The gaseous decomposition of substance M to product T occurs by the two-step mechanism shown below.
Step 1 M → N
Step 2 N → T
A chemist measures the first-order rate constants for Step 1 at two different temperatures:
Temperature (K) Rate constant k1 (s⁻¹)
298 2.4 × 10⁻⁵
338 1.2 × 10⁻³
Additional thermodynamic data are provided.
Step Activation energy, Ea (kJ mol⁻¹) Enthalpy change, ΔH (kJ mol⁻¹)
1 120 +10
2 75 –130
Answer the following questions. Assume the pre-exponential factors for the two steps are equal.
(a) Using the kinetic data, calculate an experimental value of the activation energy for Step 1.
(b) Comparing your result from part (a) with the tabulated activation energy, comment on the consistency of the experimental measurement with the mechanistic data provided.
(c) At 298 K, determine which step limits the overall rate of formation of product T. Justify your choice with reference to activation energies and any relevant kinetic reasoning.