The rate constant of a reaction of a reaction increases by `5%`
when the temperature of the reaction is increased
from 300 to 301 K where equilibrium constant increases
only by `2%`. Calculate the activation energy for the
forward as well as backward reaction.

Explanation

To solve the problem, we will use the Arrhenius equation and the Van 't Hoff equation to find the activation energies for the forward and backward reactions.

### Step 1: Calculate the activation energy for the forward reaction using the Arrhenius equation.

The Arrhenius equation relates the rate constants (K) at two different temperatures (T1 and T2) to the activation energy (EA):

\[
\log \left(\frac{K_2}{K_1}\right) = \frac{E_A}{2.303 R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)
...