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An ideal solution is prepared by dissolving n moles of a non-volatile, non-electrolyte solute in N moles of solvent. If the vapour pressure of the solution is P and the vapour pressure of the pure solvent is P0, which of the following relations is correct?

1. (P0 - P) / P = n / N
2. (P0 - P) / P0 = n / N
3. (P0 - P) / P0 = N / n
4. (P0 - P) / P = N / n

Correct answer: (P0 - P) / P0 = n / N

Solution

From Raoult's law, vapour pressure P = P0 * N/(N+n). So (P0 - P)/P0 = 1 - N/(N+n) = n/(N+n). For dilute solutions n << N this equals n/N. The standard statement of Raoult's law expresses relative lowering as (P0 - P)/P0 = n/N (dilute approximation), matching option B.

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