A chemical engineering company is evaluating the behavior of methane at high pressures and temperatures, typical of natural gas processing. As part of your role, you are to use equations of state to predict the molar volume of methane at a temperature of $400K$ and a pressure of $10$ MPa. Assume the critical properties of methane are:

$\backslash$table$[[C{H}_4,\backslash$table$[[$Molar$],[$mass$]],,\frac{T_c}{K},\frac{P_c}{\frac{?}{?}}$bar $,\frac{V_c}{c}{m}^{3}mo{l}^{-1},\frac{T_n}{K}$