7: Kinetic Mechanisms 2
- Page ID
- 516491
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 7.1: Numerical Modeling of Mechanisms
- In many cases complicated mechanisms cannot be analytically integrated to determine the time profiles of all the species involved and approximation methods (pre-equilibrium, steady-state, etc...) do not provide an adequate model to make useful predictions. There are two primary methods used for numerical modeling of reaction mechanisms: numerical integration; and stochastic modeling.
- 7.2: 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.
- 7.3: 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.
- 7.4: 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.
- 7.5: Catalysis (ozone example)
- 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.
- 7.6: 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.
- 7.7: Diffusion
- A significant fraction of how molecules move spatially in biophysics is described macroscopically by “diffusion” and microscopically through its counterpart “Brownian motion”. Diffusion refers to the phenomenon by which concentration and temperature gradients spontaneously disappear with time, and the properties of the system become spatially uniform. Brownian motion is also a spontaneous process observed in equilibrium and non-equilibrium systems.
- 7.8: Membrane Diffusion
- Membranes are barriers to molecular flow between regions. In living systems and industrial processes this allows the creation and maintenance of concentration gradients used to do useful work and separate molecules. This section focuses on the situation of semi-permeable membranes that allow some species to pass through. Diffusion facilitated by transporter molecules is also discussed.
- 7.9: Ion Mobilities
- This section introduces the concept of ion mobilities to describe the motion of ions in a solution and how their motion is impacted by an external electric field. The Grotthus mechanism is presented as an explanation for the anomalous mobility of protons in water.
- 7.10: Transport Across Cell Membranes
- It is essential for cells to be able to uptake nutrients. This function along with movement of ions and other substances is provided by proteins/protein complexes that are highly specific for the compounds they move. Selective movement of ions by membrane proteins and the ions’ extremely low permeability across the lipid bilayer are important for helping to maintain the osmotic balance of the cell and also for providing for the most important mechanism for it to make ATP.
- 7.11: Kinetics of Electron Transfer Reactions
- The kinetics of redox reactions can be impacted by the rate of electron transfer from the oxidized species to the reduced species. In this section we present the Marcus Theory for the rates of this process and using the Marcus Cross Relations for estimating these rates from experimental data.