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JEE Advanced 2024 Paper 2 · Chemistry · Solutions, Solid State and Surface Chemistry · medium

Benzene (A, p^°=120 torr) and a less volatile liquid B (p^°=40 torr) form an ideal solution. An equimolar liquid L0 is in equilibrium with its vapour…

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Benzene (A\mathrm{A}, p∘=120p^\circ=120 torr) and a less volatile liquid B\mathrm{B} (p∘=40p^\circ=40 torr) form an ideal solution. An equimolar liquid L0L_0 is in equilibrium with its vapour V1V_1. V1V_1 is condensed completely to liquid L1L_1, which is brought to equilibrium with its own vapour V2V_2, and V2V_2 is completely condensed to liquid L2L_2. The total vapour pressure (in torr) above L2L_2 at the same temperature is
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Answer: 112

Use Raoult's and Dalton's laws. For L0L_0 with xA=0.5x_A=0.5: P=0.5(120)+0.5(40)=80P=0.5(120)+0.5(40)=80 torr and the vapour has yA=0.5×12080=0.75y_A=\dfrac{0.5\times120}{80}=0.75. Complete condensation of V1V_1 gives L1L_1 with xA=0.75x_A=0.75. Its pressure is 0.75(120)+0.25(40)=1000.75(120)+0.25(40)=100 torr and yA=0.75×120100=0.90y_A=\dfrac{0.75\times120}{100}=0.90. Condensing V2V_2 gives L2L_2 with xA=0.90x_A=0.90. The total vapour pressure above L2L_2 is P=0.90(120)+0.10(40)=108+4=112P=0.90(120)+0.10(40)=108+4=112 torr. The enrichment of the more volatile component in each stage is the principle of fractional distillation.
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