You have studied the gas-phase oxidation of \(\mathrm{HBr}\) by \(\mathrm{O}_{2}\) : $$ 4 \mathrm{HBr}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{Br}_{2}(g) $$ You find the reaction to be first order with respect to HBr and first order with respect to \(\mathrm{O}_{2}\). You propose the following mechanism: $$ \begin{aligned} \mathrm{HBr}(g)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{HOOBr}(g) \\ \mathrm{HOOBr}(g)+\mathrm{HBr}(g) & \longrightarrow 2 \mathrm{HOBr}(g) \\ \mathrm{HOBr}(g)+\mathrm{HBr}(g) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Br}_{2}(g) \end{aligned} $$ (a) Confirm that the elementary reactions add to give the overall reaction. (b) Based on the experimentally determined rate law, which step is rate determining? (c) What are the intermediates in this mechanism? (d) If you are unable to detect HOBr or HOOBr among the products, does this disprove your mechanism?

Understanding how chemical reactions occur requires diving into the realm of chemical kinetics, which is the study of reaction rates and the factors that affect them. When examining the gas-phase oxidation of HBr by O₂, we see that kinetics plays a crucial role in determining the speed and outcome of the reaction. The fact that the reaction between HBr and O₂ is first order with respect to each reactant indicates how the concentration of these substances influences the reaction rate.

In practical terms, the rate law can be thought of as a recipe for the reaction rate, with each ingredient (reactant) contributing to the speed at which the reaction proceeds. For our HBr oxidation reaction, the rate law would be written as: Rate = k [HBr][O₂], where k is the rate constant, and the concentrations are signified by the square brackets. It's this precise, quantifiable relationship that allows chemists to predict how quickly a reaction will go under varying concentrations of reactants.

Dive into the chemical reaction mechanism, and you'll encounter a bustling microscopic metropolis of molecules and atoms rapidly forming, then disappearing - these elusive entities are known as reaction intermediates. In the given oxidation mechanism of HBr, the intermediates, specifically HOOBr and HOBr, play a pivotal but transient role, acting as the 'middle-men' of the reaction sequence.

As they are not present in the initial reactants or the final products, intermediates are the chemical equivalents of undercover agents in a spy film - essential to the narrative but vanishing before the end. Not being able to detect HOBr or HOOBr in the final product mix doesn't throw our mechanism off its rails, because their fleeting existence is part of the mechanism's design - to facilitate the transformation without sticking around for the applause.

In the dramatic unfolding of a chemical reaction, the rate-determining step is akin to the slowest runner in a relay race - it sets the pace for the whole sequence. It is the most time-consuming step that controls the rate at which the reaction progresses. In our specific case of HBr oxidation, we anchor our understanding by matching the experimentally determined rate law with the rate of the presumed slowest step in the proposed mechanism.

By scrutinizing the steps of the mechanism and comparing them with the Rate = k [HBr][O₂], we deduce that the initial step, HBr(g) + O₂(g) → HOOBr(g), is indeed the rate-determining step. This bottleneck step governs how fast the reaction will go, and, in essence, is the director of the reaction's tempo.

Elementary reactions are the building blocks of a complex chemical equation, and each one is a single-step process involving a specific, straightforward change from reactants to products. These little leaps, whether they involve the collision between two molecules, the dissociation of a molecule, or a molecule capturing an electron, are the steps that choreograph the dance of the complete reaction mechanism.

In the case of gas-phase oxidation of HBr, the proposed sequence is made up of three elementary reactions, each with its own discreet reactant-to-product journey. What makes these steps truly elementary is that their stoichiometry directly corresponds to their rate law. Their simplicity allows us to piece together the full picture of the intricate chemical process that transforms humble HBr and O₂ into H₂O and Br₂.