Two reactions of the same order have equal pre exponential factors but their activation energies differ by 24.9kJ `"mol"^(-1)`. Calculate the ratio between the rate constants of these reactions at `27^(@)C`. (Gas constant R = 8.314 J `K^(-1) "mol"^(-1)`)

Explanation

To solve the problem, we will use the Arrhenius equation, which relates the rate constant (k) of a reaction to its activation energy (Ea), the temperature (T), and the pre-exponential factor (A).

### Step-by-step Solution:

1. **Write the Arrhenius Equation**:
The Arrhenius equation is given by:
\[
k = A e^{-\frac{E_a}{RT}}
...