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

\frac{1}{3}

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\frac{1}{4}

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\frac{1}{5}

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\frac{1}{6}

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Solution

The correct option is D $\frac{1}{6}$
Suppose, initially pressure of $C_{6} H_{6} = P_{1}$ mm of Hg and that of $H_{2} (g) = P_{2}$ mm of Hg
$∴ P_{1} + P_{2} = 60$ mm of Hg $\to$ (1)
After the reaction, pressure of $C_{6} H_{6} (g) = 0$
Pressure of $H_{2} (g) = P_{2} - 3 P_{1}$
Total pressure: $P_{2} - 2 P_{1} = 30$ mm of Hg $\to$ (2)
solving (1) and (2) we get $P_{1} = 10$ mm of Hg and $P_{2} = 50$ mm of Hg
Now fraction of $C_{6} H_{6} (g)$ by volume =
$\frac{10}{60} = \frac{1}{6}$

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Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction: $C_{6} H_{6} (g) + 3 H_{2} (g) \to C_{6} H_{12} (g) .$ 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 benzene converted to cyclohexane, the pressure of the gas was 30 mm of Hg at same volume and temperature. The fraction of $C_{6} H_{6}$ (by volume) present in the original volume is___.