The Redlich-Kwong Equation and its Modifications

The equations of state most commonly used at the present time to represent gas behavior at moderate to high pressures are based on a simple modification of the van der Waals equation published by Redlich and Kwong in 1949  

There is no really good theoretical justification for the two changes in the denominator of the a-term but the agreement with observed data is considerably improved. .. 

In the original RK equation, the parameters a and b were constants, independent of P and T. Since the RK equation first appeared in print, it too has undergone many modifications in an attempt to further improve its fit. Many of these modified Redlich-Kwong equations are summarized by Holloway (1977) and Kerrick and Jacobs (1981), and involve writing the a and b parameters as a function of T, P, or both T and P. The MRK equation of Kerrick and Jacobs fits most of the data for H2O and CO2 at elevated P and T to better than 1 % and is chosen for discussion here. 

The MRK equation of Kerrick and Jacobs keeps b constant but writes a as a function of both P and T  

Here you can see that the repulsion term holds b constant but is more complicated (which gives it better flexibility). The a parameter in the attraction term is written as a simple polynomial function of 1 jV (hence of P) and of T. This is a MRK equation with 10 adjustable parameters, so naturally it fits real data considerably better than the original RK equation, which has only two parameters. 

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