The mole fraction of benzene in a solution in toluene is 0.40. Calculate the weight per cent of benzene in the solution.

Answer

To solve the problem of calculating the weight percent of benzene in a solution of toluene given that the mole fraction of benzene is 0.40, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mole Fraction**:
The mole fraction of benzene (C6H6) in the solution is given as 0.40. This means that in a mixture of benzene and toluene, 40% of the total moles are benzene.

2. **Assume Total Moles**:
For simplicity, assume the total number of moles in the solution is 1 mole.

3. **Calculate Moles of Benzene**:
Since the mole fraction of benzene is 0.40, the number of moles of benzene (nB) can be calculated as:
\[ n_B = 0.40 \times 1 = 0.40 \text{ moles} \]

4. **Calculate Moles of Toluene**:
The remaining moles will be toluene. Thus, the number of moles of toluene (nT) is:
\[ n_T = 1 - n_B = 1 - 0.40 = 0.60 \text{ moles} \]

5. **Find Molecular Weights**:
The molecular weight of benzene (C6H6) is 78 g/mol, and the molecular weight of toluene (C7H8) is 92 g/mol.

6. **Calculate Weight of Benzene**:
The weight of benzene can be calculated using the formula:
\[ \text{Weight of Benzene} = n_B \times \text{Molecular Weight of Benzene} = 0.40 \text{ moles} \times 78 \text{ g/mol} = 31.2 \text{ grams} \]

7. **Calculate Weight of Toluene**:
Similarly, the weight of toluene is:
\[ \text{Weight of Toluene} = n_T \times \text{Molecular Weight of Toluene} = 0.60 \text{ moles} \times 92 \text{ g/mol} = 55.2 \text{ grams} \]

8. **Calculate Total Weight of the Mixture**:
The total weight of the mixture is the sum of the weights of benzene and toluene:
\[ \text{Total Weight} = \text{Weight of Benzene} + \text{Weight of Toluene} = 31.2 \text{ grams} + 55.2 \text{ grams} = 86.4 \text{ grams} \]

9. **Calculate Weight Percent of Benzene**:
Finally, the weight percent of benzene in the solution can be calculated as:
\[ \text{Weight Percent of Benzene} = \left( \frac{\text{Weight of Benzene}}{\text{Total Weight}} \right) \times 100 = \left( \frac{31.2}{86.4} \right) \times 100 \approx 36.1\% \]

### Final Answer:
The weight percent of benzene in the solution is approximately **36.1%**.