\(30 \%\) by mass of \(\mathrm{C}_6 \mathrm{H}_6\) in \(\mathrm{CCl}_4\) means \(30 \mathrm{~g} \mathrm{C}_6 \mathrm{H}_6\) in \(100 \mathrm{~g}\) solution and mass of \(\mathrm{CCl}_4\) is \(70 \mathrm{~g}\).
\(\therefore \quad\) Number of moles of
\(\mathrm{C}_6 \mathrm{H}_6\left(\mathrm{n}_{\mathrm{C}_6 \mathrm{H}_6}\right)=\frac{30}{78}=0.385\)
(molar mass of \(\mathrm{C}_6 \mathrm{H}_6=78 \mathrm{~g}\) )
Number of moles of
\(\begin{gathered}
\mathrm{CCl}_4\left(\mathrm{n}_{\mathrm{CCl}_4}\right)=\frac{70}{154}=0.454 \\
\therefore \text { Mole fraction of benzene }=\frac{\mathrm{n}_{\mathrm{C}_6 \mathrm{H}_6}}{\mathrm{n}_{\mathrm{C}_6 \mathrm{H}_6}+\mathrm{n}_{\mathrm{CCl}_4}} \\
=\frac{0.385}{0.385+0.454}=\frac{0.385}{0.84}=0.459 \\
x_{\mathrm{CCl}_4}=1-0.459=0.542
\end{gathered}\)