Question

Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction
$C_{6}H_{6 \left(g\right)}+3H_{2 \left(g\right)} \rightarrow C_{6}H_{12 \left(g\right)}$
A mixture of $C_{6}H_{6}$ and excess $H_{2}$ has a pressure of 60 mm of Hg in an unknown volume. After the gas has been passed over a nickel catalyst and all the benzene converted to cyclohexane, the pressure of the gas was 30 mm of Hg in the same volume and temperature. The fraction of $C_{6}H_{6}$ (by volume) present in the original volume is 1/y. The value of 'y' is

Answer 1

Suppose initially, pressure of $C_{6}H_{6}\left(g\right)=P_{1}$ mm of Hg and that of $H_{2}\left(g\right)=P_{2}$ mm of Hg.
So $P_{1}+P_{2}=60$ mm of Hg …(i)
After the reaction
Pressure of $C_{6}H_{6}\left(g\right)=0$
Pressure of $H_{2}\left(g\right)=P_{2}-3P_{1}$
Pressure of $C_{6}H_{12}\left(g\right)=P_{1}$
Total pressure $=P_{2}-3P_{1}+P_{1}=30$ mm of Hg.
Or $P_{2}-2P_{1}=30$ mm of Hg…(ii)
Solving (i) and (ii) we get
$P_{1}=10$ mm of Hg
$P_{2}=50$ mm of Hg
Fraction of $C_{6}H_{6}\left(g\right)$ by volume = Fraction of moles = Fraction of pressures
$=\frac{10}{60}=\frac{1}{6}$