Advanced Potentiometry (eBook)

Contents 6
List of Definitions and Symbols 10
Preface 14
References 16
Acknowledgement 18
to 1 Introduction 19
1.1 The Titration of Weak Acids (HL, H 3 L) with a Strong Base 19
1.2 The Measurement of the Concentration of the H + or the Metal Ion B z(B)+ by Means of an Emf Cell 20
1.2.1 The Total Emf of Cell B 21
1.2.2 The Total Emf of Cell H 25
1.2.3 The Constant Ionic Medium Method 28
1.3 On the Curve-Fitting Computer Treatment [2d] 29
1.4 On the Deduction of Theoretical Equations 31
to 2 Emf Cells with Mixtures of Strong Electrolytes and Liquid Junctions of the Type AY | AY + HY + BYz(B) 35
2.1 Studies on Emf Cells Where [A + ] = C M, Constant [1] 35
2.1.1 Cell B Using an Amalgam/Ion-Selective Indicator Electrode 36
2.1.1.1 The Determination of E 0B and Some Slope Functions 36
2.1.1.2 The Estimation of the Systematic Errors in the Equilibrium Constants, 0 log 10 0 pqr , Caused by the Use of the Conditional Experimental Constant E 0B1 40
2.1.2 Cell H Using a Glass Indicator Electrode 41
2.1.2.1 The Determination of E 0H and Some Slope Functions 41
2.1.2.2 The Estimation of the Systematic Errors in the Equilibrium Constant, 0 log 10 0 pqr , Caused by the Use of the Conditional Experimental Constant E 0H1 45
2.2 Studies on Emf Cells Where [Y ] = C M, Constant [1] 46
2.2.1 Cell B Using an Amalgam/Ion-Selective Indicator Electrode 47
2.2.1.1 The Determination of E 0B and Some Slope Functions 47
2.2.1.2 The Estimation of the Systematic Errors in the Equilibrium Constant, 0 log 10 0 pqr , Caused by the Use of the Conditional Experimental Constant E 0B1 49
2.2.2 Emf Studies in Cell H Using a Glass Indicator Electrode 50
2.2.2.1 The Determination of the Constant E 0H and Some Slope Functions 50
2.2.2.2 The Estimation of the Systematic Errors in the Equilibrium Constants, 0 log 10 0 pqr , Caused by the Use of the Conditional Constant E 0H1 52
2.3 Studies on Emf Cells Where the Ionic Strength (I) = C M, Constant [1] 52
2.3.1 Emf Studies in Cell B Using an Amalgam Indicator Electrode 54
2.3.1.1 The Determination of E 0B and Some Slope Functions 54
2.3.1.2 The Estimation of the Systematic Errors in the Equilibrium Constants, 0 log 10 0 pqr , Caused by the Use of the Conditional Constant E 0B1 55
2.3.2 Emf Studies in Cell H Using a Glass Indicator Electrode 55
2.3.2.1 The Determination of E 0H and Some Slope Functions 56
2.3.2.2 The Estimation of the Systematic Errors in the Equilibrium Constants, 0 log 10 0 pqr , Caused by the Use of the Conditional Constant E 0H1 57
2.4 Conclusion on Emf Studies of Mixtures of Strong Electrolytes 57
to 3 Determination of the Ionic Molar Conductivities in Mixtures of the Strong Electrolytes HClO4 + NaClO4 + Cd(ClO4)2 65
3.1 Introduction 65
3.2 Conductivity Measurements 66
3.2.1 Conductivity Measurements in Mixtures Where [Na + ] = 30M, Constant [ 1 ] 66
3.2.1.1 Conductivity Measurements in Mixture 1 Where c B is Varied While c H is Kept Constant 66
3.2.1.2 Conductivity Measurements in Mixture 2 Where c H is Varied While c B is Kept Constant 70
3.2.1.3 Conductivity Measurements in Mixture 3 Where Both c B and c H Are Varied 73
3.2.1.4 Conclusion Which Can Be Obtained from Tables 2.2 and 3.1 73
3.2.1.5 Measurement of the Molar Conductivity of Concentrated Aqueous Cd(ClO 4 ) 2 Solutions 74
3.2.2 Conductivity Measurements in Mixtures Where [ClO 4 0 ] = 30M, Constant [ 7 ] 75
3.2.2.1 Conductivity Measurements in Mixture 2 Where c H Is Varied While c B Is Kept Constant 76
3.2.2.2 Conductivity Measurements in Mixture 1 Where c B Is Varied While c H Is Kept Constant 79
3.2.2.3 Conductivity Measurements in Mixture 3 Where Both c B and c H Are Varied 83
3.2.3 Conductivity Measurements in Mixtures Where I = C M, Constant [ 8 ] 84
3.2.3.1 Conductivity Measurements in Mixture 1 Where c B Is Varied While c H Is Kept Constant 84
3.2.3.2 Conductivity Measurements in Mixture 2 Where c H Is Varied While c B Is Kept Constant 88
3.2.3.3 Conductivity Measurements in Mixture 3 Where Both c B and c H Are Varied 91
3.3 Conclusion on Conductivity Measurements 91
3.4 Experimental Details 93
to 4 Studies on Emf Cells Where Complex Formation Takes Place Using Liquid Junctions of the Type AY AY + HY + BYz(B) + AyL and -- log10 [H+] 7 95
4.1 Deduction of the General Equations [ 1 ] 95
4.1.1 Introduction 95
4.1.2 Definitions and Symbols Used in Equilibrium Systems 96
4.1.3 Deduction of the Potential Functions E D , E Df , E B and E H 99
4.1.4 Calculation of the Ideal Diffusion Potential, E D, in Cells with Complex Formation 100
4.1.5 The Suggested Function for E D for the Preliminary Treatment of Emf Data 102
4.1.6 Calculation of the Contribution of the Activity Coefficients to the Ideal Diffusion Potential, E Df , in Cells with Complex Formation 103
4.1.7 The Suggested Function for E Df for the Preliminary Treatment of Emf Data 103
4.1.8 The Total Cell Emf in Cells with Complex Formation 104
4.1.8.1 The Total Emf of Cell B with an Amalgam Indicator Electrode 104
4.1.8.2 The Total Emf of Cell H with a H + -Sensitive Indicator Electrode 105
4.1.9 The Validity of the Equations 105
4.2 Emf Cells Where [A + ] = C M, Is Kept Constant [ 23 ] 107
4.2.1 Potential Functions for the Formation of Strong Complexes 108
4.2.1.1 The Study of the Formation of Metal Ion Complexes 108
4.2.1.2 Survey of the Potential Functions for the Protolysis of the Weak Acid HL 116
4.2.1.3 Experimental Studies 121
4.2.1.4 Survey of the Potential Functions for the Calculation of the Second Protolysis Constant of the Weak Acid H 2 L 130
4.2.2 Emf Studies on Weak Complex Formation at [A + ] = C M, Constant 133
4.3 Emf Cells Where [Y ] = C M, Constant [ 35 ] 135
4.3.1 Emf Studies Where Strong Complexes Are Formed 136
4.3.1.1 Studies on the Formation of Metal Ion Complexes According to Section 4.2.1.1 136
4.3.1.2 Survey of the Potential Functions for the Protolysis of the Weak Acid HL, According to Section 4.2.1.2 138
4.3.1.3 Experimental Studies 141
4.3.1.4 Survey of the Potential Functions for the Protolysis of the Weak Acid H 2 L 145
4.3.2 Emf Studies on Weak Complex Formation at [Y -- ] = C M, Constant 148
4.3.2.1 Critical Analysis of the So-Called Self-Medium Method for Cell H 148
4.3.3 Experimental Examples Taken from the Literature 152
4.3.3.1 The Hydrolysis of the Lanthanum Ion, La 3+ 152
4.3.3.2 Carbonate Complex Formation of the La 3+ Ion [ 37 ] 157
4.4 Emf Cells Where I = C M, Is Kept Constant [ 38 ] 160
4.4.1 Introduction 160
4.4.1.1 The Determination of the Constant E 0B 161
4.4.1.2 The Determination of the Constant E 0H 162
4.4.2 Emf Studies Where Strong Complexes Are Formed At I = C M, Constant 164
4.4.2.1 The Main Titration 164
4.4.2.2 Studies on the Formation of Metal Ion Complexes 165
4.4.2.3 The Calculation of the Total Potential Anomalies in Emf Cells Where Protolysis of the Weak Acids HL and H 2 L Takes Place, Respectively 169
4.4.3 Emf Studies on Weak Complex Formation At I = C M, Kept Constant 173
4.4.4 On the Ionic Medium Dependence of the Equilibrium Constants 175
4.4.4.1 Comparison of the Values of the Mentioned Potential Functions Q(H, V) at Different Experimental Conditions 176
4.4.4.2 The Dependence of the Equilibrium Constants (log 10 0 pqr ) on the Ionic Medium 178
4.5 Conclusion on Cells with Complex Formation 181
4.5.1 Strong Complexes Are Formed 181
4.5.2 Weak Complexes Are Formed 184
4.6 Appendix 1 185
4.6 Notation Appendix 2 186
4.5.2 Survey of the Estimated Q(H, V) Functions with V = h, b, l = [L 0 ], l = [L 20 ], 0 c A and/or 0 c Y at [A + ] = C M, Is Kept Constant 186
4.5.2 At [Y -- ] = C M, Is Kept Constant 188
4.5.2 At I = C M, Is Kept Constant 188
to 5 Estimation of the Total Potential Anomalies and the Determination of the Equilibrium Constants in Emf Cells Where Every Kind of Complex Can Be Present 192
to 6 On Emf Titrations Proposed for the Determination of Some Interaction Coefficients 197
6.1 Introduction 197
6.2 Survey of Some Emf Cells for Determination of Interaction Coefficients 198
6.2.1 Determination of the Interaction Coefficient (B,Y) 198
6.2.2 Determination of 0 (A + = Na, L) 199
6.2.3 Determination of 0 0 (B, ClO 4 ) 202
6.2.4 Determination of (H, L) 203
6.2.5 Determination of (A, Cl) 205
6.2.6 Determination of 0 0 (A, ClO 4 ) 206
6.2.7 Determination of (H, Y) 207
6.2.8 Determination of (H, Cl) 208
6.3 The Dependence of the Interaction Coefficients on the Ionic Strength 208
6.4 Experimental 210
6.5 Appendix 1 211
to 7 Emf Titrations Proposed for the Determination of Certain Transport Numbers [1] 214
7.1 Introduction 214
7.2 Survey of Emf Cells for the Determination of Transport Numbers 215
7.2.1 Determination of Transport Numbers in Strong Electrolyte A e H u L or A y L with Anionic Charges y = e + u =1, 2 or 3 215
7.2.2 The Determination of the Transport Numbers in the Strong Electrolyte BY z(B) Containing An Amalgam-Forming Cation 218
7.2.2.1 Cell 7 219
7.2.2.2 Cell 8 221
7.2.3 The Determination of the Transport Numbers in Metal Perchlorate Solutions 222
7.2.3.1 Cell 9 222
7.2.3.2 Cell 10 224
to 8 Studies on Emf Cells Where Strong Complexes Are Formed Using Liquid Junctions of the Type AY AY + BYz(B) + HY + AyL At [Y--]INTtie = C M, Constant, and -- log10 [H+] 7
8.1 Introduction 227
8.2 The Presentation of the Potential Functions 228
8.2.1 The Calculation of the Ideal Diffusion Potential Term, E D 229
8.2.2 The Calculation of the Activity Factor Contribution to the Ideal Diffusion Potential, E Df 230
8.2.3 The Total Emf of Cell B in Alkaline Solutions, with a B z(B)+ Ion-Selective Indicator Electrode and for Small Values of w/a 231
8.2.4 The Total Emf of cell H, in Alkaline Solutions, with a H + Ion-Sensitive Indicator Electrode and for Small Values of w/a 233
8.2.5 Emf Titration Suggested for the Determination of the Experimental Slope Function SL(H, l) and log 10 K 1 Value of the Weak Acid HL 235
8.2.6 The Protolysis of H 2 L in Alkaline Solutions 239
8.3 Appendix 1 (Chapter 8) The Hydrogen Electrode [13] 240
8.2.6 The Preparation of the Hydrogen Electrode by Electrolysis 240
8.2.6 The Thermal Preparation of the Hydrogen Electrode [ 14 ] 242
8.2.6 The Total Emf of Cell H with a Hydrogen Indicator Electrode 242
8.3 Presentation of a New Calibration Method for the Glass Electrode Against the Hydrogen Electrode in Alkaline Solutions 244
Index 248