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The rate of \mathrm{r_{xn}} doubles when its temperature changes from 290 K to 300 K. Activation energy of such reaction will be log [2=0.301]

Option: 1

32197


Option: 2

50140


Option: 3

24316


Option: 4

27819


Answers (1)

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\mathrm{\begin{aligned} \log \frac{k_2}{k_1} & =\frac{-E a}{2.303 R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right) \\ \log \frac{k_2}{k_1} & =\frac{E a}{2.30 B R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right) \\ \log 2 & =\frac{E a}{2.303 \times 8.314}\left(\frac{30-2 a}{8700}\right) \\ \log 2 & =\frac{E a}{2.303 \times 8.314}\left(\frac{1}{8700}\right) \\ E a & =\log 2 \times 2.303 \times 8.314 \times 8700 \\ E a & =0.301 \times 2.303 \times 8.314 \times 8700 \\ E a & =50140 \end{aligned}}

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