Skip to main content
SpringerLink
Log in

Theory of Ionic Solutions at Equilibrium

  • Chapter
The Physics and Chemistry of Aqueous Ionic Solutions

Part of the book series: NATO ASI Series ((ASIC,volume 205))

Abstract

The pair correlation function theory of ionic interactions in solution is developed using cluster theory methods. Fluctuation theory provides a natural entry to McMillan-Mayer solution theory. It is complemented by a similar operation on the Ornstein-Zernike equation which leads to important conditions on the solvent-averaged interactions among the ions. Certain inconsistencies in the theory which are identified seem to have remarkably little effect on the success of model calculations with solvent-averaged pair potentials, even for electrolyte mixture coefficients which depend on interactions in ion triples and larger clusters, and even for the rate constants of activation-controlled reactions of ionic species.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References and Footnotes

  1. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press, New York, 1976.

    Google Scholar 

  2. G. Stell in Graph Theory and Theoretical Physics, Academic Press, New York, 1967. editor F. Harary

    Google Scholar 

  3. H. L. Friedman, A Course in Statistical Mechanics, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1985.

    Google Scholar 

  4. I. R. McDonald and K. Singer, Chem. Britain, 9, 544 (1973).

    Google Scholar 

  5. For any function f(r) we denote the Fourier transform and its inverse as, respectively,F(k)=∫ f(r)eik•r d3r ; f(r) = (2π)-3 ∫ F(k) e-k•r d3k We make much use of the convolution theorem: The Fourier transform of ∫f(r-R)d3Rs(R) is the product of the transforms F(k)S(k).

    Google Scholar 

  6. G. W. Neilson and J. E. Enderby, Proc. Roy. Soc. (London) A390, 353 (1983).

    Google Scholar 

  7. The details involving graphical notation and conventions, symmetry numbers, and the three lemmas which help with analytical manipulations, are needed to take full advantage of the power of the graphical methods. See references 1–3, for example.

    Google Scholar 

  8. It is sometimes useful to notice that the prescription for B(r) in terms of f bonds may be replaced by one in terms of h bonds. See for example, R. J. Bacquet and P. J. Rossky, J. Chem. Phys. 79, 1419 (1983).

    Article  CAS  Google Scholar 

  9. D. M. Ceperley and G. V. Chester, Phys Rev. A15, 755 (1977). F. Lado, S. M. Foiles, and N. W. Ashcroft, Phys. Rev. A28, 2374 (1983).

    Google Scholar 

  10. E. Thiele, J. Chem. Phys 39, 474 (1963). M. S. Wertheim, Phys. Rev. Lett. 10, 321 (1963).

    Article  Google Scholar 

  11. L. Blum in Theoretical Chemistry Academic Press, New York, 1980, D. Henderson, editor, Vol. 5, Chapter 1. R. J. Baxter, J. Chem. Phys. 52,4559 (1968). E. Waisman and J. L. Lebowitz J. Chem. Phys. 56, 3086, 3093 (1972).

    Google Scholar 

  12. F. H. Stillinger and R. Lovett, J. Chem. Phys. 48, 3858 (1968).

    Article  CAS  Google Scholar 

  13. D. J. Mitchell, D. A. McQuarrie, A. Szabo, and J. Groeneveldt J. Stat. Phys. 17, 15 (1977).

    Article  Google Scholar 

  14. G. Stell, J. S. Høye, and G. N. Patey, Adv. Chem. Phys. 48, 183 (1981).

    Article  CAS  Google Scholar 

  15. F. H. Stillinger and R. Lovett J. Chem. Phys. 49, 1991 (1968).

    Google Scholar 

  16. H. L. Friedman and W.D.T.Dale, in Modern Theoretical Chemistry,Plenum Press, New York, Vol. 5:Statistical Mechanics, p. 85. B. J. Berne, editor.

    Google Scholar 

  17. H. L. Friedman, Faraday Disc. 64, 7 (1977).

    Article  Google Scholar 

  18. J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 19, 744 (1951).

    Article  Google Scholar 

  19. H. L. Friedman and P. S. Ramanathan, J. Phys.Chem. 74, 3756 (1970).

    Article  CAS  Google Scholar 

  20. R. L. Perry and J. P. O’Cornell, Mol. Phys. 11, 1 (1984).

    Google Scholar 

  21. W. G. McMillan and J. E. Mayer, J. Chem. Phys. 13, 276 (1945).

    Article  CAS  Google Scholar 

  22. H. L. Friedman, Ionic Solution Theory, Wiley, New York, 1962.

    Google Scholar 

  23. C. V. Krishnan and H. L. Friedman, J. Solution Chem. 3, 727 (1974).

    Article  CAS  Google Scholar 

  24. R. Triolo, L. Blum and M. A. Floriano, J. Phys. Chem. 82, 1368 (1978).

    Article  CAS  Google Scholar 

  25. W. H. Streng and W. Y. Wen, J. Solution Chem. 3, 65 (1974).

    Article  Google Scholar 

  26. P. S. Ramanathan and H. L. Friedman, J. Chem. Phys. 54, 1086 (1971).

    Article  CAS  Google Scholar 

  27. P. S. Ramanathan, C. V. Krishnan, and H. L. Friedman, J. Solution Chem. 1, 237 (1972)

    Article  Google Scholar 

  28. D. Bratko, H. L. Friedman, and E. C. Zhong, J. Chem. Phys. 85, 377 (1986).

    Article  CAS  Google Scholar 

  29. H. L. Friedman, C. V. Krishnan, and L. P. Hwang in Structure of Water and Aqueous Solutions, Verlag Chemie Gmbh, 1974. Editor W. Luck

    Google Scholar 

  30. H. L. Friedman, C. V, Krishnan, and C. Jolicouer,, Ann. New York Academy Sci. 264, 79 (1973).

    Article  Google Scholar 

  31. B. M. Pettitt and P. J. Rossky J. Chem. Phys. 84, 5836 (1986).

    Article  CAS  Google Scholar 

  32. G. N. Patey and S. L. Carnie, J. Chem. Phys, 78, 5183 (1983).

    Article  CAS  Google Scholar 

  33. M. Berkowitz, O. A. Karim, A. McCammon, and P. J. Rossky, Chem. Phys. Lett. 105 577 (1984).

    Article  CAS  Google Scholar 

  34. S. A. Adelman, Chem. Phys. Lett. 3 8, 567 (1976).

    Article  CAS  Google Scholar 

  35. S. A. Adelman J. Chem. Phys. 64, 724 (1976).

    Article  CAS  Google Scholar 

  36. J. E. Mayer, J. Chem. Phys. 18, 1426 (1950).

    Article  CAS  Google Scholar 

  37. M. Setchenow, Ann. chim. phys.,[6] 25, 226 (1892).

    Google Scholar 

  38. An exact expression for kca,b in terms of Gca,b or even Gab (!) can be obtained from Eqs. (3.4), (3.31), and (5.5). /29/ The form given here is only accurate if the solution is dilute enough so that kca,b is independent of solute concentrations, in which case it reduces to a combination of second virial coefficients./3/

    Google Scholar 

  39. G. R. Haugen and H. L. Friedman, J. Phys. Chem. 60, 1363 (1956).

    Article  CAS  Google Scholar 

  40. P. J. Rossky and H. L. Friedman, J. Phys. Chem. 84, 587 (1980).

    Article  CAS  Google Scholar 

  41. T. K. Lim, E. C. Zhong, and H. L. Friedman, J. Phys. Chem. 90, 144 (1986).

    Article  CAS  Google Scholar 

  42. H. L. Friedman, Kinam 3, 101 (1981).

    Google Scholar 

  43. L. Blum and A. J. Torruella, J. Chem. Phys. 56, 303 (1972).

    Article  CAS  Google Scholar 

  44. H. L. Friedman, J. Chem. Phys. 76, 1092 (1982).

    Article  CAS  Google Scholar 

  45. C. G. Gray and K. E. Gubbins, Theory of Molecular Fluids, Oxford, 1984.

    Google Scholar 

  46. G. Stell and J. S. Høye, Faraday Discussion. 64, 17 (1977).

    Google Scholar 

  47. J. B. Hubbard and L. Onsager, J. Chem. Phys. 68, 1649 (1977). J. B. Hubbard, P. Colonomos, and P. G. Wolynes, J. Chem. Phys. 71, 2652 (1979).

    Article  Google Scholar 

  48. P. G. Kusalik and G. N. Patey, J. Chem. Phys. 79, 4468 (1983).

    Article  CAS  Google Scholar 

  49. R. B. Cassel and R. H. Wood, J. Phys. Chem. 78, 1924 (1974).

    Article  CAS  Google Scholar 

  50. H. L. Friedman and and C. V. Krishnan, J. Phys. Chem, 78, 1927 (1974).

    Article  CAS  Google Scholar 

  51. H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolyte Solutions, 3rd edition, Reinhold, New York, 1972.

    Google Scholar 

  52. H. L. Friedman, J. Chem. Phys. 32, 1134 (1960),

    Article  CAS  Google Scholar 

  53. H. L. Friedman and B. Larsen, J. Chem. Phys. 70, 92 (1979).

    Article  CAS  Google Scholar 

  54. H. L. Friedman and B. Larsen, Pure and Applied Chem. 51, 2147 (1979).

    Article  CAS  Google Scholar 

  55. H. L. Friedman, J. Solution Chem. 1, 387, 418 (1972).

    Google Scholar 

  56. G. Brown and N. Sutin, J. Am. Chem. Soc. 101, 883 (1979).

    Article  CAS  Google Scholar 

  57. K. Laidler, Chemical Kinetics, McGraw-Hill Book Co. New York, 1965.

    Google Scholar 

  58. F. Hirata, H.L. Friedman, M. Holz, and H. G. Hertz, J. Chem. Phys. 73, 6031 (1980).

    Article  CAS  Google Scholar 

  59. P. H. Fries, N. R. Jaganathan, F. G. Herring, and G. N. Patey, J. Chem. Phys. 80, 6267 (1984).

    Article  CAS  Google Scholar 

  60. B. L. Tembe, H. L. Friedman, and M. D. Newton, J. Chem. Phys. 76 1490 (1982).

    Article  CAS  Google Scholar 

  61. A. R. Altenberger and H. L. Friedman, J. Chem. Phys., 78, 4162 (1983).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, State University of New York, Stony Brook, N.Y., 11794, USA

    Harold L. Friedman

Authors
  1. Harold L. Friedman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire Léon Brillouin (CEA-CNRS), Centre d’Estudes Nucléaires de Saclay, France

    M.-C Bellissent-Funel

  2. H. H. Witts Physics Laboratory, University of Bristol, UK

    G. W. Neilson

Rights and permissions

Reprints and permissions

Copyright information

© 1987 D. Reidel Publishing Company

About this chapter

Cite this chapter

Friedman, H.L. (1987). Theory of Ionic Solutions at Equilibrium. In: Bellissent-Funel, MC., Neilson, G.W. (eds) The Physics and Chemistry of Aqueous Ionic Solutions. NATO ASI Series, vol 205. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3911-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3911-0_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8236-5

  • Online ISBN: 978-94-009-3911-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation