Non-ideality in the gas phase

The real molar volume of the gas can be calculated from empirically derived coefficients (Dymond and Smith 1980 Table 1) for the virial equation of state Vm, where 

P is the total pressure, R the gas constant, T the temperature, and B(T) and C(T) the temperature dependent first and second order virial coefficients. Vm can be found by rearranging Equation (3) to a third-order polynomial and solving using Newton s method of approximation to 10 iterations. The real molar volume is used in turn to find the fugacity coefficient, where 

Only the fugacity change with respect to pressure and temperature variation has been considered for the pure gases. For a mixed gas system, interactions between the different gas molecules and atoms must also be taken into account. The second virial coefficient, Bm(T), for a binary mixture between molecules 1 and 2 can be expressed as 

In principle if all the second order virial coefficients of the pure components and the interaction coefficients of all the pairs of the molecules are known, the second order virial coefficient can be calculated. For the third order virial coefficient, 112 and 122 interactions 

As the molar fraction of either H2O or CO2 approaches unity, the activity of that species approaches the activity predicted by the Lewis-Randall rale. However, the activity of the minor component can be significantly higher than that predicted by ideal mixing or real gases. Maximum deviation from ideality occurs at low concentration, low temperature and high pressure. 

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