Binary mixtures of $n-$butane and $n-$hexane produce ideal solutions that obey Raoult's law. A liquid

mixture containing $50$mol$\%n-$butane and $50$mol$\%n-$hexane at pressure $P$ is heated to a temperature

of $95C,$ where it exists as a vapour$/$liquid mixture in equilibrium.

i$)$ If the mole fraction of $n-$hexane in the liquid phase is $0\mathrm{.}75,$ what is the pressure $P($in kPa $)?$

ii$)$ What molar fraction of the total fluid is vapour? What is the composition of the vapour phase?

iii$)$ If the temperature is maintained at $95C$ and the pressure increased, at what pressure would all

the vapour condense?

iv$)$ Calculate the condensation $($dew$)$ point pressure for the same mixture if maintained at $95C.$

v$)$ What is the composition of the liquid at this point?

Antoine equations for vapour pressures $(kPa)$ as a function of temperature, $T(C)$ :

n$-$butane $(1)$:

$ln(P_1^{\text{s}\text{a}\text{t}})=13\mathrm{.}6608-\frac{2154\mathrm{.}70}{T+238\mathrm{.}789}$

n$-$hexane $(2)$:

$ln(P_2^{\text{s}\text{a}\text{t}})=13\mathrm{.}8193-\frac{2696\mathrm{.}04}{T+224\mathrm{.}317}$

Raoult's law:

$y_{i}P=x_i{P}_i^{\text{s}\text{a}\text{t}}$