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Dalton's Law of Partial Pressures

Gaseous Benze...

Question

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

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

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

A

1/3

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B

1/4

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C

1/5

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D

1/6

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Solution

The correct option is D
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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