The vapour pressure of pure benzene at `88^(@)C` is `957 mm` and that of toluene at the same temperature is `379.5 mm`. The composition of benzene-toluene misture boiling at `88^(@)C` will be

Options

A. `chi_("benzene")=0.66 , chi_("toluene") = 0.34`
B. `chi_("benzene")=0.34, chi_("toluene") = 0.66`
C. `chi_("benzene")= chi_("toluene") = 0.5`
D. `chi_("benzene")=0.75, chi_("toluene") = 0.25`

Explanation

To solve the problem of finding the composition of a benzene-toluene mixture boiling at `88°C`, we can follow these steps:

### Step 1: Understand the Given Data
We are given:
- Vapor pressure of pure benzene at `88°C` (P0B) = `957 mm`
- Vapor pressure of pure toluene at `88°C` (P0T) = `379.5 mm`
- The total pressure at boiling point (Pt) = `760 mm` (standard atmospheric pressure)

### Step 2: Apply Dalton's Law of Partial Pressures
According to Dalton's Law, the total vapor pressure (Pt) of a mixture is the sum of the partial pressures of the components:
\[ P_t = P_B + P_T \]
Where:
- \( P_B = P_0B \cdot X_B \) (partial pressure of benzene)
- \( P_T = P_0T \cdot X_T \) (partial pressure of toluene)

### Step 3: Express Mole Fractions
Let:
- \( X_B \) = mole fraction of benzene in the liquid phase
- \( X_T \) = mole fraction of toluene in the liquid phase

Since \( X_T = 1 - X_B \), we can express the total pressure as:
\[ P_t = P_0B \cdot X_B + P_0T \cdot (1 - X_B) \]

### Step 4: Substitute Known Values
Substituting the known values into the equation:
\[ 760 = 957 \cdot X_B + 379.5 \cdot (1 - X_B) \]

### Step 5: Simplify the Equation
Expanding the equation gives:
\[ 760 = 957X_B + 379.5 - 379.5X_B \]
Combining like terms:
\[ 760 = (957 - 379.5)X_B + 379.5 \]
\[ 760 - 379.5 = 577.5X_B \]
\[ 380.5 = 577.5X_B \]

### Step 6: Solve for \( X_B \)
Now, we can solve for \( X_B \):
\[ X_B = \frac{380.5}{577.5} \approx 0.658 \]

### Step 7: Find \( X_T \)
Now, we can find the mole fraction of toluene:
\[ X_T = 1 - X_B = 1 - 0.658 \approx 0.342 \]

### Final Answer
Thus, the composition of the benzene-toluene mixture boiling at `88°C` is approximately:
- \( X_B \approx 0.66 \) (mole fraction of benzene)
- \( X_T \approx 0.34 \) (mole fraction of toluene)

The correct option is:
**Option A: \( X_B = 0.66, X_T = 0.34 \)**