A reaction between A(g) and B(g) to form products is studied at 500 K. The initial-rate data are collected under constant total pressure.
Experiment
[A]₀ (mol L⁻¹)
[B]₀ (mol L⁻¹)
Initial Rate (mol L⁻¹ s⁻¹)
1
0.050
0.050
1.6 × 10⁻³
2
0.100
0.050
6.4 × 10⁻³
3
0.100
0.100
1.3 × 10⁻²
Two alternative mechanisms, each with its first step rate-limiting, are proposed:
Mechanism I
Step 1 (slow): A + A → A₂‡
Step 2 (fast): A₂‡ + B → products
Mechanism II
Step 1 (slow): A + B → AB‡
Step 2 (fast): AB‡ + A → products
(a) Using the experimental data, determine the empirical rate law, including the numerical orders with respect to A and B.
(b) From Mechanism I, derive the rate law that would be expected if that mechanism were correct.
(c) From Mechanism II, derive the rate law that would be expected if that mechanism were correct.
(d) Which mechanism is consistent with the experimental data? Provide a justification that explicitly compares the predicted and empirical rate laws.
(e) Propose a specific modification to the rejected mechanism that would reconcile it with the observed kinetics, and explain how your modification changes the rate-determining step or molecularity to fit the data.