An exactly soluble model of dissociation–recombination

Abstract

A master equation for a classical collinear model of collisionally induced dissociation and recombination is solved. With the choice of impulsive interaction between diatomic molecules A2 and heat-bath particles M, the results depend strongly on the value of α =arc tan(1+2mA/mM)1/2. It is found that the approach to equilibrium is not, in general, exponential in time for α=π/4, but that the relaxation is exponential for α=0.254π and α=π/3, with, however, different degrees of deviation from the equilibrium approximation. In both of these cases the inequalities kD ?k′D?keqD and kR?k′R=keqR are satisfied, where k′D and k′R are the rate constants calculated when the appropriate reverse reactions are neglected. The rate constants kD and kR are shown to have a weak dependence on the total density of reacting species. In addition, for α=0.254π, a ’’negative activation energy’’ for recombination is obtained at high temperatures.