Multiple choice

A mixture of two miscible volatile ideal liquids P and Q (obeying Raoult's law) is kept in a vessel (molar ratio of P and Q in the mixture is m). At a suitable temperature T, the vapour above the liquid is condensed in another vessel. The liquid obtained on condensation is allowed to evaporate and establish equilibrium with its vapour. The vapour is then condensed in another vessel. The process of such evaporation and condensation is repeated for n times. If the ratio of the vapour pressure of pure P to that of pure Q is p, the molar ratio of P and Q in the condensed liquid obtained after nth cycle (for finite n > 1) is

  1. pnm

  2. pmn

  3. pn/2mn/2

  4. pnmn
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A Correct answer
Explanation

In each distillation cycle, the ratio of the more volatile component increases by a factor of p. After n cycles, the enrichment factor is p^n. Therefore, the new ratio is p^n * m.

AI explanation

For ideal miscible liquids obeying Raoult's law, the ratio of moles in the vapour phase is directly proportional to the product of their mole fraction in the liquid and their pure vapour pressures. If the initial molar ratio of P to Q is m, their mole fractions are m divided by (m+1) and 1 divided by (m+1), making the first vapour ratio mp. Because the condensed liquid becomes the new mixture, this ratio compounds with each evaporation cycle. After n such cycles, the molar ratio of P to Q in the condensed liquid becomes p to the power of n times m to the power of n.

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