The nonequilibrium kinetics of reversible bimolecular reactions.

Abstract

The master equation describing the rate of the bimolecular reaction A+BC&rlhar2;AB+C under steadystate conditions at the vibrational level of detail, is solved by a matrix technique. A computer program (MRBIM) has been written by the author to exploit the matrix technique as applied to the H + O 2 reaction. Reaction from levels v = 0 to 15 for O2 and from levels v = 0 to 9 for OH are considered for, while vibrational-translational (V -- T) energy transfer by O2, H, OH, O and He is considered as the mechanism for equilibration. The distortion to the fates of the reaction H+O2&rlhar2;OH+O caused by the non-equilibrium vibrational population distribution is investigated in detail. It is found that the ratio of forward and reverse fate coefficients, (kf/kr does not equal the equilibrium constant, Keq when the reaction proceeds far from equilibrium and this is because the individual rate coefficients are suppressed from their equilibrium values to different extents. We have applied information theory to the HBrv+Cl&rlhar2;HCl v'+Br reaction over a wide range of temperatures, and we have thus extracted an extensive set of state-to-state rate constants from scattered literature data. We also made use of microscopic-reversibility to obtain the exothermic state-to-state rates. Our values for the rate constants fit and extrapolate all existing data. Reaction from levels v' = 0 to 9 of HCl and levels v = 0 to 9 of HBr are considered, while vibrational- translational (V - T) energy transfer by HCl, HBr, Cl, Br, and Ar is considered. The measure of the nonequilibrium effect (kf/kr) / Keq is much more severe for reaction occuring far from equilibrium. The temperature dependence of the non-equilibrium factor is complex. An effort to solve the master equation analytically has resulted in closed form expressions for the rate law for reversible bimolecular reactions, as well as for the thermal rate coefficients, kf and kr, and for the ratio of kf/kr under highly reactive non-equilibrium conditions. They are in qualitative agreement with the exact numerical results, and under some conditions, also in quantitative agreement. Model calculations indicate that our analytical expressions improving on the kinetic mass action law, can be best used when reactivity is from v > 0, v' > 0, and when Keq ≈ 1. (Abstract shortened by UMI.)