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Calculation of individual isotope equilibrium constants for geochemical reactions

D.C. Thorstenson·D.L. Parkhurst
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Abstract

Theory is derived from the work of Urey (Urey H. C. [1947] The thermodynamic properties of isotopic substances. J. Chem. Soc . 562–581) to calculate equilibrium constants commonly used in geochemical equilibrium and reaction-transport models for reactions of individual isotopic species. Urey showed that equilibrium constants of isotope exchange reactions for molecules that contain two or more atoms of the same element in equivalent positions are related to isotope fractionation factors by α = (K ex ) 1/n , where n is the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example 13 C 16 O 18 O and 1 H 2 H 18 O. The equilibrium constants of the isotope exchange reactions can be expressed as ratios of individual isotope equilibrium constants for geochemical reactions. Knowledge of the equilibrium constant for the dominant isotopic species can then be used to calculate the individual isotope equilibrium constants. Individual isotope equilibrium constants are calculated for the reaction CO 2g = CO 2aq for all species that can be formed from 12 C, 13 C, 16 O, and 18 O; for the reaction between 12 C 18 O 2aq and 1 H 2 18 O l ; and among the various 1 H, 2 H, 16 O, and 18 O species of H 2 O. This is a subset of a larger number of equilibrium constants calculated elsewhere (Thorstenson D. C. and Parkhurst D. L. [2002] Calculation of individual isotope equilibrium constants for implementation in geochemical models. Water-Resources Investigation Report 02-4172. U.S. Geological Survey). Activity coefficients, activity-concentration conventions for the isotopic variants of H 2 O in the solvent 1 H 2 16 O l , and salt effects on isotope fractionation have been included in the derivations. The effects of nonideality are small because of the chemical similarity of different isotopic species of the same molecule or ion. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation factors. The derivations can be extended to calculation of individual isotope equilibrium constants for ion pairs and equilibrium constants for isotopic species of other chemical elements. The individual isotope approach calculates the same phase isotopic compositions as existing methods, but also provides concentrations of individual species, which are needed in calculations of mass-dependent effects in transport processes. The equilibrium constants derived in this paper are used to calculate the example of gas-water equilibrium for CO 2 in an acidic aqueous solution.

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D.C. Thorstenson, D.L. Parkhurst. 2004. Calculation of individual isotope equilibrium constants for geochemical reactions. https://doi.org/10.1016/j.gca.2003.11.027

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