U.S. Geological Survey
Water-Resources Investigations Report 02-4172

By Donald C. Thorstenson and David L. Parkhurst

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Theory is derived from the work of Urey 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 Equation relating fractionation factor to equilibrium constant, where is n the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example and Carbon-13, oxygen-16, oxygen-18 carbon dioxide, and Hydrogen-1, hydrogen-2, oxygen-18 water to include the effects of nonideality. The equilibrium constants of the isotope exchange reactions provide a basis for calculating the individual isotope equilibrium constants for the geochemical modeling reactions. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation factors. Equilibrium constants are calculated for all species that can be formed from Hydrogen-1, hydrogen-2Carbon-12, carbon-13, carbon-14 Oxygen-16, oxygen-18 and selected species containing Tritium, in the molecules Carbon dioxide gas, carbon dioxide aqueous Bicarbonate ionCarbonate ion Calcite Water vapor Liquid water Hydronium ion Hydroxide ion and the Sodium ion, potassium ionCalcium ion, magnesium ion ion pairs with where the subscripts g, aq, l, and s refer to gas, aqueous, liquid, and solid, respectively. These equilibrium constants are used in the geochemical model PHREEQC to produce an equilibrium and reaction-transport model that includes these isotopic species. Methods are presented for calculation of the individual isotope equilibrium constants for the asymmetric bicarbonate ion. An example calculates the equilibrium of multiple isotopes among multiple species and phases.




Isotope ratios in gaseous and aqueous CO2

Species and symmetry numbers

Equilbrium constants for intraspecies reactions among the CO2 species

Isotope ratios

Calculation of individual isotope equilibrium constants for the reaction CO2gas - CO2aqueous






14CO2, 14CO18O, and 14C18O2

Symmetry assumptions in the isotope ratios

Individual isotope equilibrium constants for bicarbonate

Individual isotope equilibrium constants for ion pairs

Application to other isotopes


Temperature dependence

Fundamental individual isotope equilibrium constants

Comparison of methods

Example calculation using PHREEQC


References cited


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