Thermodynamic and kinetic constants for isotopic fractionation modeling with or without major isotope hypothesis

Abstract

Abstract The modeling capacities of geochemical speciation and reactive transport software continue to develop, and stable isotopes are now increasingly incorporated into these codes. Isotopic fractionation associated with a given chemical reaction is commonly modeled by affecting different calculated rate and thermodynamic constants for each explicitly defined isotopologue based on the classical rate and thermodynamic constant of a reaction and the fractionation factor associated to the modeled reaction. This approach has been reliably demonstrated for cases in which one isotope is much more abundant (i.e. common) than the others (e.g. carbon, oxygen, nitrogen, etc.). Such large disparity in abundance allows the assumption that the thermodynamic constant of the isotopologue bearing the major isotope is essentially equal to the classical constant for the element. Kinetic rate constants for different isotopologues are also frequently determined by assuming that the rate of the reaction involving the major isotope is very close to the overall rate. As our ability to accurately measure more isotopic systems expands, it becomes necessary to define the scope of validity of the rare isotope hypothesis and the errors introduced in application to elements like chlorine, bromine, zinc or others that do not present a clearly abundant major isotope. This study reviews the mathematical developments of thermodynamic and kinetic rate constant calculations following the major isotope hypothesis and expands upon this basis to provide appropriate thermodynamic parameterization where this assumption could introduce errors. The results show that the assumption brought by the major isotope hypothesis is also valid in isotopic systems without a major isotope for the determination of thermodynamic constants. This verification assures our ability to employ geochemical speciation codes to handle isotopic fractionation for a large variety of elements. The validity stems from the typically small deviations of relative concentrations and small differences in behavior for different isotopes. We illustrate these developments with an application case of zinc isotope fractionation modeling during sphalerite precipitation performed with the reactive transport code Hytec. The model scripts used for the application case are provided in this study and offer the opportunity for future benchmarking of software in application to explicit modeling of stable isotope fractionation.