12: Chemical Kinetics II
- Page ID
- 84371
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In the previous chapter, we discussed the rates of chemical reactions. In this chapter, we will expand on the concepts of chemical reaction rates by exploring what the rate law implies about the mechanistic pathways that reactions actually follow to proceed from reactants to products. Typically, one determines a rate law that describes a chemical reaction, and then suggests a mechanism that can be (or might not be!) consistent with the observed kinetics. This chapter will be concerned with reconciling reaction mechanisms with predicted rate laws.
- 12.1: Reaction Mechanisms
- A reaction mechanism is a series of elementary steps that outline the path from reactants to products in a chemical reaction. Elementary reactions can be unimolecular, bimolecular, or occasionally termolecular, though the latter usually involves rapid bimolecular steps forming and stabilizing an activated complex. A valid mechanism must match the overall stoichiometry, be consistent with observed kinetics, and account for any side products.
- 12.2: Concentration Profiles for Some Simple Mechanisms
- The page discusses various types of reaction mechanisms and their impact on concentration profiles. It covers simple unimolecular conversions, reversible reactions, catalyzed reactions, reactions with intermediates, and reactions with competing pathways. For each mechanism, equations for the rate of change of concentrations are provided, explaining how they lead to specific concentration profiles over time.
- 12.3: The Connection between Reaction Mechanisms and Reaction Rate Laws
- The page discusses the value of chemical kinetics in understanding reaction mechanisms and determining rate laws. By analyzing mechanisms, one can predict rate laws and gain insights into reaction pathways. The example given shows how different mechanisms imply different orders of reaction, which cannot confirm a specific mechanism alone.
- 12.4: The Rate Determining Step Approximation
- The rate determining step approximation is a method used to deduce a rate law from a proposed reaction mechanism. It states that a reaction can proceed no faster than its slowest step. For example, if a reaction is proposed to occur through a mechanism with a slow initial step followed by a fast step, the rate law is determined based on the slow step. The same concept applies to different mechanisms, where the rate law aligns with the molecularity of the rate determining (slowest) step.
- 12.5: The Steady-State Approximation
- The page discusses the steady state approximation, a method used to simplify the analysis of reactions involving highly reactive intermediates that maintain a constant concentration over time. It explains how applying this approximation to proposed reaction mechanisms allows for determining the reaction order and rate laws. Two examples illustrate how to derive the rate law using the steady state approximation by analyzing intermediates \(A_2\) and \(A^*\).
- 12.6: The Equilibrium Approximation
- The page discusses reaction mechanisms involving intermediate compounds and the equilibrium approximation to predict reaction rate laws. It explains how, in reactions with reversible intermediate steps, the equilibrium approximation can simplify the rate law derivation. Examples illustrate how equilibrium assumptions for initial reactions lead to expressions for intermediates' concentrations, influencing the rate law.
- 12.7: The Lindemann Mechanism
- The Lindemann mechanism is a chemical model used to relate mechanisms to rate laws. It involves a reactant being collisionally activated into an energetic form that can transform into products. By applying the steady-state approximation to the intermediate \(A^*\), expressions for product production rates can be derived under different conditions.
- 12.8: The Michaelis-Menten Mechanism
- The page explains the Michaelis-Menten mechanism, a model describing enzyme-mediated reactions. It involves enzymes interacting with substrates to form an enzyme-substrate complex, leading to a product. The reaction rate is governed by parameters like the Michaelis constant (\(K_M\)) and maximum rate (\(V_{max}\)), with different derivations using equilibrium and steady-state approximations.
- 12.9: Chain Reactions
- The page describes the concept of chain reactions, which consist of initiation, propagation, and termination steps, particularly when radicals are involved. It uses the reaction between H_2 and Br_2 to produce HBr as an example. A proposed mechanism is analyzed, and steady-state approximations are applied to derive expressions for radicals involved. The resulting expression aligns with the experimentally determined rate law.
- 12.10: Catalysis
- The text describes the catalytic decomposition of ozone, highlighting the role of atomic chlorine in the process. This reaction is significant for environmental chemistry, especially regarding the issue of ozone layer depletion. The provided information explains the reaction mechanism, the rate equations involved, and how chlorine acts as a catalyst, highlighting the negative environmental impact of chlorofluorocarbons.
- 12.11: Oscillating Reactions
- The page discusses the phenomenon of oscillating reactions, where reactant concentrations fluctuate during a reaction. This can occur through autocatalysis, where a product or step catalyzes the reaction. An example is the Lotka-Voltera mechanism, a three-step autocatalytic process. This model mimics the predator-prey relationship, applicable in fields beyond chemistry, such as biology and economics, and raises the question of its potential use in understanding politics.
- 12.E: Chemical Kinetics II (Exercises)
- Exercises for Chapter 12 "Chemical Kinetics II" in Fleming's Physical Chemistry Textmap.
- 12.S: Chemical Kinetics II (Summary)
- This page provides a glossary of vocabulary and concepts related to chemical reactions and kinetics, including terms like autocatalysis, dynamic equilibrium, and reaction mechanisms. It also references several studies and scholarly articles, highlighting important contributions in the field, such as the work of Lindemann, Michaelis-Menten kinetics, and the Montreal Protocol.