Question $3$

$25$ Marks

In a petroleum refinery, liquid state hydrocarbon is stored in a vessel at $493K$ and it is in equilibrium with its vapor phase. The properties of the hydrocarton are: Density $=0\mathrm{.}63gc{m}^3,$ Critical temperature $(T_c)=562\mathrm{.}2K,$ Critical pressure $(P_c)=48\mathrm{.}98$ bar and acentric lactor $()=0210.$ The saturation pressure $($Prat$)$ is given as $1912\mathrm{.}86$kPa. The molar mass of the hydrocarbon is $78\frac{g}{m}ol.$

$($i$)$ Calculate the fugacity $($i$)$ of the hydrocarbon af saturation pressure.

$($ii$)$ Calcutate the fugacity of the liquid hydrocarbon at a total pressure of $2014\mathrm{.}7.$