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# Gaseous benzene reacts with hydrogen gas in the 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 60mm 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 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)- $\dfrac{1}{3}$(b)- $\dfrac{1}{4}$(c)- $\dfrac{1}{5}$(d)- $\dfrac{1}{6}$

Last updated date: 17th Jun 2024
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Hint: The fraction can be calculated by taking 2 equations, with initial and final process pressure. Add the 2 equations and divide it with original pressure.

Let us first write down the equation given in the question:
${{C}_{6}}{{H}_{6}}(g)+3{{H}_{2}}(g)\to {{C}_{6}}{{H}_{12}}(g)$
For the first condition,
Let the initial pressure of ${{C}_{6}}{{H}_{6}}(g)$ is ${{p}_{1}}mm$ and for ${{H}_{2}}(g)$ is ${{p}_{2}}mm$,
In the question, it is given that the mixture has a pressure of 60mm of Hg.
Therefore, the equation is-
${{p}_{1}}+{{p}_{2}}=60mm\text{ }of\text{ }Hg$ - Equation 1
For the second condition,
After heating the final pressure of ${{C}_{6}}{{H}_{6}}(g)=0$ (because all the benzene has reacted during heating)
For ${{H}_{2}}(g)={{p}_{2}}-3{{p}_{1}}$
Because the initial pressure of benzene is ${{p}_{1}}$ , hydrogen is ${{p}_{2}}$ , and cyclohexane is 0.
Final pressure of benzene is 0, hydrogen is${{p}_{2}}-3{{p}_{1}}$ , and cyclohexane is ${{p}_{1}}$
So, the total pressure is-
${{p}_{2}}-3{{p}_{1}}+{{p}_{1}}=30mm\text{ }of\text{ }Hg$
${{p}_{2}}-2{{p}_{1}}=30mm\text{ }of\text{ }Hg$--Equation 2
On solving Equation 1 and 2, we get ${{p}_{1}}=10mm\text{ and }{{p}_{2}}=50mm$
So, the fraction of ${{C}_{6}}{{H}_{6}}$ by volume is = mole fraction,
Hence, the fraction of pressure = $\dfrac{{{p}_{1}}}{{{p}_{1}}+{{p}_{2}}}=\dfrac{10}{60}=\dfrac{1}{6}$

So, the correct answer is option (d) $\dfrac{1}{6}$.

Note: The mole fraction of the initial and final pressure should be taken, and not the fraction of ${{p}_{1}}\text{ }and\text{ }{{p}_{2}}$.
So, you may get confused between option (c) and option (d).