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: $$ \begin{aligned} \mathrm{HBr}(g)+\mathrm{O}_{2}(g) & \longrightarrow \operatorname{HOOBr}(g) \\\ \mathrm{HOOBr}(g)+\operatorname{HBr}(g) & \longrightarrow 2 \operatorname{HOBr}(g) \\ \mathrm{HOBr}(g)+\operatorname{HBr}(g) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Br}_{2}(g) \end{aligned} $$ (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?

Short answer

In summary, the given mechanism's elementary reactions do add up to the overall reaction, and the rate-determining step is the first step involving both HBr and O2. The intermediates are HOOBr and HOBr. Non-detection of these intermediates does not necessarily disprove the mechanism, as they could be reacting quickly or have low concentrations, and further experiments would be needed for a conclusive decision.

Step-by-step solution

Confirm that the elementary reactions add to give the overall reaction

To verify that the elementary reactions given in the mechanism add up to the overall reaction, we will add them up and see if the result matches the overall equation. The elementary reactions are: 1. HBr(g) + O2(g) -> HOOBr(g) 2. HOOBr(g) + HBr(g) -> 2 HOBr(g) 3. HOBr(g) + HBr(g) -> H2O(g) + Br2(g) To add these reactions, let's cancel out any species that do not appear in the overall reaction: HBr(g) + O2(g) + HBr(g) + HBr(g) -> H2O(g) + Br2(g) Now combining the species on the left-hand side: 4 HBr(g) + O2(g) -> H2O(g) + Br2(g) This matches the given overall reaction, so the elementary reactions do add up to the overall reaction.

Identify the rate-determining step

The experimentally determined rate law for this reaction is first-order with respect to HBr and first-order with respect to O2. This implies that the rate-determining step must involve both HBr and O2: rate = k[HBr][O2] Comparing the given elementary reactions, we can see that the first step involves both HBr and O2: 1. HBr(g) + O2(g) -> HOOBr(g) Thus, the first step is the rate-determining step.

Identify the intermediates

Intermediates are species that are produced in one step of a reaction mechanism and consumed in a later step. To identify the intermediates, we look at the given steps and find which species get canceled out when added up. In this mechanism, the intermediates are: 1. HOOBr(g): Produced in step 1 and consumed in step 2. 2. HOBr(g): Produced in step 2 and consumed in step 3.

Discuss if non-detection of HOBr or HOOBr disproves the mechanism

If we are unable to detect HOBr or HOOBr among the products, it does not necessarily disprove the mechanism. It is possible that these two species are being formed as intermediates and that they react quickly enough to form the final products that we are unable to detect them experimentally. It is also possible that the concentrations of these intermediates are too low to be detected. Non-detection of intermediates is only one piece of evidence, and more experiments and data would be needed to conclusively disprove the proposed mechanism.

Key concepts

Elementary Reactions

Elementary reactions are the individual steps or stages that combine to form the complete mechanism of a complex chemical reaction. Each elementary reaction represents a single molecular event, such as the collision between molecules, which leads to the formation or breaking of bonds.
In the context of the gas-phase oxidation of hydrogen bromide (HBr) by oxygen (O₂), we have three proposed elementary reactions:

• 1. HBr(g) + O₂(g) → HOOBr(g)
• 2. HOOBr(g) + HBr(g) → 2 HOBr(g)
• 3. HOBr(g) + HBr(g) → H₂O(g) + Br₂(g)

These reactions collectively sum up to the overall reaction: 4 HBr(g) + O₂(g) → 2 H₂O(g) + 2 Br₂(g).
Verification involves ensuring that the sum of these individual reactions removes any intermediate species, leaving only the reactants and products of the overall reaction.

Rate-Determining Step

The rate-determining step (RDS) is the slowest step in a reaction mechanism. It acts like a bottleneck, significantly influencing the overall reaction rate. For a given mechanism, the experimentally observed rate law can guide us in identifying the RDS.
In this exercise, the reaction has been observed to be first-order with respect to both HBr and O₂, suggesting that both species are involved in the rate-determining step. When examining the proposed sequence of elementary reactions:

• 1. HBr(g) + O₂(g) → HOOBr(g)
• 2. HOOBr(g) + HBr(g) → 2 HOBr(g)
• 3. HOBr(g) + HBr(g) → H₂O(g) + Br₂(g)

Only the first step involves both HBr and O₂ directly. Therefore, the first step is likely to be the rate-determining step. This is because it matches the observed rate law: rate = k[HBr][O₂], indicating both reactants are involved in the formation of the product, influencing the speed of the whole process.

Reaction Intermediates

Reaction intermediates are transient species formed during the course of a chemical reaction. They appear in the reaction pathways but not in the overall equation, usually because they are consumed in subsequent steps.
In the discussed mechanism, two intermediates appear:

• **HOOBr(g):** Formed in the first step and consumed in the second.
• **HOBr(g):** Produced in the second step and consumed in the third.

Intermediates are crucial for understanding the detailed pathway of reactions, although they are often difficult to detect experimentally. The inability to detect intermediates such as HOBr or HOOBr in the product mixture does not necessarily invalidate the mechanism. This may be because:

• They convert quickly into products,
• Their concentrations remain very low, making them hard to pinpoint with conventional techniques.

Thus, further experiments may be needed to determine the presence and role of these intermediates.