Question $2(60$ marks$)$

The vapor$-$liquid equilibrium for a binary liquid solution containing methanol$-$ methyl acetate

methyl methacrylate $($MMA$)$ at $101\mathrm{.}3$kPa is reported by Shi et al$.($Journal of Chemical and

Engineering Data $2022,$ vol. $67,$ pp$\mathrm{.}3650-3660).$ Suppose that the activity coefficients for

methanol $(1)$ and methyl acetate $(2)$ MMA $(2)$ can be expressed by an activity coefficient model

as follows:

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

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

where $A_{12}$ and $A_{21}>0(A_{12}$ and $A_{21}$ can be considered as constant$)$

a$)$ By using Excel, construct $T-x,y$ diagram at $101\mathrm{.}3$kPa based on the suggested activity

coefficient model above and compare it with the experimental data reported in the paper.

Give your recommendation if we can use the model above for $(1)$methanol

$(2)($MMA$)$ mixture.

b$)$ Determine the fugacity of methanol and methyl metacrylate in the azeotropic solution.

State clearly the equations you use, the methods and the assumptions to solve the question.