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 , where is n the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example and , and 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 and selected species containing , in the molecules and the 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
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
Fundamental individual isotope equilibrium constants
Comparison of methods
Example calculation using PHREEQC
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