The calculations yield the following results:

• Activation energy ($E_a$): $74,851.9$ J/mol
• Pre-exponential factor ($A$): $3.839 \times 10^{11}$ s$^{-1}$
• Rate constant at $298$ K: $0.0291$ s$^{-1}$

So, the rate constant for this reaction at $298$ K is approximately $0.0291$ s$^{-1}$.

Would you like more details or have any questions?

Here are some related questions you might find useful:

1. How is the Arrhenius equation used to determine reaction rates?
2. What is the significance of the activation energy in a chemical reaction?
3. How can we determine the pre-exponential factor $A$ from experimental data?
4. Why do we use the natural logarithm of the rate constant in the Arrhenius equation?
5. How do temperature changes affect the rate of a chemical reaction?

Tip: When plotting experimental data to determine kinetic parameters, ensure accurate measurements and consistent units to obtain reliable results.