WATER A COMPREHENSIVE TREATISE

Volume 3

Aqueous Solutions of Simple Electrolytes

Volume 1

Volume 2

Volume 3

Volume 4

WATER A COMPREHENSIVE TREATISE

Edited by Felix Franks

The Physics and Physical Chemistry of Water

Water in Crystalline Hydrates; Aqueous Solutions of Simple Nonelectrolytes Aqueous Solutions of Simple Electrolytes

Aqueous Solutions of Macromolecules; Water in Disperse Systems

WATER A COMPREHENSIVE TREATISE

Edited by Felix Franks Unilever Research Laboratory

Sharnbrook, Bedford, England

Volume 3 Aqueous Solutions

of Simple Electrolytes

g:>PLENUM PRESS. NEW YORK-LONDON. 1973

200435

First Printing - May 1973 Second Printing - May 1977

Library of Congress Catalog Card Number 78-165694 ISBN 978-1-4684-2957-2 ISBN 978-1-4684-2955-8 (eBook) DOI 10.1007/978-1-4684-2955-8

© 1973 Plenum Press, New York Softcover reprint of the hardcover 1 st edition 1973

A Division of Plenum Publishing Corporation 227 West 17th Street, New York N.Y. 10011

United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Company, Ud.

Davis House (4th Floor), 8 Scrubs Lane, Harlesden, London, NWI0 6SE, England

All rights reserved

No part of this publication may be reproduced in any form without written permission from the publisher

Preface

The chapters making up this volume had originally been planned to form part of a single volume covering solid hydrates and aqueous solutions of simple molecules and ions. However, during the preparation of the manu­scripts it became apparent that such a volume would turn out to be very unwieldy and I reluctantly decided to recommend the publication of sepa­rate volumes. The most sensible way of dividing the subject matter seemed to lie in the separation of simple ionic solutions.

The emphasis in the present volume is placed on ion-solvent effects, since a number of excellent texts cover the more general aspects of electrolyte solutions, based on the classical theories of Debye, Huckel, On sager, and Fuoss. It is interesting to speculate as to when a theory becomes "classical." Perhaps this occurs when it has become well known, well liked, and much adapted. The above-mentioned theories of ionic equilibria and transport certainly fulfill these criteria.

There comes a time when the refinements and modifications can no longer be related to physical significance and can no longer hide the fact that certain fundamental assumptions made in the development of the theory are untenable, especially in the light of information obtained from the application of sophisticated molecular and thermodynamic techniques.

There is now general agreement that the description of ionic solutions in terms of only a simple electrostatic potential fU'nction modified by a bulk dielectric permittivity. can hardly represent the true situation and we are now beginning to see the development and acceptance of the second generation of electrolyte theories. The present state of flux is reflected in most of the following chapters, which might suggest that the timing of the publication of this volume is premature. However, within the framework of this treatise properties of electrolyte solutions play an important part, and I hope that bringing together some of the more recent experimental

v

vi Preface

and theoretical results in one volume will advance the development of useful working models for ion solvation and ionic interactions.

As before I should like to express my gratitude to the contributing authors for their enthusiastic cooperation which is mainly responsible for the short interval between the publication of this and the preceding volume.

Biophysics Division Unilever Research Laboratory Colworth/Welwyn Colworth House, Sharnbrook, Bedford

F. FRANKS

Contents

Contents of Volume 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xlll

Contents of Volume 2........................................ xv

Contents of Volume 4........................................ XVII

Chapter 1

Thermodynamics of Ion Hydration

H. L. Friedman and C. V. Krishnan

I. The Thermodynamic Theory of Solvation ............. . 1.1. General Remarks ............................... I 1.2. Resolution of Data into Solvation and Excess Properties 2 1.3. Standard States..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4. Reference Solvents .............................. II 1.5. Pair Interaction Coefficients ...................... 13 1.6. Temperature and Pressure. . . . . . . . . . . . . . . . . . . . . . . . 21 1.7. Single-Ion Properties ............................ 21

2. Molecular Interpretation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1. Introduction..................................... 24 2.2. The Born Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3. The Debye-Pauling Model ....................... 30 2.4. Hamiltonian Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5. A Chemical Model..... . . . . . . . . . . . . . . . . . . . . . . . . . 47

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viii Contents

3. Hydration of Gaseous Ions ........................... 54 3.1. Free Energies, Enthalpies, and Entropies of Hydration 54 3.2. Equations for Entropies of Aqueous Ions ......... 54 3.3. The Chemical Model Interpretation of Ionic Entropies 62 3.4. Transition and Rare Earth Metal Ions at Infinite Dilution 64

4. Other Thermodynamic Properties of Ions at Infinite Dilution in Water............................................. 66 4.1. Partial Molar Volume of Solute X at infinite Dilution,

VX(aq) .......................................... 66 4.2. Partial Molar Heat Capacity of Solute X at Infinite

Dilution, CX(aq).................................. 71 4.3. Partial Molar Isothermal Compressibility of Solute X

at Infinite Dilution, KTx(aq) , and Partial Molar Adia­batic Compressibility of Solute X at Infinite Dilution, KSx(aq) ......................................... 73

4.4. Partial Molal Expansibility of Solute X at Infinite Dilution, Ex (aq) ................................. 76

4.5. Variation of Heat Capacity of Solute X at Infinite Dilution with Temperature, oCx(aq)/oT ............ 78

4.6. Variation of Partial Molal Isothermal Compressibility of Solute X at Infinite Dilution with Temperature, oKTx(aq)/oT ......... ,' . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.7. Variation of Partial Molal Expansibility of Solute X at Infinite Dilution with Temperature, (oEx(aq)/oT)p . . . 80

5. Solvent-Isotope Effect in Hydration.................... 81 5.1. Introduction..................................... 81 5.2. Free Energies ................................... 82 5.3. Enthalpies...................................... 85 5.4. Entropies....................................... 100 5.5. Volumes........................................ 103 5.6. Heat Capacities ................................. 105

6. Reference Solvents ................................... 105 6.1. Free Energies in Nonaqueous Solvents ............ 105 6.2. Entropies in Nonaqueous Solvents ................ 105 6.3. Enthalpies in Nonaqueous Solvents........... . . . . . 108 6.4. Heat Capacities in Nonaqueous Solvents...... . . . . . 113

7. Ionic Hydration and Excess Properties ................. 113

Contents ix

Chapter 2

Thermodynamics of Aqueous Mixed Electrolytes

Henry L. Anderson and Robert H. Wood

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

2. Theoretical Framework ............................... 121

2.1. Symmetric, Common-Ion Mixtures................ 121

2.2. Symmetric, Multicomponent Mixtures... . . . . . . . . .. 124

2.3. Nomenclature................................... 126

3. Experimental Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4. Experimental Results and Discussion................... 128

4.1. Concentration and Common-Ion Dependence....... 128

4.2. Young's Sign Rule .............................. 139

4.3. Temperature Dependence of JmHE . . . . . . . . . . . . . . . . 140

4.4. Tetraalkylammonium Electrolytes ................. 141

Chapter 3

Hydration Effects and Acid-Base Equilibria

Loren G. Hepler and Earl M. Woolley

1. Ionization of Liquid Water ............................ 145

1.1. Ionization of Water in Aqueous Electrolyte Solutions 158

1.2. Ionization of Water in Aqueous Organic Mixtures.. 158

2. Hydration of H+ and OH- ........................... 160

2.1. Gas-Phase Hydration of H+ and OH-............. 160

2.2. Hydration of H+ and OH- in Aqueous Solution... 161

3. Organic Acids and Bases in Aqueous Solution.......... 163

3.1. Thermodynamics of Ionization Reactions .......... 165

3.2. Substituent Effects on Ionization of Organic Acids. . . 167

3.3. Examples of Hydration Effects on Acid-Base Ionization Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

x Contents

Chapter 4

Ionic Transport in Water and Mixed Aqueous Solvents

Robert L. Kay

I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

2. Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 174

3. Limiting Ionic Conductances in Binary Solutions. . . . . . .. 178

4. Mechanism of Ionic Conductance. . . . . . . . . . . . . . . . . . . . . . 180 4.1. Stokes' Law.................................... 184 4.2. Solvent Dipole Relaxation Effect ................. 186 4.3. Cosphere Effects ................................ 189 4.4. Temperature Coefficient... . . . . . . . . . . . . . . . . . . . . . . . 192 4.5. Pressure Coefficient..... . . . . . . . . . . . . . . . . . . . . . . . . . 196

5. Limiting Ionic Conductance in Aqueous Solvent Mixtures 204

Chapter 5

Infrared Spectroscopy of Aqueous Electrolyte Solutions

Ronald Ernest Verrall

I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 211

2. Information on Aqueous Ionic Solutions Obtainable from Infrared Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 212 2.1. General......................................... 212 2.2. The Effects of Ions on the Structure of Water .... 213 2.3. Far Infrared ................................... . 2.4. Fundamental Infrared ........................... 215 2.5. Near Infrared.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 218

3. Experimental Methods... . . . . . . . . . . . . .. . . . . . . . . . . . . . .. 219 3.1. General ........................................ 219 3.2. Atmospheric Absorptions ........................ 220 3.3. Cells and Cell Path Lengths ..................... 220 3.4. Temperature Variation of Sample. . . . . . . . . . . . . . . .. 222 3.5. Reflection Losses........ . . . . . . . . . . . . . . . . . . . . . . .. 223 3.6. Isotopically Dilute HDO as a Solvent ............ 224

Contents xi

4. Critical Review of Available Infrared Data ....... . . . . .. 225 4.1. Far Infrared .................................... 225 4.2. Fundamental Infrared ........................... 233 4.3. Near Infrared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 249 4.4. Effect of Water on Infrared Spectra of Inorganic Ions 261

5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 263

Chapter 6

Raman Spectroscopy of Aqueous Electrolyte Solutions

T. H. Lilley

1. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 265

2. Raman Bands Arising from Solutes . . . . . . . . . . . . . . . . . . .. 267

3. Raman Bands Arising from the Solvent: Liquid Water.. 275 3.1. Intermolecular Region Vibrations ................. 277 3.2. Intramolecular Bands of the Solvent .............. 283

4. Addendum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 296

Chapter 7

Nuclear Magnetic Relaxation Spectroscopy

H. G. Hertz

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30 I

2. Nuclear Magnetic Relaxation . . . . . . . . . . . . . . . . . . . . . . . . .. 304 2.1. Principles....................................... 304 2.2. Proton Relaxation Times and Correlation Times of

Water in Paramagnetic Electrolyte Solutions. . . . . .. 313 2.3. Oxygen-17 Relaxation in Aqueous Solutions of Para­

magnetic Ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 338 2.4. Proton Relaxation Times and Correlation Times of

Water in Diamagnetic Electrolyte Solutions...... .. 349 2.5. Quadrupolar Relaxation of Water in Diamagnetic

Electrolyte Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 379

xii Contents

2.6. Relaxation Times of Ionic Nuclei Relaxing by Magnetic Dipole-Dipole Interaction . . . . . . . . . . . . . . . . . . . . . . .. 384

2.7. Self-Diffusion Coefficients in Electrolyte Solutions ., 389 2.8. Structural Interpretation of Microdynamic Data.... 395

Chapter 8

Dielectric Properties

Reinhard Pottel

1. Basic Theory ........................................ 401 1.1. Types of Dielectric Polarization and Its Decay .... 401 1.2. Dielectric Relaxation in a Model of Pure Water. .. 404 1.3. Dielectric Relaxdtion in a Model of Aqueous Ionic

Solutions ....................................... 407 1.4. Comparison of the Molecular Rotational Correlation

Times as Derived from Dielectric Relaxation and Proton Magnetic Resonance Relaxation ........... 409

2. Experimental Methods................................ 412

3. Characteristic Quantities Derived from Complex Permittivity Measurements ....................................... , 414

4. Information from the "Static" Permittivity ............. 420

5. Information Obtainable from the Dielectric Relaxation Time with the Help of the Proton Magnetic Relaxation Rate... 423

6. The Influence of Small Cations on the Dielectric Relaxation Time................................................ 426 6.1. Electrostatic Interaction Mechanisms Independent of

the Water Structure.. . . . . . . . .. . . . . . . . . . . . . . . .. 427 6.2. Mech~ni5iils Depending on the Water Structure. . .. 428

7. Summary ........................................... , 431

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 433

Subject Index ............................................... 457

Compound Index. .. ...... . . ... ... . .. ...... .. .... ... .. ..... ... 465

Formula Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 469

Contents of Volume 1: The Physics and Physical Chemistry of Water

Chapter 1. Introduction-Water, the Unique Chemical, by F. Franks

Chapter 2. The Water Molecule, by C. W. Kern and M. Karplus

Chapter 3. Theory of Hydrogen Bonding in Water, by C. N. R. Rao

Chapter 4. The Properties of Ice, by F. Franks

Chapter 5. Raman and Infrared Spectral Investigations of Water Struc­ture, by G. E. Walrafen

Chapter 6. Nuclear Magnetic Resonance Studies on Water and Ice, by Jay A. Glasel

Chapter 7. Liquid Water: Dielectric Properties, by J. B. Hasted

Chapter 8. Liquid Water: Scattering of X-Rays, by A. H. Narten and H. A. Levy

Chapter 9. The Scattering of Neutrons by Liquid Water, by D. I. Page

Chapter 10. Thermodynamic and Transport Properties of Fluid Water, by G. S. Kell

Chapter 11. Application of Statistical Mechanics in the Study of Liquid Water, by A. Ben-Naim

Chapter 12. Liquid Water-Acoustic Properties: Absorption and Relax­ation, by Charles M. Davis, Jr., and Jacek Jarzynski

Chapter 13. Water at High Temperatures and Pressures, by Klaus TOdheide

Chapter 14. Structural Models, by Henry S. Frank

xiii

Contents of Volume 2: Water in Crystalline Hydrates; Aqueous Solutions of Simple N onelectrolytes

Chapter 1. The Solvent Properties of Water, by F. Franks

Chapter 2. Water in Stoichiometric Hydrates, by M. Falk and O. Knop

Chapter 3. Clathrate Hydrates, by D. W. Davidson

Chapter 4. Infrared Studies of Hydrogen Bonding in Pure Liquids and Solutions, by W. A. P. Luck

Chapter 5. Thermodynamic Properties, by F. Franks and D. S. Reid

Chapter 6. Phase Behavior of Aqueous Solutions at High Pressures, by G. M. Schneider

Chapter 7. Dielectric Properties, by J. B. Hasted

Chapter 8. Spectroscopic Properties, by M. J. Blandamer and M. F. Fox

Chapter 9. Acoustic Properties, by M. J. Blandamer

Chapter 10. NMR Spectroscopic Studies, by M. D. Zeidler

Chapter 11. Molecular Theories and Models of Water and of Dilute Aque­ous Solutions, by A. Ben-Nairn

xv

Contents of Volume 4: Aqueous Solutions of Macromolecules; Water in Disperse Systems

Chapter 1. The Hydrophobic Interaction, by F. Franks

Hydration and Reversible Aggregation Phenomena in Aqueous Solutions of Simple Solutes

Chapter 2. Surfactants, by G. C. Kresheck

Chapter 3. Dyestuffs, by G. H. Giles and D. G. Duff

Chapter 4. Lipids, by H. Hauser

The Role of Solute-Water Interactions in Aqueous Solutions and Gels of Macromolecules

Chapter 5.

Chapter 6.

Chapter 7.

Nucleic Acids, Peptides, and Proteins, by D. Eagland

Polysaccharides, by A. Suggett

Synthetic Polymers, by P. Molyneux

Disperse Systems

Chapter 8. Role of Water in the Stability of Hydrophobic Colloids, by D. Eagland

Chapter 9. Properties of Water in Capillaries and Thin Films, by J. Clifford

Chapter 10. The Aqueous Interface-Foams, Emulsions, by M. C. Phillips

Chapter 11. Clay-Water Systems, by E. Forslind

Chapter 12. Adsorption of Water on Well-Characterized Inorganic Sur­faces, by A. C. Zettlemoyer

Chapter 13. Specific Interactions of Water with Biopolymers, by H. Berendsen

xvii