Ethanol and n$-$propanol are mixed in a container $($molecules of these two compounds are of similar shape arld size$).$ The following vapour pressure correlation for ethanol hold, where $P_v$ is in kPa and $T$ is in $K$ :

$ln{P}_v=\frac{-4739(K)}{T}+18\mathrm{.}1$

n$-$propanol has a normal boiling point of $97\mathrm{.}72C,$ and has a vapour pressure of $12\mathrm{.}03$kPa at $50C.$

$($a$)$ From the data on n$-$propanol, develop a vapour pressure correlation for n$-$propanol.

$($b$)$ Calculate the vapour pressure of pure ethanol and pure n$-$propanol at $60C.$

$($c$)$ The mixture of ethanol and n$-$propanol is held at a temperature of $60C.$ A liquid$-$vapour two phase mixture is formed. The liquid phase contains $25\mathrm{.}82$mol of ethanol and $11\mathrm{.}07$mol of $n$ propanol.

i$.$ Determine the molar composition of the liquid phase.

ii$.$ Determine the molar composition of the vapour phase.

iii. Determine the overall molar composition of the contents of the container, given that there is $19\mathrm{.}72$mol of vapour in the container.

iv$.$ Water is spilled into the container. The vapour pressure correlation for water is given below, with $P_v$ in kPa and $T$ in $K$ :

$ln{P}_v=\frac{-4891\mathrm{.}75(K)}{T}+17\mathrm{.}728$

At a temperature of $60C,$ the liquid in this new mixture has $13\mathrm{.}11$mol of water. Determine this new mixture's vapour pressure.

v$.$ Using the correlation above, determine how much energy would be required to vapourize $30$kmol of pure water, given that the water is at its boiling point.