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AIIMS AIIMS Solved Paper-2010

  • question_answer
    The following equilibria are given I. \[{{N}_{2}}+3{{H}_{2}}\rightleftharpoons 2N{{H}_{3}};{{K}_{1}}\] II. \[{{N}_{2}}+{{O}_{2}}\rightleftharpoons 2NO;{{K}_{2}}\] III.  \[{{H}_{2}}+\frac{1}{2}{{O}_{2}}\rightleftharpoons {{H}_{2}}O;{{K}_{3}}\] The equilibrium constant for the reaction, \[2N{{H}_{3}}+\frac{5}{2}{{O}_{2}}\rightleftharpoons 2NO+3{{H}_{2}}O\] in terms of \[{{K}_{1}},{{K}_{2}}\] and \[{{K}_{3}}\] will be

    A) \[{{K}_{1}}{{K}_{2}}{{K}_{3}}\]       

    B)        \[\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{3}}}\]  

    C)        \[\frac{{{K}_{1}}K_{3}^{2}}{{{K}_{2}}}\] 

    D)        \[\frac{{{K}_{2}}K_{3}^{3}}{{{K}_{1}}}\] 

    Correct Answer: D

    Solution :

    From given equations, We have, \[{{K}_{1}}=\frac{{{[N{{H}_{3}}]}^{2}}}{[{{N}_{2}}]{{[{{H}_{2}}]}^{3}}}\] \[{{K}_{2}}=\frac{{{[NO]}^{2}}}{[{{N}_{2}}][{{O}_{2}}]}\] \[{{K}_{3}}=\frac{[{{H}_{2}}O]}{[{{H}_{2}}]{{[{{O}_{2}}]}^{1/2}}}\] For the given reaction, \[K=\frac{{{[NO]}^{2}}{{[{{H}_{2}}O]}^{3}}}{{{[N{{H}_{3}}]}^{2}}{{[{{O}_{2}}]}^{5/2}}}\] \[\frac{K{{ & }_{2}}K_{3}^{3}}{{{K}_{1}}}=\frac{{{[NO]}^{2}}{{[{{H}_{2}}O]}^{3}}}{{{[N{{H}_{3}}]}^{2}}{{[{{O}_{2}}]}^{5/2}}}\] \[K=\frac{{{K}_{2}}K_{3}^{3}}{{{K}_{1}}}\]


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