In a solution of 7.8 gm benzene `C_(6)H_(6)` and 46.0 gm toluene `(C_(6)H_(5)CH_(3))`, the mole fraction of benzene in this solution is

Options

A. `1//6`
B. `1//5`
C. `1//2`
D. `1//3`

Explanation

To find the mole fraction of benzene in the solution, we will follow these steps:

### Step 1: Calculate the moles of benzene (C₆H₆)
1. **Given mass of benzene** = 7.8 g
2. **Molar mass of benzene (C₆H₆)** = 78 g/mol

Using the formula for moles:
\[ \text{Moles of benzene} = \frac{\text{mass}}{\text{molar mass}} = \frac{7.8 \, \text{g}}{78 \, \text{g/mol}} = 0.1 \, \text{moles} \]

### Step 2: Calculate the moles of toluene (C₆H₅CH₃)
1. **Given mass of toluene** = 46.0 g
2. **Molar mass of toluene (C₆H₅CH₃)** = 92 g/mol

Using the formula for moles:
\[ \text{Moles of toluene} = \frac{\text{mass}}{\text{molar mass}} = \frac{46.0 \, \text{g}}{92 \, \text{g/mol}} = 0.5 \, \text{moles} \]

### Step 3: Calculate the total moles in the solution
\[ \text{Total moles} = \text{Moles of benzene} + \text{Moles of toluene} = 0.1 + 0.5 = 0.6 \, \text{moles} \]

### Step 4: Calculate the mole fraction of benzene
The mole fraction of benzene (X₁) is given by the formula:
\[ X_{\text{benzene}} = \frac{\text{Moles of benzene}}{\text{Total moles}} = \frac{0.1}{0.6} = \frac{1}{6} \]

### Conclusion
The mole fraction of benzene in the solution is:
\[ \text{Mole fraction of benzene} = \frac{1}{6} \]