The reaction 2 NO(g)+Cl2( g) →→2 NOCl(g) obeys the rate law, rate =k[NO]^2[Cl2]. The following m

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The reaction 2 NO(g)+Cl2( g) →→2 NOCl(g) obeys the rate law,...

The reaction $2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \rightarrow 2 \mathrm{NOCl}(g)$ obeys the rate law, rate $=k[\mathrm{NO}]^{2}\left[\mathrm{Cl}_{2}\right]$. The following mechanism has been proposed for this reaction: $$ \begin{array}{r} \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g) \\ \mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \rightarrow \rightarrow 2 \mathrm{NOCl}(g) \end{array} $$ (a) What would the rate law be if the first step were rate determining? (b) Based on the observed rate law, what can we conclude about the relative rates of the two steps?

The reaction $2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \rightarrow 2 \mathrm{NOCl}(g)$ obeys
the rate law, rate $=k[\mathrm{NO}]^{2}\left[\mathrm{Cl}_{2}\right]$. The following mechanism has been proposed for this reaction:
$$
\begin{array}{r}
\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g) \\
\mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \rightarrow \rightarrow 2 \mathrm{NOCl}(g)
\end{array}
$$
(a) What would the rate law be if the first step were rate determining? (b) Based on the observed rate law, what can we conclude about the relative rates of the two steps?

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Key Concepts

Rate Law

The rate law is an expression that relates the rate of a reaction to the concentrations of its reactants raised to specific powers. These powers are determined by the reaction mechanism, not by the overall stoichiometry, and they indicate the order of reaction with respect to each reactant.

Reaction Mechanism

A reaction mechanism is a detailed sequence of elementary steps that collectively describe the overall reaction. Each elementary step has its own rate law, and the mechanism must be consistent with the observed overall rate law, helping chemists understand the path from reactants to products.

Rate-Determining Step

The rate-determining step is the slowest step in the mechanism, which limits the overall rate of the reaction. Because it acts as a bottleneck, the overall rate law is typically dictated by the kinetics of this single elementary step.

Pre-equilibrium Approximation

When an initial step in a mechanism is fast and reversible, it can establish an equilibrium before the slower, rate-determining step occurs. This allows the concentration of intermediates to be expressed in terms of the concentrations of the reactants, bridging the gap between the steps and aligning the predicted rate law with experimental observations.

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