Chemistry

When a reaction can proceed through multiple parallel pathways, each with its own activation energy and rate constant, the overall behavior is a weighted average of all paths. The key insight is that the average activation energy $E_{AV}$ must account for how much each pathway contributes—and contribution is proportional to the rate constant of that path. Set up the weighted average where each activation energy is weighted by its corresponding rate constant, then solve for $n$.

When a reaction can proceed through multiple parallel pathways, each with its own activation energy and rate constant, the overall behavior is a weighted average of all paths. The key insight is that the average activation energy $E_{AV}$ must account for how much each pathway contributes—and contribution is proportional to the rate constant of that path. Set up the weighted average where each activation energy is weighted by its corresponding rate constant, then solve for $n$.