The specific rate constant of a particular reaction quadruples when temperature is changed from `27^@" to "47^@C`. Find activation energy for the reaction.

Explanation

To find the activation energy (Ea) for the reaction, we can use the Arrhenius equation and the information given in the problem. The specific rate constant quadruples when the temperature changes from 27°C to 47°C. Here’s a step-by-step solution:

### Step 1: Understand the relationship between rate constants and temperature
The Arrhenius equation relates the rate constant (k) to temperature (T) and activation energy (Ea):
\[ k = A e^{-\frac{E_a}{RT}} \]
Where:
- \( A \) = pre-exponential factor
- \( R \) = universal gas constant (8.314 J/mol·K or 2 cal/mol·K)
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