Question

Gaseous Benzene reacts with hydrogen gas in presence of a Nickel catalyst to form gaseous cyclohexane according to the Reaction

$C_6{H}_6+3H_2⟶C_6{H}_{12}$

A mixture of $C_6{H}_6$ and excess $H_2$ has a pressure of 60mm of Hg in an unknown volume. After the gas had been passed over a Ni catalyst and all the benzene converted to cyclohexane, the pressure of the gas was 30mm of Hg in the same volume at the same temperature. The fraction of $C_6{H}_6$ (by volume) present in the original volume is

• A. 1/3
• B. 1/4
• C. 1/5
• D. 1/6

Answer 1

The correct option is D

1/6

Let initial pressure of $C_6{H}_6=P_{1}mm.$ And that of $H_2=P_{2}mm.$
$\therefore P_1+P_2=60mm.⟶\left(1\right)$
After the Reaction, pressure of $C_6{H}_6=0$
(As all has reacted)
Pressure of $H_2=P_2-3P_1$
Pressure of $C_6{H}_{16}=P_1$

Total Pressure = $P_2-3P_1+P_1=30mm$

Or, $P_2-2P_1=30mm⟶\left(2\right)$
Solving (1) and (2) we get
$P_1=10mm,P_2=50mm$

Fraction of $C_6{H}_6$ by volume = fraction of moles = fraction of pressure = $\frac{10}{60}=\frac{1}{6}$