Two reactions of the same order have equal pre-exponential factors, but their activation energies differ by 24.9 kJ per mole. Calculate the ratio between the rate constants of these reactions at `27^@C`.

Explanation

To solve the problem, we need to find the ratio of the rate constants \( k_1 \) and \( k_2 \) for two reactions with different activation energies but equal pre-exponential factors. Let's denote the activation energies as \( E_a1 \) and \( E_a2 \), where \( E_a1 - E_a2 = 24.9 \, \text{kJ/mol} \).

### Step-by-Step Solution:

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