Final answer:
The rate law for the reaction O2 + 2NO(g) → 2NO2, given the proposed mechanism, is rate = k'[NO]^2[O2]. The rate-determining step is O2 + N2O2 → 2NO2, and after applying the steady state approximation for the intermediate N2O2, we express the rate law in terms of the reactant's concentrations.
Step-by-step explanation:
The proposed mechanism for the reaction O2 + 2NO(g) → 2NO2 is comprised of two steps. The first step is the fast equilibrium 2NO → N2O2 with forward rate constant k1 and reverse rate constant k-1. The second step is the slow reaction O2 + N2O2 → 2NO2. According to the rate-determining step approximation, the rate law for a reaction mechanism is determined by the slowest step, because it acts as a bottleneck for the reaction progress. Therefore, the rate law predicted by this mechanism is rate = k[N2O2][O2]. However, since N2O2 is an intermediate and is not present in the rate law for a bimolecular reaction, we apply the steady state approximation for N2O2. By setting the formation rate of N2O2 equal to its consumption rate, we can solve for the concentration of N2O2 in terms of NO's concentration. Substituting this into our rate law yields rate = k'[NO]^2[O2] where k' is a constant derived from the original rate constants k1 and k-1.