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Ideal Gas Equation

Gaseous benze...

Question

Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction: $C_{6} H_{6} (g) + 3 H_{2} (g) \to C_{6} H_{12} (g) .$ 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___.

A

$\frac{1}{3}$

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B

$\frac{1}{4}$

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C

$\frac{1}{5}$

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D

$\frac{1}{6}$

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Solution

The correct option is D
$\frac{1}{6}$

$C_{6} H_{6} (g) + 3 H_{2} (g) \to C_{6} H_{12} (g) .$

Let the pressure of benezene is x then the pressure of $H_{2}$ = 60 - x.

$C_{6} H_{6} (g) + 3 H_{2} (g) \to C_{6} H_{12} (g) .$

x 60-x 0

x-x=0 60-x-3x 0+x

60-x-3x+x = 30 $\Rightarrow$ x=10.

$∴$ Fraction of $C_{6} H_{6}$ present in original volume = $\frac{10}{60} = \frac{1}{6}$

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