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

Abstract

Intramolecular isotope fractionation within a molecule containing two exchangeable atoms in structurally non-equivalent positions (E.G., the two sulfur atoms in thiosulfate) leads to the complexity of the isotopic exchange between the molecule and another compound (E.G., H 2S). We have derived a rate law for the isotopic exchange reactions in a homogeneous (gaseous or aqueous) system of two-compound ( X and AB) system with three exchangeable components ( X, A, and B) where one overall intramolecular exchange ( A ⇔ B) and two overall intermolecular exchange ( X ⇔ A and X ⇔ B) reactions exist. The isotopic δ value of each component ( X, A, and B) at any time can be expressed as a function of the initial δ values of the three components, the concentrations of the two compounds, and the overall rate constants for the intra- and intermolecular isotope exchange reactions. Differing from the isotopic exchange behavior in a simple two-compound system described by previous investigators (E.G., Ohmoto and Lasaga, 1982), the changes with time of the δ values of X, A, and B may not be monotonie, because the isotopic exchange rates may not be identical for the three overall isotope exchange reactions ( A ⇔ B, X ⇔ A, and X ⇔ B). The In (1 − F) vs. time curve for the overall reaction between the two compounds ( X ⇔ AB) is generally non-linear. The rate law derived in this study was applied to a set of experimental data obtained by Uyama et al. (1985) on sulfur isotope exchange reactions between H 2S and thiosulfate (Run 120-A), where the δ 34S values of H 2S( X) and sulfane sulfur ( A) and sulfonate sulfur ( B) of thiosulfate were measured during reaction for various run times at 120°C and at near-neutral pH. From their experimental data, we were able to deduce the following sets of rate constants and equilibrium fractionation factors: logk H 2S ⇔ SH of thiosulfate = −1.4 , log k H 2S ⇔ SO 3H of thiosulfate = −2.6 , log k SH ⇔ 2SO 3H of thiosulfate = −8 , 1000 In α SH of thiosulfate-H 2S = −4.6 , 1000 In α SO 3H of thiosulfate-H 2S = 29.2 and 1000 In α SO 3H-SH of thiosulfate = 33.7 .