Question

You want to test the following proposed mechanism for the oxidation of HBr. $$\begin{array}{c} \mathrm{HBr}+\mathrm{O}_{2} \stackrel{k_{1}}{\longrightarrow} \mathrm{HOOBr} \\\ \mathrm{HOOBr}+\mathrm{HBr} \stackrel{k_{2}}{\longrightarrow} 2 \mathrm{HOBr} \\\ \mathrm{HOBr}+\mathrm{HBr} \stackrel{k_{3}}{\longrightarrow} \mathrm{H}_{2} \mathrm{O}+\mathrm{Br}_{2} \end{array}$$ You find that the rate is first order with respect to HBr and to \(\mathrm{O}_{2}\). You cannot detect HOBr among the products. (a) If the proposed mechanism is correct, which must be the rate-determining step? (b) Can you prove the mechanism from these observations? (c) Can you disprove the mechanism from these observations?

Short answer

The rate-determining step for the mechanism is the first one. Based on the provided data, it isn't possible to confirm or prove that this mechanism is correct and the absence of HOBr in the reaction products suggests that the proposed mechanism is incorrect.

Step-by-step solution

Determine the Rate-Determining Step

A rate-determining step is the slowest step in a reaction mechanism and this step determines the overall reaction rate. The given information states that the rate of the reaction is first order with respect to both HBr and O2, which indicates that the concentration of both these molecules affect the rate of reaction. Additionally, both HBr and O2 are in the first step of the mechanism. Therefore, the first step must be the rate-determining step: \nHBr + O2 -> HOOBr

Check the Possibility of Proving the Mechanism

To prove a mechanism, it's necessary to validate each step either experimentally or through strong theoretical justification. In this case, even though the first step matches the reaction's order, there are still possibilities for other mechanisms that could also satisfy the order. Especially, we have no validations (experimental or theoretical) for the remaining steps. So based on the observations we cannot unequivocally prove this mechanism.

Analyze the Mechanism for Disproof

The product, HOBR, which is a major intermediate product (according to the proposed mechanism), is not detected during the reaction. This evidence contradicts the second and third steps of the proposed mechanism. Therefore, we can say that the proposed mechanism is most probably wrong.

Key concepts

Rate-Determining Step

In any chemical reaction mechanism, the rate-determining step is crucial. This step is like the bottleneck in the overall reaction pathway. It's the slowest step and therefore dictates the reaction rate. When a reaction proceeds, it can be visualized as a sequence of elementary steps. The rate at which the entire reaction occurs is limited by the slowest of these steps. This is analogous to a group of runners completing a relay race—in this case, the speed of the team depends on the slowest runner.
In the oxidation of HBr, we identify the rate-determining step by analyzing which elementary step matches the overall reaction rate order. Given that the rate is first order with respect to both HBr and O2, and both these molecules are only present in the first step of the mechanism, this step, HBr + O2 → HOOBr, is determined as the rate-determining step. This step decides the pace at which products are formed.

Reaction Order

Reaction order is an important concept in chemical kinetics. It tells us how the rate of a reaction depends on the concentration of the reactants. Understanding this helps predict how changes in concentrations will affect the reaction rate.
In the given oxidation of HBr, we know the rate is first order in respect to both HBr and O2. This means if the concentration of HBr is doubled, while keeping O2 constant, the reaction rate will double. Similarly, if O2 is doubled while keeping HBr constant, the rate also doubles.

• First order: Rate changes linearly with concentration changes.
• Second order: Rate changes exponentially with concentration changes.
• Zero order: Rate is independent of concentration changes.

In our case, the first reaction step aligns with the given rate order, indicating it's consistent with observed experimental data.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the speed or rate at which chemical reactions occur. It reveals information about reaction pathways, the role of catalysts, and the mechanism by which reactions proceed.
Through chemical kinetics, we can infer information about reaction intermediates and transition states. By measuring how a reaction proceeds over time, we gain insight into the underlying process. In the oxidation of HBr scenario, the absence of HOBr as a detectable product indicates that it may be an undetectable intermediate in the mechanism. Chemical kinetics allows us to hypothesize or disprove possible mechanisms.
In summary, understanding chemical kinetics aids in the exploration of complex reactions, guiding both theoretical and practical aspects of chemistry. It assists chemists in designing experiments, creating new materials, and employing time management strategies to control reactions efficiently.