VMMC VMMC Medical Solved Paper-2015

  • question_answer
    For a first order reaction involving decomposition   of\[{{N}_{2}}{{O}_{5}},\]following information is available \[2{{N}_{2}}{{O}_{5}}(g)\xrightarrow[{}]{{}}4N{{O}_{2}}(g)+{{O}_{2}}(g),\] Rate\[=k[{{N}_{2}}{{O}_{5}}]\] \[{{N}_{2}}{{O}_{5}}(g)\xrightarrow[{}]{{}}2N{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g),\] Rate\[=k[{{N}_{2}}{{O}_{5}}]\] Which of following expression is true?

    A) \[k=k'\]               

    B) \[k'=2k\]

    C) \[k'=\frac{1}{2}k\]                          

    D) \[k>k'\]

    Correct Answer: B

    Solution :

    \[2{{N}_{2}}{{O}_{5}}(g)\xrightarrow[{}]{{}}4N{{O}_{2}}+{{O}_{2}}(g)\] Rate\[=-\frac{1}{2}\frac{[{{N}_{2}}{{O}_{5}}]}{dt}=k[{{N}_{2}}{{O}_{5}}]\] or Rate\[=-\frac{d[{{N}_{2}}{{O}_{5}}]}{dt}=2k[{{N}_{2}}{{O}_{5}}]\] For\[{{N}_{2}}{{O}_{5}}\xrightarrow[{}]{{}}2N{{O}_{2}}+\frac{1}{2}{{O}_{2}}\] \[-\frac{d[{{N}_{2}}{{O}_{5}}]}{dt}=k'[{{N}_{2}}{{O}_{5}}]\] or Rate\[=-\frac{d[{{N}_{2}}{{O}_{5}}]}{dt}=k'[{{N}_{2}}{{O}_{5}}]\] Since, rate must be .same, k' = 2k


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