Abstract
A kinetic model, with only one kinetic variable κ, is developed to describe the isotope-exchange reaction CD+5 + CH4 → products (and its mirror-isotope counterpart). Each reaction yields four products and, at a particular temperature, a single value of κ is able to specify all eight rate constants. According to the model, the reactants form the intermediate CD+5 · CH4, which can then rearrange to CD4 · CH4+ etc., by a sequence of intramolecular proton/deuteron transfers. The rearrangement (characterized by a rate constant k1) competes with the dissociation of the intermediates (characterized by a rate constant k2). The kinetic variable, κ, is shown to be κ = k1/k2. where κ is identified as the average number of proton/deuteron jumps occurring during the lifetime of the intermediate.
Average proton/deuteron jump times within the intermediate (l/k1) range from 220 ps at 80K to 20 ps at 475K. These values are derived by fitting the model to the kinetic data and from estimates of the intermediates' lifetimes (measured from three-body association).
Kinetic isotope effects are identified and are predicted by the model. Isotope effects on k2 alter the relative product distribution—the most endothermic channels becoming increasingly disfavored as the temperature is reduced. Isotope effects on k1 affect the overall rate constant at the highest temperature. Where the lifetime is very short, effectively only one jump occurs; the proton is shown to jump almost twice as fast as the deuteron.
The overall kinetics show a negative temperature dependence, k ∝ T−1. The model shows this to be a compromise. The lifetime of the intermediate shows a T−3 temperature dependence and this is moderated by the temperature dependence for the proton/deuteron jumping, k1 ∝ T1.5.
The model is also applied to the corresponding reactions for the water and ammonia systems. Because isotopic exchange is effectively complete at all the temperatures investigated, only upper bounds are derived for the average proton/deuteron jump times for these two systems.