The rate constant for a first order reaction becomes six times when the temperature is raised from 350 to 400 K. Calculate the energy of activation for the reactions.

Explanation

To calculate the activation energy for the given first-order reaction, we can use the Arrhenius equation in the form of the logarithmic relationship between the rate constants at two different temperatures. Here’s a step-by-step solution:

### Step 1: Write down the Arrhenius equation
The Arrhenius equation in logarithmic form is given by:
\[ \log \left( \frac{k_2}{k_1} \right) = \frac{E_a}{2.303 R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \]
where:
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