Journal of Solution Chemistry

, Volume 4, Issue 3, pp 249–265 | Cite as

Thermodynamics of electrolytes. V. effects of higher-order electrostatic terms

  • Kenneth S. Pitzer


The contribution of higher-order electrostatic terms (beyond the Debye-Hückel approximation) to the thermodynamic properties of mixed and pure electrolytes is investigated. It is found that these effects are important for cases of unsymmetrical mixing, especially when one ion has a charge of three units or more. The appropriate correction can be made by a purely electrostatic function since the mutual repulsion of ions of the same sign keeps them far enough apart that short-range forces have little effect. This function is evaluated, and several convenient approximations are also given. Application is made to systems mixing ions of the type 1–2 and 1–3. Higher-order limiting laws exist for symmetrical mixtures and for pure, unsymmetrical solutes, but these effects were not found to be significant in relationship to existing activity or osmotic-coefficient data.

Key words

Activity coefficient osmotic coefficient thermodynamics electrolytes solution theory 


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  1. 1.
    K. S. Pitzer,J. Phys. Chem. 77, 268 (1973). Minor typographical errors in refs. 1–4 are corrected in subsequent papers of the series.Google Scholar
  2. 2.
    K. S. Pitzer and Guillermo Mayorga,J. Phys. Chem. 77, 2300 (1973).Google Scholar
  3. 3.
    K. S. Pitzer and Guillermo Mayorga,J. Solution Chem. 3, 539 (1974).Google Scholar
  4. 4.
    K. S. Pitzer and Janice J. Kim,J. Am. Chem. Soc. 96, 5701 (1974).Google Scholar
  5. 5.
    T. H. Gronwall, V. K. LaMer, and K. Sandved,Physik. Z. 29, 558 (1928).Google Scholar
  6. 6.
    H. P. Stock and B. Plewinsky,Ber. Bunsenges. Physik. Chem. 76, 694 (1972). Supplementary details have also been kindly provided by the authors through correspondence.Google Scholar
  7. 7.
    H. L. Friedman,Ionic Solution Theory (Interscience Publishers, New York, 1962).Google Scholar
  8. 8.
    R. A. Robinson, R. H. Wood, and P. J. Reilly,J. Chem. Thermodyn. 3, 461 (1971).Google Scholar
  9. 9.
    J. E. Mayer,J. Chem. Phys. 18, 1426 (1959).Google Scholar
  10. 10.
    H. S. Harned and R. Gary,J. Am. Chem. Soc. 77, 1994 (1955).Google Scholar
  11. 11.
    H. S. Harned and T. R. Paxton,J. Phys. Chem. 57, 531 (1953).Google Scholar
  12. 12.
    H. S. Harned and R. Gary,J. Am. Chem. Soc. 77, 4695 (1955).Google Scholar
  13. 13.
    H. S. Harned and C. M. Mason,J. Am. Chem. Soc. 53, 3377 (1931).Google Scholar
  14. 14.
    H. S. Harned and R. Gary,J. Am. Chem. Soc. 76, 5924 (1954).Google Scholar
  15. 15.
    H. S. Harned and C. G. Geary,J. Am. Chem. Soc. 59, 2032 (1937).Google Scholar
  16. 16.
    C. J. Downes,J. Chem. Soc., Faraday Trans. I. 68, 1964 (1972).Google Scholar
  17. 17.
    S. Lindenbaum, R. M. Rush, and R. A. Robinson,J. Chem. Thermodyn. 4, 381 (1972).Google Scholar
  18. 18.
    Y. C. Wu, R. M. Rush, and G. Scatchard,J. Phys. Chem. 72, 4048 (1968);73, 2047, 4433, 4434 (1969).Google Scholar
  19. 19.
    R. A. Robinson and V. E. Bower,J. Res, Nat. Bur. Std. 70A, 313 (1966).Google Scholar
  20. 20.
    R. A. Robinson and V. E. Bower,J. Res. Nat. Bur. Std. 69A, 19 (1965).Google Scholar
  21. 21.
    C. J. Downes,J. Chem. Eng. Data 18, 412 (1973).Google Scholar
  22. 22.
    R. A. Robinson and A. K. Covington,J. Res. Nat. Bur. Std. 72A, 239 (1968).Google Scholar
  23. 23.
    R. A. Robinson and V. E. Bower,J. Res. Nat. Bur. Std. 69A, 439 (1965).Google Scholar
  24. 24.
    R. A. Robinson, R. F. Platford, and C. W. Childs,J. Solution Chem. 1, 167 (1972).Google Scholar
  25. 25.
    M. Randall and G. F. Breckenridge,J. Am. Chem. Soc. 49, 1435 (1927).Google Scholar
  26. 26.
    M. H. Lietzke and R. W. Stoughton,J. Phys. Chem. 71, 662 (1967).Google Scholar
  27. 27.
    M. H. Lietzke and M. D. Danford,J. Chem. Eng. Data 17, 459 (1972).Google Scholar
  28. 28.
    C. M. Mason and D. B. Kellam,J. Phys. Chem. 38, 689 (1934).Google Scholar
  29. 29.
    H. S. Harned and A. B. Gancy,J. Am. Chem. Soc. 62, 627 (1958). See also appendix of ref. 4.Google Scholar
  30. 30.
    H. S. Harned and O. E. Schupp, Jr.,J. Am. Chem. Soc. 52, 3892 (1930).Google Scholar
  31. 31.
    J. S. Falcone, A. S. Levine, and R. H. Wood,J. Phys. Chem. 77, 2137 (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • Kenneth S. Pitzer
    • 1
  1. 1.Inorganic Materials Research Division of the Lawrence Berkeley Laboratory and Department of ChemistryUniversity of CaliforniaBerkeley

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