On the theory of the strange and unconventional isotopic effects in ozone formation

Abstract

The strange mass-independent isotope effect for the enrichment of ozone and the contrastingly unconventional strong mass-dependent effect of individual reaction rate constants are studied using statistical (RRKM)-based theory with a hindered-rotor transition state. Individual rate constant ratios of recombination reactions and enrichments are calculated. The theory assumes (1) an “η-effect,” which can be interpreted as a small deviation from the statistical density of states for symmetric isotopomers, compared with the asymmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. A partitioning effect controls the recombination rate constant ratios. It arises from small differences in zero-point energies of the two exit channels of dissociation of an asymmetric ozone isotopomer, which are magnified into large differences in numbers of states in the two competing exit channel transition states. In enrichment experiments, in contrast, this partitioning factor disappears exactly [Hathorn and Marcus, J. Chem. Phys. 112, 9497 (2000)], and what remains is the η-effect. Both aspects can be regarded as “symmetry driven” isotopic effects. The two experiments, enrichments and rate constant ratios, thus reveal markedly different theoretical aspects of the phenomena. The calculated low-pressure ozone enrichments, the low-pressure recombination rate constant ratios, the effects of pressure on the enrichment, on the individual recombination rate constant ratios, and on the recombination rate constant are consistent with the experimental data. The temperature dependence of the enrichment and of the recombination rate constant ratios is discussed and a variety of experimental tests are proposed. The negative temperature dependence of the isotopic exchange rate constant for the reaction O+16O18O→18O16O+18O18 at 130 K and 300 K is used for testing or providing information on the nature of a variationally determined hindered-rotor transition state. The theory is not limited to ozone formation but is intended to apply to other reactions where a symmetrical stable or unstable gas phase molecule may be formed.