Problem $6.$ Consider a mixture of $C{H}_4(1)$ and $H_{2}S(2)$ at $444K$ and $70$ bar. Calculate the fugacity and the fugacity coefficient of methane in an equimolar mixture using each of the following:

$($a$)$ the van der Waals equation of state

$($b$)$ the Redlich$-$Kwong equation of state

$($c$)$ the Peng$-$Robinson equation of state

$($Assume $k_{12}=0)$

Compare the results.