Answer

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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.

Complete step by step answer:

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).

Complete step by step answer:

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).

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