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Ch.14 - Chemical Kinetics
Brown - Chemistry: The Central Science 15th Edition
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Tutti i libri di testoBrown 15th EditionCh.14 - Chemical KineticsProblema 74b
Capitolo 14, Problema 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?

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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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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 Law Fundamentals

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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Rate Law Determination

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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Reaction Mechanism Overview
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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:

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