If Pₐ and P_b are 108 and 36 torr respectively, what will be the mole fraction of A in the vapor phase if B has a mole fraction of 0.5 in the solution?

• A. 0.25
• B. 0.75
• C. 0.60
• D. 0.35

To find the mole fraction of component A in the vapor phase, we can use Raoult's Law and Dalton's Law of partial pressures. Given that the mole fraction of B in the solution is 0.5, the mole fraction of A will also be 0.5 since the total must equal 1.

Step-by-Step Calculation

1. **Identify the mole fractions**: - Mole fraction of A (Xₐ) = 0.5 - Mole fraction of B (X_b) = 0.5

2. **Calculate the partial pressures**: - Partial pressure of A (Pₐ) = Xₐ * Pₐ (vapor pressure of A) - Partial pressure of B (P_b) = X_b * P_b (vapor pressure of B)

Using the given pressures: - Pₐ = 108 torr - P_b = 36 torr

3. **Calculate the partial pressures**: - Pₐ (A) = 0.5 * 108 = 54 torr - P_b (B) = 0.5 * 36 = 18 torr

Total Pressure

The total pressure (P_total) in the vapor phase is the sum of the partial pressures:

P_total = Pₐ (A) + P_b (B) = 54 torr + 18 torr = 72 torr

Mole Fraction of A in Vapor Phase

The mole fraction of A in the vapor phase (Yₐ) is given by:

Yₐ = Pₐ (A) / P_total = 54 torr / 72 torr

Calculating this gives:

Yₐ = 0.75

Final Answer

The mole fraction of A in the vapor phase is 0.75, which corresponds to option B.