11: Chemical Kinetics I
- Page ID
- 84364
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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.
- 11.1: 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.
- 11.2: Measuring Reaction Rates
- Several methods exist to measure chemical reaction rates, including spectrophotometry, which tracks concentration changes by monitoring light absorption. Measuring product appearance is often preferred due to lower background interference. The stopped-flow method uses flow control to mix reactants quickly for spectrophotometric analysis, and is common in physical chemistry labs.
- 11.3: 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.
- 11.4: 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.
- 11.5: 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.
- 11.6: 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.
- 11.7: 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.
- 11.8: The Method of Half-Lives
- The page explains how the behavior of a reaction's half-life can help determine its order by examining its dependence on concentration. For a 0th order reaction, the half-life decreases as concentration decreases. For a 1st order reaction, the half-life is constant and independent of concentration, while for a 2nd order reaction, the half-life increases with decreasing concentration.
- 11.9: 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.
- 11.10: 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 \(N_2O_5\).
- 11.11: 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.
- 11.E: Chemical Kinetics I (Exercises)
- Exercises for Chapter 11 "Chemical Kinetics I" in Fleming's Physical Chemistry Textmap.
- 11.S: Chemical Kinetics I (Summary)
- Summary for Chapter 11 "Chemical Kinetics I" in Fleming's Physical Chemistry Textmap.