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.
Abstract
Introduction
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
CO18O
C18O2
13CO2
13CO18O
13C18O2
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
Nonideality
Temperature dependence
Fundamental individual isotope equilibrium constants
Comparison of methods
Example calculation using PHREEQC
Summary
References cited
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