The Master Equation for the Dissociation of a Dilute Diatomic Gas. VI. Solution of Coupled Sets of Master Equations

Abstract

Three coupled sets of master equations, representing the equilibration of X, + Y , e 2XY via atoms only, have been solved by the normal-mode technique; the set of 57 simultaneous differential equations describing the H2/D,/2HD system was considered as a suitable trial model. It was found that at times ( t ) in excess of the longest vibrational relaxation time, even though some of the populations in the system appeared highly nonBoltzmann, all the phenomenological rate constants were well-behaved: they were either constant and obeyed the rate-quotient law, or they were dependent on t2.The paper concludes with a discussion of the information required before a full solution of the X, + Y+ F! 2XY reaction could be contemplated, and suggests methods by which an approximation to such a solut~on could be obtained. IntroductionEarlier papers in this series (1-5) have been concerned with the dissociation and recombination of a homonuclear diatomic gas at infinite dilution in a bath of rozully inert atoms, and at such temperatures that rotational equilibration can be considered infinitely rapid.' In most of this work, the H, molecule has been used as a model, and having only 15 vibrational levels, can be represented by a set of 16 simultaneous differential equations; Part V addressed itself to the problem having a rather more dense energy-level spectrum, using D, as a model, and giving rise to a master equation of order 23. It is hoped that in future work, a more realistic description of the dissociation and recombination of a dilute homonuclear diatomic gas can be achieved by considering both rotational and vibrational interchanges; it should be mentioned in passing that for H,, this will require the solution of almost 400 simultaneous differential equations and the assignment of some 70 000 translational-vibrational transition probabilities; for D, the problem is even more forbidding,