Calculation of the second virial coefficient for the Hayden-O'Connell equation of state

The second virial coefficient is a correction to the ideal gas law to consider vapor-phase interactions. For a simple system with only the classical electrostatic forces (that is, no polar or association contributions), the molecular interactions include bound, metastable bound, and free types, and we can include the corresponding contributions to the virial coefficient. For the polar and association contributions, Hayden and O'Connell1 developed correlations to account for the polar and associating components. They correlated the polar (attractive) contribution to the free contribution by empirically fitting data for polar and non-associating compounds. They then correlated the association contribution to the bound contribution as an equilibrium constant for the association reaction in terms of an association (or solvation for unlike molecules) parameter. They also developed suitable mixing rules for unlike pair interactions.

We can use the following necessary equations to calculate the virial coefficients for both polar and nonpolar systems:

Please see the references by Hayden and O'Connell1 and Prausnitz et al.2 for details on the correlations for each contribution.