At low pressure, the solubility of CO_{2} gas is given by Henry's law:

At pressures above about 20 atm, 2 effects start playing a role. First, the active pressure, or *fugacity*, of the gas becomes different from its (partial) pressure:

[*P*_{CO2}] = φ_{CO2} *P*_{CO2} / *P*_{0},

where φ is the fugacity coefficient. The gas pressure is divided by the standard state (*P*_{0} = 1 atm) to make the [activity], or [fugacity] dimensionless.

Second, the pressure affects Henry's constant by the volume change of the reaction (as explained in *Pressure effects on solubility*).

The fugacity coefficient can be obtained by comparing an equation of state for the gas with the ideal gas law. For example, the Van der Waals equation:

where *b* is the gas' minimal volume, and *a* and *α* are Van der Waals attraction factors.

Peng and Robinson (1976) have devised formulas to relate these coefficients to the critical pressure and temperature, and the acentric factor of a gas. The Peng-Robinson formulas enable a remarkably accurate estimate of the *P*-*V _{m}* relationship for a gas. Calculated (lines) and measured (symbols) data on CO

From the equation of state, the fugacity coefficient is:

and the solubility can be calculated with:

.

CO_{2} solubilities calculated with PHREEQC input file *CO2_conc.phr* are compared with measured data from *CO2.dat* in the figure.

If you run the file with phreeqc, put the 2 files in the same directory on your computer, and uncomment the line that reads:

# -plot_csv_file co2.dat

in the input file.

See Appelo, Parkhurst and Post, *doi.org/10.1016/j.gca.2013.10.003* for detailed information on Peng-Robinson calculations and effects in gas-mixtures.