A Theory of Ion Association as a Complement of the Debye-Hückel Theory

Abstract

Abstract The classical Debye-Hückel theory of strong electrolyte solutions was re-examined in order to explain ion association. Regarding a symmetrical electrolyte in very dilute solutions, a more precise expression was derived for excess chemical potential due to electrostatic ion-ion interactions. This expression has, in addition to the Debye-Hückel term, a supplementary term resulting from a more proper account of the energy of the interactions of ions existing near each other. If the concept of ion association is taken as a complement of the Debye-Hückel theory, the contribution to the chemical potential of the electrolyte from ion association should correspond to the supplementary term. The following equation was thus obtained for the ion-association constant: K=(8πNa^3/1000) \overset∞\undersetn=1∑b^2n+2/[(2n+2)! (2n-1)] This equation is in agreement with that derived by Ebeling on the basis of the cluster theory and has an asymptotic representation (at b→∞) in common with Bjerrum’s. For practical b values, the present equation has the merit that it gives moderate K values, decreasing monotonously with an increase in the a value, and eliminates the disadvantages of Fuoss’s result, giving a minimum K value at b=3, and of Bjerrum’s, giving K=0 at ≤2.