pH and Buffer TheoryA 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
Series Preface
Acknowledgements
Notation
1
2
xi
xv
xvii
xix
Monoprotic Weak Acids and Bases and Their Salts with
Strong Bases and Acids
Summary
1 pH — A Controversial Physico-chemical Concept
2 Thermodynamic and Stoichiometric Dissociation
Constants
3 Titration Curves
4 Buffer Power
5 Buffer Range
6 The pH of Solutions of Monoprotic Weak Acids
and Bases
7 The pH of Solutions of Salts of a Weak Acid and a Strong
Base and Vice Versa
8 The pH of Buffer Solutions
8.1 Exact Equations
8.2 Henderson's Equation
19
22
22
23
Biprotic Weak Protolytes and Their Salts with Strong Acids
and Bases
Summary
1 Introduction
2 Titration Curves
3 Buffer Power
3.1 General Equation
3.2 Intrinsic and Titration Dissociation Constants
27
27
27
30
31
31
36
1
1
1
3
6
11
12
13
CONTENTS
vi
4
5
6
7
8
3.3 Existence and Locations of Buffer Power Maxima .
3.4 Magnitudes of Maxima and Minima
Buffer Range
Ionic Strength
The pH of Solutions of Biprotic Protolytes
6.1 Biprotic Acids
6.2 Biprotic Bases
6.3 Biprotic Ampholytes
The pH of Solutions of Salts of Biprotic Protolytes
7.1 Monovalent Salts
7.2 Bivalent Salts
Buffer Solutions of Biprotic Protolytes
8.1 Deduction from the Mean Valence
8.2 Deduction from the Electroneutrality Equation
8.3 Interpretation of Equation (83)
3 Binary Mixtures of Monoprotic Weak Protolytes
Part 1 Buffer Solutions Composed of One Monoprotic Weak Acid
and One Monoprotic Weak Base
Summary
1 Introduction
2 Basic Equations
3 Approximate Solutions
3.1 Solutions Outside the Neutral Range 6 < pH < 8 .
3.2 Solutions more Concentrated than 0.01 M at a pH
Between 4 and 10
3.2.1 Buffer Power
3.2.2 Buffer Range
3.2.3 Ionic Concentrations and Degree
of Hydrolysis
4 Accurate Analysis
4.1 The pH of Solutions of the Neutral Salt
4.1.1 Salts Isoprotic Below pH 6
4.1.2 Salts Isoprotic Above pH 8
4.1.3 Salts Isoprotic Between pH 6 and 8
4.1.4 Comparison with Previous Literature
4.2 Buffer Power in the Case of Non-Negligible Water
Ion Concentrations
Part 2 Binary Equimolar Mixtures of Two Monoprotic Protolytes
Summary
1 Introduction
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73
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CONTENTS
vii
2
3
74
76
4
5
Titration Curve
Consequences Concerning Intrinsic Dissociation Constants
Tri- and Polyprotic Protolytes and Their Salts with Strong
Acids and Bases
Summary
1 Introduction
2 Basic Equations for a Triprotic Weak Acid
3 Titration Curves
4 Buffer Power
4.1 General Equation
4.2 Intrinsic and Titration Constants
4.3 The Case of Symmetry
4.4 The Case of Great Asymmetry
4.5 The Case of Moderate Asymmetry
4.6 Multiprotic Weak Protolytes
5 Ionic Strength
5.1 Buffers of Triprotic Weak Acids with Monovalent
Strong Base
5.2 Buffers of Triprotic Weak Bases with Monovalent
Strong Acids
6 Residual Charges at the Isoprotic Points
7 The pH of Solutions of Triprotic Protolytes
7.1 Triprotic Acids H3A
7.2 The Ampholyte H2Am
7.3 The Ampholyte HAm
7.4 Triprotic Bases
8 The pH of Solutions of Monovalent Salts
8.1 Monovalent Salts of Triprotic Acids
8.2 Monovalent Salts of Ampholytes НгАт
8.3 Monovalent Salts of Ampholytes HAm
8.4 Monovalent Salts of Triprotic Bases
9 The pH of Solutions of Bivalent Salts
9.1 Bivalent Salts of Triprotic Acids
9.2 Bivalent Salts of Ampholytes H2Am
9.3 Bivalent Salts of Ampholytes HAm
9.4 Bivalent Salts of Triprotic Bases
10 Trivalent Salts of Triprotic Acids and Bases
11 Survey of the Isoprotic Points of Triprotic Protolytes, and
Salts of Polyprotic Acids and Bases
The Debye-Hückel Theory for Strong Electrolytes
Summary
79
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81
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83
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107
109
109
CONTENTS
viii
1 Historical
2 The Principle of Electroneutrality for Atomic
Volume Elements
3 The Potential in the Electric Field Around an
Individual Ion
4 The Concept of Ionic Strength
5 The Activity Factor of an Individual Ion
6 Numerical — Güntelberg's Equation
7 The Activity Factor of a Binary Electrolyte
8 Explicit Approximate Expressions for the Mean Activity
Coefficient
9 Correction to Curves Calculated on the Basis of Constant
Dissociation Constants
10 Guggenheim's and Davies' Extensions of the Range of
Applicability of the Debye-Hückel Theory
6
7
110
110
Ill
114
115
116
117
120
121
123
Buffer Power and the Titration Curve of Water
Summary
1 The Ion Product of Water
2 The Buffer Power of Water
2.1 Basic Equations
2.2 The Buffer Power in Moderately Acidic Media
2.3 The Buffer Power in Strongly Acidic Media
2.4 Activity Coefficients in HCl Solutions from
Guggenheim's Equation
2.5 The Buffer Power in Moderately Alkaline Media ..
2.6 The Buffer Power in Strongly Alkaline Media
2.7 Activity Coefficients in NaOH Solutions from
Guggenheim's Equation
3 The pK Values of Water
4 The Titration Curve of Water
125
126
126
126
126
127
130
Experimental Determination of pK and ApA" Values as well
as Isoprotic Points
Summary
1 Introduction
2 Use of Henderson's Equation
2.1 pA"' Values Between 4 and 10
2.2 Extension to Low and High pK' Values
2.3 Conversion to Thermodynamic Dissociation
Constants
2.3.1 Monoprotic Protolytes
147
134
135
136
139
139
143
147
148
149
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CONTENTS
2.3.2 Biprotic Protolytes
2.3.3 Triprotic Protolytes
3 Experimental Determination of ApA"' Values
3.1 Biprotic Protolytes
3.2 Triprotic Protolytes
3.3 Conversion to Thermodynamic ApK Values
4 Experimental Determination of Isoprotic Points
4.1 Historical
4.2 Biprotic Protolytes
4.2.1 Conversion of Stoichiometric to Thermodynamic Isoprotic Points
4.2.2 The Minimum Concentration Required to
Measure an Isoprotic Point and Correction to
the Same
4.2.3 Comparison with Bates' Equation
4.2.4 Experimental Procedure
4.3 Triprotic Protolytes
4.3.1 The Ionic Strengths at the Isoprotic Points
4.3.2 Conversion to Thermodynamic Isoprotic
Points
5 Simultaneous Determination of Isoprotic Points and ApK;
Values From Titration Data
5.1 Integral Contra Differential Methods
5.2 Biprotic Protolytes
Appendix
References
Author Index
Subject Index
ix
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153
160
161
161
161
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163
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166
167
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170
111
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177
183
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189