Kinetics of heterogeneous isotopic exchange reactions: derivation of an Elovich equation

Abstract

A derivation is presented for an Elovich equation, d θ /d t = A exp (– Bθ ), describing the kinetics of heterogeneous isotopic exchange reactions involving non-uniform surfaces of solids. By considering a small element of the surface, an equation was obtained relating the rate of transfer of isotope to the rate at which all the molecules of the exchanging species undergo exchange at that element; the effect on kinetics due to the development of excess isotope concentrations on more labile surface sites during isotopic exchange was taken into account. The Elovich equation for exchange over the whole surface was then obtained by an approximate integration procedure previously used in the kinetics of chemisorption of gases on solids, assuming that the activation energies for exchange were a linear function of θ . The term θ was related to the experimentally measured fraction exchange F by θ = bF/[ b + a (1 – F)] where a and b are the concentrations of the exchanging species in the system, in the adsorbed and free states respectively. The derivation indicates methods for obtaining concentration independent rate constants from the parameters A and B .