On the rate constant for reactions between ions in solution: a simple unification of the Born and Debye–Hückel models

Abstract

The rate of reaction between ions in solution depends on solvent properties like permittivity and ionic strength. The influence of a solution's ionic strength is described by the Brønsted–Bjerrum equation. We show how this equation can be derived directly from transition-state theory without introducing the concept of activity coefficients. The electrostatic contribution to the activation energy is extracted from the electric potential of an ion, according to the Debye–Hückel theory. The derivation also gives a contribution to the activation energy, which corresponds to the Born model for ions represented as spherical charged particles. That is, for a given solvent permittivity, the dependence on ion radii is also displayed. This approach provides enhanced physical insights into the description of reactions where ions are participating.