Page 24 - MODERN ELECTROCHEMISTRY

CONTENTS xxiii

3.4.2. The Physical Significance of Activity Coefficients ............ 253
3.4.3. The Activity Coefficient of a Single Ionic Species Cannot Be Measured . 255
3.4.4. The Mean Ionic Activity Coefficient .................... 256
3.4.5. Conversion of Theoretical Activity-Coefficient Expressions into a Testable
Form .................................... 257
3.4.6. Experimental Determination of Activity Coefficients ........... 260
3.4.7. How to Obtain Solute Activities from Data on Solvent Activities ..... 261
3.4.8. A Second Method to Obtain Solute Activities: From Data on Concentration
Cells and Transport Numbers ............................ 263
Further Reading ................................. 267

3.5. The Triumphs and Limitations of the Debye–Hückel Theory of
Activity Coefficients ......................... 268
3.5.1. How Well Does the Debye–Hückel Theoretical Expression for Activity
Coefficients Predict Experimental Values? ................ 268
3.5.2. Ions Are of Finite Size, They Are Not Point Charges ........... 273
3.5.3. The Theoretical Mean Ionic-Activity Coefficient in the Case of Ionic
Clouds with Finite-Sized Ions ....................... 277
3.5.4. The Ion Size Parameter a .......................... 280
3.5.5. Comparison of the Finite-Ion-Size Model with Experiment ........ 280
3.5.6. The Debye–Hückel Theory of Ionic Solutions: An Assessment.......... 286
3.5.7. Parentage of the Theory of Ion–Ion Interactions.................... 292
Further Reading ................................ 293
3.6. Ion–Solvent Interactions and the Activity Coefficient ....... 293
3.6.1. Effect of Water Bound to Ions on the Theory of Deviations from Ideality 293
3.6.2. Quantitative Theory of the Activity of an Electrolyte as a Function of the
Hydration Number ............................. 295
3.6.3. The Water Removal Theory of Activity Coefficients and Its Apparent
Consistency with Experiment at High Electrolytic Concentrations .... 297
3.7. The So-called “Rigorous” Solutions of the Poisson–Boltzmann
Equation ............................... 300
3.8. Temporary Ion Association in an Electrolytic Solution: Formation
of Pairs, Triplets ........................... 304
3.8.1. Positive and Negative Ions Can Stick Together: Ion-Pair Formation . . . 304
3.8.2. Probability of Finding Oppositely Charged Ions near Each Other ..... 304
3.8.3. The Fraction of Ion Pairs, According to Bjerrum ............. 307
3.8.4. The Ion-Association Constant of Bjerrum ............... 309
3.8.5. Activity Coefficients, Bjerrum’s Ion Pairs, and Debye’s Free Ions .... 314
3.8.6. From Ion Pairs to Triple Ions to Clusters of Ions ............. 314
3.9. The Virial Coefficient Approach to Dealing with Solutions .... 315
Further Reading ................................. 318
3.10. Computer Simulation in the Theory of Ionic Solutions ....... 319