Question

What is the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride ?

• A. 0.540
• B. 0.459
• C. 0.500
• D. 0.300

Hint:

Mole fraction is a dimensionless quantity. Always ensure you calculate moles using the correct molar masses ($C=12, H=1, Cl=35.5$).

Answer 1

The Correct Option is B

Let the total mass of the solution be 100 g.
Mass of Benzene (C$_6$H$_6$) = 30 g. Mass of Carbon tetrachloride (CCl$_4$) = 100 - 30 = 70 g.
Molar mass of Benzene (C$_6$H$_6$) = $12(6) + 1(6) = 78$ g/mol.
Molar mass of CCl$_4$ = $12 + 35.5(4) = 12 + 142 = 154$ g/mol.
Moles of Benzene ($n_B$) = $\frac{30}{78} \approx 0.385$ mol.
Moles of CCl$_4$ ($n_A$) = $\frac{70}{154} \approx 0.455$ mol.
Total moles = $0.385 + 0.455 = 0.840$ mol.
Mole fraction of Benzene ($X_B$) = $\frac{n_B}{n_{total}} = \frac{0.385}{0.840} \approx 0.4583$.
This value is closest to 0.459.