Starting with the simplest form of virial equation prove that the fugacity of a pure liquid species at a pressure $($P$)$ and temperature $($T$)$ is given by the following expression

f $=$ psut exp

$[$Bpxat$+$v$($P$-$psat$)]$ RT

where B$,$ psat and v$\text{'}$ are second virial coefficient, saturation vapour pressure and molar volume of the pure liquid, respectively. List your assumptions