ELLIPTIC INTEGRAL SOLUTIONS FOR THE KINETICS OF AUTOCATALYTIC TERMOLECULAR REACTIONS WITH REACTIVE INTERMEDIATE SPECIES

The kinetics of an autocatalytic termolecular reaction with overall st oichiometry of A + B --> C + D was investigated. It is assumed that ea ch of the three components A, B and C dissociate into reactive interme diate species, with equilibrium always established in all three cases. The rate-limiting step is then assumed to be the reaction between the intermediates formed from A and B, respectively, catalyzed by the rea ctive intermediate formed from product C. Integration of the different ial equation describing the chemical kinetics of this process was perf ormed for various special cases of initial reactant concentrations-sto ichiometric and non-stoichiometric. The analytical solution in the lat ter case incorporates incomplete elliptic integrals of the first kind. Numerical values of reaction times may then be readily computed with the aid of various extensive compilations of elliptic integrals. (C) 1 997 Elsevier Science S.A.