$(5)$ A liquid mixture of $CC{l}_4$ et $CHC{l}_3$ with $x_{CHC{l}_3}^{(liq)}=0\mathrm{.}50$ at $25C$ has a total vapour pressure of

$p_{\text{t}\text{o}\text{t}}=167\mathrm{.}3$ torr and gas$-$phase equilibrium composition of $x_{CHC{l}_3}^{(vap)}=0\mathrm{.}61.$ At the same temperature,

the pure$-$component vapour pressures are $p_{CHC{l}_3}^{**}=200$torr and $p_{CC{l}_4}^{**}=143$torr, and their second

virial coefficients are $B_2^{(CHC{l}_3)}=-526c\frac{m^3}{m}o{l}^3$ and $B_2(CC{l}_4)=-691c\frac{m^3}{m}ol.$

$($a$)$ Use the Lewis$-$Randall rule to compute the fugacity coefficients for the vapours.

$($b$)$ Determine the activity coefficients for the components in the solution at equilibrium by

using the "convention I", but taking into consideration that vapours are real gases.