One of the reactions that occurs in polluted air in urban...

One of the reactions that occurs in polluted air in urban areas is $2 \mathrm{NO}_{2}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{O}_{2}(g) . \mathrm{It}$ is believed that a species with the formula $\mathrm{NO}_{3}$ is involved in the mechanism, and the observed rate law for the overall reaction is rate $=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{O}_{3}\right] .$ Propose a mechanism for this reaction that includes the species $\mathrm{NO}_{3}$ and is consistent with the observed rate law.

Key Concepts

Pre-Equilibrium Assumption

The pre-equilibrium assumption is used when an early step in the mechanism is fast and reversible, allowing an intermediate to be in equilibrium with reactants before a slower, rate-determining step occurs. This assumption permits the concentration of the intermediate to be expressed in terms of the reactants, reconciling the mechanism with the observed rate law.

Rate Law

The rate law is an expression that correlates the reaction rate with the concentrations of reactants, usually derived from the slowest, or rate-determining, step of the mechanism. It is a critical piece of experimental data, and any proposed mechanism must result in a rate law that matches the observed concentration dependencies.

Reaction Intermediate

A reaction intermediate is a species formed during one step of the mechanism that does not appear in the overall balanced equation. Intermediates like the NO3 species can facilitate the transformation by providing an alternative pathway. Their existence must be reconciled within the mechanism, ensuring that they are generated and consumed appropriately.

Reaction Mechanism

A reaction mechanism details the sequence of elementary steps that occur in a reaction and collectively account for the observed overall reaction. It includes the formation and consumption of intermediate species and must be consistent with the overall stoichiometry of the reaction. In proposing a mechanism, each step should be justified based on how it contributes to the overall reaction pathway and the observed rate dependence.

Elementary Reaction

Elementary reactions are the individual steps in a reaction mechanism that take place in a single event. Each elementary reaction has its own rate law that reflects the molecularity of the step, meaning the number of molecules involved directly in that path. Analyzing elementary reactions allows us to link the mechanistic steps with the experimentally observed kinetics.

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