The vapour pressures of pure liquids `A` and `B` are `400` and `600 mmHg`, respectively at `298K`. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid `B` is `0.5` in the mixture. The vapour pressure of the final solution, the mole fractions of components `A` and `B` in vapour phase, respectively are:

Options

A. `450 mmHg. 0.4,0.6`
B. `500 mmHg,0.5,0.5`
C. `450 mmHg,0.5,0.5`
D. `500mmHg,0.4,0.6`

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify Given Data
- Vapor pressure of pure liquid A, \( P^0_A = 400 \, \text{mmHg} \)
- Vapor pressure of pure liquid B, \( P^0_B = 600 \, \text{mmHg} \)
- Mole fraction of liquid B in the mixture, \( X_B = 0.5 \)
- Mole fraction of liquid A in the mixture, \( X_A = 1 - X_B = 0.5 \)

### Step 2: Apply Raoult's Law
According to Raoult's Law, the vapor pressure of the solution \( P_T \) is given by:
\[ P_T = P^0_A \cdot X_A + P^0_B \cdot X_B \]

### Step 3: Substitute Values
Substituting the values we have:
\[ P_T = (400 \, \text{mmHg} \cdot 0.5) + (600 \, \text{mmHg} \cdot 0.5) \]
\[ P_T = 200 \, \text{mmHg} + 300 \, \text{mmHg} \]
\[ P_T = 500 \, \text{mmHg} \]

### Step 4: Calculate Mole Fractions in Vapor Phase
Using Dalton's Law of Partial Pressures, we can find the mole fractions of components A and B in the vapor phase. The mole fraction of A in the vapor phase \( Y_A \) is given by:
\[ Y_A = \frac{P^0_A \cdot X_A}{P_T} \]
Substituting the values:
\[ Y_A = \frac{400 \, \text{mmHg} \cdot 0.5}{500 \, \text{mmHg}} \]
\[ Y_A = \frac{200}{500} = 0.4 \]

### Step 5: Calculate Mole Fraction of B in Vapor Phase
Since the total mole fraction must equal 1:
\[ Y_B = 1 - Y_A = 1 - 0.4 = 0.6 \]

### Final Results
- Vapor pressure of the final solution, \( P_T = 500 \, \text{mmHg} \)
- Mole fraction of A in vapor phase, \( Y_A = 0.4 \)
- Mole fraction of B in vapor phase, \( Y_B = 0.6 \)

### Summary of Answers
- Vapor pressure of the final solution: \( 500 \, \text{mmHg} \)
- Mole fraction of A in vapor phase: \( 0.4 \)
- Mole fraction of B in vapor phase: \( 0.6 \)