KVPY Sample Paper KVPY Stream-SX Model Paper-27

Two liquids 'A' and 'B' are mixed in the molar ratio of 1 : 2 and the vapour pressure of the solution is 24 torr. When the two liquids are mixed in the reverse ratio, the vapour pressure of the solution increases by a fraction of \[\frac{1}{4}.\] The vapour pressures of pure 'A' and 'B' are respectively.

A) 20 torr, 40 torr

B) 40 torr, 20 torr

C) 36 torr, 18 torr

D) 18 torr, 36 torr

Correct Answer: C

Solution :

\[2\,\,\left[ 24=\frac{1}{3}p_{A}^{0}+\frac{2}{3}p_{B}^{0}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(1) \right]\]
\[24\times \left( 1\frac{1}{4} \right)=\frac{2}{3}p_{A}^{0}+\frac{1}{3}p_{B}^{0}\]	...(2)
subtracting we get
\[p_{B}^{0}=18\,\,\text{torr}\]
Hence \[p_{A}^{0}=36\,\,\text{torr}.\]