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A reaction mechanism consists of a series of elementary steps that describe the pathway from reactants to products. Each individual step involves a small number of molecules colliding and reacting. These steps can help us understand how a reaction takes place at the molecular level.

In this given problem, the mechanism includes two steps: a fast equilibrium step and a subsequent conversion, which together describe the overall reaction.

• The first step: \( \mathrm{NO} + \mathrm{Cl}_2 \underset{k_{r}}{\stackrel{k_{f}}{\rightleftharpoons}} \mathrm{NOCl}_2 \), shows a fast equilibrium involving NO and Clâ‚‚ to form an intermediate, NOClâ‚‚.
• The second step: \( \mathrm{NOCl}_2 + \mathrm{NO} \stackrel{k_{2}}{\longrightarrow} 2 \mathrm{NOCl} \), illustrates the conversion of the intermediate to the final product, NOCl.

Macroscopically, the entire mechanism provides the framework needed to deduce important kinetic properties like the rate law.

Intermediate species are molecules or atoms that are formed and consumed during the reaction mechanism. They are not present in the overall balanced equation of the reaction as they appear only temporarily.

In this specific example, \( \mathrm{NOCl}_2 \) is an intermediate species. It is formed in the first fast equilibrium step and consumed in the rate-determining step.

• Formation: \( \mathrm{NO} + \mathrm{Cl}_2 \rightleftharpoons \mathrm{NOCl}_2 \).
• Consumption: \( \mathrm{NOCl}_2 + \mathrm{NO} \rightarrow 2 \mathrm{NOCl} \).

Understanding intermediates is crucial because they directly affect the rate law of the reaction, linking different steps in the mechanism.

An equilibrium expression relates the concentrations of reactants and products in a reaction that is at equilibrium. It is derived from the law of mass action and allows us to express concentration relationships through an equilibrium constant \( K \).

For this reaction, the first step involves a fast equilibrium:

• \( \mathrm{NO} + \mathrm{Cl}_2 \rightleftharpoons \mathrm{NOCl}_2 \).

The expression for this equilibrium is \( K = \frac{[\mathrm{NOCl}_2]}{[\mathrm{NO}][\mathrm{Cl}_2]} \).
Rearranging the equilibrium expression provides a way to express the concentration of the intermediate, \( [\mathrm{NOCl}_2] = K [\mathrm{NO}][\mathrm{Cl}_2] \). This relationship allows us to substitute \( [\mathrm{NOCl}_2] \) in the rate law of the subsequent reaction step, bridging the two stages of the mechanism.

The rate-determining step of a reaction is the slowest step in a reaction mechanism. It essentially "bottlenecks" the reaction, controlling the overall rate. In many cases, it is the step that energy considerations show to be the hardest to occur.

In the given mechanism, the second step is generally the rate-determining step. This is because it follows a fast initial equilibrium step:

• \( \mathrm{NOCl}_2 + \mathrm{NO} \rightarrow 2 \mathrm{NOCl} \).

Because the first step is at equilibrium, the system quickly reaches a balance between forward and reverse formations of the intermediate, and the slower second step crucially affects how fast the products are formed.
The rate law for this step can initially be written as \( \text{rate} = k_2 [\mathrm{NOCl}_2][\mathrm{NO}] \). By substituting the expression for \( [\mathrm{NOCl}_2] \) from the equilibrium step, we achieve the overall rate law: \( \text{rate} = k_2 K [\mathrm{NO}]^2[\mathrm{Cl}_2] \), where \( k_2 K \) is the observed rate constant \( k_{obs} \). This highlights the significance of the rate-determining step in shaping the rate law.