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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 42

  • question_answer
    A reaction takes place in three steps: the rate constant are \[{{k}_{1}},{{k}_{2}},\] and\[{{k}_{3}}\]. The overall rate constant \[k={{k}_{1}}{{k}_{3}}/{{k}_{2}}\]. If the energies of activation are \[40,\text{ }30\] and \[20\text{ }kJ\text{ }mo{{l}^{-1}},\] the overall energy of activation is (assuming A to be constant for all)

    A) \[10\]                     

    B)        \[15\]                     

    C) \[30\]        

    D)        \[60\]

    Correct Answer: C

    Solution :

    [c] The overall rate constant \[k=\frac{{{k}_{1}}{{k}_{3}}}{{{k}_{2}}}\] We know;  \[k=A{{e}^{-Ea/RT}}\] \[\therefore \,\,\,\,\,\,\,\,k=\frac{{{k}_{1}}{{k}_{3}}}{{{k}_{2}}}=A{{e}^{-({{E}_{a1}}+{{E}_{a3}}-{{E}_{a2}})/RT}}\] \[=A{{e}^{-(40-30+20)/RT}}=A{{e}^{-30/RT}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,{{E}_{a}}=30\,kJ\,mo{{l}^{-1}}\]           


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