Problem 74 - Chemistry: The Central Science in SI Units, Global Edition

Question

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 \(\mathrm{HBr}\) and first order with respect to \(\mathrm{O}_{2}\). You propose the following mechanism: $$ \begin{aligned} \operatorname{HBr}(g)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{HOOBr}(g) \\\ \mathrm{HOOBr}(g)+\mathrm{HBr}(g) & \longrightarrow 2 \mathrm{HOBr}(g) \\ \mathrm{HOBr}(g)+\mathrm{HBr}(g) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Br}_{2}(g) \end{aligned} $$ (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?

Step-by-Step Solution

Answer

(a) Yes, the elementary reactions add up to the overall reaction: \(4 \mathrm{HBr}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2}\mathrm{O}(g)+2 \mathrm{Br}_{2}(g)\). (b) The rate-determining step is the first step: \(\mathrm{HBr}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{HOOBr}(g)\). (c) The intermediates in this mechanism are \(\mathrm{HOOBr}(g)\) and \(\mathrm{HOBr}(g)\). (d) Not detecting \(\mathrm{HOBr}\) or \(\mathrm{HOOBr}\) among the products does not necessarily disprove the proposed mechanism because they are intermediates and might be present in very low concentrations or decompose into other products during the reaction.

Step 1: (a) Confirming the elementary reactions add to the overall reaction

To confirm that the given elementary reactions add up to the overall reaction, we can simply add the equations for each reaction and then cancel out any species that appear on both the reactant and product sides. Let's do that: Step 1: HBr(g) + O2(g) → HOOBr(g) Step 2: HOOBr(g) + HBr(g) → 2 HOBr(g) Step 3: HOBr(g) + HBr(g) → H2O(g) + Br2(g) Adding all three equations: [HBr(g) + O2(g)] + [HOOBr(g) + HBr(g)] + [HOBr(g) + HBr(g)] → [HOOBr(g)] + [2 HOBr(g)] + [H2O(g) + Br2(g)] After canceling out the species that appear on both sides: 4 HBr(g) + O2(g) → 2 H2O(g) + 2 Br2(g) The overall reaction obtained by adding the elementary reactions is the same as the given overall reaction. So the answer is: yes, the elementary reactions add up to the overall reaction.

Step 2: (b) Determining the rate-determining step

The reaction is found to be first order with respect to HBr and first order with respect to O2. The rate law can be expressed as: Rate = k[HBr]^1[O2]^1 To find the rate-determining step, we need to look at the proposed mechanism and identify the step that involves HBr and O2 as reactants. In this case, it is the first step: HBr(g) + O2(g) → HOOBr(g) Since the rate law agrees with this step's reactants, it is the rate-determining step.

Step 3: (c) Identifying intermediates in the mechanism

Intermediates are the species that are produced in one step and consumed in a subsequent step. In the proposed mechanism, we can identify the following intermediates: 1. HOOBr(g): It is produced in Step 1 and consumed in Step 2. 2. HOBr(g): It is produced in Step 2 and consumed in Step 3. Hence, the intermediates in this mechanism are HOOBr(g) and HOBr(g).

Step 4: (d) Impact of not detecting HOBr or HOOBr on the proposed mechanism

Not being able to detect HOBr or HOOBr among the products does not necessarily disprove the proposed mechanism. The reason is that these two species are intermediates, which means they are produced and consumed during the reaction process, and they might be present in very low concentrations. They could be consumed faster than they are produced or might decompose into other products during the reaction. Therefore, their absence in the final products does not disprove the proposed mechanism. Additional experiments and analyses would be required to confirm or disprove the mechanism.

Key Concepts

Gas-phase Reactions

Gas-phase reactions occur when the reactants involved are gases. These types of reactions are often encountered in atmospheric and industrial processes. The advantage of gas-phase reactions is that the reactants can mix more thoroughly, allowing for more uniform reactions compared to reactions in the solid or liquid phase.

In the case of the oxidation of hydrogen bromide ( HBr) by oxygen ( O_2), the reaction produces water (H_2O) and bromine (Br_2), both in the gaseous phase. The ability of gases to move and collide freely results in potentially faster reactions, but it also requires appropriate conditions such as temperature and pressure to be maintained.

• Gases have high kinetic energy, allowing molecules to mix and collide effectively.
• Collisions between gas molecules can lead to chemical reactions when there is enough energy.
• Conditions like temperature and pressure influence the rate and success of these reactions.

Reaction Mechanisms

Reaction mechanisms provide a step-by-step sequence of elementary reactions by which the overall chemical change occurs. Each elementary reaction involves a few reactants and products, and collectively, these steps explain how the overall reaction proceeds.

Understanding the mechanism helps in identifying the steps where reactants are converted into products. In our example, the oxidation of HBr involves multiple elementary steps, where each step represents a simple reaction that may involve the formation of intermediate species. This mechanistic view allows chemists to comprehend not just how the reactants produce the final products, but also what happens in between.

• Mechanisms are a series of elementary reactions.
• They offer insight into the path of a reaction.
• Each step in a mechanism usually involves only two molecules interacting at once.

Reaction Intermediates

Reaction intermediates are species that are formed in one step of a reaction mechanism and consumed in a subsequent step. They are crucial for understanding the full mechanism but do not appear in the overall chemical equation because they are not present at the start or end of the reaction.

In our specific reaction, the intermediates identified are HOOBr and HOBr. These intermediates are important because they transform into other species or enable further reactions to take place. Often, intermediates are unstable, which makes them challenging to detect experimentally, and they usually exist only transiently during the reaction sequence.

• Intermediates do not exist in the final reaction equation.
• They appear and vanish throughout the process.
• Detection of intermediates can be difficult due to their transient nature.

Rate-determining Step

The rate-determining step is the slowest step in a reaction mechanism and essentially controls the overall rate of the chemical reaction. It acts as a bottleneck, and the rate of the overall reaction cannot surpass this step.

For the oxidation of HBr by O_2, the first step involving the combination of HBr and O_2 into HOOBr is the rate-determining step, as indicated by the rate law. Since the reaction is first order concerning both reactants ( HBr and O_2), this supports the evidence that this initial step limits how fast the overall reaction can occur.

• The slowest step is the rate-determining step.
• This step dictates the speed of the entire reaction.
• Analyzing the rate law helps to identify the rate-determining step.