Perturbation expansion for Onsager's linear law for wien dissociation of a weak electrolyte

Abstract

The partial differential equation governing the distribution function for oppositely charged ion pairs in a weak electrolyte in the presence of a uniform applied electric field, is separated into two ordinary differential equations. By means of a perturbation expansion in terms of the field dependent parameter β_q, where β is proportional to the magnitude of the applied field and q is the Bjerrum association distance, these ordinary differential equations are solved to first order in β_q. Using this result, the linear law for the relative increase in the dissociation constant due to the application of the external field is derived. This result agrees with Onsager's well known closed from expression to first order in β_q. The possibility of extending this method to terms of higher order in β_q is discussed.