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JCECE Engineering JCECE Engineering Solved Paper-2012

  • question_answer
    Equilibrium constants \[{{K}_{1}}\] and \[{{K}_{2}}\] for the following equilibria\[NO(g)+\frac{1}{2}{{O}_{2}}N{{O}_{2}}(g)\]and\[2N{{O}_{2}}(g)2NO(g)+{{O}_{2}}(g)\]are related as

    A) \[{{K}_{2}}=\frac{1}{{{K}_{1}}}\]                               

    B) \[{{K}_{2}}=K_{1}^{2}\]

    C) \[{{K}_{2}}=\frac{{{K}_{1}}}{2}\]                               

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

    Correct Answer: D

    Solution :

    (i)\[NO(g)N{{O}_{2}}(g)\] So\[,\]  \[{{K}_{1}}=\frac{[N{{O}_{2}}]}{[NO]{{[{{O}_{2}}]}^{1/2}}}\]                        ? (i) (ii)\[2N{{O}_{2}}(g)2NO+{{O}_{2}}(g)\] So\[,\]  \[{{K}_{2}}=\frac{{{[NO]}^{2}}[{{O}_{2}}]}{{{[N{{O}_{2}}]}^{2}}}\]                             ? (ii) From Eq. (i)                 \[K_{1}^{2}=\frac{{{[N{{O}_{2}}]}^{2}}}{{{[NO]}^{2}}[{{O}_{2}}]}\] or            \[\frac{1}{K_{1}^{2}}=\frac{{{[NO]}^{2}}[{{O}_{2}}]}{{{[N{{O}_{2}}]}^{2}}}\]                         ? (iii) From Eqs. (ii) and (iii)                 \[{{K}_{2}}=\frac{1}{K_{1}^{2}}\]


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