Consider a complex multi-step reaction whose effective overarching rate constant simplifies algebrai — Chemical Kinetics Chemistry Question
Question
Consider a complex multi-step reaction whose effective overarching rate constant simplifies algebraically to $k_{eff} = k_1 \sqrt{\frac{k_2}{k_3}}$. Applying standard Arrhenius logarithm derivatives to this composite constant directly validates which of the following conclusions?
💡 Solution & Explanation
By substituting $k_i = A_i e^{-E_{ai}/RT}$ into the composite formula, we get $k_{eff} = A_1 e^{-E_{a1}/RT} \sqrt{\frac{A_2 e^{-E_{a2}/RT}}{A_3 e^{-E_{a3}/RT}}}$. Collecting constants gives B, and summing exponents dictates $E_{a(eff)} = E_{a1} + 0.5E_{a2} - 0.5E_{a3}$ (A is correct). If the negative $-0.5E_{a3}$ term dominates the positive terms, the sum drops below zero (C is correct). D is false; if $E_{a(eff)}$ is positive, the rate will predictably increase with temperature.