The activation energy for a reaction which doubles the rate when the temperature is raised from $298…

The activation energy for a reaction which doubles the rate when the temperature is raised from $298 \mathrm{~K}$ to $308 \mathrm{~K}$ is
  1. $59.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  2. $39.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  3. $52.9 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  4. $29.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$

Solution

Activation energy can be calculated from the equation. $ \begin{aligned} & \frac{\log K_2}{\log K_1}=\frac{-E_a}{2.303 R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right) \\ & \text { Given } \frac{\log K_2}{\log K_1}=2 \quad T_2=308 ; \quad T_1=298 \\ & \therefore \quad \log 2=\frac{-E_a}{2.303 \times 8.314}\left(\frac{1}{308}-\frac{1}{298}\right) \\ & E_a=52.9 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned} $

Asked in: JEE Main 2012 (26 May Online)

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