pH and Buffer Theory-A New Approach

H. Rilbe Chalmers University of Technology Gothenburg, Sweden

Wiley Series in Solution Chemistry

Volume 1

JOHN WILEY & SONS Chichester • New York • Brisbane • Toronto • Singapore

I

Contents

Preface xi Series Preface xv Acknowledgements xvii Notation xix

1 Monoprotic Weak Acids and Bases and Their Salts with Strong Bases and Acids 1

Summary 1 1 pH — A Controversial Physico-chemical Concept 1 2 Thermodynamic and Stoichiometric Dissociation

Constants 3 3 Titration Curves 6 4 Buffer Power 11 5 Buffer Range 12 6 The pH of Solutions of Monoprotic Weak Acids

and Bases 13 7 The pH of Solutions of Salts of a Weak Acid and a Strong

Base and Vice Versa 19 8 The pH of Buffer Solutions 22

8.1 Exact Equations 22 8.2 Henderson's Equation 23

2 Biprotic Weak Protolytes and Their Salts with Strong Acids and Bases 27

Summary 27 1 Introduction 27 2 Titration Curves 30 3 Buffer Power 31

3.1 General Equation 31 3.2 Intrinsic and Titration Dissociation Constants 36

vi CONTENTS

3.3 Existence and Locations of Buffer Power Maxima . 37 3.4 Magnitudes of Maxima and Minima 38

4 Buffer Range 39 5 Ionic Strength 39 6 The pH of Solutions of Biprotic Protolytes 43

6.1 Biprotic Acids 43 6.2 Biprotic Bases 45 6.3 Biprotic Ampholytes 47

7 The pH of Solutions of Salts of Biprotic Protolytes 49 7.1 Monovalent Salts 49 7.2 Bivalent Salts 50

8 Buffer Solutions of Biprotic Protolytes 54 8.1 Deduction from the Mean Valence 54 8.2 Deduction from the Electroneutrality Equation 54 8.3 Interpretation of Equation (83) 56

3 Binary Mixtures of Monoprotic Weak Protolytes 57

Part 1 Buffer Solutions Composed of One Monoprotic Weak Acid 57 and One Monoprotic Weak Base Summary 57

1 Introduction 57 2 Basic Equations 58 3 Approximate Solutions 59

3.1 Solutions Outside the Neutral Range 6 < pH < 8 . 59 3.2 Solutions more Concentrated than 0.01 M at a pH 60

Between 4 and 10 3.2.1 Buffer Power 60 3.2.2 Buffer Range 62 3.2.3 Ionic Concentrations and Degree

of Hydrolysis 63 4 Accurate Analysis 65

4.1 The pH of Solutions of the Neutral Salt 65 4.1.1 Salts Isoprotic Below pH 6 65 4.1.2 Salts Isoprotic Above pH 8 65 4.1.3 Salts Isoprotic Between pH 6 and 8 67 4.1.4 Comparison with Previous Literature 68

4.2 Buffer Power in the Case of Non-Negligible Water Ion Concentrations 69

Part 2 Binary Equimolar Mixtures of Two Monoprotic Protolytes 73

Summary 73 1 Introduction 73

CONTENTS v i i

2 Titration Curve 74 3 Consequences Concerning Intrinsic Dissociation Constants 76

4 Tri- and Polyprotic Protolytes and Their Salts with Strong Acids and Bases 79

Summary 79 1 Introduction 79 2 Basic Equations for a Triprotic Weak Acid 80 3 Titration Curves 80 4 Buffer Power 81

4.1 General Equation 81 4.2 Intrinsic and Titration Constants 82 4.3 The Case of Symmetry 83 4.4 The Case of Great Asymmetry 85 4.5 The Case of Moderate Asymmetry 88 4.6 Multiprotic Weak Protolytes 88

5 Ionic Strength 91 5.1 Buffers of Triprotic Weak Acids with Monovalent

Strong Base 91 5.2 Buffers of Triprotic Weak Bases with Monovalent

Strong Acids 91 6 Residual Charges at the Isoprotic Points 93 7 The pH of Solutions of Triprotic Protolytes 94

7.1 Triprotic Acids H3A 94 7.2 The Ampholyte H2Am 98 7.3 The Ampholyte HAm 99 7.4 Triprotic Bases 100

8 The pH of Solutions of Monovalent Salts 101 8.1 Monovalent Salts of Triprotic Acids 101 8.2 Monovalent Salts of Ampholytes НгАт 101 8.3 Monovalent Salts of Ampholytes HAm 103 8.4 Monovalent Salts of Triprotic Bases 103

9 The pH of Solutions of Bivalent Salts 104 9.1 Bivalent Salts of Triprotic Acids 104 9.2 Bivalent Salts of Ampholytes H2Am 104 9.3 Bivalent Salts of Ampholytes HAm 105 9.4 Bivalent Salts of Triprotic Bases 106

10 Trivalent Salts of Triprotic Acids and Bases 107 11 Survey of the Isoprotic Points of Triprotic Protolytes, and

Salts of Polyprotic Acids and Bases 107

5 The Debye-Hückel Theory for Strong Electrolytes 109

Summary 109

viii CONTENTS

1 Historical 110 2 The Principle of Electroneutrality for Atomic

Volume Elements 110 3 The Potential in the Electric Field Around an

Individual Ion I l l 4 The Concept of Ionic Strength 114 5 The Activity Factor of an Individual Ion 115 6 Numerical — Güntelberg's Equation 116 7 The Activity Factor of a Binary Electrolyte 117 8 Explicit Approximate Expressions for the Mean Activity

Coefficient 120 9 Correction to Curves Calculated on the Basis of Constant

Dissociation Constants 121 10 Guggenheim's and Davies' Extensions of the Range of

Applicability of the Debye-Hückel Theory 123

6 Buffer Power and the Titration Curve of Water 125

Summary 126 1 The Ion Product of Water 126 2 The Buffer Power of Water 126

2.1 Basic Equations 126 2.2 The Buffer Power in Moderately Acidic Media 127 2.3 The Buffer Power in Strongly Acidic Media 130 2.4 Activity Coefficients in HCl Solutions from

Guggenheim's Equation 134 2.5 The Buffer Power in Moderately Alkaline Media .. 135 2.6 The Buffer Power in Strongly Alkaline Media 136 2.7 Activity Coefficients in NaOH Solutions from

Guggenheim's Equation 139 3 The pK Values of Water 139 4 The Titration Curve of Water 143

7 Experimental Determination of pK and ApA" Values as well 147 as Isoprotic Points

Summary 147 1 Introduction 148 2 Use of Henderson's Equation 149

2.1 pA"' Values Between 4 and 10 149 2.2 Extension to Low and High pK' Values 149 2.3 Conversion to Thermodynamic Dissociation

Constants 151 2.3.1 Monoprotic Protolytes 151

CONTENTS ix

2.3.2 Biprotic Protolytes 151 2.3.3 Triprotic Protolytes 152

3 Experimental Determination of ApA"' Values 153 3.1 Biprotic Protolytes 153 3.2 Triprotic Protolytes 160 3.3 Conversion to Thermodynamic ApK Values 161

4 Experimental Determination of Isoprotic Points 161 4.1 Historical 161 4.2 Biprotic Protolytes 162

4.2.1 Conversion of Stoichiometric to Thermody­namic Isoprotic Points 163

4.2.2 The Minimum Concentration Required to Measure an Isoprotic Point and Correction to the Same 163

4.2.3 Comparison with Bates' Equation 166 4.2.4 Experimental Procedure 167

4.3 Triprotic Protolytes 168 4.3.1 The Ionic Strengths at the Isoprotic Points 169 4.3.2 Conversion to Thermodynamic Isoprotic

Points 170 5 Simultaneous Determination of Isoprotic Points and ApK; 111

Values From Titration Data 5.1 Integral Contra Differential Methods 171 5.2 Biprotic Protolytes 172

Appendix 177 References 183 Author Index 187 Subject Index 189