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

$C_{6} H_{6} + 3 H_{2} ⟶ C_{6} H_{12}$

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

\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 $\frac{1}{6}$
Let initial pressure of $C_{6} H_{6} = P_{1} m m .$ And that of $H_{2} = P_{2} m m .$
$∴ P_{1} + P_{2} = 60 m m . ⟶ (1)$
After the Reaction, pressure of $C_{6} H_{6} = 0$
(As all has reacted)
Pressure of $H_{2} = P_{2} - 3 P_{1}$
Pressure of $C_{6} H_{16} = P_{1}$

Total Pressure = $P_{2} - 3 P_{1} + P_{1} = 30 m m$

Or, $P_{2} - 2 P_{1} = 30 m m ⟶ (2)$
Solving (1) and (2) we get
$P_{1} = 10 m m, P_{2} = 50 m m$

Fraction of $C_{6} H_{6}$ by volume = fraction of moles = fraction of pressure = $\frac{10}{60} = \frac{1}{6}$

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Similar questions

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

C_{6} H_{6} + 3 H_{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

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___.