Mathematics of wien dissociation for weak electrolytes

Abstract

Starting with Onsager's integral expression for the distribution function describing oppositely charged ion pairs in a weak electrolyte in the presence of a uniform external electric field, an alternative derivation to Onsager's is given of the closed form expression for the dependence of the electrolyte's dissociation constant on the applied field intensity. This result is independent of the choice of the spherical surface of integration, centred on the origin, of the flux of the associated ion pairs. Thus Onsager's technique of evaluating this integral “by specialization to small r”, r being the radius of the sphere centred on the origin over whose surface the integration is performed, is shown to involve no approximation in the result for the dependence of the dissociation constant on the applied field intensity.