If the first order rate constants for the decomposition of ethyl iodide at 600 K and 700 K are 2.0×10-5 s-1 and2.0×10-4 s-1 respectively, th activation energy for this reaction in kJmol-1 is

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If the first order rate constants for the decomposition of ethyl iodide at $600 K$ and $700 K$ are $2.0 \times 10^{- 5} s^{- 1}$ and $2.0 \times 10^{- 4} s^{- 1}$ respectively, th activation energy for this reaction in ${kJmol}^{- 1}$ is

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60.3

40.2

80.4

20.1

answer is A.

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Detailed Solution

$\log \frac{K_{2}}{K_{1}} = \frac{E_{a}}{2.303 \times R} (\frac{1}{T_{1}} - \frac{1}{T_{2}}) \log (\frac{2 \times 10^{- 4}}{2 \times 10^{- 5}}) = \frac{E_{a}}{2.303 \times 8.314} (\frac{1}{600} - \frac{1}{700}) \log_{10} = \frac{E_{a}}{19.147} (2.38 \times 10^{- 4}) As \log_{10} = 1 E_{a} = \frac{19.147 \times 10^{4}}{2.38} = 8.04 \times 10^{4}$