Mixture of volatile components A and B has a total vapour pressure (in torr)p=`254-119 x_(A)`is where`x_(A)`mole fraction of A in mixture .Hence`P_(A)^@`and `P_(B)^@`are(in torr)

Options

A. `254,119`
B. `119,254`
C. `135,254`
D. `154,119`

Explanation

To solve the problem, we need to find the values of the vapor pressures \( P_A^0 \) and \( P_B^0 \) for components A and B, respectively, using the given total vapor pressure equation.

### Step-by-Step Solution:

1. **Understand the Given Equation**:
We are given the total vapor pressure \( P \) of the mixture as:
\[ P = 254 - 119 x_A \]
where \( x_A \) is the mole fraction of component A in the mixture.

2. **Apply Raoult's Law**:
According to Raoult's law, the total vapor pressure \( P \) of a mixture is given by:
\[ P = P_A^0 x_A + P_B^0 x_B \]
where \( x_B = 1 - x_A \) (since the sum of mole fractions must equal 1).

3. **Substitute \( x_B \)**:
Substitute \( x_B \) into the equation:
\[ P = P_A^0 x_A + P_B^0 (1 - x_A) \]
This simplifies to:
\[ P = P_A^0 x_A + P_B^0 - P_B^0 x_A \]
Rearranging gives:
\[ P = (P_A^0 - P_B^0) x_A + P_B^0 \]

4. **Set the Two Equations Equal**:
Now, we equate the two expressions for total vapor pressure:
\[ 254 - 119 x_A = (P_A^0 - P_B^0) x_A + P_B^0 \]

5. **Compare Coefficients**:
By comparing coefficients from both sides of the equation, we can identify:
- The constant term: \( P_B^0 = 254 \)
- The coefficient of \( x_A \): \( P_A^0 - P_B^0 = -119 \)

6. **Substitute \( P_B^0 \)**:
Substitute \( P_B^0 \) into the second equation:
\[ P_A^0 - 254 = -119 \]
Solving for \( P_A^0 \):
\[ P_A^0 = 254 - 119 \]
\[ P_A^0 = 135 \]

7. **Final Values**:
Thus, we have:
\[ P_A^0 = 135 \text{ torr} \]
\[ P_B^0 = 254 \text{ torr} \]

### Final Answer:
- \( P_A^0 = 135 \text{ torr} \)
- \( P_B^0 = 254 \text{ torr} \)