The rate constant, $\mathrm{k}$ for a first order reaction, $\mathrm{C}_2 \mathrm{H}_5…

The rate constant, $\mathrm{k}$ for a first order reaction, $\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}(\mathrm{g}) \rightarrow \mathrm{C}_2 \mathrm{H}_4(\mathrm{~g})+\mathrm{HI}(\mathrm{g})$ is $\mathrm{xs}^{-1}$ at $600 \mathrm{~K}$ and $4 \mathrm{x} \mathrm{s}^{-1}$ at $700 \mathrm{~K}$. The energy of activation of the reaction (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) is
  1. $48.16$
  2. $58.16$
  3. $38.16$
  4. $28.16$

Solution

$\log \frac{\mathrm{K}_2}{\mathrm{~K}_1}=\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{R}}\left(\frac{\mathrm{T}_2-\mathrm{T}_1}{\mathrm{~T}_1 \mathrm{~T}_2}\right)$ $\begin{aligned} & \log \left(\frac{4 \mathrm{x}}{\mathrm{x}}\right)=\frac{\mathrm{E}_{\mathrm{a}}}{2.303(8.314)}\left(\frac{700-600}{700 \times 600}\right) \\ & 0.602=\frac{\mathrm{E}_{\mathrm{a}}}{19.147}\left(2.38 \times 10^{-4}\right) \\ & \Rightarrow \mathrm{E}_{\mathrm{a}}=48548.3 \mathrm{~J}=48.54 \mathrm{~kJ} \\ & \approx 48.16 \mathrm{~kJ} .\end{aligned}$

Asked in: AP EAMCET 2023 (19 May Shift 1)

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