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VIT Engineering VIT Engineering Solved Paper-2015

  • question_answer
    Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction,  \[{{C}_{6}}{{H}_{6}}\left( g \right)+3{{H}_{2}}\left( g \right)\to {{C}_{6}}{{H}_{12}}\left( g \right)\] 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 30 mm 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                       

    B) 1/4   

    C) 1/5                        

    D) 1/6

    Correct Answer: D

    Solution :

    Suppose initially, pressure of \[\tau =MB\sin {{45}^{\circ }}=\frac{MB}{\sqrt{2}}\] mm and that of \[W=\left( \sqrt{2}-1 \right).\tau \] \[\therefore \]         \[\tau =\frac{W}{\left( \sqrt{2}-1 \right)}\] After the reaction, Pressure of  \[B={{10}^{3}}gauss\] (as all has reacted) Pressure of   \[={{10}^{3}}\times {{10}^{-4}}T=0.1T\] Pressure of     \[A=5c{{m}^{2}}=5\times {{10}^{-4}}{{m}^{2}}\] Total pressure \[\theta ={{80}^{\circ }}\] or,            \[\therefore \] Solving (i) and (ii), we get                 \[\phi =NBA\cos \theta \] Fraction of \[=20\times 0.1\times 5\times {{10}^{-4}}\times \cos {{30}^{\circ }}\] by volume = fraction of moles fraction of pressure \[=10\times {{10}^{-4}}\times \frac{\sqrt{3}}{2}\]


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