• # 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) $4\times {{10}^{-4}}{{s}^{-1}}$

 $\ell n=\ell nA-\frac{Ea}{RT}$$=\ell nA-\frac{4606}{T}$ $\ell n\left( \frac{k}{{{10}^{-5}}} \right)=\left( \frac{Ea}{R} \right)\times \frac{500-400}{500\times 400}$ $\ell n\left( \frac{k}{{{10}^{-5}}} \right)=4606\times \frac{1}{2000}=2.303=\ell n10$ $\ell n\left( \frac{k}{{{10}^{-5}}} \right)=\ell n10$ $k={{10}^{-4}}.$