# Calculate the mole fraction of benzene in solution containing 30%

Question:

Calculate the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride.

Solution:

Let the total mass of the solution be 100 g and the mass of benzene be 30 g.

Mass of carbon tetrachloride = (100 − 30)g

= 70 g

Molar mass of benzene (C6H6) = (6 × 12 + 6 × 1) g mol−1

= 78 g mol−1

$\therefore$ Number of moles of $\mathrm{C}_{6} \mathrm{H}_{6}=\frac{30}{78} \mathrm{~mol}$

= 0.3846 mol

Molar mass of carbon tetrachloride (CCl4) = 1 × 12 + 4 × 35.5

= 154 g mol−1

$\therefore$ Number of moles of $\mathrm{CCl}_{4}=\frac{70}{154} \mathrm{~mol}$

= 0.4545 mol

Thus, the mole fraction of C6H6 is given as:

$=\frac{0.3846}{0.3846+0.4545}$

= 0.458