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Electrolyte Solutions at Equilibrium

  • Harold L. Friedman
  • William D. T. Dale
Part of the Modern Theoretical Chemistry book series (MTC, volume 5)

Abstract

This chapter describes statistical—mechanical tools for the study of ionic solutions at equilibrium. We have attempted to cover those topics which are essential to prospective workers in the field, assuming only that the reader is familiar with the main features of grand ensemble theory, including spatial distribution functions.(1–3)

Keywords

Electrolyte Solution Hard Sphere Black Circle Ionic Solution Pair Correlation Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    T. L. Hill, Statistical Mechanics, McGraw-Hill, New York (1956).Google Scholar
  2. 2.
    S. A. Rice and P. Gray, The Statistical Mechanics of Simple Liquids, Wiley ( Interscience ), New York (1965).Google Scholar
  3. 3.
    P. A. Egelstaff, An Introduction to the Liquid State, Academic Press, New York (1967).Google Scholar
  4. 4.
    C. W. Outhwaite, in: Statistical Mechanics (K. Singer, ed.), Vol. 2, p. 188, The Chemical Society, London (1975).Google Scholar
  5. 5.
    H. C. Andersen, The structure of liquids, Ann. Rev. Phys. Chem. 26, 145 (1975).CrossRefGoogle Scholar
  6. 6.
    F. Vaslow, in: Water and Aqueous Solutions ( R. A. Home, ed.), p. 465, Wiley, New York (1972).Google Scholar
  7. 7.
    H. L. Anderson and R. H. Wood, in: Water, A Comprehensive Treatise (F. Franks, ed.), Vol. 3, p. 119, Plenum Press, New York (1974).Google Scholar
  8. 8.
    J. C. Rasaiah, A view of electrolyte solutions, J. Solution Chem. 2, 301–338 (1973); also in: The Physical Chemistry of Aqueous Systems (R. L. Kay, ed.), Plenum Press, New York (1974).Google Scholar
  9. 9.
    H. L. Friedman, in: Modern Aspects of Electrochemistry (J. O’M. Bockris and B. E. Conway, eds.), Vol. 6, p. 1, Plenum Press, New York (1971).Google Scholar
  10. 10.
    R. A. Robinson and R. H. Strokes, Electrolyte Solutions, Butterworths, London (1955).Google Scholar
  11. 11.
    H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions, 3rd ed., Reinhold Publishing Co., New York (1958).Google Scholar
  12. 12.
    H. S. Harned and R. A. Robinson, Multicomponent Electrolyte Solutions, Pergamon Press, Oxford (1968).Google Scholar
  13. 13.
    H. Falkenhagen, Electrolytes (R. F. Bell, tr.), Clarendon Press, Oxford (1934).Google Scholar
  14. 14.
    H. L. Friedman, Ionic Solution Theory Based on Cluster Expansion Methods, Wiley ( Interscience ), New York (1962).Google Scholar
  15. 15.
    S. Baer, Correlations among ions, electrons, and screened potentials in a hot dilute gas, Phys. Rev. A 2, 2454 (1970).CrossRefGoogle Scholar
  16. 16.
    H. Popkie, H. Kistenmacher, and E. Clementi, Study of the structure of molecular complexes. IV. The Hartree-Fock potential for the water dimer and its application to the liquid state, J. Chem. Phys. 59, 3336 (1971).Google Scholar
  17. 17.
    A. Rahman and F. H. Stillinger, Molecular dynamics study of liquid water, J. Chem. Phys. 55, 3336 (1971).CrossRefGoogle Scholar
  18. 18.
    J. A. Barker and R. O. Watts, Structure of water; a Monte Carlo Calculation, Chem. Phys. Letters 3, 144 (1969).CrossRefGoogle Scholar
  19. 19.
    K. Heinziger and P. C. Vogel, A molecular dynamics study of aqueous solutions. I. First results for LiCI in H2O, Z. Naturforsch. 29a, 1164 (1974).Google Scholar
  20. 20.
    H. C. Andersen, Cluster methods in equilibrium statistical mechanics of fluids, Chapter 1 of this volume.Google Scholar
  21. 21.
    B. M. Ladanyi and D. Chandler, New type of cluster theory for molecular fluids: Interaction site cluster expansion, J. Chem. Phys. 62, 4308 (1975).CrossRefGoogle Scholar
  22. 22.
    H. L. Lemberg and F. H. Stillinger, Central force model for liquid water, J. Chem. Phys. 62, 1677 (1975).CrossRefGoogle Scholar
  23. 23.
    W. G. McMillan and J. E. Mayer, The statistical thermodynamics of multicomponent systems, J. Chem. Phys. 13, 276 (1945).CrossRefGoogle Scholar
  24. 24.
    H. L. Friedman, On the limiting law for electrical conductance in ionic solutions, Physica 30, 537 (1964).CrossRefGoogle Scholar
  25. 25.
    J. M. Deutch and I. Oppenheim, Molecular theory of Brownian motion for several particles, J. Chem. Phys. 54, 3547 (1971).CrossRefGoogle Scholar
  26. 26.
    I. Amdur and J. E. Jordan, Elastic scattering of high-energy beams: Repulsive forces, Advan. Chem. Phys. 10, 29 (1966).CrossRefGoogle Scholar
  27. 27.
    E. A. Guggenheim and M. L. McGlashan, Repulsive energy in sodium chloride and potassium chloride crystals, Discuss. Faraday Soc. 40, 76 (1965).CrossRefGoogle Scholar
  28. 28.
    R. G. Gordon and Y. S. Kim, Theory of the forces between closed shell atoms and molecules, J. Chem. Phys. 56, 3122 (1972).CrossRefGoogle Scholar
  29. 29.
    L. Pauling, Nature of the Chemical Bond, Cornell University Press, Ithaca, New York (1960).Google Scholar
  30. 30.
    P. S. Ramanathan and H. L. Friedman, Study of a refined model for aqueous 1–1 electrolytes, J. Chem. Phys. 54, 1086 (1971).CrossRefGoogle Scholar
  31. 31.
    H. L. Friedman, Mayer’s ionic solution theory applied to electrolyte mixtures, J. Chem. Phys. 32, 1134 (1960).CrossRefGoogle Scholar
  32. 32.
    S. Levine and D. K. Rozenthal, in: Chemical Physics of Ionic Solutions ( B. E. Conway and R. G. Barradas, eds.), p. 119, Wiley, New York (1966).Google Scholar
  33. 33.
    S. Levine and H. E. Wrigley, The specific interaction of two ions in a strong aqueous electrolyte, Discuss. Faraday Soc. 24, 43 (1957).CrossRefGoogle Scholar
  34. 34.
    C. V. Krishnan and H. L. Friedman, Model calculations for Setchenow coefficients, J. Solution Chem. 3, 727 (1974).CrossRefGoogle Scholar
  35. 35.
    H. L. Friedman and C. V. Krishnan, in: Water, A Comprehensive Treatise (F. Franks, ed.), Vol. 3, p. 1, Plenum Press, New York (1974).Google Scholar
  36. 36.
    H. A. Kolodziej, G. P. Jones, M. Davies, High field dielectric measurements in water, J.C.S. Faraday II 71, 269 (1975).CrossRefGoogle Scholar
  37. 37.
    R. W. Gurney, Ions in Solution, Dover Publications, New York (1962).Google Scholar
  38. 38.
    Henry S. Frank in: Chemical Physics of Ionic Solutions (B. E. Conway and R. G. Barradas, eds.), p. 53, Wiley, New York (1966).Google Scholar
  39. 39.
    H. L. Friedman, C. V. Krishnan, and L. P. Hwang, in: Structure of Water and Aqueous Solutions (W. Luck, ed.), p. 169, Verlag Chemie-Physikk, Weinheim (1974).Google Scholar
  40. 40.
    G. Stell, Ionic solution theory for nonideal solvents, J. Chem. Phys. 59, 3926 (1973).CrossRefGoogle Scholar
  41. 41.
    G. N. Patey and J. P. Valleau, A Monte Carlo method for obtaining the interionic potential of mean force in ionic solution, J. Chem. Phys. 63, 2334 (1975).CrossRefGoogle Scholar
  42. 42.
    I. R. McDonald and J. C. Rasaiah, Monte Carlo simulation of the average force between two ions in a Stockmayer solvent, in: Report of Workshop on Ionic Liquids (K. Singer, ed.), p. 230, CECAM Orsay, France (1974).Google Scholar
  43. 43.
    L. Blum, Solution of a model for the solvent-electrolyte interactions in the mean spherical approximation, J. Chem. Phys. 61, 2129 (1974).CrossRefGoogle Scholar
  44. 44.
    H. L. Friedman, Modern advances in solvation theory, Chem. Br. 9, 300 (1973).Google Scholar
  45. 45.
    C. V. Krishnan and H. L. Friedman, Solvation enthalpies of various ions in water, propylene carbonate, and dimethyl sulfoxide, J. Phys. Chem. 73, 3934 (1969).CrossRefGoogle Scholar
  46. 46.
    B. G. Cox and A. J. Parker, Solvation of ions. XVII. Free energies, heats, and entropies of transfer of single ions from protic to dipolar aprotic solvents, J. Am. Chem. Soc. 95, 402 (1973).CrossRefGoogle Scholar
  47. 47.
    G. N. Lewis, M. Randall, K. S. Pitzer, and L. Brewer, Thermodynamics, 2nd ed., McGraw-Hill, New York (1961).Google Scholar
  48. 48.
    H. L. Friedman, Thermodynamic excess functions for electrolyte solutions, J. Chem. Phys. 32, 1351 (1960).CrossRefGoogle Scholar
  49. 49.
    J. C. Rasaiah and H. L. Friedman, Integral equation methods in the computation of equilibrium properties of ionic solutions, J. Chem. Phys. 48, 2742 (1968).CrossRefGoogle Scholar
  50. 50.
    V. B. Parker, Thermal Properties of Aqueous Uni-Univalent Electrolytes, U.S. National Bureau of Standards NSRDS-NBS2, Washington, D.C. (1965).Google Scholar
  51. 51.
    K. S. Pitzer, Thermodynamics of electrolytes. V. Effects of higher-order electrostatic terms, J. Solution Chem. 4, 249 (1975).CrossRefGoogle Scholar
  52. 52.
    H. L. Friedman and P. S. Ramanathan, Theory of mixed electrolyte solutions and application to a model for aqueous lithium chloride-cesium chloride, J. Phys. Chem. 74, 3756 (1970).CrossRefGoogle Scholar
  53. 53.
    H. L. Friedman, On the thermodynamics of the interaction between the solutes in dilute ternary solutions, J. Phys. Chem. 59, 161 (1955).CrossRefGoogle Scholar
  54. 54.
    H. L. Friedman, C. V. Krishnan, and C. Jolicoeur, Ionic interactions in water, Ann. N.Y. Acad. Sci. 204, 79 (1973).CrossRefGoogle Scholar
  55. 55.
    J. E. Enderby, W. S. Howells, and R. A. Howe, The structure of aqueous solutions, Chem. Phys. Lett. 21, 109 (1973).CrossRefGoogle Scholar
  56. 56.
    J. Waser and V. Schomaker, The Fourier inversion of diffraction data, Rev. Mod. Phys. 25, 671 (1953).CrossRefGoogle Scholar
  57. 57.
    A. H. Narten, Liquid water: Atom pair correlation functions from neutron and X-ray diffraction, J. Chem. Phys. 56, 5681 (1972).CrossRefGoogle Scholar
  58. 58.
    E. Kâlmân, S. Lengyel, L. Haklik, and A. Eke, A new experimental technique for the study of liquid structure, J. Appl. Crys. 7, 442 (1974).CrossRefGoogle Scholar
  59. 59.
    E. Kâlmân and G. Pâlinkâs, in: Collected Abstracts, Second European Crystallographic Meeting, p. 494, Keszthely, Hungary (1974).Google Scholar
  60. 60.
    L. Onsager, Theories of concentrated electrolytes, Chem. Rev. 13, 73 (1933).CrossRefGoogle Scholar
  61. 61.
    G. S. Rushbrooke, On the statistical mechanics of assemblies whose energy-levels depend on the temperature, Trans. Faraday Soc. 36, 1055 (1940).CrossRefGoogle Scholar
  62. 62.
    H. L. Friedman, Lewis-Randall to McMillan-Mayer conversion for the thermodynamic excess functions of solutions. Part I. Partial free energy coefficients, J. Solution Chem. 1, 387 (1972).CrossRefGoogle Scholar
  63. 63.
    H. L. Friedman, Lewis-Randall to McMillan-Mayer conversion for the thermodynamic excess functions of solutions. Part II. Excess energy and volume, J. Solution Chem. 1, 413 (1972).CrossRefGoogle Scholar
  64. 64.
    H. L. Friedman, Lewis-Randall to McMillan-Mayer conversion for the thermodynamic excess functions of solutions. Part III. Common-ion mixtures of two electrolytes, J. Solution Chem. 1, 419 (1972).CrossRefGoogle Scholar
  65. 65.
    J. C. Rasaiah and H. L. Friedman, Integral equation computations for aqueous 1–1 electrolytes. Accuracy of the method, J. Chem. Phys. 50, 3965 (1969).CrossRefGoogle Scholar
  66. 66.
    J. E. Mayer and M. G. Mayer, Statistical Mechanics, Wiley, New York (1940).Google Scholar
  67. 67.
    J. Riordan, An Introduction to Combinatorial Analysis, Wiley, New York (1958).Google Scholar
  68. 68.
    T. Morita and K. Hiroike, A new approach to the theory of classical fluids. III., Progr. Theor. Phys. 25, 537 (1961).CrossRefGoogle Scholar
  69. 69.
    C. DeDominicis, Variational formulations of equilibrium statistical mechanics, J. Math. Phys. 3, 983 (1962).CrossRefGoogle Scholar
  70. 70.
    G. Stell, in: The Equilibrium Theory of Classical Fluids ( H. L. Frisch and J. L. Lebowitz, eds.), p. II - 171, Benjamin, New York (1964).Google Scholar
  71. 71.
    G. Stell, in: Graph Theory and Theoretical Physics ( F. Harary, ed.), p. 281, Academic Press, New York (1967).Google Scholar
  72. 72.
    J. K. Percus, in: The Equilibrium Theory of Classical Fluids ( H. L. Frisch and J. L. Lebowitz, eds.), p. II - 33, Benjamin, New York (1964).Google Scholar
  73. 73.
    J. E. Mayer, The theory of ionic solutions, J. Chem. Phys. 18, 1426 (1950).CrossRefGoogle Scholar
  74. 74.
    J. C. Poirier, Thermodynamic functions from Mayer’s theory of ionic solutions. II. The stoichiometric mean ionic molar activity coefficient, J. Chem. Phys. 21, 972 (1953).CrossRefGoogle Scholar
  75. 75.
    E. Meeron, Mayer’s treatment of ionic solutions, J. Chem. Phys. 26, 804 (1957).CrossRefGoogle Scholar
  76. 76.
    H. L. Friedman and C. V. Krishnan, Charge-asymmetric mixtures of electrolytes at low ionic strength, J. Phys. Chem. 78, 1927 (1974).CrossRefGoogle Scholar
  77. 77.
    G. Stell and J. L. Lebowitz, Equilibrium properties of a system of charged particles, J. Chem. Phys. 49, 3706 (1968).CrossRefGoogle Scholar
  78. 78.
    G. Stell, The Percus-Yevick equation for the radial distribution function of a fluid, Physica 29, 517 (1963).CrossRefGoogle Scholar
  79. 79.
    J. Groeneveld, in: Graph Theory and Theoretical Physics ( F. Harary, ed.), p. 229, Academic Press, New York (1967).Google Scholar
  80. 80.
    E. Meeron, Nodal expansions. III. Exact integral equations for particle correlation functions, J. Math. Phys. 1, 192 (1960).CrossRefGoogle Scholar
  81. 81.
    L. S. Ornstein and F. Zernike, in: The Equilibrium Theory of Classical Fluids ( H. L. Frisch and J. L. Lebowitz, eds.), p. III - 2, Benjamin, New York (1964).Google Scholar
  82. 82.
    D. D. Carey, Radial distributions of ions for a primitive model of an electrolyte solution, J. Chem. Phys. 46, 3783 (1967).CrossRefGoogle Scholar
  83. 83.
    A. R. Allnatt, Integral equations in ionic solution theory, Mol. Phys. 8, 533 (1964).CrossRefGoogle Scholar
  84. 84.
    H. L. Friedman, D. M. Zebolsky, and E. Kâlmân, Calculated X-ray scattering functions for models for aqueous Ph4AsC1 which fit the osmotic coefficient data, J. Solution Chem. 5, (1976).Google Scholar
  85. 85.
    E. Thiele, Equation of state for hard spheres, J. Chem. Phys. 39, 474 (1963).CrossRefGoogle Scholar
  86. 86.
    M. S. Wertheim, Exact solution of the Percus-Yevick integral equation for hard spheres, Phys. Rev. Lett. 10, 321 (1963).CrossRefGoogle Scholar
  87. 87.
    E. Waisman and J. L. Lebowitz, Mean spherical model integral equation for charged hard spheres. I and II., J. Chem. Phys. 56, 3086, 3093 (1972).CrossRefGoogle Scholar
  88. 88.
    L. Blum, Mean spherical model for asymmetric electrolytes. I: Method of solution, Mol. Phys. 30, 1529 (1975).CrossRefGoogle Scholar
  89. 89.
    M. S. Wertheim, Exact solution of the mean spherical model for fluids of hard spheres with permanent electric dipole moments, J. Chem. Phys. 55, 4291 (1971).CrossRefGoogle Scholar
  90. 90.
    E. Waisman, The radial distribution function for a fluid of hard spheres at high densities. Mean spherical integral equation approach, Mol. Phys. 25, 45 (1973).CrossRefGoogle Scholar
  91. 91.
    R. G. Palmer and J. D. Weeks, Exact solution of the mean spherical model for charged hard spheres in a uniform neutralizing background, J. Chem. Phys. 58, 4171 (1973).CrossRefGoogle Scholar
  92. 92.
    L. Blum, Invariant expansion. II. The Ornstein—Zernike equation for nonspherical molecules and an extended solution to the mean spherical model, J. Chem. Phys. 57, 1862 (1972).CrossRefGoogle Scholar
  93. 93.
    L. Blum, Invariant expansion III: The general solution of the mean spherical model for neutral spheres with electrostatic interactions, J. Chem. Phys. 58, 3295 (1973).CrossRefGoogle Scholar
  94. 94.
    D. A. Maclnnes and I. E. Farquhar, Exact solution of the mean spherical model for fluids of non-spherical molecules II., Mol. Phys. 30, 889 (1975).CrossRefGoogle Scholar
  95. 95.
    R. Triolo, J. R. Grigera, and L. Blum, Simple electrolytes in the mean spherical approximation, J. Phys. Chem. 17, 1858 (1976).CrossRefGoogle Scholar
  96. 96.
    J. S. Hoye, J. L. Lebowitz, and G. Stell, Generalized mean spherical approximations for polar and ionic fluids, J. Chem. Phys. 61, 3253 (1974).CrossRefGoogle Scholar
  97. 97.
    G. Stell and S. F. Sun, Generalized mean spherical approximation for charged hard spheres. The electrolyte regime. J. Chem. Phys. 63, 5333 (1975).CrossRefGoogle Scholar
  98. 98.
    H. C. Andersen, D. Chandler, and J. D. Weeks, Roles of repulsive and attractive forces in liquids. The equilibrium theory of classical fluids, Adv. Chem. Phys. 34, 105 (1976).CrossRefGoogle Scholar
  99. 99.
    W. R. Smith, in: Statistical Mechanics (K. Singer, ed.) Vol. 1, p. 71, The Chemical Society, London (1973).Google Scholar
  100. 100.
    F. Hirata and K. Arakawa, The computation of the thermodynamic properties of aqueous electrolyte solutions by means of the perturbation theory of fluids, Bull. Chem. Soc. Jpn. 48, 2139 (1975).CrossRefGoogle Scholar
  101. 101.
    J. C. Rasaiah and H. L. Friedman, Charged square-well model for ionic solutions, J. Phys. Chem. 72, 3352 (1968).CrossRefGoogle Scholar
  102. 102.
    J. C. Rasaiah, Computations for higher valence electrolytes in the restricted primitive model, J. Chem. Phys. 56, 3071 (1972).CrossRefGoogle Scholar
  103. 103.
    F. H. Stillinger and R. Lovett, Ion-pair theory of concentrated electrolytes. I. Basic concepts, J. Chem. Phys. 48, 3858 (1968).CrossRefGoogle Scholar
  104. 104.
    F. H. Stillinger and R. Lovett, General restriction on the distribution of ions in electrolytes, J. Chem. Phys. 49, 1991 (1968).Google Scholar
  105. 105.
    T. L. Hill, On the theory of the Donnan membrane equilibrium, Discuss. Faraday Soc. 21, 31 (1956).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • Harold L. Friedman
    • 1
  • William D. T. Dale
    • 1
  1. 1.Department of ChemistryState University of New York at Stony BrookStony BrookUSA

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