The correction to the equilibrium rate of reaction in a one‐component reactive system is calculated from the perturbation of the velocity distribution function obtained by solving the Chapman–Enskog and Burnett equations. A method of solution of the Chapman–Enskog equation with a Sonine polynomial expansion is described that is not limited by the number of terms retained and is applicable to realistic systems characterized by elastic and reactive cross sections which may be available only in tabulated form. The convergence of the Sonine polynomial expansion is demonstrated for a variety of model reactions with and without activation energy and for a set of cross sections obtained with a semiempirical potential for the reaction H2(i) + H2(j) → (products), where i and j denote the vibrational quantum numbers. The Sonine polynomial method is compared with the recent variational solutions of Present and Morris. It is shown that the extent of the departure from equilibrium is due to the deviation of the reacti...

Nonequilibrium Contributions to the Rate of Reaction. I. Perturbation of the Velocity Distribution Function

The phenomenological rate equations for reactions in which three or more chemical species are simultaneously interconverting are derived from a microscopic stochastic model. Particular attention is focused on the establishment of long chemical relaxation times, and on an important orthogonality property which guarantees that the principle of detailed balancing is obeyed. By developing a quantum mechanical analog, the mathematical origins of both of the above properties are related to a resonance phenomenon associated with three or more wells separated by high energy barriers. The quantum analog is itself equivalent to a stochastic master equation, the rate constants of which are analytically determined. These are shown to contain the expected Arrhenius factors and to obey the principle of the independent coexistence of reactions.

Stochastic models of the interconversion of three or more chemical species

https://science.sciencemag.org/content/sci/148/3677/1555.full.pdf

Molecular Transitions and Chemical Reaction Rates: The stochastic model relates the rate of a chemical reaction to the underlying transition probabilities.

The technique described in previous papers of this series has been used to measure separately the rate coefficients k1 for the reaction Cl + H2 → HCl + H over the temperature range 251°–456°K, and k−1 for the reverse reaction over 195°–497°K. Both sets of data are Arrhenius linear and obey (cm3 mole − 1·sec − 1) k1 = 1.2 × 1013exp ( − 4300 / RT); k − 1 = 2.3 × 1013exp ( − 3500 / RT). Interpretation of the individual rate coefficients is made in terms of absolute rate theory with no tunneling, using a potential surface constructed by the semiempirical Sato method for a linear transition complex. The properties of the complex give a theoretical pre‐exponential factor for the forward reaction about 2.5 times higher than experiment, while that for the reverse reaction is in fair agreement with experiment. It is shown that the ratio k1 / k − 1 is a factor of 2–3 below the thermodynamic equilibrium constant over the experimental temperature range. A possible qualitative explanation for this deviation from the s...

Atom–Molecule Kinetics using ESR Detection. IV. Results for Cl + H2 ⇄ HCl + H in Both Directions

Three distinct topics in the theory of stochastic models of chemical reaction kinetics are discussed. The first, treated in Sec. II, concerns the case of two or more simultaneous reactions, as typified by the mutual interconversion of three or more species. The formula that relates the rate constants to the microscopic transition rates is discussed. The same formula, alternatively interpreted, is then seen also to be the relation that one would use to derive experimental rate constants from the amplitudes and time constants that are the primary experimental data. The second topic is that treated in Sec. III, which is on a class of stochastic models for which the conventional steady‐state approximation is essentially exact. The origins and implications of that circumstance are discussed. The third subject is that of Sec. IV, on a fundamental difference between three‐center exchange reactions A+BC⇄AB+C and (bimolecular) isomerizations A⇄B. The difference is in certain dynamical features of the respective collision mechanisms, which in one case imply that an ``equilibrium'' approximation to the rate constant, such as that given by transition‐state theory, would be a good approximation, and in the other case not.

O. K. Rice

Papers

On the relation between an equilibrium constant and the nonequilibrium rate constants of direct and reverse reactions1