Equations for the Hayden-O'Connell equation of state

The Hayden-O'Connell equation of state incorporates the chemical theory of dimerization. It is a virial equation of state that accounts for the association and chemical bonding in the vapor phase in the computation of the second virial coefficient. In this approach, we truncate the general virial equation of state to the second virial coefficient term:

where

B is the second virial coefficient that concerns interactions between two molecules

We can develop the relationship between the fugacity coefficient and the vapor-phase P, V, and T relations directly from the definitions of the fugacity and fugacity coefficient:

We can substitute the virial equation into the preceding equation to produce an equation that requires only an expression for the virial coefficients:

We use this equation when the vapor mixture does not contain one or more species of polar or dimerizing compounds, such as carboxylic acids. At moderate densities (densities less than approximately one half of the critical density), this equation provides a very good approximation.