$($b$)$ A vapor$-$liquid mixture of carbon tetrachloride$(1)$ and $n-$heptane$(2)$ is at $100$kPa. The activity coefficients can be derived from Wilson equation as follows:

$ln{}_1=-ln(x_1+x_2{}_{12})+x_2(\frac{{}_{12}}{x_1+x_2{}_{12}}-\frac{{}_{21}}{x_2+x_1{}_{21}})$

$ln{}_2=-ln(x_2+x_1{}_{21})-x_1(\frac{{}_{12}}{x_1+x_2{}_{12}}-\frac{{}_{21}}{x_2+x_1{}_{21}})$

${}_{12}=1\mathrm{.}5410$ and ${}_{21}=0\mathrm{.}5197$

$($i$)$ Determine the temperature and its equilibrium composition at $x_1=0\mathrm{.}4.$