Biogeochemistry of Sulfur Isotopes

TL;DR: In this paper, the natural abundances of stable sulfur isotopes have been investigated and the generalized isotope equilibrium between two chemical species is presented in Equation (3), where an equilibrium constant, Keq, may be found.

Abstract: Sulfur, with an atomic weight of 32.06, has four stable isotopes. By far the most abundant is 32S, representing around 95% of the total sulfur on Earth. The next most abundant isotope is 34S, followed by 33S, and finally 36S is the least abundant contributing only 0.0136% to the total (Table 1⇓). The natural abundances of sulfur isotopes, however, vary from these values as a result of biological and inorganic reactions involving the chemical transformation of sulfur compounds. For thermodynamic reasons, the relative abundance of sulfur isotopes can vary between coexisting sulfur phases. This is because lighter masses partition more of the total bond energy into vibrational rather than translational modes. Bonds with a higher vibrational energy are also more easily broken which is why lighter isotopes are generally enriched in the reaction products in chemical reactions with associated fractionation. Thus, for a nonreversible chemical reaction, as often occurs in biological systems, independent reactions may be written for the transformation of the light, L, and heavy, H, isotopes of reactant, A, to product, B (Eqns. 1 and 2). View this table: Table 1. Natural abundance ofstable sulfur isotopesa \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[A\_{H}\ {{\rightarrow}\_{}^{k\_{H}}}\ B\_{H}\] \end{document}(1) \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[A\_{L}\ {{\rightarrow}\_{}^{k\_{L}}}\ B\_{L}\] \end{document}(2) Each of these reactions has associated rate constants, kH and kL, and as described above, kH is generally less than kL, yielding an enrichment of the lighter isotope in the product. Fractionations associated with a unidirectional process are referred to as kinetic fractionations. Fractionations can also occur between two chemical species at equilibrium. The basis for equilibrium fractionations is thermodynamic and, as with kinetic fractionations, is related to mass-dependent differences in bond energies between light and heavy isotopes. The generalized isotope equilibrium between two chemical species is presented in Equation (3). \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[x\ A\_{L}\ +\ y\ B\_{H}\ {\leftrightarrow}\ x\ A\_{H}\ +\ y\ B\_{L}\] \end{document}(3) From Equation (3) an equilibrium constant, Keq, may be …