C. Carruthers et H. Teitelbaum, NONEQUILIBRIUM KINETICS OF BIMOLECULAR REACTIONS .6. TRANSIENT RATE COEFFICIENTS, Canadian journal of chemistry, 72(3), 1994, pp. 714-720
The master equation is solved numerically for the time dependence of t
he 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 vibrat
ional equilibration subject to Landau-Teller T-V excitation. Strong de
viations from Boltzmann distributions are found. A wide range of react
ant concentrations, diluent concentrations and temperatures were explo
red. It was found that no significant reaction occurs before the estab
lishment of a steady vibrational population distribution, confirming t
hat the rate coefficient for non-equilibrium bimolecular exchange reac
tions can be determined from a simple analytical steady state treatmen
t (J. Chem. Sec. Faraday Trans. 87, 229 (1991)). The rate of an isolat
ed elementary bimolecular reaction, A + BC --> AB + C, under non-equil
ibrium conditions can deviate seriously from the standard expression,
k(eq)[A][BC], and is better given by the law d[BC]/dt = -k(eq)4[A] [BC
]/{1+1/(a+g[R]/[A])} where [R] is the concentration of the collisional
equilibrator, R, and a and g are constants depending only on temperat
ure. 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 rev
erse reaction.