On the theory of Wien dissociation for weak electrolytes

Onsager's integral expression for the distribution function of oppositely charged ion pairs in a weak electrolyte in the presence of a uniform external electric field is rewritten as a sum of ordinary Bessel functions ranging from order zero to order plus infinity. Starting from this result a derivation of Onsager's expression for the dependence of the electrolyte's dissociation constant on the field intensity is given. It is shown that this requires only the zero order term in the above summation. Further, it is proved rigorously that the remaining higher order terms make no contribution to the dissociation constant. A non-zero contribution from these higher order terms would have implied dependence on the choice of the surface over which integration is performed at an intermediate stage of the analysis.