A reaction mechanism converts reactant X to product Z through three successive elementary steps. Rate constants for each step were measured at two temperatures; the data are summarized below.
Step k298 (s⁻¹) k450 (s⁻¹)
1 1.8 × 10⁴ 9.6 × 10⁵
2 7.0 × 10² 8.0 × 10⁵
3 3.5 × 10⁵ 2.2 × 10⁶
Answer the following questions. Assume first-order kinetics for every step and constant pre-exponential factors.
(a) Use the rate constants provided to calculate the activation energy Ea for each elementary step.
(b) At 298 K, identify the step that controls the overall reaction rate. Support your conclusion quantitatively.
(c) Using your calculated activation energies, predict the rate-determining step at 450 K and explain whether the identity of the slowest step changes with temperature.
(d) Briefly discuss how the temperature dependence you found in part (c) illustrates the kinetic competition among the elementary steps in a multistep mechanism.