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For a set of parallel first-order reactions (, ) and (, ), the overall effective activation energy fChemical Kinetics Chemistry Question

Question

For a set of parallel first-order reactions $A \rightarrow B$ ($k_1$, $E_{a1}$) and $A \rightarrow C$ ($k_2$, $E_{a2}$), the overall effective activation energy $E_{a(eff)}$ for the destruction of A is expressed by which formula?

Answer: B

💡 Solution & Explanation

Taking the Arrhenius derivative $d(\ln k)/dT = E_a/RT^2$ of the overall rate constant $k_{eff} = k_1 + k_2$ mathematically yields a weighted average of the activation energies, explicitly defined as $\frac{k_1 E_{a1} + k_2 E_{a2}}{k_1 + k_2}$.

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