Two liquids A and B from an ideal solution. The solution has a vapour pressure of 700 torr at 80°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 vapour pressure of the residue at 80°C is 600 Torr, which of the following is/are true?

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

The composition of A in the original liquid was $X_{A}^{} = 0.4.$

$P_{B}^{0} = 500 T o r r .$

$P_{A}^{0} = \frac{2500}{3} T o r r .$

answer is A, C, D.

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Detailed Solution

$X_{A} P_{A}^{0} + X_{B} P_{B}^{0} = 700; X_{A} = 0.6; X_{B} = 0.4...... (i)$

$X_{A}^{'} P_{A}^{0} + X_{B}^{'} P_{B}^{0} = 0.30 P_{A}^{0} + 0.70 P_{B}^{0} = 600........ (i i)$

If moles of A & B initially are x & y then

$x = 0.75 \times \frac{2}{3} (x + y) + 0.30 \times \frac{1}{3} (x + y) .... (i i i)$

Solving (iii) $\frac{x}{y} = \frac{3}{2}$

$\Rightarrow X_{A} = \frac{x}{x + y} = \frac{3}{5} = 0.6 (i n t h e o r i g i n a l l i q u i d)$

Solving (i) and (ii) the get $P_{A}^{0} = \frac{2500}{3} T o r r a n d P_{B}^{0} = 500 T o r r$

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