Consider a two$-$phase binary system of n$-$heptane $+$ toluene. Assume that the both liquid and vapor phases behave ideally, assuming Raoult's law is valid.

a$)$ Prepare and plot $y-x,$ and $T-x-y$ diagrams at $101\mathrm{.}3$kPa, where $x$ and $y$ are mole fractions of the more volatile component. For vapor pressure of pure component, use Antoine equation of question #$1.[15$ marks$]$

b$)$ From the following experimental data, plot the experimental $y-x,$ and $T-x-y$ diagrams on the same figure as part $($a$).$ Then compare the experimental $y-x$ and $T-x-y$ diagrams with those from Raoult's law in part $($a$),$ and comment on the accuracy of the Rault's law for n$-$heptane $+$ toluene system. $[10$ marks$]$

Table $2$: VLE experimental data for n$-$heptane $+$ toluene mixture at $1$atm.$x$&$y$ are mole fractions. Ref: Steinhauser and White $[$Ind$.$ Eng. Chem., $41,2912(1949)]$

$\backslash$table$[[x_{nhhptane},y_{n-heptane},T[C]$