Solveeit Logo
Login

Question

Question: Gaseous benzene reacts with hydrogen gas in the presence of a nickel catalyst to form gaseous cycloh...

Gaseous benzene reacts with hydrogen gas in the presence of a nickel catalyst to form gaseous cyclohexane according to the reaction,
C6H6(g)+3H2(g)→C6H12(g){{C}_{6}}{{H}_{6}}(g)+3{{H}_{2}}(g)\to {{C}_{6}}{{H}_{12}}(g)
A mixture of C6H6{{C}_{6}}{{H}_{6}} and excess H2{{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 C6H6{{C}_{6}}{{H}_{6}} (by volume) present in the original volume is:
(a)- 13\dfrac{1}{3}
(b)- 14\dfrac{1}{4}
(c)- 15\dfrac{1}{5}
(d)- 16\dfrac{1}{6}

Explanation

Solution

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:
C6H6(g)+3H2(g)→C6H12(g){{C}_{6}}{{H}_{6}}(g)+3{{H}_{2}}(g)\to {{C}_{6}}{{H}_{12}}(g)
For the first condition,
Let the initial pressure of C6H6(g){{C}_{6}}{{H}_{6}}(g) is p1mm{{p}_{1}}mm and for H2(g){{H}_{2}}(g) is p2mm{{p}_{2}}mm,
In the question, it is given that the mixture has a pressure of 60mm of Hg.
Therefore, the equation is-
p1+p2=60mm of Hg{{p}_{1}}+{{p}_{2}}=60mm\text{ }of\text{ }Hg - Equation 1
For the second condition,
After heating the final pressure of C6H6(g)=0{{C}_{6}}{{H}_{6}}(g)=0 (because all the benzene has reacted during heating)
For H2(g)=p2−3p1{{H}_{2}}(g)={{p}_{2}}-3{{p}_{1}}
Because the initial pressure of benzene is p1{{p}_{1}} , hydrogen is p2{{p}_{2}} , and cyclohexane is 0.
Final pressure of benzene is 0, hydrogen isp2−3p1{{p}_{2}}-3{{p}_{1}} , and cyclohexane is p1{{p}_{1}}
So, the total pressure is-
p2−3p1+p1=30mm of Hg{{p}_{2}}-3{{p}_{1}}+{{p}_{1}}=30mm\text{ }of\text{ }Hg
p2−2p1=30mm of Hg{{p}_{2}}-2{{p}_{1}}=30mm\text{ }of\text{ }Hg--Equation 2
On solving Equation 1 and 2, we get p1=10mm and p2=50mm{{p}_{1}}=10mm\text{ and }{{p}_{2}}=50mm
So, the fraction of C6H6{{C}_{6}}{{H}_{6}} by volume is = mole fraction,
Hence, the fraction of pressure = p1p1+p2=1060=16\dfrac{{{p}_{1}}}{{{p}_{1}}+{{p}_{2}}}=\dfrac{10}{60}=\dfrac{1}{6}

So, the correct answer is option (d) 16\dfrac{1}{6}.

Note: The mole fraction of the initial and final pressure should be taken, and not the fraction of p1 and p2{{p}_{1}}\text{ }and\text{ }{{p}_{2}}.
So, you may get confused between option (c) and option (d).