Question

\( P_A \) and \( P_B \) are the vapor pressures of pure liquid components A and B, respectively, in an ideal binary solution. If \( X_A \) represents the mole fraction of component A, the total pressure of the solution will be:

• A. \( P_A + X_A (P_B - P_A) \)
• B. \( P_B + X_A (P_B - P_A) \)
• C. \( P_A + X_A (P_A - P_B) \)
• D. \( P_B + X_A (P_A - P_B) \)

Hint:

Raoult’s law states that the total vapor pressure of an ideal solution is the sum of the partial pressures of the components.

Answer 1

The Correct Option is D

Step 1: Applying Raoult’s Law.
- According to Raoult’s Law, the total vapor pressure of an ideal binary solution is: \[ P_{{total}} = P_A X_A + P_B X_B \] - Since \( X_B = 1 - X_A \), we substitute: \[ P_{{total}} = P_A X_A + P_B (1 - X_A) \] \[ = P_A X_A + P_B - P_B X_A \] \[ = P_B + X_A (P_A - P_B) \] Step 2: Identifying the correct answer.
- This matches option (D), so the correct answer is (D).