Redlich-Kwong equation of state

The Redlich-Kwong equation of state is:

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

where

$a=0.4278{\frac {R^{2}T_{c}^{2.5}}{P_{c}}}$

and

$b=0.0867{\frac {RT_{c}}{P_{c}}}$

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:

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

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:

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

or equivalently:

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