The master equation is solved numerically for the time dependence of the vibrational level populations of HCl (treated as a simple harmonic oscillator) during the bimolecular exchange reaction, Br + HCl → HBr + Cl, taking into account the competition between reaction and vibrational equilibration subject to Landau–Teller T–V excitation. Strong deviations from Boltzmann distributions are found. A wide range of reactant concentrations, diluent concentrations and temperatures were explored. It was found that no significant reaction occurs before the establishment of a steady vibrational population distribution, confirming that the rate coefficient for non-equilibrium bimolecular exchange reactions can be determined from a simple analytical steady state treatment (J. Chem. Soc. Faraday Trans. 87, 229 (1991)). The rate of an isolated elementary bimolecular reaction, A + BC → AB + C, under non-equilibrium conditions can deviate seriously from the standard expression, Keq [A][BC], and is better given by the law[Formula: see text]where [R] is the concentration of the collisional equilibrator, R, and a and g are constants depending only on temperature. This generalized rate law describes not only the initial rate but also the rate all the way up to completion, in the absence of the reverse reaction.
Initial Non-Equilibrium Vibrational Population Distribution in Splitting of Four-Atomic Complex [ABCD] into AB+C+D
