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Ch.14 - Chemical Kinetics
All textbooksBrown 14th EditionCh.14 - Chemical KineticsProblem 74b
Chapter 14, Problem 74b

You have studied the gas-phase oxidation of HBr by O2: 4 HBr(g) + O2(g) → 2 H2O(g) + 2 Br2(g)
You find the reaction to be first order with respect to HBr and first order with respect to O2. You propose the following mechanism:
HBr(g) + O2(g) → HOOBr(g)
HOOBr(g) + HBr(g) → 2 HOBr(g)
HOBr(g) + HBr(g) → H2O(g) + Br2(g)
(b) Based on the experimentally determined rate law, which step is rate determining?

Verified step by step guidance
1
1. The rate law for a reaction is determined by the slowest step in the reaction mechanism, also known as the rate-determining step. The rate law is an expression that shows the relationship between the rate of a reaction and the concentrations of the reactants.
2. The problem states that the reaction is first order with respect to HBr and first order with respect to O2. This means that the rate of the reaction depends on the concentration of HBr and O2 to the first power.
3. Looking at the proposed mechanism, the first step involves one molecule of HBr and one molecule of O2. This step is consistent with the experimentally determined rate law, as it involves one molecule of each reactant.
4. The second and third steps in the mechanism only involve HBr and other species, but not O2. Therefore, these steps cannot be the rate-determining step because the rate law shows that the reaction rate depends on both HBr and O2.
5. Therefore, based on the experimentally determined rate law, the first step (HBr(g) + O2(g) → HOOBr(g)) is the rate-determining step in the reaction mechanism.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rate Law

The rate law of a reaction expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is determined experimentally and indicates how the rate depends on the concentration of each reactant, often represented as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B, respectively.
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Rate Determining Step (RDS)

The rate determining step is the slowest step in a reaction mechanism that dictates the overall rate of the reaction. It is crucial because even if other steps are faster, the RDS limits how quickly the entire reaction can proceed. Identifying the RDS helps in understanding the kinetics of the reaction and is often inferred from the rate law.
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Mechanism of Reaction

A reaction mechanism is a step-by-step description of the pathway taken by reactants to form products. Each step in the mechanism represents a single molecular event, and the overall reaction is the sum of these steps. Understanding the mechanism is essential for predicting the rate law and identifying the rate determining step, as it provides insight into how reactants interact and transform during the reaction.
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Related Practice
Textbook Question

The reaction 2 NO1g2 + Cl21g2¡2 NOCl1g2 was performed and the following data were obtained under conditions of constant 3Cl24:

(a) Is the following mechanism consistent with the data? NO1g2 + Cl21g2ΔNOCl21g2 1fast2 NOCl21g2 + NO1g2¡2 NOCl1g2 1slow2

Textbook Question

You have studied the gas-phase oxidation of HBr by O2: 4 HBr(g) + O2(g) → 2 H2O(g) + 2 Br2(g)

You find the reaction to be first order with respect to HBr and first order with respect to O2. You propose the following mechanism:

HBr(g) + O2(g) → HOOBr(g)

HOOBr(g) + HBr(g) → 2 HOBr(g)

HOBr(g) + HBr(g) → H2O(g) + Br2(g)

(a) Confirm that the elementary reactions add to give the overall reaction.

Textbook Question

(a) What is a catalyst? (b) What is the difference between a homogeneous and a heterogeneous catalyst?

Textbook Question

(c) Do catalysts affect the overall enthalpy change for a reaction, the activation energy, or both?