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

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 reactive collision number R(0)(c) from a special form R̄(0)(c). It was found that for the realistic systems considered here the decrease in the equilibrium rate of reaction due to a perturbation of the velocity distribution function by reaction is very small (≲1%) and that the Burnett correction to the distribution function can be neglected. For the set of (H2, H2) reactions, the greatest decrease in the equilibrium rate of reaction is 0.66% at 6400°K for (i, j) = (3, 2). A formal transport theory description of reaction rates analogous to the description of heat conduction and viscous flow by Chapman and Cowling is also presented.