Molecular and phenomenological rate coefficients of fast reactions in solutions

Abstract

The paper is concerned with the problem of formulating chemical rate equations for reversible reactions in solution in terms of concentration-independent, phenomenological rate coefficients. These time-dependent rate coefficients approach, after an initial transient, the rate constants that can be obtained in a relaxation experiment. We start with the coupled evolution equations for the macroscopic concentrations, and for the two-particle distribution functions describing association–dissociation (A+B=C), bimolecular isomerization (A+B=B+C), and double decomposition (A+B=C+D). The effects of interparticle forces and long-ranged reactivity are included. We derive general identities linking the reactants and products radial distribution functions. For association–dissociation this leads to relations among the molecular rate coefficients which are valid for both contact and long ranged reactivities. For the other two reaction types, we were able to derive analogous relations only for contact reactivities. We demonstrate how the phenomenological rate coefficients can be defined via the solutions of the corresponding diffusional boundary-value problems. This approach is quite general, and valid for both contact and long-ranged reactivities and if interaction forces are included.