Redlich-Kwong equation of state

The Redlich-Kwong equation of state is :

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

The Redlich-Kwong equation of state has a critical point compressibility factor of :

$Z_c=\frac{p_c{v}_c}{R{T}_c}=\frac{1}{3}$

leading to

$a=\frac{1}{9(2^{1/3}-1)}\frac{R^2{T}_c^{5/2}}{p_c}\approx 0.4274802336\frac{R^2{T}_c^{5/2}}{p_c}$

and

$b=\frac{(2^{1/3}-1)}{3}\frac{R{T}_c}{p_c}\approx 0.08664034995\frac{R{T}_c}{p_c}$

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:

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