The rate constant of a reaction is `1.2 xx10^(-3) s^(-1)` at `30^@C` and `2.1xx10^(-3)s^(-1)` at `40^@C`. Calculate the energy of activation of the reaction.

Explanation

To calculate the energy of activation (Ea) for the reaction, we can use the Arrhenius equation in its logarithmic form. Here’s a step-by-step solution:

### Step 1: Identify the given data
We have two rate constants at two different temperatures:
- \( k_1 = 1.2 \times 10^{-3} \, \text{s}^{-1} \) at \( T_1 = 30^\circ C = 303 \, K \)
- \( k_2 = 2.1 \times 10^{-3} \, \text{s}^{-1} \) at \( T_2 = 40^\circ C = 313 \, K \)

### Step 2: Use the Arrhenius equation in logarithmic form
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