Redlich-Kwong equation of state

The Redlich-Kwong equation of state is:

$[p+\frac{a}{T^{1/2}v(v+b)}](v-b)=RT$

where

$a=0.4278\frac{R^2{T}_c^{2.5}}{P_c}$

and

$b=0.0867\frac{R{T}_c}{P_c}$

where $p$ is the pressure, $T$ is the temperature and $R$ is the molar gas constant. $T_c$ is the critical temperature and $P_c$ is the pressure at the critical point.

Soave Modification

A modification of the the Redlich-Kwong equation of state was presented by Giorgio Soave in order to allow better representation of non-spherical molecules. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentricity factor:

$\alpha (T)={(1+(0.48508+1.55171\omega -0.15613{\omega }^2)(1-\sqrt{\frac{T}{T_c}}))}^2$

where $T_c$ is the critical temperature and $\omega$ is the acentric factor for the gas. This leads to an equation of state of the form:

$[p+\frac{a\alpha (T)}{v(v+b)}](v-b)=RT$

or equivalently:

$p=\frac{RT}{v-b}-\frac{a\alpha (T)}{v(v+b)}$