Question

An ideal aqueous solution containing liquid $A(M.Wt=128)$ $64$% by weight has a vapour pressure of $145mm$ $Hg$. If the vapour pressure of $A$ is $x$ $mm$ of $Hg$ and that of water is $155mm$ $Hg$ at the same temperature. Then find $\frac{x}{5}$. The solutions is ideal.

Answer 1

For two miscible liquids,

$P_{total}$ = mole fraction of $A$ $\times P_A^{\circ }$ + mole fraction of $B$ $\times P_B^{\circ }$

Number of moles of $A=$ $\frac{64}{128}=0.5$

Number of moles of $B=$ $\frac{36}{18}=2$

$⟹x=43{\Lambda }_A=\frac{0.5}{2.5}=0.2;{\Lambda }_B=\frac{2}{2.5}=0.8⟹145=\left(0.2\right)\left(x\right)+\left(0.8\right)\left(155\right)$

$⟹\left(\frac{x}{5}\right)=145-\frac{4}{5}\times 155=21$ mm of Hg