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Two liquids A and B are mixed at 25 deg C to form a solution where the mole fraction of B is X_B = 0.92. The total vapour pressure of the solution is 0.95 atm. The vapour pressure of pure A is 300 torr and that of pure B is 800 torr. Which of the following is correct for this solution?

1. delta_H_mix > 0, delta_V_mix > 0
2. delta_H_mix < 0, delta_V_mix < 0
3. delta_H_mix = 0, delta_V_mix = 0
4. delta_H_mix < 0, delta_V_mix > 0

Correct answer: delta_H_mix < 0, delta_V_mix < 0

Solution

Mole fractions: X_B = 0.92, X_A = 0.08. Ideal vapour pressure by Raoult's law: P_ideal = X_A * P_A° + X_B * P_B° = 0.08*300 + 0.92*800 = 24 + 736 = 760 torr = 1 atm. Observed pressure = 0.95 atm = 722 torr. Observed P < P_ideal. This is NEGATIVE deviation from Raoult's law. Negative deviation: intermolecular interactions in the mixture are STRONGER than in pure components => delta_H_mix < 0 (exothermic mixing) and delta_V_mix < 0 (volume contraction). So delta_H_mix < 0 and delta_V_mix < 0.

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