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  4. Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction C6H6(g)+3H2(g) arrow C6H12(g) A mixture of C6H6 and excess H2 has a pressure of 60 mm of Hg in an unknown volume. After the gas had been passed over a nickel catalyst and all the benzene converted to cyclohexane, the pressure of the gas was 30 mm of Hg in the same volume at the same temperature. The fraction of C6H6 (by volume) present in the original volume is

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Q. Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction
$C_{6}H_{6\left(g\right)}+3H_{2\left(g\right)} \rightarrow C_{6}H_{12\left(g\right)}$
A mixture of $C_6H_6$ and excess $H_2$ has a pressure of $60 \,mm$ of $Hg$ in an unknown volume. After the gas had been passed over a nickel catalyst and all the benzene converted to cyclohexane, the pressure of the gas was $30\, mm$ of $Hg$ in the same volume at the same temperature. The fraction of $C_6H_6$ (by volume) present in the original volume is

States of Matter

Solution:

Let, initial pressure of $C_6H_{6(g)} = P_1\, mm$ and that of $H_{2(g)} = P_2\, mm$
$\therefore P_1+P_2=60\,mm\,...(i)$
After the reaction,
pressure of $C_6H_{6(g)} = 0\,\,$ (as all has reacted)
pressure of $H_{2(g)} = P_2 - 3P_1$
pressure of $C_6H_{12(g)} = P_1$
Total pressure $= P_2 - 3P_1 + P_1 = 30 \,mm$
or $P_2 - 2P_1 = 30 \,mm\,...(ii)$
Solving (i) and (ii), we get
$P_1 = 10\, mm, P_2 = 50\, mm$
Fraction of $C_6H_6$ by volume = Fraction of moles
= Fraction of pressure $=\frac{10}{60}=\frac{1}{6}$