Q$1.($a$)$ One mole of $A(P_A^{**}=36\mathrm{.}6$kPa$)$ is mixed with five moles of $B(P_B^{**}=22\mathrm{.}8$kPa$)$ at $25C$

to form an ideal solution. Assuming the vapour behaves ideally, answer the following:

$($i$)$ At what pressure will the solution boil?

$($ii$)$ What is the composition of the first bubble of vapour?

$($iii$)$ Show that $Y_B=x_B\frac{P_B^{**}}{P_A^{**}+x_B(P_B^{**}-P_A^{**})},$ where $x_B$ and $Y_B$ are the liquid and

vapour phase mole fractions of $B,$ respectively.

$($iv$)$ Write down an expression for the chemical potential of $A$ in the ideal solution,

defining the terms used.

$($v$)$ Hence, calculate the difference in the chemical potential of $A$ in the pure liquid

and in the solution.

$[14$ marks$]$

$($b$)$ Sketch a boiling$-$temperature vs$.$ composition diagram for a solution of two liquids $C$ and

D $($C being more volatile than $D)$ which shows large positive deviations from Raoult's

law. Label the important regions of the diagram and use the Gibbs phase rule to

determine the degrees of freedom for each labelled region. Remember that the external

pressure is constant.

$[7$ marks$]$

$($c$)$ The vapour pressure of a pure liquid solvent is $11\mathrm{.}73$kPa at $25C.$ When $0\mathrm{.}2$mol of a

non$-$volatile solute are added to $0\mathrm{.}8$mol of the solvent at the same temperature, the

vapour pressure of the solvent above the solution drops to $5\mathrm{.}33$kPa. What is the activity

coefficient of the solvent in the solution?