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Manipal Medical Manipal Medical Solved Paper-2008

  • question_answer
    A hypothetical reaction\[{{A}_{2}}+{{B}_{2}}\xrightarrow[{}]{{}}2AB\]follows the mechanism as given below, \[{{A}_{2}}\rightleftharpoons A+A\] (fast) \[A+{{B}_{2}}\xrightarrow[{}]{{}}AB+B\] (slow) \[A+B\xrightarrow[{}]{{}}AB\] (fast) The order of the overall reaction is

    A)  2               

    B)  1

    C)  \[1\frac{1}{2}\]              

    D)  0

    Correct Answer: C

    Solution :

     From slow step, rate\[=k[{{B}_{2}}][A]\] From 1st equation\[{{K}_{eq}}=\frac{{{[A]}^{2}}}{[{{A}_{2}}]}\] Or     \[[A]=\sqrt{{{K}_{eq}}[{{A}_{2}}]}=K_{eq}^{1/2}A_{2}^{1/2}\] Hence, rate\[=k[{{B}_{2}}]K_{eq}^{1/2}{{[{{A}_{2}}]}^{1/2}}\] \[=k{{[{{A}_{2}}]}^{1/2}}[{{B}_{2}}]\] Hence, order\[=1\frac{1}{2}\]


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