Revision needed for the predicted standard free energy of aqueous CO2 at elevated temperatures and pressures

In the deep Earth cycle of carbon, CO₂ is thought to play a key role. The Helgeson-Kirkham-Flowers (HKF) standard state thermodynamic properties of CO₂ dissolved in water are well established by experiment and equations of state at ambient conditions and at upper crustal pressures and geothermal temperatures (Shock et al., 1989). They have been widely used to compute aqueous equilibria and mineral-fluid equilibria with other carbon species in codes such as SUPCRT92. Extrapolation of the HKF standard state Gibbs free energy equation of state of CO₂ to higher pressures and temperatures, widely used in the Deep Earth Water (DEW) model, has not been adequately tested. Experimentally determined mineral solubilities provide such a test. However, under deep Earth conditions, the solubilities of mineral assemblages, such as classic decarbonation equilibria involve large amounts of dissolved CO₂. As a consequence, model solubilities depend on the aqueous activity coefficient of CO₂ as well as its standard state free energy. Fortunately, the activity coefficients for aqueous CO₂ have been measured (Aranovich and Newton, 1999). In the same study, the decarbonation equilibria give us measured solubilities of CO₂ when the mole fractions of CO₂ are converted to molalities. Knowledge of the experimental activity coefficients and solubilities enable a direct test of predicted standard state free energies.

For example, at 1.0 GPa and 800°C, using the hypothetical 1.0 m standard state for aqueous CO₂, experimentally measured activity coefficients and solubilities in molality can be combined to give experimental activities of aqueous CO₂. For two different equilibria at 1.0 GPa and 800°C, wollastonite-calcite-quartz (high CO₂) and enstatite-magnesite quartz (low CO₂), the experimental CO₂ activities are close to two orders of magnitude lower than the values computed using the HKF equation of state The same discrepancy at 1.0 GPa and 800°C is obtained using the experimental solubility of graphite (Tumiati et al., 2017). The consistency of these three tests, all at 1.0 GPa and 800°C, requires a substantial revision to the HKF prediction of the aqueous standard state free energy of CO₂. The latter becomes more positive than previously at elevated pressures and temperatures. In turn, a revised equation of state characterization of aqueous CO₂ will imply less of the molecule CO₂ relative to other aqueous carbon-bearing species under deep Earth conditions.

Shock, E. L., H. C. Helgeson and D. A. Sverjensky (1989). "Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Standard partial molal properties of inorganic neutral species." Geochimica et Cosmochimica Acta 53: 2157-2184.

Aranovich, L. and R. Newton (1999). "Experimental determination of CO2-H2O activity-composition relations at 600-1000 C and 6-14 kbar by reversed decarbonation and dehydration reactions." American Mineralogist 84(9): 1319-1332.

Tumiati, S., C. Tiraboschi, D. A. Sverjensky, T. Pettke, S. Recchia, P. Ulmer, F. Miozzi and S. Poli (2017). "Silicate dissolution boosts the CO₂ concentrations in subduction fluids." Nature Communications 8(1): 616.