Question
Explain the composition of vapour phase above a liquid mixture.

Answer

Consider a liquid mixture of two liquids $A$ and $B$ having vapour pressures $P_{ A }^0$ and $P_{ B }^0$ and mole fractions $x_1$ and $x_2$ respectively in the liquid phase.
By Raoult's law, the vapour pressures of two liquids will be,
$P _{ A }= x _1 P_{ A }^0 \text { and } P _{ B }= x _2 P_{ B }^0$
The total vapour pressure of this liquid mixture is,
$\begin{aligned}
& P _{ T }= P _{ A }+ P _{ B } \\
& P _{ T }= x _1 P_{ A }^0+ x _2 P_{ B }^0
\end{aligned}$
The vapour above liquid surface contains $A$ and $B$. If $y_1$ and $y_2$ are the mole fractions of $A$ and $B$ components respectively in the vapour phase, then by Dalton's law of partial pressures,
$P _A= y _1 P _{ T } \text { and } P _{ B }= y _2 P _{ T }$
and total vapour pressure is,
$P _{ T }= y _1 P _{ T }+ y _2 P _{ T } .$

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