Rayleigh equation for evolution of stable isotope ratios in contaminant decay chains
Résumé
In isotope geochemistry, the Rayleigh equation describes the evolution of isotope ratios in a parent compound as a function of reaction progress, and associated equations describe isotope ratios in an instantaneous product and an accumulated product. The Rayleigh equation is commonly used for fitting fractionation factors of processes undergoing kinetic isotope fractionation such as biochemical reactions. This work extends the equations associated with the Rayleigh equation for describing the isotope ratios in intermediate products in a chain of reacting species degrading with first-order kinetics. A general solution is presented for decay chains of any length, and explicit examples are presented for the biodegradation of a substrate or a mixture of substrates through 3 intermediate products to a final product. Applications of these analytical solutions for the fitting of enrichment factors for intermediate compounds in laboratory experiments are demonstrated with a spread-sheet. This avoids separate experiments to measure each intermediate product. The utility of the equations for the assessment of slopes in dual isotope plots is furthermore illustrated, and limitations of its use are critically discussed. (C) 2013 Elsevier Ltd. All rights reserved.