$(4)$ The critical temperature and pression of $N_2$ are $T_c=126\mathrm{.}2K$ and $p_c=3\mathrm{.}394$MPa, respectively.

Assuming that the gas can be described by the van der Waals model, then:

$($a$)$ Determine the fugacity coefficient at $5$atm and $30C.[$The relations between the critical

parameters and the gas parameters a and $b$ are $b=R\frac{T_c}{8p_c}$ and $a=27R^2\frac{T_c^2}{64p_c}.]$

$($b$)$ Use the Lewis$-$Randall rule to determine the fugacity of $N_2$ in a mixture of $0\mathrm{.}4$mol

of $N_2$ and $0\mathrm{.}9$mol of $O_2$ at $30C$ and $5$atm. $($Discuss all the assumptions made.$)$