A perturbation solution to the problem of Wien dissociation in weak electrolytes

Abstract

The problem of Wien dissociation of a weak electrolyte in the presence of a uniform applied electric field, X , is analysed by using a perturbation technique. The partial differential equation for the ion-pair distribution function is first reduced to an infinite system of ordinary differential equations by taking the Legendre transform . Explicit expressions for the relative increase in the dissociation constant, K ( X )/ K (0), due to the applied electric field, are calculated to second order in the expansion parameter 2 βq , where β is proportional to X and q is the Bjerrum association distance. Further, by induction, the m th term of this expansion is derived. The infinite series obtained in this way for K ( X )/ K (0) is convergent for all values of βq , and when summed, agrees with a formula in terms of an ordinary Bessel function of order one, given by onasager (1934) whose derivation has been published in full.