Find the specific volume $(V_m)$ of n$-$propane at $393\mathrm{.}3K$ and $16\mathrm{.}6$atm using the Redlich$-$Kwong Soave EOS. $Tc=369\mathrm{.}8K,Pc=42\mathrm{.}05$atm,$=0\mathrm{.}153$ and $R=0\mathrm{.}08206L-at\frac{m}{g}$molK.

$P=\frac{RT}{V_m-b}-\frac{a}{V_m(V_m+b)}$

$a=\frac{0\mathrm{.}42747R^2{T}_c^2}{P_c}$

$b=\frac{0\mathrm{.}08664R{T}_c}{P_c}$

$=(1+(0\mathrm{.}48508+1\mathrm{.}55171-0\mathrm{.}15613{}^2)(1-\sqrt[2]{T_r}){)}^2$

$T_r=\frac{T}{T_c}$