An approximate theory of the ozone isotopic effects: Rate constant ratios and pressure dependence

Abstract

The isotopic effects in ozone recombination reactions at low pressures are studied using an approximate theory which yields simple analytic expressions for the individual rate constant ratios, observed under "unscrambled" conditions. It is shown that the rate constant ratio between the two competing channels XYZ→ X + YZ and XYZ→ XY+ Z is mainly determined by the difference of the zero-point energies of diatomic molecules YZ and XY and by the efficiency of the deactivation of the newly formed excited ozone molecules, whereas the mass-independent fractionation depends on a "nonstatistical" symmetry factor and the collisional deactivation efficiency. Formulas for the pressure effects on the enrichment and on the rate constant ratios are obtained, and the calculated results are compared with experiments and more exact calculations. In all cases, ratios of isotope rates and the pressure dependence of enrichments, the agreement is good. While the initial focus was on isotope effects in the formation of O 3 , predictions are made for isotope effects on ratios of rate constants in other reactions such as O + CO → CO 2 , O+NO→ NO 2 , and O + SO → SO 2 .

Timescales for the evolution of oxygen isotope compositions in the solar nebula

“…The deficiency in intramolecular energy redistribution occurs for the symmetric isotopomers because there are roughly half as many states available as for the asymmetric isotopomers, making anharmonic and other couplings less effective (Gao and Marcus, 2001;Marcus, 2008). Application of unimolecular dissociation theory, with the inclusion of the symmetric density of states at a value $85% of the statistical density of states, yields excellent agreement Marcus, 2001, 2002) with measured isotopomer-specific rate coefficients (Mauersberger et al, 1999), and with the measured temperature and pressure dependence of the MIF signature in ozone (Gao and Marcus, 2007). It has been proposed (e.g., Thiemens, 1999) that symmetry-dependent isotopic reactions analogous to O 3 formation occurred among CAI precursors in hot regions of the solar nebula.…”

Use of Isotope Effects To Understand the Present and Past of the Atmosphere and Climate and Track the Origin of Life

“…[34][35][36][37][38] Subsequent to the discovery of Thiemens and Heidenreich, [19] besides the range of experimental quantification of parameters that influence the isotope effect, there were many attempts to develop theories that could accommodate measurements. [34][35][36][37][38] Subsequent to the discovery of Thiemens and Heidenreich, [19] besides the range of experimental quantification of parameters that influence the isotope effect, there were many attempts to develop theories that could accommodate measurements.…”

“…Thetheory behind the mass independent ozone effect has advanced considerably.T he first quantitative theory was developed by Marcus and his colleagues. [34][35][36][37][38] Subsequent to the discovery of Thiemens and Heidenreich, [19] besides the range of experimental quantification of parameters that influence the isotope effect, there were many attempts to develop theories that could accommodate measurements. Marcus developed anew approach that successfully accounted for observations.…”

Mass-Independent Isotopic Composition of Terrestrial and Extraterrestrial Materials

“…While these assumptions are valid for a gas-phase molecular reaction, they do not account for the totality of the experimental ozone isotopic observations. At present, the most complete model for the ozone effect is that of Markus and colleagues (Gao and Marcus, 2007;Hathorn and Marcus, 1999 in accounting for many of the experimental observations. RRKM theory is employed in its development, which quantitatively describes the energetics of gas-phase atomic-molecular encounters and the relevant parameters leading to either stabilization and product formation or re-dissociation to atomic and molecular species, with the energetic intermediate being a critical species.…”