Liquid A & B form ideal solution over the entire range of composition. At temp T. equilimolar binary solution of liquid A & B has vapour pressure of 45 Torr. At the same Vapour pressure of 22.5 Torr. The value of $X_{A} / X_{B}$ in the new solution is _____
(given that the vapour pressure of pure liquid A is 20 Torr at temp T)

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answer is 19.

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Detailed Solution

$\begin{array}{l} X_{A} = 0.5 \\ X_{B} = 0.5 \\ P_{T} = 45 Torr \\ P_{T} = P_{A}^{0} X_{A} + P_{B}^{0} X_{B} \\ 45 = P_{A}^{0} 0.5 + P_{B}^{0} 0.5 \\ P_{B}^{0} = 70 Torr \\ 22.5 = 20 X_{A} + 70 X_{B} \\ 22.5 = 20 (X_{A}) + 70 (1 - X_{A}) (∴ X_{B} = 1 - X_{B}) \\ X_{A} = 0.95 \\ X_{B} = 0.05 \\ \frac{X_{A}}{X_{B}} = \frac{0.95}{0.05} = 19 \end{array}$

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