Question

At 300 K, the vapour pressures of A and B liquids are 500 and 400 mm Hg respectively. Equal moles of A and B are mixed to form an ideal solution. The mole fraction of A and B in vapor state is respectively.

• A. \( 0.5, 0.5 \)
• B. \( 0.666, 0.333 \)
• C. \( 0.444, 0.555 \)
• D. \( 0.555, 0.444 \)

Hint:

Mole fraction in ideal solutions can be found by dividing the vapor pressure of the component by the total vapor pressure.

Answer 1

The Correct Option is D

We are given the following information:
Vapour pressures of A and B at 300 K are 500 mm Hg and 400 mm Hg, respectively.
Equal moles of A and B are mixed to form an ideal solution. We are asked to find the mole fraction of A and B in the vapor phase. Step 1: Use Raoult's Law Raoult's Law states that the partial pressure of each component in the vapor phase is directly proportional to its mole fraction in the liquid phase: \[ P_A = x_A P_A^0 \quad \text{and} \quad P_B = x_B P_B^0 \] Where:
\( P_A \) and \( P_B \) are the partial pressures of A and B in the vapor phase,
\( x_A \) and \( x_B \) are the mole fractions of A and B in the liquid phase,
\( P_A^0 \) and \( P_B^0 \) are the vapor pressures of pure A and B at 300 K. Since equal moles of A and B are mixed, the mole fraction of A and B in the liquid phase is: \[ x_A = x_B = \frac{1}{2} \]
Step 2: Calculate the partial pressures of A and B in the vapor phase Using Raoult's Law, the partial pressures of A and B in the vapor phase are: \[ P_A = x_A P_A^0 = \frac{1}{2} \times 500 = 250 \, \text{mm Hg} \] \[ P_B = x_B P_B^0 = \frac{1}{2} \times 400 = 200 \, \text{mm Hg} \]
Step 3: Calculate the total pressure The total pressure of the system is the sum of the partial pressures of A and B: \[ P_{\text{total}} = P_A + P_B = 250 + 200 = 450 \, \text{mm Hg} \]
Step 4: Calculate the mole fraction of A and B in the vapor phase The mole fraction of A and B in the vapor phase is given by: \[ y_A = \frac{P_A}{P_{\text{total}}} = \frac{250}{450} = 0.555 \] \[ y_B = \frac{P_B}{P_{\text{total}}} = \frac{200}{450} = 0.444 \] Thus, the mole fractions of A and B in the vapor phase are approximately 0.555 and 0.444, respectively.