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.