7: Kinetics
- Page ID
- 556324
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chemical kinetics is the study of how fast chemical reactions proceed from reactants to products. This is an important topic because while thermodynamics will tell us about the direction of spontaneous change, it is silent as to how fast processes will occur. But additionally, the power of studying reaction rates is that it gives us insight into the actual pathways chemical processes follow to proceed from reactants to products.
- 7.1: Reaction Rate
- The page explains the definition of the rate of a chemical reaction, emphasizing the need to consider stoichiometric coefficients. It provides a general formula for calculating reaction rates using concentration changes of reactants and products. An example illustrates these concepts, demonstrating how to calculate the time-rate of change for concentrations in a reaction between nitrogen and hydrogen forming ammonia.
- 7.2: Rate Laws
- The text discusses rate laws in chemistry, which relate the concentration of reactants or products in a chemical reaction to time. Rate laws can be complex, involving experimentally determined values and may include concentrations of catalysts or enzymes. The order of a reaction is determined by the exponents on the concentrations, which can be fractional or negative. Understanding the rate law is essential for gaining insights into reaction pathways.
- 7.3: 0th order Rate Law
- The summary of the page is: For a zeroth-order reaction, the rate of change of concentration of reactant [A] can be expressed as \(-\frac{d[A]}{dt} = k\), leading to the relation \([A] = [A]_0 - kt\). A plot of concentration versus time yields a straight line with a slope of \(-k\) and intercept \([A]_0\), confirming zeroth-order kinetics if linear.
- 7.4: 1st order rate law
- The page explains the derivation of a first-order rate law in chemical kinetics. It describes how to separate variables and integrate the equations to determine the relationship between concentration and time. It states that plotting ln[A] against time should produce a linear graph with the slope of -k. An example with kinetic data is provided, demonstrating first-order kinetics with a rate constant determined from the graph.
- 7.5: 2nd order Rate Laws
- The page provides an explanation of second-order reaction kinetics, focusing on deriving rate laws and integrating them to find expressions for concentration over time. For a reaction \(A \rightarrow P\), the integrated rate law is derived, showing that plotting \(1/[A]\) vs. time yields a straight line with slope \(k\). For reactions \(A + B \rightarrow P\), the integration involves stoichiometry, and a plot of \(\ln([B]/[A])\) vs. time produces a linear relation.
- 7.6: The Method of Initial Rates
- The method of initial rates is used to determine rate laws by measuring the initial rate of reactions under varying initial concentrations. By analyzing the rates from different concentration conditions, the orders of the reactants in the rate law can be deduced using ratios of the rates. In this example, the rate law was determined to be first-order in reactant A and second-order in reactant B, resulting in an overall third-order reaction with a rate constant calculated as \(3.
- 7.7: Temperature Dependence
- The page discusses the relationship between temperature and chemical reaction rates, noting that increased temperature generally enhances reaction rates due to more frequent molecular collisions and increased kinetic energy. The empirically derived Arrhenius model describes this relationship, introducing parameters like the activation energy (\(E_a\)), which represents the energy barrier for reactions.
- 7.8: Collision Theory
- Collision Theory, introduced by Max Trautz and William Lewis in the 1910s, explains the rate of chemical reactions based on molecular collisions, their energy, and the orientation of reacting molecules. The theory predicts the reaction rate using factors like collision frequency and activation energy. Although initially applicable to bimolecular reactions, it can also elucidate first-order reactions involving bimolecular initiation steps, as demonstrated in the decomposition of \(N_2O_5\).
- 7.9: Transition State Theory
- Transition state theory, proposed by Henry Erying in 1935, explains chemical reaction rates by considering an intermediate state called the transition state. When molecules collide, they form an activated complex, partially breaking and forming bonds. The theory expresses reaction rates as a product of transition state concentration and decomposition frequency. It relates these rates to equilibrium constants, free energy, and vibrational frequency of bonds.
- 7.10: 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.
- 7.11: 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.
- 7.12: 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.
- 7.13: 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 \(A^*\).
- 7.14: 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.