Question

Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction
$C_6{H}_{6\left(g\right)}+3H_{2\left(g\right)}\to C_6{H}_{12\left(g\right)}$
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

Answer: 6

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
$=\frac{10}{60}=\frac{1}{6}$