Question

The vapour pressures of A and B at 25°C are 75 mm Hg and 25 mm Hg, respectively. If A and B are mixed such that the mole fraction of A in the mixture is 0.4, then calculate the mole fraction of B in the vapour phase.

Hint:

- Raoult’s Law: The partial vapour pressure of each component in an ideal solution is proportional to its mole fraction. - The component with a lower vapour pressure contributes less to the total vapour pressure.

Answer 1

The mole fraction of B in the vapour phase is \( 0.33 \)
Step 1: Calculate Total Vapour Pressure Using Raoult’s Law, \[ P_T = P_A^0 X_A + P_B^0 X_B \] Substituting values: \[ P_T = (75 \times 0.4) + (25 \times 0.6) \] \[ P_T = 30 + 15 = 45 \text{ mm Hg} \] Step 2: Calculate Partial Pressure of B \[ P_B = y_B \times P_T \] \[ y_B = \frac{P_B}{P_T} = \frac{P_B^0 X_B}{P_T} \] \[ y_B = \frac{(25 \times 0.6)}{45} = \frac{15}{45} = \frac{1}{3} = 0.33 \]