Transfer of vibrational-rotational energy in thermal reactions: approximations, application to diatomics

Abstract

A thermal system is considered, consiting of a reactant diluted in a heat bath of inert gas, undergoing decomposition at low pressure; thus collisional activation is the rate-determining process. If collissions are assumed to transfer both vibrational and rotational energy, the master equation becomes two-dimensional, ultimately involving an intractable four-fold integration. Two approximate solutions are developed that permit removing one of the dimensions from the integrations. On the basis of a simplified model, involving exponential vibrational and rotational transition probabilities, it is shown that the socalled fixed- v approximation is the most reasonable one. It represents essentially the rate of rotational dissociation at a given vibrational energy, averaged over an appropriate non-equilibrium vibrational distribution function. The model and the approximation are tested on the thermal dissociation of H 2 and shown to give excellent results. The treatment can be readily generalized to polyatomic reactants and other forms of the transition probabilities.