$(2)$ Benzene and toluene form an ideal solution at $20C,$ but a nonideal solution at $120C.$ For the latter

solution, we have the following experimental data for the compositions and total vapour pressures:

$($a$)$ Knowing that the vapour pressures of pure benzene and toluene are $2\mathrm{.}98$atm and $1\mathrm{.}34$atm

at $120C,$ respectively, estimate the activity coefficients and the activities for the solute and solvent

for a solution with composition $x_{\text{B}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}^{(liq)}=0\mathrm{.}40.$ Discuss carefully the conventions used for the

computation of the activities, and any simplification you had to make.

$($b$)$ Estimate the $G_{\text{m}\text{i}\text{x}}$ for preparing the solution with composition $x_{\text{B}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}^{(liq)}=0\mathrm{.}40.$