Problem $1.$ Methanol and Ethanol form an ideal solution. Vapour pressures of ethanol and methanol at various temperatures are given below:

$\backslash$table$[[$Vapour pressure, mm Hg$,200,400,760,1520],[$Temperature$,C,$ Ethanol,$48\mathrm{.}4,62\mathrm{.}5,78\mathrm{.}4,97\mathrm{.}5],[$Temperature$,C,$ Methanol,$34\mathrm{.}8,49\mathrm{.}9,64\mathrm{.}7,84\mathrm{.}0]]$

$($a$)$ Draw the curves showing the variation of vapour pressure as a function of temperature for both the components.

$($b$)$ Compute the VLE data at $760mmHg$ pressure.

$($c$)$ Draw the $T-x-y$ diagram from the VLE data computed.

$($d$)$ Draw the equilibrium $(x-y)$ curve from the $T-x-y$ diagram drawn in part $($c$).$

Problem $2.$ Mixtures of n$-$hexane and n$-$octane form essentially ideal solutions.

$($a$)$ Prepare the bubble point, dew point and equilibrium curves $(T-x-y$ and $x-y$ plots$)$ at $1$ atm total pressure.

$($b$)$ Calculate the values of the relative volatility of $n-$hexane and $n-$octane in mixtures containing $10$ mole$\%$ and $90$mole$\%$ hexane. Do these values suggest that the solutions may be ideal?

Data given: Antoine Equation: $ln{P}_A^v=A-\frac{B}{C+T}$;$P_A^v$ in $mmHg$;$T$ in ${?}^{0}C$

$\backslash$table$[[,B{P}^{0}C,A,B,C$