Vapour Pressure Of Binary Liquid Mixtures
Two volatile liquids A (vapour pressure 400 mmHg) and B (vapour pressure 100 mmHg) are mixed in equal molar proportions to form an ideal solution. What is the total vapour pressure of the mixture and the mole fraction of A in the vapour phase?
Select the correct option:
Solution
TotalP=250mmHg;yA=0.80
For an ideal solution of two volatile components, Raoult's law applies to both. With equal molar proportions: x_A = x_B = 0.5. By Raoult's law: P_A = x_A × P°_A = 0.5 × 400 = 200 mmHg; P_B = x_B × P°_B = 0.5 × 100 = 50 mmHg. Total vapour pressure: P_total = P_A + P_B = 200 + 50 = 250 mmHg. The mole fraction of A in the vapour phase: y_A = P_A / P_total = 200 / 250 = 0.80. This demonstrates that the more volatile component is enriched in the vapour phase — y_A = 0.80 > x_A = 0.50. Option B incorrectly adds the pure vapour pressures without accounting for mole fractions. Option C correctly gives the total pressure but assigns equal vapour mole fractions, ignoring volatility difference. Option D invents an incorrect total pressure. The enrichment of the more volatile component in the vapour phase is the basis of fractional distillation. Plausibility check: total pressure (250 mmHg) lies between P°_A and P°_B, as required by Raoult's law, and y_A > x_A confirms enrichment of the more volatile component.
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About This Question
- Subject
- chemistry
- Chapter
- solutions
- Topic
- vapour pressure of binary liquid mixtures
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
TotalP=250mmHg;yA=0.80
For an ideal solution of two volatile components, Raoult's law applies to both. With equal molar proportions: x_A = x_B = 0.5. By Raoult's law: P_A = x_A × P°_A = 0.5 × 400 = 200 mmHg; P_B = x_B × P°_B = 0.5 × 100 = 50 mmHg. Total vapour pressure: P_total = P_A + P_B = 200 + 50 = 250 mmHg. The mole fraction of A in the vapour phase: y_A = P_A / P_total = 200 / 250 = 0.80. This demonstrates that the more volatile component is enriched in the vapour phase — y_A = 0.80 > x_A = 0.50. Option B incorrectly adds the pure vapour pressures without accounting for mole fractions. Option C correctly gives the total pressure but assigns equal vapour mole fractions, ignoring volatility difference. Option D invents an incorrect total pressure. The enrichment of the more volatile component in the vapour phase is the basis of fractional distillation. Plausibility check: total pressure (250 mmHg) lies between P°_A and P°_B, as required by Raoult's law, and y_A > x_A confirms enrichment of the more volatile component.
This medium difficulty chemistry question is from the chapter solutions, covering the topic of vapour pressure of binary liquid mixtures. It appeared in the 2025 exam.
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