KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    For a certain reaction consider the plot of \[\ell nk\] versus 1/T given in the figure. If the rate constant of this reaction at 400 K is \[{{10}^{-5}}{{s}^{-1}},\]then the rate constant at 500 K is:

    A) \[{{10}^{-6}}{{s}^{-1}}\]

    B) \[2\times {{10}^{-4}}{{s}^{-1}}\]

    C) \[{{10}^{-4}}{{s}^{-1}}\]

    D) \[4\times {{10}^{-4}}{{s}^{-1}}\]

    Correct Answer: C

    Solution :

    \[\ell n=\ell nA-\frac{Ea}{RT}\]\[=\ell nA-\frac{4606}{T}\]
    \[\ell n\left( \frac{k}{{{10}^{-5}}} \right)=\left( \frac{Ea}{R} \right)\times \frac{500-400}{500\times 400}\]
    \[\ell n\left( \frac{k}{{{10}^{-5}}} \right)=4606\times \frac{1}{2000}=2.303=\ell n10\]
    \[\ell n\left( \frac{k}{{{10}^{-5}}} \right)=\ell n10\]

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