Question

In a solution 30 mass percent of benzene is dissolved in carbon tetrachloride. Calculate mole fraction of benzene.

Hint:

Always convert mass percent composition into actual masses by assuming 100 g of solution. Then, calculate moles using molar masses before applying the mole fraction formula.

Answer 1

We are given 30 mass percent benzene in the solution. This means:
- Mass of benzene = 30 g
- Mass of carbon tetrachloride (CCl$_4$) = 70 g
Molar masses:
- Molar mass of benzene (C$_6$H$_6$) = 78 g/mol
- Molar mass of carbon tetrachloride (CCl$_4$) = 154 g/mol

Step 1: Calculate moles of benzene.
\[ n_{\text{benzene}} = \frac{30}{78} = 0.385 \, \text{mol} \]

Step 2: Calculate moles of carbon tetrachloride.
\[ n_{\text{CCl}_4} = \frac{70}{154} = 0.455 \, \text{mol} \]

Step 3: Calculate mole fraction of benzene.
\[ \chi_{\text{benzene}} = \frac{n_{\text{benzene}}}{n_{\text{benzene}} + n_{\text{CCl}_4}} = \frac{0.385}{0.385 + 0.455} = \frac{0.385}{0.840} = 0.458 \] \[ \boxed{\chi_{\text{benzene}} = 0.458} \] Thus, the mole fraction of benzene is 0.458.