Kinetics of isotope exchange reactions involving intra- and intermolecular reactions: 1. Rate law for a system with two chemical compounds and three exchangeable atoms

For an isotopic exchange reaction between two compounds (X and AB) in a homogeneous system, such as a gaseous or aqueous system, where one (AB) of them possesses two exchangeable atoms in non-equivalent positions and where one intramolecular isotope exchange (A ↔ B) and two intermolecular isotope exchange reactions (X ↔ A and X ↔ B) may occur, its rate law no longer obeys a pseudo-first order rate equation described for simple two-component systems by many previous investigators. The change with time of the δ value of each of the three components (X, A, and B) in a closed and homogeneous system is a complicated function of the initial δ values of the three components, the chemical concentrations of the two compounds, and the overall rate constants of the forward and reverse reactions involving the two intermolecular and one intramolecular reactions of isotope exchanges. Also, for some one of the three components, the change of its δ value with time may not be monotonic, and the relationship of 1n (1 - F) with time may be non-linear in a plot of 1n (1 - F) vs. t. In addition, the rate law of the isotope exchange reaction in this system also provides a quantitative method to estimate the overall rate constants for the one-intra-and two intermolecular isotope exchanges and the equilibrium isotopic fractionation factors among the three components