Methanol and ethanol solutions are basically ideal.

a$)$ Calculate the vapor$-$liquid equilibria for this system at $1$ and $5$ atm absolute pressure and plot the xy and txy diagrams at each pressure.

b$)$ For each pressure, calculate the relative volatilities and determine an average value.

c$)$ Using equation $(9\mathrm{.}2)$ with the average volatilities, compare the values of $\backslash ($y$^\{($a$)\}\backslash )$ at each value of $\backslash ($x$\backslash )$ obtained in this way with the values calculated directly from the vapor pressures.$=\frac{\frac{y^{*}}{1-y^{*}}}{\frac{x}{1-x}}=\frac{y^{*}(1-x)}{x(1-y^{*})}$