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. `119,373`

Explanation

To solve the problem, we need to find the vapor pressures of pure components A and B, denoted as \( P_A^0 \) and \( P_B^0 \) respectively. We are given the total vapor pressure \( P \) as a function of the mole fraction of component A, \( x_A \).

### Step-by-Step Solution:

1. **Understand the Given Equation**:
The total vapor pressure \( P \) of the mixture is given by the equation:
\[ P = 254 - 119 x_A \]
Here, \( x_A \) is the mole fraction of component A in the mixture.

2. **Identify the Relationship**:
According to Raoult's Law, the total vapor pressure of a mixture of two volatile components A and B can be expressed as:
\[ P = P_A^0 x_A + P_B^0 x_B \]
where \( x_B = 1 - x_A \).

3. **Substituting for \( x_B \)**:
We can 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. **Comparing Coefficients**:
Now we can compare the coefficients of \( x_A \) from both expressions for \( P \):
- From the given equation: The coefficient of \( x_A \) is \(-119\).
- From our rearranged equation: The coefficient of \( x_A \) is \( P_A^0 - P_B^0 \).

Therefore, we have:
\[ P_A^0 - P_B^0 = -119 \quad \text{(1)} \]

5. **Finding the Constant Term**:
The constant term from the given equation is \( 254 \), which corresponds to \( P_B^0 \) in our rearranged equation:
\[ P_B^0 = 254 \quad \text{(2)} \]

6. **Substituting to Find \( P_A^0 \)**:
Now we can substitute \( P_B^0 \) from equation (2) into equation (1):
\[ P_A^0 - 254 = -119 \]
Solving for \( P_A^0 \):
\[ P_A^0 = 254 - 119 = 135 \]

7. **Final Results**:
Thus, the vapor pressures of pure components A and B are:
\[ P_A^0 = 135 \, \text{torr} \]
\[ P_B^0 = 254 \, \text{torr} \]

### Summary of Results:
- \( P_A^0 = 135 \, \text{torr} \)
- \( P_B^0 = 254 \, \text{torr} \)