5: Kinetic Mechanisms 1
- Page ID
- 516489
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 5.1: 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.
- 5.2: Relaxation Methods
- Relaxation methods can be used to monitor the kinetics of fast reactions by starting with a system at equilibrium and rapidly changing the physical conditions to shift the equilibrium. Then the "relaxation" to the new equilibrium is monitored. In this section we summarize the theory behind these techniques and look at examples of temperature and pressure jumps to shift the equilibrium.
- 5.3: Representative Reaction Mechanisms
- A major goal in chemical kinetics is to determine the sequence of elementary reactions, or the reaction mechanism, that comprise complex reactions. In the following sections, we will derive rate laws for complex reaction mechanisms, including reversible, parallel and consecutive reactions.
- 5.4: 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.
- 5.5: 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.
- 5.6: 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 \(A^*\).