Question

The total pressure observed by mixing two liquids $A$ and $B$ is $350mm$ Hg when their mole fractions are $0.7$ and $0.3$ respectively.
The total pressure becomes $410mmHg$ if the mole fractions are changed to $0.2$ and $0.8$ respectively for $A$ and $B$. The vapour pressure of pure $A$ is _________$mmHg$. (Nearest integer) Consider the liquids and solutions behave ideally.

Answer 1

Answer: 314

Let V.P. of pure $A$ be $P_A^0$
Let V.P of pure $B$ be $P_B^0$
When $X_A=0.7\&X_B=0.3$
$P_s=350$
$\Rightarrow P_A^0\times 0.7+P_B^0\times 0.3=\mathrm{350....}$(i)
When $X_A=0.2\&X_B=0.8$
$P_s=410$
$\Rightarrow P_A^0\times 0.2+P_B^0\times 0.8=410,......$(ii)
Solving (i) and (ii)
$P_A^0=314mmHg$
$P_B^0=434mmHg$
$=(314)$