Non-equilibrium kinetics of bimolecular exchange reactions. Part 2.—Improved formalism and applications to H + H2→ H2+ H and its isotopic variants

Abstract

The master equation describing the steady thermal-exchange reaction, A + BC → AB + C, is solved. Reaction from any vibrational level of BC is considered, and BC can become vibrationally excited by A, by BC, and by any inert diluent. An exact analytical expression is obtained for the phenomenological rate of reaction and for the non-equilibrium vibrational population distribution of BC. The latter is described by a non-equilibrium statistical partition function. The validity of an even simpler but more approximate rate law of a previous study (J. Chem. Soc., Faraday Trans. 2, 1988, 84, 1889) is also confirmed.The distortion to the rates of the reactions H(D)+ H2(D2) is investigated in detail. Microscopic rate constants for reaction and V–T energy transfer are taken from the literature and used in the exact expression. The depression of the reaction rate is most pronounced at intermediate temperatures of ca. 2500 K, at intermediate ratios of atom-to-diatom concentrations of, for example, ca. 1 : 100, and reaches a limiting value of ≲ 20% in the absence of an inert diluent. The effect is more pronounced in the presence of Ar than in the presence of He. Of the four isotopic variations, the H + D2 reaction is the most susceptible to non-equilibrium effects which are prominent at ca. 1500 K. On the other hand, the H + H2 reaction is the least affected, but the distortion persists at temperatures as high as 6000 K. Non-equilibrium effects do not contribute to non-Arrhenius curvature below room temperature in the hydrogen-exchange reaction.