Numerical answer
Two volatile liquids and form an ideal solution. At a given temperature the vapour pressures of pure and are and respectively. An equimolar liquid mixture of and is placed in a closed vessel and the vapour above it is completely condensed into a second liquid. This second liquid is then allowed to come to equilibrium with its own vapour. If the mole fraction of in the vapour above the second liquid is , then the value of is
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Answer: 8
Use Raoult's law and Dalton's law at each stage: .
Stage 1 (liquid with ): .
Complete condensation of this vapour gives the second liquid with the same composition, , .
Stage 2 (vapour above the second liquid): .
Hence . The enrichment in the more volatile component at each stage () is the principle of fractional distillation. A common slip is to use the mole fraction of the liquid (0.5) directly in the second stage, which gives and the wrong answer .
Stage 1 (liquid with ): .
Complete condensation of this vapour gives the second liquid with the same composition, , .
Stage 2 (vapour above the second liquid): .
Hence . The enrichment in the more volatile component at each stage () is the principle of fractional distillation. A common slip is to use the mole fraction of the liquid (0.5) directly in the second stage, which gives and the wrong answer .
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