The specific rate constant for a reaction increases by a factor of 4, if the temperature is changed from `27^(@)C" to "47^(@)C`. Find the activation energy for the reaction.

Explanation

To find the activation energy (Ea) for the reaction given the specific rate constant increases by a factor of 4 when the temperature changes from 27°C to 47°C, we can use the Arrhenius equation in its logarithmic form. Here’s a step-by-step solution:

### Step 1: Convert Temperatures to Kelvin
First, we need to convert the temperatures from Celsius to Kelvin since the Arrhenius equation requires temperatures in Kelvin.

- For T1 (27°C):
\[
T_1 = 27 + 273 = 300 \, \text{K}
...