For a set of parallel first-order decomposition paths (, activation energy ) and (, activation energ — Chemical Kinetics Chemistry Question
Question
For a set of parallel first-order decomposition paths $A \rightarrow B$ ($k_1$, activation energy $E_{a1}$) and $A \rightarrow C$ ($k_2$, activation energy $E_{a2}$), the overall effective activation energy $E_{a(eff)}$ for the destruction of A is rigorously expressed by which Arrhenius derivation?
Answer: B
💡 Solution & Explanation
Taking the Arrhenius derivative $d(\ln k)/dT = E_a/RT^2$ of the sum of the composite overall rate constant $k_{eff} = k_1 + k_2$ mathematically generates 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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