Statistical Interpretations of Unimolecular Reaction Rates

Abstract

Consistency theorems are derived from the general Lindemann theory of unimolecular reaction rates; one can make several general statements about the signs of the slopes and curvatures of plots of observed rate constants against a function of the pressure. Observed rate constants and simple combinations of observed rate constants are interpreted in terms of Tolman's distribution function, the distribution of molecules which react. Moments of the ratio of rate constant for decomposition to that for deactivation by collision, ci/bi, can be found at any pressure. By means of Schwarz's inequality one can find several dimensionless quantities which provide consistency tests with respect to the statistical interpretations and which provide a check against a wrong assignment of the high- or low-pressure limit. These methods are used to examine the data for cyclobutane, cyclopropane, nitrogen pentoxide, and nitrous oxide. Previous interpretations given to the data on the last two cases are revised. The average detailed rate constants for molecules which react are estimated using an approximate relation.