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 pure vapor pressures \( P^0_A \) and \( P^0_B \) of components A and B, respectively, using the given total vapor pressure equation.

### Step-by-Step Solution:

1. **Write the expression for total vapor pressure**:
The total vapor pressure \( P \) of a mixture of two volatile components A and B can be expressed as:
\[ P = P^0_A \cdot x_A + P^0_B \cdot x_B \]
where \( x_A \) is the mole fraction of A and \( x_B \) is the mole fraction of B. Since \( x_B = 1 - x_A \), we can rewrite the equation as:
\[ P = P^0_A \cdot x_A + P^0_B \cdot (1 - x_A) \]

2. **Substitute the total vapor pressure equation**:
According to the problem, the total vapor pressure is given by:
\[ P = 254 - 119 \cdot x_A \]
We can now equate the two expressions for total vapor pressure:
\[ P^0_A \cdot x_A + P^0_B \cdot (1 - x_A) = 254 - 119 \cdot x_A \]

3. **Rearranging the equation**:
Rearranging the equation gives:
\[ P^0_B - P^0_A \cdot x_A = 254 - 119 \cdot x_A \]
This implies:
\[ P^0_B - P^0_A = 254 \]
and
\[ P^0_A = 119 \]

4. **Solving for \( P^0_B \)**:
From the equation \( P^0_B - P^0_A = 254 \), we substitute \( P^0_A = 135 \):
\[ P^0_B - 135 = 254 \]
Therefore, solving for \( P^0_B \):
\[ P^0_B = 254 \]

5. **Final results**:
We have determined that:
\[ P^0_A = 135 \, \text{torr} \]
\[ P^0_B = 254 \, \text{torr} \]

### Summary of Results:
- \( P^0_A = 135 \, \text{torr} \)
- \( P^0_B = 254 \, \text{torr} \)