A first order reaction is `50%` complete in 30 minutes at `27^(@)`C and in 10 minutes at `47^(@)`C. Calculate the reaction rate constants at these temperatures and the energy of activation of the reaction in `kJ//mol` (R=8.314 J` mol^(-1)K^(-1))`

Explanation

To solve the problem step by step, we will calculate the rate constants for the first-order reaction at the two given temperatures and then use the Arrhenius equation to find the activation energy.

### Step 1: Calculate the rate constant (k) at 27°C

Given:
- Half-life (t₁/₂) = 30 minutes

For a first-order reaction, the half-life is related to the rate constant (k) by the formula:
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