Mole fraction of vapour of `A` above solution in mixture of `A` and `B(X_(A) = 0.4)` will be `(P_(A)^(@) = 100mm, P_(B)^(@) = 200 mm)`:

Options

A. 0.4
B. 0.8
C. 0.25
D. None of these

Answer

To solve the problem of finding the mole fraction of vapor of component A above a solution of A and B, we will follow these steps:

### Step 1: Identify Given Values
We have the following values provided:
- Mole fraction of A in the solution, \( X_A = 0.4 \)
- Vapor pressure of pure A, \( P^0_A = 100 \, \text{mm} \)
- Vapor pressure of pure B, \( P^0_B = 200 \, \text{mm} \)

### Step 2: Calculate Mole Fraction of B
Since the total mole fraction must equal 1, we can calculate the mole fraction of B:
\[ X_B = 1 - X_A = 1 - 0.4 = 0.6 \]

### Step 3: Calculate Total Vapor Pressure
The total vapor pressure \( P_{total} \) of the solution can be calculated using Raoult's Law:
\[ P_{total} = P^0_A \cdot X_A + P^0_B \cdot X_B \]
Substituting the values:
\[ P_{total} = (100 \, \text{mm} \cdot 0.4) + (200 \, \text{mm} \cdot 0.6) \]
Calculating each term:
\[ P_{total} = 40 \, \text{mm} + 120 \, \text{mm} = 160 \, \text{mm} \]

### Step 4: Calculate Vapor Pressure of A
The vapor pressure of A above the solution can be calculated as:
\[ P_A = P^0_A \cdot X_A = 100 \, \text{mm} \cdot 0.4 = 40 \, \text{mm} \]

### Step 5: Calculate Mole Fraction of A in the Vapor
The mole fraction of A in the vapor phase \( Y_A \) can be calculated using the formula:
\[ Y_A = \frac{P_A}{P_{total}} \]
Substituting the values:
\[ Y_A = \frac{40 \, \text{mm}}{160 \, \text{mm}} = 0.25 \]

### Conclusion
The mole fraction of vapor of A above the solution is \( Y_A = 0.25 \).