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Solution of Onsager's equation in closed form

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  • McIlroy, Douglas K.

Abstract

The problem of the Wien dissociation of a weak electrolyte to which a uniform electric field X is applied is analysed by direct solution of the partial differential equation governing the distribution of pairs of associated ions in the electrolyte (Onsager's equation). The method of solution is based on the correct choice of the characteristic numbers of the weak electrolyte which leads to a transformation of Onsager's equation into two parts both of which are identically zero in this problem. The solution reproduces Onsager's result (see L. Onsager, J. Chem. Phys. 2 (1934) 599) in the form of a definite integral for the distribution function describing associated ion pairs. The mathematical details of Onsager's solution have apparently never been published previously for this result which leads directly to his well known equation for the relative increase, KX/K0, in the dissociation constant of the weak electrolyte.

Suggested Citation

  • McIlroy, Douglas K., 1988. "Solution of Onsager's equation in closed form," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 152(3), pages 459-468.
    • Handle: RePEc:eee:phsmap:v:152:y:1988:i:3:p:459-468
    DOI: 10.1016/0378-4371(88)90200-2
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