The following mechanism has been proposed for the reaction between nitric oxide and bromine: Step \(1 \mathrm{NO}+\mathrm{Br}_{2} \longrightarrow \mathrm{NOBr}_{2}\) (slow) Step \(2 \mathrm{NOBr}_{2}+\mathrm{NO} \longrightarrow \mathrm{NOBr}+\mathrm{NOBr}\) (fast) Write the rate law for the formation of NOBr implied by this mechanism.

Understanding the rate law is fundamental in chemical kinetics as it describes the relationship between the reactants' concentration and the rate at which the reaction occurs. The rate law is generally expressed in the form \( Rate = k[\text{A}]^{m}[\text{B}]^{n} \) where \( k \) is the rate constant, \( [\text{A}] \) and \( [\text{B}] \) are the concentrations of reactants A and B, and \( m \) and \( n \) are the orders of the reaction with respect to A and B, respectively.

The orders of a reaction are not necessarily the stoichiometric coefficients seen in the overall balanced equation; instead, they are determined experimentally or through the rate-determining step of a reaction mechanism. An essential aspect of the rate law is that it only includes reactants, not products or intermediates, and it reflects the slowest step in the reaction mechanism—the rate-determining step.

The rate-determining step, often the slowest step in a reaction mechanism, governs the reaction rate. It's like a bottleneck in a process that restricts the flow—the rate of the entire reaction cannot go faster than this slow step.

In our example, Step 1, \( \text{NO} + \text{Br}_{2} \rightarrow \text{NOBr}_{2} \), is the rate-determining step because it is described as slower compared to the subsequent steps in the mechanism. As a result, the rate law directly reflects this step. A common misstep for students is assuming that all steps influence the rate law, but it is the kinetics, not stoichiometry, that determines which step dictates the pace of the reaction.

A reaction mechanism outlines the sequence of elementary steps that lead to the conversion of reactants to products. Each step involves a transition state and possibly the formation of intermediates—species that are produced in one step of the mechanism and consumed in another.

While the overall equation provides a summary of the reaction, the mechanism gives insight into the 'how' and 'why' behind the process. It's a more detailed picture that explains the individual steps involved and their respective speeds, and it is critical for deducing the rate law. In our exercise, the mechanism consists of two steps, with the first being the slow, rate-determining step and the second being a fast step that involves the intermediate \( \text{NOBr}_{2} \). This information allows us to construct a rate law that reflects the actual process accurately.

Stoichiometry deals with the quantitative relationships between reactants and products in a chemical reaction. It's the math behind chemistry, allowing us to predict how much of each substance is needed or produced. While stoichiometry is based on the balanced chemical equation, when it comes to reaction rates, the stoichiometric coefficients are not necessarily related to the reaction order in the rate law.

For instance, the stoichiometric coefficient of a reactant in the balanced equation doesn't automatically indicate the reactant's order in the rate law. The rate law focuses on the mechanism's steps, especially the rate-determining step, rather than the overall balanced equation. In educational practice, emphasizing the distinction between stoichiometric coefficients and reaction orders can help students understand why not all reactants or their amounts appear in the rate law.