The data in Table are molar volume of carbon dioxide at $423\mathrm{.}15K.$ The fugacity coefficient $)=(\frac{f_i}{P}.$ a dimensionless property, is a measure of the ideal gas behavior, which may will calculated from the volumetric data. According to the definition, the fugacity coefficient is given by residual Gibbs free energy as

$ln\frac{O}{{?}_i}=\frac{G_{{?}_{?}}(i)-G_i^{IG}}{RT}at$ constant $T$

$(1)$ Derive the equation of fugacity coefficient in terms of PVT properties.

$(2)$ Calculate the fugacity coefficient of carbon dioxide at pressure of $\frac{300}{b}ar.$

Table Molar volume of carbon dioxide at $423\mathrm{.}15K.$

$\backslash$table$[[P($bar$),V_{c{m}^3*mo{l}^{-1}},($bar$),V_{c{m}^3*mo{l}^{-1}}$