The linear mixture formula in non-equilibrium chemical kinetics

Abstract

The recent extensions of the 'eigenvalue approximation' of non-equilibrium kinetics proposed by Bartis and Widom to explain in a direct qualitative sense some general features of phenomenological chemical kinetics in ideal gas systems, have been used to investigate the problem of the 'linear mixture formula' applied to non-equilibrium kinetics of reactions proceeding in mixtures. For isomerization reactions in mixtures dilute in reactant, the model of Bartis and Widom, without further embellishment, has been shown to justify such an equation. Extrapolation of this result to account for recent empirical successes of a linear mixture formula in dissociation–recombination reactions of diatomic molecules X2 is not straightforward; the physical implications of the mathematical approximations employed are examined, and the non-linear recombination term is accounted for in the present purely qualitative context by an appropriate linearization. However, the appreciable contributions from X2–X2 collisions, under the conditions of the experiments cited, introduce inescapable non-linearities if vibration–vibration exchange, for example, is important. Problems associated with the role of the free atom X as a collision partner seem likely to be less important.