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NEET AIPMT SOLVED PAPER SCREENING 2005

  • question_answer
                    Equilibrium constants \[{{K}_{1}}\] and \[{{K}_{2}}\] for the following equilibria:                 \[{{N}_{2}}(g)+\frac{1}{2}{{O}_{2}}\,N{{O}_{2}}(g)\,and\,\]          \[2N{{O}_{2}}(g)\,2NO(g)+{{O}_{2}}(g)\]                 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) \[NO(g)+\frac{1}{2}{{O}_{2}}(g)N{{O}_{2}}(g)\]                         \[So\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{K}_{1}}=\frac{[N{{O}_{2}}]}{[NO]\,{{[{{O}_{2}}]}^{1/2}}}.....(i)\]                 (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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