University Chemistry Chapter 14: Chemical Kinetics Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2 Chemical Kinetics Thermodynamics – does a reaction take place? Kinetics – how fast does a reaction proceed? Reaction rate is the change in the concentration of a reactant or a product with time (M s -1 ). Kinetics: The area of chemistry concerned with the rates at which chemical reactions occur.

3 A B time rate = -  [A] tt rate = [B][B] tt

4 A B  [A] = change in concentration of A over time period  t Because [A] decreases with time,  [A] is negative.  [B] = change in concentration of B over time period  t

5 Br 2 (aq) + HCOOH (aq) 2Br - (aq) + 2H + (aq) + CO 2 (g) time  [Br 2 ]   Absorption 393 nm light Detector red

6 Br 2 (aq) + HCOOH (aq) 2Br - (aq) + 2H + (aq) + CO 2 (g) average rate = -  [Br 2 ] tt = - [Br 2 ] final – [Br 2 ] initial t final - t initial slope of tangent slope of tangent slope of tangent instantaneous rate = rate for specific instance in time

7 rate  [Br 2 ] rate = k [Br 2 ] k = rate [Br 2 ] k = 3.50 x s -1 rate constant—a constant of proportionality between the reaction rate and the concentration of reactant. ~ rate law

8 2H 2 O 2 (aq) 2H 2 O (l) + O 2 (g) PV = nRT P = RT = [O 2 ]RT n V [O 2 ] = P RT 1 measure  P over time PP

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10 Reaction Rates and Stoichiometry 2A B Two moles of A disappear for each mole of B that is formed. aA + bB cC + dD

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13 The Rate Law The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers. aA + bB cC + dD reaction is xth order in Areaction is yth order in B reaction is (x +y)th order overall overall reaction order is defined as the sum of the powers to which all reactant concentrations appearing in the rate law are raised. rate = k [Br 2 ]

14 F 2 (g) + 2ClO 2 (g) 2FClO 2 (g) rate = k [F 2 ] x [ClO 2 ] y Double [F 2 ] - [ClO 2 ] constant Rate doubles x = 1 Quadruple [ClO 2 ] - [F 2 ] constant Rate quadruples y = 1 rate = k [F 2 ][ClO 2 ]

15 F 2 (g) + 2ClO 2 (g) 2FClO 2 (g) rate = k [F 2 ][ClO 2 ] Rate laws are always determined experimentally. Reaction order is always defined in terms of reactant (not product) concentrations. ( = ?) The order of a reactant is not related to the stoichiometric coefficient of the reactant in the balanced chemical equation. 1 Reaction order is not always an integer. It can be a fractional number.

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20 Using calculus, the rate laws can be transformed by the process of integration to give integrated rate laws, which tell us the concentrations of reactants at any time during the course of a reaction. Integrated Rate Laws: Relationship Between Reactant Concentration and Time A first-order reaction is a reaction whose rate depends on the reactant concentration raised to the first power (v = k[A] 1 ). A second-order reaction is one whose rate depends on the concentration of one reactant raised to the second power or on the concentrations of two different reactants, each raised to the first power (v = k[A] 2 or k[A] 1 [B] 1 ). Zero-order reaction is independent of reactant concentration (v = k[A] 0 ).

21 First-Order Reactions A product k = rate [A] = 1/s or s -1 M s -1 M = [A] is the concentration of A at any time t [A] 0 is the concentration of A at time t=0 or

22 For gas phase reactions P ref is an arbitrary reference pressure (often 1 bar).

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27 Least squares linear regression gives 5.76 x s -1

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30 Half-Life The half-life, t ½, is the time required for the concentration of a reactant to decrease to half of its initial concentration. t ½ = t when [A] = [A] 0 /2 Independent of the initial concentration of the reactant.

31 A product First-order reaction # of half-lives [A] = [A] 0 /n

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33 Second-Order Reactions A product k = rate [A] 2 = M -1 s -1 M s -1 M2M2 = [A] is the concentration of A at any time t [A] 0 is the concentration of A at time t=0

34 t ½ = t when [A] = [A] 0 /2 Half-Life inversely proportional to the initial reactant concentration Half-life should be shorter in the early stage of the reaction when more reactant molecules are present to collide (react) with each other. The half-life is much less useful in describing second- order reactions

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37 pseudo–first-order reaction. If

38 Zero-Order Reactions A product k = rate [A] 0 = M s -1 [A] is the concentration of A at any time t [A] 0 is the concentration of A at time t=0 t ½ = t when [A] = [A] 0 /2 t ½ = [A] 0 2k2k

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40 Parallel Reactions Reactions that are occurring simultaneously. Total rate of consumption of A is the sum of the rates. More Complex Reactions

41 Consecutive Reactions The product from the first step becomes the reactant for the second step, and so on.

42 If the first reaction is the slowest (k 1 << k 2 ) If the second reaction is the slowest (k 2 << k 1 ) The slowest reaction is referred to as the rate-determining step. If k 1 = k 2

43 Reversible Reactions net rate law at equilibrium Principle of detailed balance which states that, at equilibrium, the rates of forward and reverse processes are equal.

44 Temperature Dependence of Rate Constants The Arrhenius Equation - an experimental result activation energy frequency factor (pre-exponential factor) slopey-intercept For two temperatures:

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48 transition state (or activated complex). intermediate state at which the potential energy is maximum Physical Meaning of the Activation Energy Reaction pathway: specific sequence in which the reaction occurs.

49 Activation energy (E a ) : the minimum amount of energy required for a chemical reaction to proceed. Endothermic Exothermic energy barrier

50 Effect of temperature on the number of molecules capable of crossing the energy barrier More molecules possess E a

51 Collision Theory of Reaction Rates Account for effective collisions

52 temperature dependence concentration dependence

53 orientation factor (or steric factor) More complex reactions involve orientation for an effective collision

54 Effect of orientation

55 Transition-State Theory Useful to predict reaction rates for more complex molecules or molecules in solution. The reactants A and B are in equilibrium with the transition state AB ‡. necessary to ensure that k has the appropriate units c 0 is the standard concentration m is the reaction order Can be calculated theoretically

56 Reaction Mechanisms The overall progress of a chemical reaction can be represented at the molecular level by a series of simple elementary steps or elementary reactions. The sequence of elementary steps that leads to product formation is the reaction mechanism. 2NO (g) + O 2 (g) 2NO 2 (g) N 2 O 2 is detected during the reaction! Elementary step:NO + NO N 2 O 2 Elementary step:N 2 O 2 + O 2 2NO 2 Overall reaction:2NO + O 2 2NO 2 +

57 2NO (g) + O 2 (g) 2NO 2 (g)

58 Elementary step:NO + NO N 2 O 2 Elementary step:N 2 O 2 + O 2 2NO 2 Overall reaction:2NO + O 2 2NO 2 + Intermediates are species that appear in a reaction mechanism but not in the overall balanced equation. An intermediate is always formed in an early elementary step and consumed in a later elementary step. The molecularity of a reaction is the number of molecules reacting in an elementary step. Unimolecular reaction – elementary step with 1 molecule Bimolecular reaction – elementary step with 2 molecules Termolecular reaction – elementary step with 3 molecules

59 Unimolecular reactionA productsrate = k [A] Bimolecular reactionA + B productsrate = k [A][B] Bimolecular reactionA + A productsrate = k [A] 2 Rate Laws and Elementary Steps Writing plausible reaction mechanisms: The sum of the elementary steps must give the overall balanced equation for the reaction. The rate-determining step should predict the same rate law that is determined experimentally. The rate-determining step is the slowest step in the sequence of steps leading to product formation.

60 Sequence of Steps in Studying a Reaction Mechanism

61 Example:

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63 Rapid Pre-equilibrium contains intermediate in terms of reactants

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66 The Steady-State Approximation Not all reactions have a single rate-determining step. A reaction may have two or more comparably slow steps. In such cases it is useful to assume that the concentration of intermediates is constant over much of the reaction progress. Assume at some point steady state For gas A

67 steady-state approximation steady-state rate law

68 For an ideal gas

69 Experimental Support for Reaction Mechanisms Isotopic labeling Label:

70 CH 2 2 CH 2 2 Femtochemistry

71 A catalyst is a substance that increases the rate of a chemical reaction without itself being consumed. EaEa k rate catalyzed > rate uncatalyzed E a c < E a UncatalyzedCatalyzed

72 In heterogeneous catalysis, the reactants and the catalysts are in different phases. In homogeneous catalysis, the reactants and the catalysts are dispersed in a single phase, usually liquid. Haber synthesis of ammonia Ostwald process for the production of nitric acid Catalytic converters Acid catalysis Base catalysis

73 N 2 (g) + 3H 2 (g) 2NH 3 (g) Fe/Al 2 O 3 /K 2 O catalyst Haber Process Fe/Al 2 O 3 /K 2 O

74 Ostwald Process Pt-Rh catalysts used in Ostwald process Pt-Rh catalyst recycle

75 Catalytic Converters CO + Unburned Hydrocarbons + O 2 CO 2 + H 2 O catalytic converter 2NO + 2NO 2 2N 2 + 3O 2 catalytic converter

76 Homogenous Catalysis Addition of an acid H+H+ The rate is determined solely by the catalyzed portion of the reaction. Ester hydrolysis – reactants and products miscible liquids

77 Enzyme Catalysis Enzymes are biological catalysts.

78 Enzyme Kinetics study initial rates uncatalyzedcatalyzed enzyme substrateintermediate product

79 Enzyme is conserved. Michaelis-Menten equation

80 Michaelis-Menten reaction mechanism correctly describes the experimentally observed rate data