1. Chemical Kinetics: Rates and Mechanisms of Chemical Reactions General Chemistry: An Integrated Approach Hill, Petrucci, 4 th Edition Mark P. Heitz State University of New York at Brockport © 2005, Prentice Hall, Inc.

2. Chapter 13: Chemical Kinetics2 Chemical Kinetics: A Preview Chemical kinetics is the study of the rates of chemical reactions, the factors that affect these rates, and the reaction mechanisms by which reactions occur Reaction rates vary greatly – some are very fast (e.g., burning) and some are very slow (e.g., disintegration of a plastic bottle in sunlight) EOS Catalysts are substances that speed up a reaction but emerge unchanged by the reaction. How catalysts work is covered later in the chapter

3. Chapter 13: Chemical Kinetics3 Predicting Reaction Rates Variables of control are: Concentrations of reactants: Reaction rates generally increase as the concentrations of the reactants are increased Temperature: Reaction rates generally increase rapidly as the temperature is increased EOS Surface area: For reactions that occur on a surface rather than in solution, the rate increases as the surface area is increased

4. Chapter 13: Chemical Kinetics4 Meaning of the Reaction Rate The rate of a reaction is the change in concentration of a species per unit of time Example: rate of formation of productA  P EOS The rate of reaction has the units of moles per liter per (unit of) time, expressed as mol L –1 s –1 Appearance of product Or … Disappearance of reactant

5. Chapter 13: Chemical Kinetics5 A Conceptual Example EOS

6. Chapter 13: Chemical Kinetics6 Graphing Changes EOS

7. Chapter 13: Chemical Kinetics7 General Reaction Rate General reaction rate: calculated by dividing rate expressions by stoichiometric coefficients Consider: 2 H 2 O 2  2 H 2 O + O 2 EOS For aA + bB  cC + dD,

8. Chapter 13: Chemical Kinetics8 Average Reaction Rate Rates of chemical reaction tends to slow down as time goes on in the reaction EOS At the beginning of the reaction, the rate is faster than the average and near the end of the reaction, the rate is slower than the average The average rate of the reaction is calculated by dividing the change in concentration over the time interval of the reaction

9. Chapter 13: Chemical Kinetics9 Measuring Reaction Rates In general, the greater the concentration of a reactant, the faster the reaction goes EOS

10. Chapter 13: Chemical Kinetics10 Measuring Reaction Rates The average rate of reaction during an experiment is the negative of the slope of the reaction rate EOS The instantaneous rate at the beginning of a reaction is called the initial rate of reaction

11. Chapter 13: Chemical Kinetics11 Rate Law Expressions The rate law for a chemical reaction relates the rate of reaction to the concentrations of reactants For aA + bB  cC + dD The rate law is Rate = k[A] m [B] n EOS The exponents in a rate law must be determined by experiment. They are not derived from the stoichiometric coefficients in an overall chemical equation

12. Chapter 13: Chemical Kinetics12 Rate Laws The values of the exponents in a rate law establish the order of a reaction Rate = k[A] m [B] n For reactant A, if m = 1, reaction is first order in A if m = 2, reaction is second order in A EOS The proportionality constant, k, is the rate constant and its value depends on the reaction, the temperature, and the presence or absence of a catalyst

13. Chapter 13: Chemical Kinetics13 Distinctions between Rate and the Rate Constant, k The rate constant remains constant throughout a reaction, regardless of the initial concentrations of the reactants For reaction orders other than zero, the rate and rate constant are numerically equal only when the concentrations of all reactants are 1 M, units are different EOS The rate and the rate constant have the same values and units only in zero- order reactions Rate = k[A] 0

14. Chapter 13: Chemical Kinetics14 Method of Initial Rates The method of initial rates involves a series of experiments in which the initial concentrations of some reactants are held constant and others are varied in convenient multiples in order to determine the rate law for that reaction EOS Rate = k[NO] 2 [Cl 2 ]

15. Chapter 13: Chemical Kinetics15 Reaction Order and Concentration The effects of doubling one initial concentration: For zero-order reactions, no effect on rate For first-order reactions, the rate doubles For second-order reactions, the rate quadruples EOS For third-order reactions, the rate increases eightfold

16. Chapter 13: Chemical Kinetics16 First-Order Reactions A first-order reaction is a reaction in which a single reactant yields products. Rate = k[A] 1 = k[A] The integrated rate law is an equation that describes the concentration of a reactant as a function of time ln{[A] t /[A] 0 } = ln[A] t – ln[A] 0 = –kt EOS ln[A] t = –kt + ln[A] 0 y= mx + b

17. Chapter 13: Chemical Kinetics17 First Order Example EOS

18. Chapter 13: Chemical Kinetics18 Half-life of a Reaction The half-life (t ½ ) of a reaction is the time in which one-half of the reactant originally present is consumed ln[A] t – ln[A] 0 = ln½[A] 0 – ln[A] 0 = –kt ½  ln(½) = –kt ½ EOS t ½ = –ln(½)/k = –(–0.693)/k = 0.693/k

19. Chapter 13: Chemical Kinetics19 Half-life of a Reaction For a first-order reaction, the half-life is a constant; it depends only on the rate constant, k, and not on the concentration of reactant If k is known, t ½ can be calculated, and if t ½ is known, k can be calculated EOS Common application is in half-life of radioactive isotopes – e.g., medicine, nuclear energy, etc.

20. Chapter 13: Chemical Kinetics20 Zero-Order Reactions The rate of reaction remains constant throughout and is equal to the rate constant k and to the negative of the slope EOS

21. Chapter 13: Chemical Kinetics21 Zero-Order Reactions Rate has the same value at all points, and is independent of initial reactant concentration EOS The half-life is proportional to the initial reactant concentration

22. Chapter 13: Chemical Kinetics22 Second-Order Reactions A second-order reaction has a rate law with a sum of the exponents equal to 2 Rate = k[A][B]m + n = 2 Rate = k[A] 2 m = 2 The integrated rate law which expresses [A] as a function of time has the following form 1/[A] t = kt + 1/[A] o EOS Second-order half life ist ½ = 1/k[A] o

23. Chapter 13: Chemical Kinetics23 Second Order Illustrated EOS Bimolecular Reaction

24. Chapter 13: Chemical Kinetics24 Summary of Kinetic Data EOS

25. Chapter 13: Chemical Kinetics25 Collision Theory Before atoms, molecules, or ions can react, they must first come together, or collide EOS An effective collision between two molecules puts enough energy into key bonds to break them

26. Chapter 13: Chemical Kinetics26 Collision Theory The activation energy (E a ) is the minimum energy that must be supplied by collisions for a reaction to occur EOS The spatial orientations of the colliding species also affect the reaction rate

27. Chapter 13: Chemical Kinetics27 Transition State Theory The configuration of the atoms at the time of the collision is called the transition state The transitory species having this configuration is called the activated complex EOS Heat of Reaction (  H) Activation Energy

28. Chapter 13: Chemical Kinetics28 Effect of Temperature on Rates In 1889, Svante Arrhenius proposed the following mathematical expression for the effect of temperature on the rate constant, k k = Ae – E a /RT EOS ln k = –E a /RT + ln A

29. Chapter 13: Chemical Kinetics29 The Arrhenius Equation The constant A, called the frequency factor, is the product of the collision frequency and a probability factor that takes into account the orientation required for effective molecular collisions EOS The expression e – E a /RT represents the fraction of molecular collisions sufficiently energetic to produce a reaction

30. Chapter 13: Chemical Kinetics30 Reaction Mechanisms A reaction mechanism is a series of simple steps that ultimately lead from the initial reactants to the final products of a reaction An elementary reaction represents a single stage in the progress of the overall reaction EOS The mechanism must account for the experimentally determined rate law

31. Chapter 13: Chemical Kinetics31 Elementary Reactions The molecularity of an elementary reaction refers to the number of free atoms, ions, or molecules that enter into the reaction EOS

32. Chapter 13: Chemical Kinetics32 Elementary Reactions The rate-determining step is the slowest step in establishing the rate of the overall reaction Slow – rate determining EOS Fast step

33. Chapter 13: Chemical Kinetics33 Effect of Catalyst on Reaction Enhances reaction rate by reducing the activation energy EOS

34. Chapter 13: Chemical Kinetics34 Homogeneous Catalysis Reaction profile for the uncatalyzed and catalyzed decomposition of ozone EOS

35. Chapter 13: Chemical Kinetics35 Heterogeneous Catalysis Many reactions are catalyzed by the surfaces of appropriate solids EOS

36. Chapter 13: Chemical Kinetics36 Enzyme Catalysis Enzymes are high-molecular-mass proteins that usually catalyze one specific reaction—or a set of quite similar reactions—but no others EOS

37. Chapter 13: Chemical Kinetics37 Concentrations and Rates EOS [Enzyme] = const [Substrate] = const

38. Chapter 13: Chemical Kinetics38 Summary of Concepts Rates of reactions are based on the rate of disappearance of a reactant or formation of a product An integrated rate law relates concentration and time The half-life of a reaction is the time in which one-half of the reactant initially present is consumed EOS Chemical reactions occur when sufficiently energetic molecules collide in the proper orientation

39. Chapter 13: Chemical Kinetics39 Summary of Concepts Reactions generally go faster at higher temperatures or in the presence of a catalyst EOS Reaction mechanisms provide a plausible explanation of how a reaction proceeds