`P_(A)=(235y -125xy)mm` of `HgP_(A)` is partial pressure of `A,x` is mole fraction of B in liquid phase in the mixture of two liquids A and B and y is the mole fraction of A in vapour phase, then `P_(B)^(@)` in mm of Hg is:

Options

A. 235
B. 0
C. 110
D. 125

Explanation

To solve the problem, we need to find the value of \( P_B^0 \) (the vapor pressure of pure B) given the equation for the partial pressure of A, \( P_A = (235y - 125xy) \) mm Hg. Here are the steps to derive the solution:

### Step 1: Rewrite the given equation
The equation for the partial pressure of A can be factored:
\[ P_A = 235y - 125xy = y(235 - 125x) \]
This is our Equation (1).

### Step 2: Apply Dalton's Law
According to Dalton's Law, the partial pressure of A can also be expressed as:
\[ P_A = X_A \cdot P_{total} \]
where \( X_A \) is the mole fraction of A in the liquid phase and \( P_{total} \) is the total pressure. This is our Equation (2).

### Step 3: Compare Equations
By comparing Equation (1) and Equation (2):
\[ y(235 - 125x) = X_A \cdot P_{total} \]
From this, we can express the total pressure:
\[ P_{total} = \frac{y(235 - 125x)}{X_A} \]
This is our Equation (3).

### Step 4: Express Total Pressure in terms of Vapor Pressures
The total pressure can also be expressed as:
\[ P_{total} = P_A^0 \cdot X_A + P_B^0 \cdot X_B \]
Since \( X_A + X_B = 1 \), we can write \( X_A = 1 - X_B \). Substituting this into the equation gives:
\[ P_{total} = P_A^0(1 - X_B) + P_B^0 X_B \]
Rearranging this, we get:
\[ P_{total} = P_A^0 + P_B^0 - P_A^0 X_B \]
This is our Equation (4).

### Step 5: Compare Equations (3) and (4)
Now we compare Equation (3) and Equation (4):
\[ P_A^0 + P_B^0 - P_A^0 X_B = y(235 - 125x) \]
From this, we can isolate \( P_B^0 \):
\[ P_B^0 = y(235 - 125x) + P_A^0 X_B \]

### Step 6: Substitute and Solve for \( P_B^0 \)
From the earlier steps, we know:
1. \( P_A^0 = 235 \) mm Hg (from the context of the problem).
2. Rearranging gives us \( P_B^0 = -125 + P_A^0 \).

Substituting \( P_A^0 \):
\[ P_B^0 = -125 + 235 = 110 \text{ mm Hg} \]

### Final Answer
Thus, the value of \( P_B^0 \) is:
\[ \boxed{110 \text{ mm Hg}} \]