liter (g/L) and is obtained by multiplying to percent TA by 10. So, a TA of 0.60% is expressed as 6g/L. pH is defined as the measure of the strength of acid in a solution.

Although water is a poor conductor of electricity. Pure water does ionize through a process known as autoprotolysis. The dissociation of water is represented by equation given below: H3O+ + OH–

2 H2O K

=

[H3O + ] + [OH − ] [H 2 O]2

K[H2O]2 = [H3O+] + [OH–] Since concentration of H 2O is constants therefore [H2O]2 equals to another constant Kw Kw is known as ionic product of water. The numerical value of Kw varies with temperature and at 25 °C it is approximately 1 × 10–14.

5.5 Ionization of Acids and Bases base according to their power of ionization in aqueous (aq.) solution. e.g. if we compare 1NHCl (aq.) and 1N acetic acid, HCl is better conductor of electricity, react much more readily with, metals, crystals certain reactions are neutralize identical amount of alkali which is known as titratable acidity. That means 1000 ml of 1N acetic acid will require same amount of alkali to get neutralized as by 1000ml of 1N HCl Similarly 1000 ml of 1N sodium hydroxide and NH4OH will require equal amount of acid to neutralize. This difference in the properties of the two acids/ bases is attributed to difference in their tendency to get ionized. Kw = [H3O+][OH–] The ionization of weak acid (incompletely ionized acid) may be considered as reversible type of reaction MA Molecular acid

M+ + A+

Anion

An equilibrium expression based on law of Mass action may be applied to the reaction [M+][A–] Ka = [MA] a is constant as the concentration is varied provided acid is weak however, deviation occurs in case of strong acids.

Physical Pharmacy and Instrumental Methods of Analysis

60

For monoprotic acid the ionization can be represented as below A–+ M3O+

MA + H2O K =

...(10)

[A  ] [M 3O + ] [MA][H 2O]

...(11)

[H 2 PO 4 −1 ] [H 2O + ] [H3PO 4 ]

Ka =

...(12)

For polyprotic acid the ionization can be represented as H3PO4–1 + H3O+

H3PO4 + H2O –1

–2

H2PO4 + H2O

HPO4 + H3O

–2

–3

HPO4 + H2O

PO4 + H3O -2

+

[H 2 PO 4-1 ] [HPO 4-2 ] [H 3O + ]

K2 =

[H 2 PO 4-1 ]

K3 =

...(13) ...(14) ...(15)

+

[HPO 4 ] [H 3O ]

K1 =

+

...(16) ...(17)

[PO 4 −3 ] [H3O + ] [HPO 4 −2 ]

[PO 4 −3 ] [H 2O + ]3 K4 = H3PO 4

Each of the successive ionization is suppressed by the hydronium ion formed from proceeding stage. The successive K value is always small in value. Similarly the ionization of base is represented as below: NH4OH

NH4+ + OH– +

...(18)

–

[NH ][OH ] Kb = [NH OH] 4

...(19)

According to Bronsted and Lewis when base NH3 is dissolved in water, the water acts as acid donating a proton to NH3, which pH scale: The pH scale, accepts it by offering a share of pair of electrons the standard measurement on the nitrogen atom. This reaction is written as; of acidity, was developed by the head of Carlsberg NH4+ + OH– ...(20) NH4 + H2O Kb

[NH+][OH–] = [NH OH] 4

...(21)

Equation (21) is identical to eq. (19) because [NH3] is numerically identical with [NH4OH]. But when the concentration of an acid is increased this does not holds good. It has been observed experimentally that conductivity of 1.4 N solution of the strong acid is only about normal with respect to H+ ion concentration. Now

Laboratory’s Chemical Department in 1909. Dr Søren Sørensen (18681939) developed the pH scale during his pioneering research into proteins, amino acids and enzymes the basis of today’s protein chemistry.

Ionization and Ionic Equilibria

61

when concentration of an acid is progressively decreased by the dilution or by neutralization. The H+ion concentration fall as to 0.01, 0.001, 0.0001 and so on example dissociation of water and the concentration of respective ions is given by the following equation [H3+O] = [OH–] = Kw = 1 × 10–7 th

+

...(22) –

This solution is 1/10 million normal with respect to H & OH such small Thus, in pure water where H3+O and OH– ions are present in same concentration CH+ = COH– = 1.01 × 10–7 gm ion /litr. Therefore; Kw = CH+ × COH– =1.02 × 10-14 at 25 °C. Now, if the H3+O ion concentration in higher than 1 × 10–7 the solution is said to be acidic and if the OH– concentration is higher than 1 × 10–7gm ion /liter solution is said to be basic. That means the hydrogen ion concentration of a solution varies from approximately 1 in a 1M solution of a strong acid to about 1 × 10–14 in a 1M solution of a strong base, and the calculations often become cumbersome. To reduce this concentration. He established the term pH, which was originally written as pH+, reciprocal of the hydrogen ion concentration: pH = log 1/[H3O+]

...(23)

According to the rules of logarithms, this equation can be written as pH = log 1 – log [H3O+] +

and since the logarithm of 1 is zero, pH = – log [H3O ]

...(24) ...(25)

Equations (23) and (25) are identical; they are acceptable for approximate calculations involving pH. The relation between H3+O ion concentration & pH may also be represented as [H3O+] =10–pH

...(26)

Similar symbol has been represented for the OH– ion concentration. Thus for N/10 alkali, [OH–] concentration equal 1 × 10–1 i.e. pOH =1 The pH of a solution may be considered in terms of a numeric scale having values from 0 to 14, which expresses in a quantitative way the degree of acidity (7 to 0) and alkalinity (7 to 14). The value 7 at which the hydrogen and hydroxyl ion concentrations are about equal at room temperature is referred to as the neutral point, or neutrality. The neutral pH at 0°C is 7.47, and at 100°C it is 6.15. The scale relating pH to the hydrogen and hydroxyl ion concentration of a solution is given in Table 5.1.

Physical Pharmacy and Instrumental Methods of Analysis

62

Table 5.1: The pH Scale and Corresponding Hydrogen and Hydroxyl Ion Concentrations

pH

[H30+ ] (moles/liter)

[OH–] (moles/liter)

0

10° = 1

10 –14

1

10–1

10–13

2

10–2

10–12

3

10–3

10–11

4

10–4

10–10

5

10–5

10–9

6

10–6

10–8

7

10–7

10–7

8

10

–8

–6

9

10–9

10–5

10

10–10

10–4

11

10–11

10–3

12

10–12

10–2

13

10–13

10–1

14

10–14

10° = 1

10

Acidic

Neutral

Basic

>f

5.5.1 Conversion of Hydrogen Ion Concentration to pH. The pH of a solution can be easily converted to determine the hydrogen ion concentration of the solution and vice versa. Following examples will help students to understand how to do that.

pH of a solution is 5.3, what is the hydronium ion concentration? pH = – log [H3O+] = 5.3 log [H3+O] = – 5.3 = -6 + 0.7 [H3+O] = antilog 0.7 × antilog (–6) [H3O+] = 5 × 10–6 moles/liter 3O

+

concentration of solution is 0.25 M calculate the pH of solution pH = – log [H+] = – log [0.25] = – log [25 × 10-2] = – log 25 – (–2 log 10) = 1.39 – 0.70 = 0.69

Ionization and Ionic Equilibria

63

3.24 × 10–3 M. What is the pH of the solution? pH = – log (3.24 × 10-3) = 3 – log 3.24 = 2.49 +

The H3O ion concentration of weak acids are much lower than their total concentration and are governed by their dissociation constant. The value for [H3O+] in case of weak acid can be calculated from its dissociation constant. e.g.

H3O+ + A–

HA+ H2O

Let the concentration of acid ‘HA’ be ‘C’ moles/liter, Let the dissociation is very small and after applying the law of mass action we get.

[A  ][H3O  ] ...(27) [HA] [At equilibrium concentration of positive and negative charged ions will be same] Ka =

Ka [HA] = [A-] [H3O+] Ka C = [A-]2 or [H3O+]2 [H3O+] =

KaC

= [Ka C]

1/2

pH = – log [Ka C]1/2 = –1/2[– log Ka – log C] pH = ½ pKa – ½ log C

...(28) ...(29) ...(30) ...(31) ...(32) ...(33) ...(34)

Example: What is the pH of N/10 acetic acid solution, the dissociation constant of acetic acid is, Ka = 1.8 × 10–5 = 1/2 [– log (1.8 × 10-5)] – 1/2 log 1 × 10-1 = 1/2 [5 – 1.8] – 0.5 = 1/2 (5 – log 1.8) – 0.5 = 1/2 [5 – 0.25] – 0.5 = 4.75 /2 – 0.5 = 2.88 *Strong acid and strong bases do not follow law of mass action. pH and pOH . The use of pH to designate the negative logarithm of hydronium ion concentration has proved to be so convenient that expressing numbers less than unity in “p” notation has become a standard procedure. The term “p” is used to express the negative logarithm of the term following the “p”. For example, pOH

Physical Pharmacy and Instrumental Methods of Analysis

64

expresses –log [OH–], pKw is –log Kw, and pKa is used for –log Ka. Thus, equations (35) can be expressed as or we can write

pH + pOH = pKw

...(35)

p Ka + pKb = pKw

...(36)

in which pK is often called the dissociation exponent. Electronegativity and dissociation constant: If an electronegative atom is attached to the weak acid its ionization increases e.g. Chloro acetic acid.

5.5.2 Common Ion Effect Common ion effect is observed in weak electrolytes only because they do not dissociate completely when present in aqueous medium. In such solutions when their salt is added, the dissociation of the acid is further diminished. For example dissociation of acetic acid very weak. CH3COOH + H2O

CH3COO– + H3O+

On addition of sodium acetate to a solution of acetic acid the dissociation of acetic acid is suppressed which is already very small. The equilibrium is pushed toward to left hand side. The result is mixture of weak acid and its salt. The H + concentration of a mixture of weak acid and its highly dissociated salt can be calculated as: HA

H+ + A-

Ka = [A–] [N+] / [HA] [H3O+] = Ka [HA] / [A–] This equation has been derived on the basis of the dissociation constant of acid [HA] alone, and it holds good whatever be the source of H+ and A– ions. Now suppose the molar concentration and of weak acid is C1 and we added its salt of molar concentration C2. The dissociation of acid is further reduced while the salt is assumed to be completely dissociated, by convention it follows that the ionic concentration i.e. concentration of A– 2 and concentration of unionized acid i.e. HA as C1 from equation alone Therefore, [H3O+] = Ka

C1 C2

...(37)

Above equation may be expressed in logarithmic form, with the signs reversed – log [H3O+] = – log Ka – log [acid] + log [salt] (Eq. 38) This equation can be rewritten as

pH = pKa – log pK a  log [acid]

Or

[salt] [salt ] pH = pKa + log pK a  log [acid]

...(38)

Ionization and Ionic Equilibria

65

Therefore, H3O+ ion concentration of a mixture of weak acid and its salt is given by the dissociation constant of acid and ratio of concentration of acid to salt. Since pKa is constant, H3O+ is directly related with ratio of salt / acid.

5.6 Buffers Buffers are compounds or mixture of compounds that by their presence in solution, resist change in pH upon the addition of small quantities of acid /alkali. The resistance to change in pH in known as buffer action. If small amount of 0.1N HCl solution is added to water or a solution of NaCl, the pH of water or the salt solution changes considerably from 7 to 3. On the other hand if same amount of HCl of similar concentration is added to a solution containing equal quantities of acetic acid and sodium acetate. The pH is changed only by 0.009 pH units. This is because the base Ac– ties up the hydrogen ion according to reaction. Ac– + H3O+

HAc + H2O

...(40)

(feebly dissociated)

If strong base NaOH is added, acetic acid neutralize the OH– ions as shown in following reaction H2O + Ac–

HAc + OH–

...(41)

5.6.1 Buffer of Weak Acid and Its Salt Buffer mixture of weak acid and its salt e.g. acetic acid and sodium acetate. CH3COO– + H+

...(42)

[CH3COO − ][H3O + ] [CH3COOH ]

...(43)

K a [CH3COOH ] [CH3COO]

...(44)

CH3COOH Ka = [H3O+] =

[acid] [H3O+] = K a [salt ] pH = pK a  log

...(45) [acid] [salt ]

...(46)

pH = pK a  log

[salt ] ...(47) [acid] This is Henderson’s equation. This equation is same as the one derived in common ion effect. What is pH of 0.1 M acetic acid solution before and after enough sodium acetate has been added to make the solution 0.1 M w.r.t. this salt pKa = 4.76 pH of acetic acid = ½ pKa – ½ log C = 2.88

Physical Pharmacy and Instrumental Methods of Analysis

66

pH = pK a  log pH = 4.76 + log

[salt ] [acid] [0.1] [0.1]

pH = 4.76 pH = 4.76 This shows an addition of two pH units i.e. the acidity has reduced to about one hundredth of its value by addition of equal concentration of a salt with common ion that suggest the repression of ionized addition of a common ion.

5.6.2 Buffer of Weak base and its Salt: NH4OH & NH4Cl Basic solution from weak base and their salt are not generally preferred because of their volatility (e.g. NH3), their instability and also due to the dependence of their pH on pKw which is often affected by temperature changes. Buffer equation for weak base and salt. NH4+ + OH–

NH4OH Kb =

[ NH 4 + ][OH + ] [ NH 4 OH]

[OH–] = Kb

...(48)

[ NH 4 OH]

...(49)

[ NH 4 + ]

[OH–] = Kb pK a  log

[base] [salt ]

pOH = pKb – pK a  log We know

[base] log [salt ]

(50) ...(51)

pOH + pH = pKw pH = pKw – pOH Putting value of pOH we get [base] pH = pK w − pK a + log [salt ]

...(52)

This equation shows the dependence of pH of a basic buffer solution of the concentration ration of salt to base and also on the pKw Example: What is the pH of a solution containing 0.1 mole of ephedrine and 0.01 mole of ephedrine HCl per/litre of solution. pKb of ephedrine = 4.64 pH = 14 – 4.64 + log 0.1/0.01 = 9.36 + log 10 = 10.36

Ionization and Ionic Equilibria

67

5.6.3 Buffer Capacity The magnitude of the resistance of a buffer to pH change is referred to as the buffer

...(53)

pH

pH e.g. consider an acetate buffer having 0.1 mole of acetic acid (HAc) and 0.1 mole of sodium acetate (NaAc). HAc + NaOH

NaAc+ H2O,

Now if we add 0.1 mole of NaOH to this solution the concentration of HAc reduce to 0.1– 0.01 mol and that of salt AcNa increase to 0.1+ 0.01 mol. The pH of the solution can be calculated as per the equation pH = pK a  log [salt ] [acid] = 4.76 + log [0.1+ 0.01] 0.11/[0.1– 0.01] 0.09 = 4.285 There is very slight change in pH of the solution and this is the buffer capacity of the solution. Buffer capacity is maximum when ratio of log [salt] / [acid] = 1 i.e.

pH = pKa

If the ratio salt to acid decreases, buffer capacity also decreases. If concentration of buffer species is increased, greater alkaline and acid reserve is produced. That is why buffers are said to have reserve acidity and alkalinity Koppel and Spiro/Vanslyke developed more exact equation of buffer capacity increment of strong base (or acid) to the small change in pH brought about by this pH gives only approximate calculation for buffer capacity however, the equation given below developed by Koppel and Spiro / Vanslyke give more exact calculations K a [ H 3O  ]

( K a  [ H 3O  ])2

...(54)

Where C is total buffer concentration (sum of molar concentration of acid and salt). From this equation buffer capacity at any hydrogen ion concentration can be calculated. e.g. At a [H3O+] ion concentration 1.5 × 10-5. What is capacity of a buffer containing 0.15 mole each of acetic acid and sodium acetate per litre of solution Ka = 1.75 × 10-5 (1.5 × 10−5 ) × (1.5 × 10−5 ) [(1.75 × 10−5 ) + (1.5 × 10−5 )]2

Physical Pharmacy and Instrumental Methods of Analysis

68

5.6.4 Maximum Buffer Capacity Buffer capacity is maximum when pH = pKa [H3O + ]2

max

= 2.303C

max

2.303 C 4 = 0.0576 C ...(56)

...(55)

(2[H3O + ]) 2

Neutralization: The rate of reaction of an equivalent of an acid with an equivalent of a base is called neutralization

In which C is total concentration of buffer species.

 %XIIHU&DSDFLW\ȕ DQG1HXWUDOL]DWLRQ&XUYH Consider a titration curve of strong HCl and weak acid (acetic acid ; HAc) when they are mixed with increasing quantities of alkali (NaOH). The reaction of strong acid and weak acid with strong alkali can be represented as follows: H3O+Cl– + Na+OH– = H2O + H2O + Na+ + Cl– +

–

+

HAc + Na OH = H2O + Na Ac +

–

...(57) ...(58)

–

H3O Cl is hydrated form of HCl in water. Consider neutralization of strong acid with strong base. The reaction between hydronium and hydroxyl ions is usually written as H3O+ + OH- = 2H2O 14

12

10

Excess of base

8

Salt

pH 6

Curve II HAc Buffer region

4

Curve I

2

HCl 0

5

10

15

20

ml of 0.1 N NaOH Neutralization of a strong acid and weak acid by a strong base

Ionization and Ionic Equilibria

69

Since Na+ + Cl– appear on the both sides of the equation (58). They may be base almost proceeds to completion. However reaction of weak acid (HAc) and strong base remains incomplete, since Ac– ion reacts in parts with water that is it hydrolyzes to regenerate the free acid. The neutralization of 10 ml of 0.1 N HCl (curve I) and 10 ml of 0.1 N acetic acid

of NaOH is added the hydrogen ion concentration of 0.1N HCl is 10–1 mol/l and pH of solution is1 assuming that HCl is completely dissociated. The addition of 5ml of 0.1N NaOH neutralizes 5 ml of 0.1 N HCl, leaving 5 ml of original HCl in 10 + 5 =15 ml of solution or [H3O+] = 5 /15 × 0.1 = 3.3 × 10-2 moles per litre, and pH becomes 1.48 When 10 ml of bases is added all the HCl is converted to NaCl, and the pH of the solution (NaCl) is 7. This is equivalence points of the titration (curve I in pH does not change markedly until nearly all the HCl is neutralized. Hence a solution of strong acid has high buffer capacity below a pH of 2. Likewise strong base has a high buffer capacity above pH -12. The buffer capacity of a solution of a strong acid was shown by Van Slyke to be directly proportional to the hydrogen ion concentration + 3O ) The buffer capacity of a solution of a strong base is similarly proportional to the hydroxyl ion concentration – ) pH is a sum of separate capacities. + – 3O ) + (OH )] In case of neutralization of weak acid Acetic acid (HAc) with strong base The pH of solution before O.1 N NaOH is added to 10 ml of 0.1 N HAc is given by; pH = ½ pKa – ½ log C pKa = 4.76, concentration 0.1 N -1 = 4.76 / 2 - ½ log 10 = 2.88 At equivalence point when acid has been completely converted into sodium ions and acetate ion the pH is computed by following equation (i.e. equation for a salt of a weak acid and strong base) pH = ½ pKw + ½ pKa + ½ log C = ½ pKw + ½ Ka + ½ log 0.05 = 7.00 + 2.38 + ½ log (5 × 10–2) = 8.73

Physical Pharmacy and Instrumental Methods of Analysis

70

The concentration of the acid is given as 0.05 because the solution has been reduced to half its original value by mixing it with an equal volumes of base at equivalence point. Between these points (from the start of NaOH to neutralization) sodium ion converts some acid to its conjugate base Ac- to form buffer mixture & pH of the solution in which 5 ml of NaOH is added. pH = pKa + log [salt] / [acid] = 4.76 + log 5/5 = 4.76 The slope of the curve is minimum and buff capacity is maximum at this point where the solution shows smallest pH change per gm equivalent of base added. The buffer capacity of the solution is reciprocal of the slope of the curve at a point is max and slope of the line is minimum at half neutralization, where pH = pKa

5.7 Hydrolysis of Salt Water dissociates to a very small extent into H+ and OH– ions 2 H2O K =

H3O+ + OH–

[H3O + ] + [OH] [H 2 O]2

Kw = [H3O+] [OH–] Pure water is neutral as concentration of H+ = OH– Salts are of strong electrolyte therefore, dissociate completely into positive and negative ions. In some salts anion react with H+ ions resulting in increased OH– ion concentration rending the solution basic and in some salt cation react with OH– ions resulting increased H3O+ ion concentration rending the solution acidic. The phenomenon of the interaction of anion and cation of the salt with H+ and OH ions furnished by water yielding acidic or alkaline or sometimes even neutral solution is known as salt hydrolysis. –

Hydrolysis may be considered as the reverse of neutralization. Neutralization involves consumption of H+ or OH- ions whereas hydrolysis leads to formation of H+ or OH- ions. For convenience salt are divided into 4 categories 1. Salt of strong acid and strong base e.g. KCl, NaNO3 2. Salt of weak acid and strong base e.g. KCN, sodium acetate 3. Salt of strong acid and weak base e.g. NH4Cl, Aniline hydrogen chloride 4. Salt of weak acid and weak base e.g. Ammonium acetate 1. Salts of strong acid and strong base: Salt of strong acid & strong base do not hydrolyze e.g. when KCl or KOH are dissolved in water, they form the acid or base which themselves are highly dissociable, therefore do not hydrolyse.

Ionization and Ionic Equilibria

71

2. Salt of weak acid and strong base: Salt of this category undergo hydrolysis to give alkaline solution e.g. sodium acetate CH3 COO Na ___ CH3 COO– + Na+ CH3 COO– + H+ ___ CH3 COOH The sodium acetate dissociates in acetate ion and sodium ions. The acetate ion furnished react with the hydrogen ion form water and converts to acetic acid. This results in increase in hydroxyl ion concentration and solution becomes alkaline.

5.7.1 Hydrolysis Constant CH3 COO– + Na+ + H2O

CH3 COO H + Na+ + OH–

Sodium ion (Na+) is common on both side therefore can be eliminated from the equation CH3 COO– + H2O ___ CH3 COOH + OHKh (hydrolysis constant) =

[CH3COOH ] + [OH − ] [CH3COOH ]2

Relationship between Kh, Ka & Kw CH3COOH = CH3COO– + H+] Applying law of mass action Kh =

[CH3COOH ] + [H + ] [CH3COOH ]2

...(59)

Water dissociates in hydroxyl and hydrogen ions H2O = H+ + OH– Kw = [H+] [OH-]

We know that

...(8)

Dividing eq. 8 by eq. 59 we get Kw [H3O + ][OH − ][CH3COOH ] = Ka [CH3COO − [OH − ]

...(60)

Right hand side of the equation is hydrolysis constant, therefore the equation can be written as Kw = Kh ...(61) Ka Evidently Kh of salt varies with Ka weaker the acid higher the hydrolysis constant

5.7.2 Degree of Hydrolysis

gone hydrolysis in the attainment of equilibrium)

72

Physical Pharmacy and Instrumental Methods of Analysis

CH3 COO– + H2O

CH3 COOH + OH– 2

Kh = Kh

2

...(62)

2

= Kh /C h /C ...(63) w / Ka C Degree of hydrolysis can be calculated form above equation at any concentration. As temperature effects other properties hydrolysis is also affected by it. With an increase in temperature, hydrolysis increases. Also with increase in dilution, hydrolysis increases. Example Ka = 1.75 × 10-5, Kw = 1008 × 10–14 Kh = Kw / Ka = 1.008 × 10–14/1.75 × 10–5 = 5.76 × 10-10 –10

/0.1

h

–5

= 7.589 × 10 pH of hydrolyzed salt solution [OH– [OH–

h /C

Ÿ (Kh C)1/2 = (C Kw / Ka )1/2 = ½ pKw – ½ log C – ½ p Ka = 14 = 14 – ½ pKw + ½ log C + ½ pKa hC

Or

OH–] pOH pH + pOH pH

...(64)

Example: Calculate p a of acetic acid is given as 1.75 × 10–5 We know that pKw = 14; pKa = – log Ka = – log (1.75 × 10–5) = 4.26 Log C = log (10–2) = – 2

Ionization and Ionic Equilibria

73

Therefore pH = 14 – ½ (14) + ½ (–2) + ½ (4.76) pH of the solution is 8.38

5.7.3 Salt of Weak Base and Strong Acid The example of salt of weak base and strong acid is ammonium chloride. The ionization of ammonium chloride is represented as NH4 Cl

NH4+ + Cl–

In “water, ammonium chloride undergoes almost complete dissociation into NH4+ and Cl– ions. The ammonium ions take up OH– ions furnished by water to form the feebly dissociated base, ammonium hydroxide (NH4OH). The undissociated water further ionizes to maintain the constant value of Kw. This causes increase in the concentration of hydrogen ions and decrease in the concentration of hydroxyl ions. The solution, therefore, becomes acidic. Thus, an aqueous solution of a salt of a weak base arid a strong acid is acidic because of hydrolysis. Hydrolysis Constant. The hydrolytic reaction of ammonium chloride may be represented as NH4+ + Cl– + H2O

NH4OH + Cl– + H+

Since Cl– is common on both sides of the equation, it may be left out and the equation may be rewritten as NH4+ + H2O

NH4OH

Unhydrolysed salt

Free base

Applying the law of chemical equilibrium, we have [NH4OH][H+] Kh = [NH4+]

+

H+ Free acid

...(65)

Kh is already known as hydrolysis constant. Relationship between Kh, Kb & Kw NH4OH

NH4+ + OH–

According following equation should hold good. [NH+][OH–] Kh = [NH4OH]

...(66)

Kb is dissociation constant of base Kw = [H+] [OH–]

We know that

(Eq. 8)

Dividing eq. 8 by eq. 19 we get Kw Ka

=

[H  ][ NH 4 OH] [ NH + ]

...(67)

Physical Pharmacy and Instrumental Methods of Analysis

74

Right hand side of the equation is hydrolysis constant of base, therefore the equation can be written as Kw = Kh Kb

...(68)

Evidently Kh of salt varies with Kb weaker the acid higher the hydrolysis constant Degree of Hydrolysis: Suppose ‘C’ mole/liter be initial concentration of salt concentration of various species at equilibrium is given as NH4+ + H2O Initial Concentration

C

NH4OH + H+

excess

0

0

Therefore, 2

=

Kh =

Kh 2

2

= Kh /C h /C w/

Kb C

...(69)

As in case of salt of weak base and strong acid the degree of hydrolysis can be calculated form above equation at any concentration. Similarly with an increase in temperature & dilution, hydrolysis of the salt increases.

5.7.4 Salt of Weak Acid and Weak Base CH3 COO– + NH4+ + H2O

CH3 COOH + NH4 OH

Although the hydrolysis of salt takes place but the solution remains neutral Because OH– and H+ ions are taken up in equal amounts. Applying the law of mass action Kh =

[CH3COOH][NH 4 OH] [CH3COO  ][NH + ]

...(70)

Also acetic acid and ammonium hydroxide formed in the reaction are feebly dissociated like CH3 COOH NH4 OH

CH3 COO– + H+ NH4+ + OH–

Ionization and Ionic Equilibria

75

Applying the law of mass action we get Ka = [CH3 COO] Kb = We also know

...(71)

[CH3COOH] [NH4+OH–]

H2O = H+ + OH-

...(72)

Dividing equation 8 by equation 70 and 71 gives

[CH3COO H ][NH4OH] Kw = ⇒ Kh ...(73) K a Kb [CH3COO - ][NH 4 + ] (hydrolysis constant) Degree of hydrolysis CH3 COO– + NH4+ + H2O

CH3COOH + NH4OH

C 2α2 α2 = = Kh 2 C (1 − α)2 (1 − α) 2 By convention the denominator is dismissed therefore the equation remains as 2

= Kh

h

Kw K a Kb

5.8 Solubility Product In saturated solution of a salt an equilibrium exists between the excess of the solute and the ion furnished by that part of solute which has gone in solution. For example a sparingly soluble salt AgCl when dissolved in water, a small amount of salt dissociates into silver and chloride ion and the rest remain as solid. The solid salt remain in equilibrium with ion furnished by the dissolved salt. AgCl solid in solution

Ag+ + Cl– (In solution)

Applying the law of chemical equilibrium and writing equilibrium constant aAg + × aCl ...(74) aAgcl The activity of solid is unity by convention therefore above equation 74 becomes K=

Ksp = aAg × aCl

...(75)

Ksp is known as solubility product of the salt and this is constant at given temperature. It is more convenient to use concentration terms than activity. The concentration term of the equation (74) can be written as Ksp’ = [Ag+] [Cl–]

76

Physical Pharmacy and Instrumental Methods of Analysis

Ksp’ is known as concentration solubility product and square brackets represents concentration terms. Since the ionic concentration of sparingly soluble salt are very low and activity of each ion is almost equivalent to its concentration. Therefore Ksp = Ksp’ Ksp = [Ag+] [Cl-] In case of silver sulphate the equilibrium can be written as 2Ag+ + SO42–

Ag2SO4

The solubility of such equation can be written as Ksp = [Ag+]2 [SO42–] Thus the solubility product of sparing soluble salt forming a saturated solution in water is given by the product of the concentration of the ions raised to a power equal to the number of times the ions occur in the equation representing the dissociation of the electrolyte. A general equation for a salt of type MmAn m Mz+ + nAz–

MmAn Where z+ and z- is vacancy

The solubility product of the salt can be written Ksp = [M2+]m + [Az–]n Application of solubility product Determination of solubilities of sparing solubility salt: This can be calculated from equation e.g. if solubility of AgCl is S mol/l Ksp = [Ag+] [Cl-] = S2 S2 = Ksp sp

The solubility of AgCl at given temperature is determined by preparing AgCl solution in presence of KCl of known concentration say b moles/l. The concentration of Ag in determined by EMF and suppose it is a mol per/l. The concentration of Cl– ion is (a+b) i.e. concentration due to silver chloride and potassium chloride. Therefore the solubility product of silver chloride is given by Ksp = [Ag+] [Cl-] = [a] [a + b] Since a & b are known, the solubility product Ksp of silver chloride can be determine. Predicting precipitation reaction: Soluble substances tend to precipitate when the ionic product of the substance (i.e. product of concentration of its ion present in a solution) exceeds the value of solubility product. Therefore from the solubility product of a sparing soluble substance its precipitation can be predicted from the solution under given condition.

Ionization and Ionic Equilibria

77

Judge Yourself 1. 2. 3. 4. 5. 6. 7.

Explain the concept of acid base. How is Arrhenius Theory different from Lewis theory of acids and bases? Explain the term pH and pH scale. How will you determine the pH of acidic solution? Why acidic buffers are preferred over basic buffers? What do you understand by buffer capacity and maximum buffer capacity? What is the Relationship between Kh, Kb & Kw? ‰‰‰

6 Chemical Kinetics Learning Objectives 

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6.1 INTRODUCTION Chemical kinetics is the study and discussion of chemical reactions with respect to reaction rates, effect of various variables, re-arrangement of atoms, formation of intermediates etc. In general reaction kinetics is the study of rate of chemical change and the way

pressure and temperature. Reaction kinetics permits formulation of models for the intermediate steps

p

p pH p

of p © The Author(s) 2023 M. Akhter and M. M. Alam, Physical Pharmacy and Instrumental Methods of Analysis, https://doi.org/10.1007/978-3-031-36777-9_6

79

3K\VLFDO3KDUPDF\DQG,QVWUXPHQWDO0HWKRGVRI$QDO\VLV

80

6.2 Rate and Order of Reaction

dc/dt. Where dc dt.

proportional to the product of the molar concentration of the reactant each raised

1 d [ A] = k[A]a [B]b a dt 1 d [ B] a − = k[A]a [B]b b dt k is proportionality constant known as rate constant or velocity constant the exponents (a + b known as order of reaction.

Rate of reaction (r

−

a

b

…(2)

…(3)

a+b the sum of the exponents of the concentration terms involved in the rate equation. Example: Reaction of ethyl acetate with sodium hydroxide in aqueous solution 3

2H 5

+ NaOH 3 d [CH3COOC 2 H5 ]  dt a

2H5OH

(b order (a + b interested in the rate of disappearance of the reactant species or in rate of appearance

&KHPLFDO.LQHWLFV

81

k → A 

d [A] dt

d [B] = −k[A] dt

…(6)

6.3 Molecularity

and so on.

e.g. 2

H2 + I2

2HI 2

and one of I2 must

come together to form two molecules of HI. complex reactions 2NO + O2

2NO2

apparently looks as termolecular i.e. two NO would collide simultaneously with

2NO N2 O 2 + O 2

N2O2 2NO2

3K\VLFDO3KDUPDF\DQG,QVWUXPHQWDO0HWKRGVRI$QDO\VLV

82

 6SHFL¿F5DWH&RQVWDQW k appearing in the rate law associated with a single step reaction is termed as the VSHFL¿FUDWHFRQVWDQW

rate constant is taken in consideration. Any change in the nature of a step due to

6.5 Units of Basic Rate Constant (i) Zero order rate constant dA moles/liter moles dt second liter second (ii) First order rate constant

k

dA 1 moles/liter dt A second-moles/liter (iii) Second order rate constant

k

k

second

1 second

liter second −1 −dA 1 moles/liter liter = = = dt A 2 second-(moles/liter)2 mole-second moles −1

A is molar concentration of reactant.

6.6 Calculation of Reaction Rate

−

∂[A] ∂[B] ∂[P1] ∂[P2] =− = = 2∂t 3∂t 2∂t ∂t

&KHPLFDO.LQHWLFV

83

6.7 Zero Order Reaction

A

P is written as the equation −

∂A dt

…(7)

k

is done. d

k

At

…(8)

dt t

Or

At

…(9) t

When t

. kt k.

6.7.1 Characteristics of Zero Order Reaction (i (ii

t

i.e tcompletion

(i

time .

6.7.2 Example of Zero Order Reaction

d d

k dt

dt

k

kt

3K\VLFDO3KDUPDF\DQG,QVWUXPHQWDO0HWKRGVRI$QDO\VLV

84

d At

dt t

Or

At

t k

slope of the line. In other words it is time required for one half of the material to disappear or time when A is decreased to ½ A. t½

/k

6.7.3 Apparent Zero Order Kinetics

drug decomposes in solution more of drug is released from the suspended particles.

r Or

k

d

k dt d [A] 1 dt [A]

we may write k

k

d [A] dt

k

apparent zero order

6.8 First Order Reaction Reactions in which rate of reaction depends on concentration one of the reactant in A

products

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dc/dt

kc

(c is concentration left after time t dc/c

k term at time t k dt

ln c

log c log c

k (t

c

c

kt

log c/ c

kt

k

kt

t log c0/c

…(25)

kt

…(26)

order. c Or

e

c c decreases exponentially as a function of

k. let the new unit k Or

k

…(27)

na/n(a x)

t log a/(a – x)

…(28) k

Plotting log c or ln c/c

k.

k . concentration to fall from c to c /2.

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,Q>$@YVWLPH

>$@YVWLPH –2.0

0.2 0.15

t

t t

–3.0 ,Q>$@

t

>$@ 0.1 PRO

t

0.05

N VORSH

t

t

t

t

–4.0

t

t

t –5.0

0.00

5

10

15

20

5 10 7LPH6HF

7LPH6HF

k

2.303 a log t (a  x)

15

20

…(29)

Where a a-x a

t

t½ x

½

k

a 2.303 log t½ (a  (a / 2))

k

2.303 2.303 0.693 × 0.3010 = log 2 = t½ t½ t½

½

nd rd

at these expressions into equation (22) and rearranging to yield In 0.90 t k

proportional to the concentration of a drug.

…(32)

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6.8.1 Examples of Order Rate Kinetics (i) Decomposition of H2O2 in aqueous solution H2O2 Pt → H2O2

2 2

solution and determining the unchanged concentration of H2O2 (ii) Decomposition of ammonium nitrates in aqueous solution 2H2O + N2 NH2NO2 (iii 6H5 2O 6H 5

2

Problem 1:

k

2.303 800 log 20 550

0.01875 day

k

2.303 800 log 0.0187 400

37.1 day

6.9 Second Order Reaction proportional to the concentration of each of the two reactants or to the second power of the concentration of the one reactant is termed as second order reaction. It can

of the concentration of the reactant. A and B P 

d [A] dt

−

d [B] = k[A][B] dt

…(33) x is the concentration

dx dt where dx/dt

k(a – x) (b – x) a – x) and (b – x) are the concentrations of

t

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in the same concentration so that a

–

At

∫0

b

d [A] =–k dt

d [A] dt

k

d[A] [A]2

kdt

2

2

Another method of expression dx = −k (a − x)2 dt on integrating using conditions x t x=x at t=t x t dx ∫0 (a − x)2 = −k ∫0 dt x = kt a(a − x)

t

1 d A = - k ∫ dt [A]2 

…(35)

A

1 t = – kt [A] 0 1 = kt + C [A]

k=

1 1  [A] [A]0

a−x

−

a

t

…(37)

1 1 = Kt  [A]0 [A]

…(38)

t produces a straight line with slope k

.

When the concentrations of the two reactants are different the integration of

Or

b( a  x ) 2.303 log ab a (b  x)

b( a  x ) 2.303 log t ( a  b) a(b  x)

kt

…(39) 6ORSH N

1 >$@

k

...

of log b (a x)/a (b x) against t should yield a straight line with a slope of (a – b)k

1 >$@0 W

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a-x v/s t k is expressed for a second-order reaction are

t

liter/(mole sec) or liter mole sec . Summary Reaction Order

Differential Rate Law

Integrated Rate Law

0

- kt

1st

e - kt

Linear Plot

2nd

Slope of Linear Plot

Units of Rate Constant ·s s

k 2

·s

+ kt

When

6.10 Methods for Determination of Order of a Reaction

6.10.1 Method of Integration (Hit and trial method)

is the one corresponding to the order of reaction. If all the reactants are at the same a/(a-x x/a-x); for second order reactions when concentration of two reactants is same a-b) log b(a-x)/a(b-x) for second order reactions when concentration of two reactants is not same

6.10.2 Graphical Method If the plot of log concentration (a – x a – x) or log b(a – x)/a(b – x reaction follows second order. a-x)2

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6.10.3 Half Life Method t t

a a and a2

t ) and (t )2 t t

and

t( ) /t( )2 log t( ) /t( )2 n

an a2 n a2/a )n a2/a t( ) /t( )2/(a2/a

6.11 Factors that Affect Reaction Rate

6.11.1 Concentration For a reaction to commence the reactant molecules must collide and collide in

rate laws. Rate laws

applies to homogeneous reactions in which all reactants and products are in one phase (solution).

6.11.2 Pressure

i.e reaction rate is therefore expected to increase with increase in pressure in gaseous reaction.

6.11.3 Surface Area

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3

6.11.4 Nature of Reactants

each of these metals is dropped into a concentrated hydrochloric acid solution in

+

to molecular hydrogen gas.

Mg(s) + Mg(s) + 2H+(aq)

2(aq)

Mg2+(aq) + H2(g)

+

2(aq)

+ 2H+(aq) For copper +

+ H2(g)

+ H2(g)

2+

(aq) + H2(g)

——X

+ 2H+(aq) ——X

2(aq)

2+

+ H2(g)

(aq) + H2(g)

) from the acid is reduced

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reduced form and the hydrogen in ionic form (H+ 2+ +

than H

3

+ +

3)2(aq)

3(aq)

+ 2NO2(g) + 2H2O(l)

2+

+

(aq) + 2NO3 (aq)

and NO3-

(aq) + 2NO2(g) + 2H2O(l) 3 and would react + ions 3 is

6.11.5 Temperature

k

Ae

a

Ea a

where A is a constant known as the Arrhenius factor k Ea is the a

4.0

Ea

3.0

ORJN

Ea and 2.0

stronger the temperature dependence of the rate constant.

molecule reactions and radical-radical

the rate decreases as the temperature complex reaction mechanism.

1.0

0

2.4

2.5 7

2.6

2.7

Fig. $SORWRIORJNDJDLQVW7 IRUWKHWKHUPDOGHFRPSRVLWLRQ RIJOXFRVHORJNLVXVHGWR HOLPLQDWHWKHQHJDWLYHYDOXHV DORQJWKHD[LV

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93

across the graph.

6.12 Theories of Chemical Kinetics

6.12.1 Collision Theory

25

28

in case

requirement is met results in reaction which means that the reactants need to collide

the following form.

fi

i/N

N

e

i i

i

i.

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94

molecules leads to reaction. i.e i

the equation leads to the conclusion that K = (PZ) e

i

…(52)

…(53)

A = PZ

Ea as the minimum kinetic energy a molecule Ea = Ei

6.12.2 Transition State Theory

‡

complex ‡ ‡

‡

‡

‡

‡ ‡

k k

‡

(k has units of s )

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k

k

‡

(M

)

where M is molarity and m is the molecularity of the reaction.

6.13 Decomposition and Stabilization of Medicinal Agents

interested reader should consult the original papers for more details.

p p at p

pH 5.85.

reason for chloramphenicol decomposition. Although the rate of degradation was low and independent of p p approximately 3 years. function of p p pH is aqueous solutions.

6.14 Summary

rates.

studies.

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Judge Yourself i

ii

iii)

reaction order and (iv would determine order of the reaction.

life of a second order reaction.

6. Write down the Arrhenius equation relating the rate constant k and the

‰‰‰

7 Catalysis Learning Objectives z

Concept of catalysis

z

Intermediate compound formation theory

z

The adsorption theory

z

Homogenous and Heterogeneous catalysis

z

Autocalysis, catalytic poisioning

z

Application

7.1 Introduction When the addition of a small amount of a chemical substance changes the rate of attainment of chemical equilibrium but the substance itself does not gets consumed or does not undergo any chemical change, then the reaction is called a catalytic reaction. The substance that affects the reaction rate is called a catalyst and the phenomena is known as catalysis. Most of the reactions require energy to move in forwarding direction and catalysts are used to providing alternative mechanism involving a different transition state of lower energy. In reversible reactions, catalyst affects both the rates of the forward and reverse reaction without changing the equilibrium.

speed up the rate of the reaction without being consumed or produced in the process. The catalysis can be traced back to ancient times, for example, the fermentation processes, an example of biocatalysis. As for the industrial catalytic processes, catalytic production of sulfuric acid through lead chamber process was performed in the presence of a mixture of nitric oxides (NO/NO-,) as a catalyst, way back in the eighteenth century. However, catalysis started to play a major impact in the © The Author(s) 2023 M. Akhter and M. M. Alam, Physical Pharmacy and Instrumental Methods of Analysis, https://doi.org/10.1007/978-3-031-36777-9_7

97

Physical Pharmacy and Instrumental Methods of Analysis

98

chemical industry from the beginning of the twentieth century, nowadays more than 95% of chemicals are being produced via a process that includes at least one catalytic step. In 1903, ammonia oxidation on the platinum gauge was developed by Ostwald for nitric acid production. Another major breakthrough was ammonia synthesis with promoted iron in 1908-1914 by Mittasch, Bosch and Haber. The development of shape selective catalysts such as molecular sieves or zeolites for cracking (1964) resulted in the production of exclusively shape selective products. The concept of the catalyst is closely linked to the mechanism of the chemical reaction. The catalyst is capable of accelerating the reaction rate or to change the selectivity of the reaction towards different products with respect to the situation when the reaction occurs in the absence of the catalyst. To explain these concepts, let us consider a general chemical reaction which is described by the following equation k yC + zD ... (1) wA + xB Where A, B and C, D represent the reagents and the products respectively and

r=–

1 d [C] 1 d [D] 1 d [B] 1 d [A] = × =– × = × × dt a dt c d b dt dt

The square brackets is conventionally employed to indicate the concentration of the different species in mol L-1. This can be described by a kinetic law as r1 = k1 [A]a[B]b

...(2)

where a and b represent the reaction order with respect to reagents A and B, k1 is the kinetic constant for the reaction (1). In this case the contribution of the reverse reaction to the overall reaction rate has not considered. This contribution would be of like r-1 = k-1 [C]c[D]d

...(3)

where the minus sign is conventionally used to indicate the reverse process. Under conditions where the contribution of the reverse process to the overall reaction rate cannot be neglected Eq. (3) must obviously be subtracted from Eq. (2) to obtain the net reaction rate. The reaction rate’s dependency on temperature has been well described by Arrhenius and in this book it is discussed in chapter titled chemical kinetics. 'Ea k1 = A × e RT

...(4)

where A is the geometric factor, R the universal gas constant (8.32 J mol-1 K-1), T temperature at which reaction is proceeding in Kelvin (K) and Ea is the activation energy (J mol-1) for the reaction. be overcome by the system so that products are formed in the reaction. That means in order to transform the reactants into products, molecules must overcome the energy

Catalyst

99

barrier represented by the activation energy. The role of the catalyst is therefore to activation energy compared to non-catalyzed system, can be offered, resulting in higher reaction rates under comparable reaction conditions as dictated by Eq (4). In certain reactions, one of the product may itself act as a catalyst, such a phenomena is known as autocatalysis. E.g. as the reaction progresses. This acceleration is due to the presence of Mn2+ ions which are formed during reaction. Autocatalysis: A chemical Thus Mn2+ ions act as catalyst and since it is reaction is said to have generated from the reaction, the phenomena is undergone autocatalysis, or be autocatalytic, if the auto-catalysis. 2KMnO4 + 5H2C2O4 + 3 H2SO4 = 2MnSO4 + K2SO4 + 8H2O + 10CO2 ... (5) very slow in the beginning, but gradually the reaction becomes faster due to the formation of nitrous acid during the reaction which acts as an auto-catalyst.

reaction product itself acts as a catalyst for that reaction. Or Catalysis by an agent formed/produced during a reaction.

In some cases a catalyst decreases the velocity of a reaction, it’s called negative catalyst. Actually negative catalyst often may be changed permanently during a reaction, and should be called inhibitors rather than catalysts. Catalyst is considered to operate in the following way. Catalyst combines with the reactant known as the substrate and forms an intermediate known as complex, which then decomposes to regenerate the catalyst and yield the products. In this way catalyst decreases the energy of activation. Alternately, a catalyst may act by production the free radical such as CH3 Chain reactions are reactions consisting of a series of steps involving free atoms or radicals that act as intermediates.

7.2 Types of Catalyst 7.2.1 Catalyst Poison There are certain substances which decrease or destroy the activity of the catalyst. Such substances are known as catalytic poisons. E.g. arsenic destroys the catalytic activity of the platinum catalyst in the manufacture of sulphuric acid.

7.2.2 Induced Catalysis ordinary conditions, the phenomenon is known as induced catalysis. For examples sodium arsenite solution is not oxidised by air. If, however, air is passed through

Physical Pharmacy and Instrumental Methods of Analysis

100

a mixture of the solution of sodium arsenite and sodium sulphite, both of them undergo simultaneous oxidation. The oxidation of sodium sulphate, thus, induces the oxidation of sodium arsenite

7.2.3 Catalyst Promoter There are certain substances which increase the activity of the catalyst. Such substances are known as catalyst promoters Promoters is a sube.g. Molybdenum acts as a promoter in the manufacture stance which has no catalytic properties o of ammonia by Haber’s process. N 2 + H2

Fe (Catalyst) Mo (promoter)

2NH3

... (6)

Bosch process of preparation of H2, where Cr2O3 acts as a promoter for catalyst Fe2O3.

f its own but when added to a catalyzed reaction enhances the activity of a catalyst.

Catalyst Poison or Promoter does not act like a catalyst.

7.2.4 Autocatalysis When one of the products of reaction itself acts as a catalyst for that reaction the phenomenon is called autocatalysis In autocatalysis the initial rate of the reaction rises as the catalytic product is

Examples of Autocatalysis ethanol of these product acetic acid acts as a catalyst for the reaction. CH3COOC2H5 + H2 COOH + C2H5OH 3 permanganate, manganous sulfate produced during the reaction acts as a catalyst for the reaction. 2KMnO4 + 5H2C2O4 + 3 H2SO4 = 2MnSO4 + K2SO4 + 8H2O + 10CO2

7.3 Characteristics of a Catalyst (i) The catalyst remains unchanged (in mass and chemical composition) in the reaction (Activity of catalyst.) (ii) A small quantity of the catalyst is required e.g. One mole of colloid Pt catalyzes 108L H2O2 (iii) The catalyst cannot does the position of equilibrium (iv) The catalyst does not change the equilibrium constant. But the equilibrium approaches earlier. (v) The catalyst exhibits maximum activity at a particular temperature which is known as optimum temperature.

Catalyst

101

(vi) The catalyst does make impossible reaction to occur and does not initiate a reaction. (vii

7.4 Theories of Catalysis There are two main theories of catalysis 7.4.1. Intermediate compound formation theory 7.4.2. The adsorption theory

7.4.1 The Intermediate Compound Formation Theory Catalysis functions by providing a new pathway of lower activation energy. In homogenous catalysis, it does so by forming an intermediate compound with one of the reactants. The highly reactive intermediate compound then reacts with the second reactant to yield the product, releasing the catalyst. For example C

A+B A+C

AB

... (7)

AC

AC + B

Intermediate

AB + C3

... (8) ... (9)

The activation energies of the reaction 8 and 9 are lower than that of the reaction 7. Hence the involvement of the catalyst in the formation of the intermediate compound and its subsequent decomposition, accelerates the rate of the reaction which was originally very low Example 1. Catalytic oxidation of sulphur dioxide (SO2) in the presence of nitric oxide (NO) as catalyst. NO

2SO2 + O2 2

2SO3

... (10)

2NO2 (intermediate compound) ... (11)

NO2 + SO2

SO3 + NO

... (12)

Example 2. Preparation of diethyl ether, (C2H5)O, from ethanol (C2H5OH) using sulphuric acid as catalyst. C2H5OH + C2H5OH 2

H5OH + H2SO4

C2H5HSO4 + C2H5OH

H2SO4

(C2H5)2O + H2O

C2H5HSO4 + H2O (C2H5)2O + H2SO4

... (13) ... (14) ... (15)

Physical Pharmacy and Instrumental Methods of Analysis

102

Charcoal potential energy

Uncatalysed complex Energy barrier Catalysed complex

Ea

Eac ER

Er

Reactarts Initial state

(A + B)

'G° of reaction Products (C + A)

Final state

Reaction sequence

Fig. 7.1 Graph showing energy of the uncatalyzed and catalysed reaction

7.4.2 The Adsorption Theory This theory explains the mechanism of a reaction between two gases catalysed by a solid. Here the catalyst functions by the adsorption of the reacting molecule on its surface. Generally, four steps can be put forward for heterogenous catalyst. For example, if the reaction is A(g) + B(g)

catalyst

C(g) + D(g)

Step 1 Adsorption of reactant molecules The reactant molecules A and B strike the catalytic surface. They are hold up at the surface by week Van der Waals forces. Step 2 Formation of activated complex The particles of the reactants adjacent to one another join to form an intermediate complex (A – B). the activated complex is unstable. It has Step 3 Decomposition of activated complex The activated complex breaks to form the product C and D. The separated particles of the products hold to the catalyst surface by partial chemical bonds. Step 4 Desorption of products The particles of the products are desorbed or release from the surface. They are stable and can lead an independent existence.

Catalyst

103

7.5 Types of Catalysis 7.5.1 Homogenous Catalysis Homogenous catalysis occurs when the catalyst and the reactants are in the same phase. Acid-Base catalysis is the most important type of homogenous catalysis. A great variety of homogenous catalyst are known, ranging from acids and bases used in organic synthesis to biocatalysts. Some examples of homogenous catalysis acid. H2SO4(l)

CH3COOH (l) + CH3CH2OH (l)

CH3COOCH2CH3 (l) + H2O (l) ... (16)

hydrogen ion concentration. H+

C12H22O11 + H2O

C12H22O11 + C6H12O6

Sucrose

Glucose

... (17)

Fructose

Invert sugar

and ethanol catalysed by hydrogen ions CH3COOH3 + H2O

H+

CH3COOH3 + CH2OH

... (18)

O RHC = CH2 + CO + H2

Co(l) or Rh(l)

R

H

... (19)

O CH3OH + CO

H R

[RHI2(CO)2]

COOR + H2

–

H3C

[Ph(DiPAMP)2]+

NHCOR

OH

... (20)

COOR RH2CC*—H NHCOR

... (21)

7.5.2 Heterogeneous Catalysis In heterogeneous catalysis the catalyst and the reactants are in different phases may be the walls of the container or molecular sieve. The heterogeneous catalysis

Physical Pharmacy and Instrumental Methods of Analysis

104

has emerged as one of the most important tools in industrial research. Enormous quantities of solid-state catalysts are used in petroleum industry for ‘cracking’ which increases the yield of gasoline from petroleum and for ‘reforming’ which causes the rearrangement of the molecular structures and raises the octane rating of gasoline. Since the catalysis occurs at the surface of the solid it is sometimes referred as contact catalysis. The reactant molecules are absorbed at various points or active centers on the rough surface of the catalyst. Presumably, the absorption weakens the bonds of the reactant molecules and lowers the activation energy. The activated molecules then gets converted in the products and diffuse away from the surface. According to Langmuir-Hinshelwood mechanism, a surface reaction can be divided 1. Diffusion of reactants to surface. 2. Adsorption of reactants at the surface. 3. Chemical reaction on the surface. 4. Desorption of products from the surface. 5. Diffusion of products away from the surface. These steps are consecutive. The step with slower rate constant among the others, becomes the rate-determining step. Steps 1 and 5 are usually very fast. Also, steps 2 and 4 are generally faster than step 3 though they may sometimes be slower. It is generally believed that the kinetics of surface reactions can be treated 1. The rate-determining step is the chemical reaction at the surface, i.e., reaction of the adsorbed molecules on the surface, i.e., step 3 given above. 2. Chemisorption plays an important role in heterogeneous catalysis. In chemisorption chemical bonds are formed between the adsorbate and the surface resulting in a monolayer (Langmuir adsorption). 3. The reaction-rate per unit surface area is proportional to 9, the fraction of the surface covered. The value of 9 is given by the Langmuir adsorption isotherm. The reason for heterogeneous catalytic activity is the same as for homogeneous catalysis, i.e., lowering of the activation energy of the rated determining step. It increases the rate at which equilibrium is attained. Examples of heterogeneous catalysis The hydrogenation of ethene using hydrogen and a nickel metal catalyst is a good example. CH2= CH2 (g) + H2 (g)

Ni(s)

CH3— CH3 (g)

... (22)

Platinum, palladium and rhodium are common heterogeneous catalyst which acts as catalytic converter. 2CO + 2NO

Pt/Pd/Rh

CO2 + N2

... (23)

Catalyst

105

Table 7.1: comparison of homogenous and heterogeneous catalysis Property

Homogenous

Heterogeneous

Catalyst recovery

Easy and cheap

Selectivity

Excellent to good

Good to poor

Thermal Stability

Poor

Good

7.5.3 Enzyme Catalysis Enzymes are the biological catalysts. Living organisms carry out thousands of chemical reactions which take place in dilute solution at ordinary temperature and pressure. For example they can use small molecules to assemble complex biopolymers such as proteins and DNA. Organisms can produce molecules that combat bacterial invaders. They can break down large, energy-rich molecules in many steps to extract chemicals energy in small portions to drive their many activities. Enzymes act with great speed and precision, they increase the rate of chemical reactions by lowering the free energy barrier that separates the reactants and products. Enormous variety of chemical reactions within a cell are mediated by enzymes 6

– 1012 pH, ...)

Table 7.2: Catalytic Power of some enzymes Enzyme

Nonenzymatic reaction rate ( s–1)

Enzymatic reaction ( s–1)

Rate enhancement

Carbonic anhydrase

1.3 × 10–1

1 × 106

7.7 × 106

Chorismate mutase

2.6 × 10–5

50

1.9 × 106

Triosphosphate isomerise

4.3 × 10

4300

1.0 × 109

Carboxypeptidase A

3.0 × 10–9

578

1.9 × 1011

AMP nucleosidase

1.0 × 10–11

60

6.0 × 1012

–13

95

5.6 × 1014

Staphylococcal nuclease

–6

1.7 × 10

Source: Radzika A and Wolfenden R, Science 267, 91, (1995) Table 7.3: &ODVVL¿FDWLRQRIHQ]\PHVDFFRUGLQJWRUHDFWLRQW\SH Class Hydrolases

Type of reaction catalysed

Remark

Hydrolysis reactions hydrolysis of ester bonds. Exohydrolase enzymes cut the molecules at the end of the chain, and endohydrolase do so in the middle of the chain.

Physical Pharmacy and Instrumental Methods of Analysis

106

Oxidoreductases

Oxidation reduction reactions

Transfer of electrons from one molecule (the reductant) to another (the oxidant). These reactions are vital to life for their role in essential metabolic processes like glycolysis.

Transferases Transfer of functional group such as methyl second molecule is called the acceptor Isomerases

Isomerization

Lyases

Group elimination to form double bonds

Lysis reactions are the kind of elimination reactions that are not hydrolytic or oxidative. The lyases are also sometimes called synthase enzymes

Ligases

Bond formation coupled with ATP hydrolysis

Ligation means joining together. Chemical potential energy is usually required for this reaction to occur, so it is often paired with the hydrolysis of a diphosphate bond.

7.6 Catalytic Poisoning Catalytic poisoning means partial or total deactivation of a catalyst by exposure to or interaction with other chemical compounds. Very often a heterogeneous catalyst is rendered ineffective by the presence of small amount of impurities in the reactants. Sometimes poisoning may be desirable when it results in improved selectivity e.g. Lindlar’s catalyst A substance which destroys the activity of the catalyst to accelerate a reaction, is called a poison and the process is called catalytic poisoning. Poisoning involves compounds which bonds chemically to the active surface sites of a catalyst. There are two ways by which poisoning may happen (1) the total number of catalytic sites decreases or the part of the total surface area that has the capability of promoting reaction reduces, (2) the average distance that a reactant molecule must diffuse on the catalyst before undergoing reaction may increase. Examples of catalytic poisoning 1. The platinum catalyst used in the oxidation of sulphur dioxide (contact process), is poisoned by arsenic oxide (As2O3) SO2 + O2 = 2SO3 ... (24) 2. The iron catalyst used in the synthesis of ammonia (Haber Process) is poisoned by H2S. N2 + 3H2 = 2NH3

7.7 Applications of Catalysis of industrial processes.

... (25)

Catalyst

107

(i) pollution control (air and waste streams; stationery and mobile) (ii) clean oxidation/halogenations processes using O2, H2O2 (C2H4O, C3H6O) (iii) avoiding toxic chemicals in industry (HF, COCl2 etc.) (iv) fuel cell generation. NO) that are the result of combustion of fuel in vehicle engines. breakdown of ozone. These radicals are formed by action of UV radiation on CFCs. (i) natural gas processing (ii (iii coating, surfactants) those of heavy industry.

Judge Yourself 1. 2. 3. 4. 5.

What do you understand by catalysis, autocatalysis, and promoters? How is homogeneous catalysis different from heterogeneous catalysis? How does catalytic poisoning reduces catalytic activity? Discuss theories of catalysis. What types of reactions are catalyzed by enzymes? Name different types of enzyme catalysed reactions. 6. What are the different steps involved in heterogeneous catalysis? ‰‰‰

8 Electrochemistry Learning Objectives z

Concept of electrolysis

z

Differences between metallic and electrolytic conductance

z

Laws of electric current

z

Electrolytic conductance and its Mechanism

z

Factors affecting electrolytic conductance

z

Conductivity cell and types of Conductivity cell

z

Applications of electrochemistry Objectives

8.1 Introduction Electrochemistry is the study of the interchange of chemical and electrical energy i.e. transformation of electrical energy into chemical energy and vice-versa. It deals with the relationship between electrical, chemical phenomena and the laws of interaction governing them. The study of electrochemistry is important in many There are two main processes of electrochemistry (i) where electrical energy is used to cause chemical change e.g. electrolysis of water to obtain H2 and O2. The equipment is called electrolytic cell. (ii) Where electric energy is generated from chemical reactions and the process is called the electromotive process. The equipment is called electrochemical cell. Electrochemistry mainly deal with the conductance in aqueous solutions. Conductance of a solution is its ability to pass an electric current. In solutions the current is carried by cations and anions in contrast to metals where it is carried by electrons.

© The Author(s) 2023 M. Akhter and M. M. Alam, Physical Pharmacy and Instrumental Methods of Analysis, https://doi.org/10.1007/978-3-031-36777-9_8

109

Physical Pharmacy and Instrumental Methods of Analysis

110

 'H¿QLWLRQRI7HUPV 8.2.1 Conductance (c) is reciprocal of resistance. C =1/R expressed in ohms or mhos.

N.

R =1/k l/a k =1/R l/a ohm–1cm–1 If l =1 cm and a =1 square centimeter then

solution of length 1 centimeter and area of 1 square centimeter cross section and is exposed in mhos / cm.

8.2.2 Resistance Resistance conductor. Resistance (R) of a conductor is directly proportional to length (l) and inversely proportional to its area (a) of cross section.

R= If l =1 cm and a =1 square centimeter respectively conductor having a length of 1 cm and area of cross section of 1 square centimeter.

8.2.3 Conductivity In solution or aqueous medium electricity is conducted by ions. Conductivity is the ability of a solution to pass current. The conductivity of a solution changes with changes in temperature.

C = conductance (S), where G = 1/R –1

)

Electrochemistry

111

8.2.4 Resistivity Resistivity is the reciprocal of the conductivity and is measured in ohm cm. It is generally used to measure the conductivity of ultrapure water.

8.2.5 Molar Conductance

electrodes which are 1 cm apart. It is denoted by µ. It units are ohm–1 cm2 mol–1.

concentration of the solution in g mole per litre, then It is conducting power of all the ions produced by one mole of an electrolyte in a given solution m.

8.2.6 Equivalent Conductance Equivalent conductance is the conductance of solution containing 1 gm equivalent 1 cm apart. It is denoted by v where ‘Q’ is volume in cc containing 1 gm equivalent of electrolyte dissolved in it. It is measured in ohms–1 or mhos. Equivalent conductance = (Molar conductance)/n where

n = (Molecular mass)/(Equivalent mass)

 7\SHVRI&RQGXFWRUV Following are the various types of conductors: (a) Metallic or electronic: In metallic conductors electrons are carries of current. (b) Electrolytic or ionic: In case of electrolytic or ionic conductors ions are the carriers of current. Differences between metallic and electrolytic conductance Metallic conductance

Electrolytic conductance

Conductance is carried by electrons i.e. due to migration of electrons

Conductance is carried by ions i.e. due to migration of ions. In electrolytic solution of ions migrate to different electrodes.

No chemical change is involved

The decomposition of the conductor takes place.

Conductance is inversely related to temperature i.e. with increase in temperature the conductance decreases

Electrolytic conductance is directly related to temperature i.e. conductance increases with increase in temperature

There is no transfer of any matter.

This involves the transfer of matter

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112

 /DZVRI(OHFWULF&XUUHQW  2KPV/DZ Ohms law (proposed by G.S. Ohms) is more related to metallic conductors. It states

and inversely proportional to resistance (R) of the conductor. i.e. Unit of current is amperes and of resistance is ohms C E CR = E C = E/R R – constant called resistance

Both metallic and electrolytic conductors follow Ohm’s law.

 )DUDGD\CV/DZRI(OHFWURO\VLV Michael Faraday described two important laws of electrolysis. The relationship between the quantity of electric charge passed through an electrolyte and the amount of the substance deposited at the electrodes was presented by Michael Faraday in 1834, in the form of laws of electrolysis.

8.4.2.1 First Law It states that the amount of any substance that in deported or liberated at an electrode is directly proportional to the quantity of electricity (Coulombs) passed through the electrolyte. If ‘m’ be the mass of the substance deposited by passing Q coulomb of charge, then according to the law, we have the relation: m-mass in gm of substance deposited m = ZQ Z is a constant of proportionality and is known as electrochemical equivalent

if we put Q = 1 (coulomb) Z=m

Electrochemical equivalent of any substance is the amount of the substance deposited on passing of 1 coulomb through its solution.

Electrochemistry

113

8.4.2.2 Second Law the mass of the substances deposited at the respective electrodes are proportional to their respective chemical equivalent or equivalent weight. m1/m2 = E1/E2 For example if same quantity of electric current is passed through two voltametres containing solutions of CuSO4 and AgNO3 with copper and silver and in the second, silver will be deposited. (Mass of copper) (Mass of silver)

=

(Equivalent mass of copper) (Equivalent mass of silver)

These masses are in the ratio of their equivalent masses. From these masses, the amount of electric charge required to deposit one equivalent of copper or silver can be calculated.

z1/z2 = E1/E2

8.4.3 Kohlrausch’s Law

irrespective of the nature of the ion with which it is associated. The equivalent constituent ions, i.e., anions and cations. Thus, /

-

+

are the ionic conductance of anion and cation + respectively. The ionic conductances are proportional to their ionic mobilities.

+

= ku+

–

= ku–

114

where P+ and P–

Physical Pharmacy and Instrumental Methods of Analysis

i.e., one Faraday. Ionic mobility = (Ionic velocity)/(Potential gradient) = (Ionic velocity (cm/sec)) / (Potential gradient (volt)/ electrode Separation) Thus, assuming that increase in equivalent conductance with dilution is due to increase in the degree of dissociation of the electrolyte; it is evident that the electrolyte achieves the degree of dissociation as unity when it is completely ionized proportional to the degree of dissociation. Thus, Degree of dissociation ( ) = / / (/ )

= (Equivalent conductance at a given concentration)/(Equivalent

8.4.4 Electrolytic Conductance solubility product, dissociation constant and other properties of electrolyte solution. Conductance is an additive property of a solution depending on all the ions present restricts the quantitative analytical use of this technique to situation where only a single electrolyte is present or where the total ionic species need to be ascertained. In these situation however conductance measurement are highly sensitivity. In conductometric titration the solution remain neutral electrically during the titration as the conductivity involves the migration of both types of ions i.e. cation and anions. The ability of ions to transport charge depends on the mobility of the ion. The mobility of an ion is essentiality its rate of movement through the solution under gradient. The mobility of an ion is affected by factors such as the charge, size, mass and extent of solvation. The measurement of conductance of a solution is known as conductometry and is used in direct and indirect methods of physicochemical analysis. It is widely used in complexometric, precipitation titrations and chemical kinetics etc. Most conductive solutions measured are aqueous solutions, as water has the capability of stabilizing the ions formed by a process called solvation. of ions when potential difference is applied between two electrodes. The cations move toward negatively charged electrode i.e., cathode whereas anions move towards positively charged electrode anodes. Since ions are charged particles of

in an electrolytic solution results in chemical reaction at the electrodes.

Electrochemistry

115

 0HFKDQLVPRI(OHFWURO\WLF&RQGXFWDQFH Electrolytic conductivity means ability of ions to carry an electric current in an electrolytic solution. The electric current is carried by the migration of ions under Exception to this occurs only under abnormal conditions e.g. high voltage or high frequency current. For an applied EMF (E) maintained constant but at a value that the electrodes immersed in the electrolyte will vary inversely with the resistance of the electrolytic solution (R). 1/R =k a/d a – area of electrode d – Distance between them The electric conductance of a solution is summation of contribution from all the ions present, depending upon there number per unit volume and the velocities with

the current per c.c. solution). However, to express the ability of individual ion to conduct the current, a function equivalent conductance in used. In above equation ‘a’ is area of two electrodes set 1 cm apart and holding between them a solution containing one equivalent of solute. If Cs is the concentration of the solution in gm equivalent per liter then volume of solution in c.c per equivalent

each ion contributes its part to the total conductance + +

)

-

-

dilution

generally lower the ionic mobilities. The conductivity of a solution is quite temperature dependent and increase of temperature invariably results in increase in ionic conductance and for most ions this amounts to about 2% per degree rise. For precise work conductance cells must be immersed in a constant temperature bath. For relative measurement as titration the conductance cell need only attain thermal equilibrium with its surrounding before proceeding with conductance measurement.

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116

7DEOHConductivity of various anions and cations in water at 298 K Cation

Conductivity (Ohm-1 cm2)

H+

Conductivity (Ohm-1 cm2)

Anion OH-

+

Br+

NH4

73.4

Na+

78.4

-

Cl

NO3-

2+

½ Ba

½ SO

71.44

4-

8.6 Conductivity Cell Parts of a voltaic or a galvanic cell: Anode—the electrode where oxidation occurs. After a period of time, the anode may appear to become smaller as it falls into solution. Cathode—the anode where reduction occurs. After a period of time it may appear larger, due to ions from solution plating onto it. Inert electrodes—used when a gas is involved OR ion to ion involved such as Fe3+ being reduced to Fe2+ rather than Fe . Made of Pt or graphite. Salt bridge—a device used to maintain electrical neutrality in a galvanic replaced with a porous cup. Voltmeter—measures the cell potential (emf) usually measured in volts. A conductivity cell is generally made of pyrex glass and contains platinum electrodes of one square centimeter area separated by a distance of one centimeter dipped in an electrolytic solution. Between the two electrodes exactly 1 cc of solution is covered. The resistance between the two electrodes is measured which gives the

 7\SHVRI&RQGXFWLYLW\&HOO Water Flow

a R1

Electric current

Electrodes

Conductivity Cell

R2

b

c

D

Processor R4

R5 d S

Wheatstone bridge

Electrochemistry

117

A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a Bridge circuit, one leg of which includes the unknown component. It was invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. a K

A R1

R D

C

R3

+ D

B

VG

b

c

d

Rx

R2 C

S

is the unknown resistance to be measured; R1, R2 and R3 are x resistors of known resistance and the resistance of R2 is adjustable. If the ratio of the two resistances in the known leg (R2/R1) is equal to the ratio of the two in the unknown leg (Rx/R3), then the voltage between the two midpoints (B & D) will . If the g bridge is unbalanced, the direction of the current indicates whether R2 is too high or too low. R2 is varied until there is no current through the galvanometer, which then reads zero. Detecting zero current with a galvanometer can be done to extremely high accuracy. Therefore, if R1, R2 and R3are known to high precision, then Rx can disrupt the balance and x are readily detected. At the point of balance, the ratio of R2/R1= Rx/R3 Therefore, Rx = (R2/R1) *R3 Alternatively, if R1, R2 and R3 are known, but R2 is not adjustable, the voltage value of Rx setup is frequently used in strain gauge and resistance thermometer measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage. In case of electrolytes: The resistance should be of about the same order as that of the solution under examination in the cell. The sliding contact is moved along wire AB until a point of minimum sound in the head phone is detected. At this stage Resistance of the solution length XB = Resistance R XA Three of them are known the fourth can be calculated. The conductance of a solution is measured by applying a high frequency (low Hz) alternating voltage to a Wheatstone bridge. The conductivity cell (C) being

Physical Pharmacy and Instrumental Methods of Analysis

118

placed in one arm and a standard resistance R1 another arm the two other arms of the bridge consists of a slide wire calibrated in terms of the ratio of the resistance (R2 and R3) tapped off at all possible setting of this sliding contact. This contact is adjusted until the sound from head phone (H) is a minimum. Resistance box R

Conductivity cell

X T

A

B

Telephone head Thermostat Secondary

Test solution

S Primary

Induction coil

Then knowing the R,XA and XB resistance conductance of solution can be calculated.

8.6.2 Cell Constant

only if the electrodes are exactly 1 cm2 in area and 1 cm apart. This is not usually the case. The value of the conductance obtained will therefore have to be multiplied cell constant. l/a* conductance Hence, the conductance measured in a cell has to be multiplied by a factor l/a l/a is cell constant where l is distance between two electrodes in cm and a is area of cross section of electrode in cm2. Therefore unit of cell constant is cm–1 and in SI m–1 Instead of determining cell constant from the dimension of the cell it is more conductance at a given temperature. For this purpose standard solution of potassium

7DEOH6SHFL¿F&RQGXFWDQFH6P–1) of various KCl solutions at different temperatures

Concentration 1M

0°C

18°C

25°C 11.173

Electrochemistry

119

in ‘c’ then

N Cell constant =

Measured conductance

can be easily obtained from its measured conductance.

 )DFWRUV$IIHFWLQJ(OHFWURO\WLF&RQGXFWDQFH  1DWXUHRI(OHFWURO\WH The conductance of an electrolytic solution is due to ions and therefore depends upon the number of ions present in the solution. Greater the number of ions in the solution the greater is the conductance. The number of ions produced by any electrolyte depends on its nature (weak or strong). The strong electrolytes dissociate almost completely in the solutions whereas weak electrolytes do not. Therefore strong electrolytes have more conducting power than weak electrolytes.

 &RQFHQWUDWLRQRIWKH6ROXWLRQ The molar conductance of strong as well as weak electrolyte increases with increase in dilution. However the variation is different for strong electrolyte and weak electrolyte.

 7HPSHUDWXUH Electricity is carried through the solution of an electrolyte by migration of ions. With increase in temperature the conductivity of an electrolyte increases because of increased mobility of ions in the solution.

 $SSOLFDWLRQV  'HWHUPLQDWLRQRI'HJUHHRI'LVVRFLDWLRQRI:HDN(OHFWURO\WH

a =

m

o m

m

º m

Molar conductance and can be found experimentally

Physical Pharmacy and Instrumental Methods of Analysis

120

 %DVLFLW\RI2UJDQLF$FLGV The basicity of organic acids is calculated from the relationship suggested by Ostwald – 32 B = 32

neutralized by adding concentrated acid using suitable indicator. When neutralization dilution. The equivalent conductance in then measured and the basicity in calculated.

 'HWHUPLQDWLRQRI6ROXELOLW\DQG6ROXELOLW\3URGXFWRI 6SDULQJO\6ROXEOH6DOW Determination of solubility of sparingly soluble salts like AgCl, BaSO4, PbSO4etc. cannot be done by chemical method very accurately as they are generally regarded as insoluble. The solubility of such salts can be determined accurately by using can be done by repeatedly washing the salt with conductivity water to remove any soluble impurity and then suspending it in conductivity water. It is warmed and settle down. The conductance is measured as usual. The conductance of the water used for the preparation of solution is also determined. The difference between the to dissolved salt. Suppose solution of AgCl, is x mole/cm3 Concentration of AgCl in solution in c = x mol m–3 The molar concentration of solution will be given as m

= k/c = (k/x) S m2mol–1

Since the solubility of AgCl is extremely low the minimum quantity that in

mAgCl

Ag+

+

– Cl

–4

(k/x) S m2mol–1

–4

S m2mol–1

–4

S m2mol–1

k S m2mol–1 x =

–4

S m2mol–1

k m–3mol =

–4

Electrochemistry

121 –4

m–3mol

–4

–3

gm dm .

 ,RQLF3URGXFWRI:DWHU Water is known to be slightly dissociated as H2O H+ + OH– According to law of chemical equilibrium [H+] + [OH –] = C H2O = [H+] + [OH–] is known as ionic product of water w w

i.e. the product of concentration of [H+] + [OH–] ions expressed in molar /dm3 w

Sm–1 3 –1

Sm

of water will be

3

Sm2

The molecular conductance of water, if it completely ionizes to give one mole of [H+] and [OH–] ion is sum of molar conductance of [H+] and [OH–] ion. –4 –4 Molecular conductance of [H+] and [OH– Sm2 –1 mol –4 -4 -4

Sm2 mol–1

Sm2 mol–1

Sm2 mol–1

It follow that when the molar conductance of 1 m3 of water is The number of molecules of H+ions /m3 will be –4 –4

mol m–3

 'HWHUPLQDWLRQRI7RWDO'LVVROYHG6ROLGV7'6 LQ:DWHU

cations and anions in water. Ions and ionic compounds making up TDS usually calcium, magnesium, sodium, and potassium. The Total dissolved solids in water can be easily determined by using conductivity cell. It consists in dipping the cell in water to be tested and consists of platinum electrodes, coated with platinum black bridge and the conductance is measured directly. The bridge uses a low voltage through conductance cells are also available.

122

Physical Pharmacy and Instrumental Methods of Analysis

The resistance of the liquid between the electrodes is measured, which is converted into conductivity using the relation. l = distance between electrodes (cm); a = surface area of electrodes (cm2); R = resistance (Siemens, S) Since the conductivity is highly temperature dependent all conductivity measurements are done in thermostat. The conductivity cell is calibrated by using a solution of known conductivity and measurements are done for samples. The following approximate equation gives the total concentration of salts with a reasonable accuracy. –1

)

-XGJH