A binary system at $110C$ exhibit VLE behavior as shown by the following phase diagram.

$($a$)$ Read VLE at $x_1=0\mathrm{.}02$ and $0\mathrm{.}98$ to evaluate ${}_1^{}$ and ${}_2^{}$

$($b$)$ Use $($a$)$ to estimate the van Laar parameters $M_{12}$ and $M_{21},$ and then predict the composition of azeotrope for the binary system. Is it close to that reported by the phase diagram? $($Hint: you may want to consider $\frac{{}_1^{az}}{{}_2^{az}}=\frac{P_2^{\text{s}\text{a}\text{t}}}{P_1^{\text{s}\text{a}\text{t}}}).$

$($c$)$ Use $($a$)$ to estimate the Wilson parameters, ${}_{12}$ and ${}_{21},$ for the binary system and then the vapor composition at $x_1=0\mathrm{.}2.$