$($a$)$ Define Raoult's law and describe circumstances in which it

may be obeyed for a liquid mixture in equilibrium with its

vapour.

$(5$ marks$)$

$($b$)$ Explain why, for an ideal vapour phase and a non$-$ideal

solution liquid phase, the condition for equilibrium is given

by:

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

You can use Raoult's law as a starting point for your

answer. Any terms in this equation that are not defined in

your answer to part $($a$)$ should be defined in your answer to

this equation.

$(2$ marks$)$

$($c$)$ A binary liquid mixture has components $($ A and $B)$ with

saturated pressures of $9\mathrm{.}0$kPa and $33$kPa respectively.

Raoult's law predicts a vapour pressure of $15$kPa.

$($i$)$ What is the mole fraction of $A$ in the liquid mixture?

$($ii$)$ What is the predicted partial pressure of $B?$

$(4$ marks$)$

$($d$)$ The mixture described in $($c$)$ above is measured, and it is

found that vapour pressure is in fact $12$kPa. The activity

coefficient for $A$ is determined to be $0\mathrm{.}9.$

$($i$)$ What is the activity coefficient for $B?$

$($ii$)$ What is the fugacity of $A?$

$(5$ marks$)$

$($e$)$ Describe why Raoult's law is relevant for distillation and

why non$-$ideal mixtures are not usually relevant.

$(4$ marks$)$