Two liquids A and B form an ideal solution. The solution has vapor pressure of 700 torr at $80^{\circ} C$ .It is distilled till 2/3rd of the solution is collected as condensate. The composition of the condensate is $X_{A}^{'} = 0.75$ and that of the residue is $X_{A}^{''} = 0.30$ . If the vapor pressure of the residual liquid at $80^{\circ} C$ is 600 torr, Which of the following is/are true?

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The composition of the original liquid was $X_{A} = 0.6$

The composition of the original liquid was $X_{A} = 0.2$

$P_{B}^{\circ} = 500 t o r r$

$P_{A}^{\circ} = \frac{2500}{3} t o r r$

answer is A, C, D.

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Detailed Solution

The vapour pressure of solutions is 700 torr Hence, $X_{A} P_{A}^{O} + X_{B} P_{B}^{O} = 700$ .
The vapour pressure of the residue is 600 torr.
Hence, $X_{A}^{"} P_{A}^{O} + {X^{"}}_{B} P_{B}^{O} = 0.30 P_{A}^{O} + 0.7 P_{B}^{O} = 600........... (i i)$
Let x and y represent initial moles of A and B respectively.
$x = 0.75 \times \frac{2}{3} (x + y) + 0.30 \times \frac{1}{3} (x + y) ....... (i i i)$
And $X_{A} = \frac{x}{x + y} = 0.6$
These equations are solved
$X_{A} = 0.6, X_{B} = 0.4, P_{A}^{o} = \frac{2500}{3} t o r r; P_{B}^{o} = 500 t o r r$