1. Chapter 14 Chemical Kinetics Dr. Subhash Goel South GA State College Douglas, GA 31533 Lecture Presentation © 2012 Pearson Education, Inc.

2. Chemical Kinetics In kinetics we study the rate at which a chemical process occurs. Besides information about the speed at which reactions occur, kinetics also sheds light on the reaction mechanism (exactly how the reaction occurs). © 2012 Pearson Education, Inc.

3. Chemical Kinetics Factors That Affect Reaction Rates Physical state of the reactants. –In order to react, molecules must come in contact with each other. –The more homogeneous the mixture of reactants, the faster the molecules can react. © 2012 Pearson Education, Inc.

4. Chemical Kinetics Factors That Affect Reaction Rates Concentration of reactants –As the concentration of reactants increases, so does the likelihood that reactant molecules will collide. Temperature –At higher temperatures, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy. © 2012 Pearson Education, Inc.

5. Chemical Kinetics Factors That Affect Reaction Rates Presence of a catalyst. –Catalysts speed up reactions by changing the mechanism of the reaction. –Catalysts are not consumed during the course of the reaction. © 2012 Pearson Education, Inc.

6. Chemical Kinetics Reaction Rates Rates of reactions can be determined by monitoring the change in concentration of either reactants or products as a function of time. © 2012 Pearson Education, Inc.

7. Chemical Kinetics Rate of Reaction from Figure Shown in Previous Slide Problem: Calculate the average rate at which A disappears over the time interval from 20 s to 40 s. Problem: Calculate the average rate of appearance of B over the time interval from 0 s to 40 s.

8. Chemical Kinetics Reaction Rates In this reaction, the concentration of butyl chloride, C 4 H 9 Cl, was measured at various times as shown in Table on next slide C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) © 2012 Pearson Education, Inc. Consider following reaction:

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10. Chemical Kinetics Reaction Rates The average rate of the reaction over each interval is the change in concentration divided by the change in time: C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) Average rate =  [C 4 H 9 Cl]  t © 2012 Pearson Education, Inc.

11. Chemical Kinetics Reaction Rates Note that the average rate decreases as the reaction proceeds. This is because as the reaction goes forward, there are fewer collisions between reactant molecules. C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) © 2012 Pearson Education, Inc.

12. Chemical Kinetics Reaction Rates A plot of [C 4 H 9 Cl] versus time for this reaction yields a curve like on next slide. The slope of a line tangent to the curve at any point is the instantaneous rate at that time. C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) © 2012 Pearson Education, Inc.

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14. Chemical Kinetics Reaction Rates All reactions slow down over time. Therefore, the best indicator of the rate of a reaction is the instantaneous rate near the beginning of the reaction. C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) © 2012 Pearson Education, Inc.

15. Chemical Kinetics Exercise: Calculating an Instantaneous Rate of Reaction Using Figure on previous slide calculate the instantaneous rate of disappearance of C 4 H 9 Cl at t = 0 s (the initial rate).

16. Chemical Kinetics Reaction Rates In this reaction, the ratio of C 4 H 9 Cl to C 4 H 9 OH is 1:1. Thus, the rate of disappearance of C 4 H 9 Cl is the same as the rate of appearance of C 4 H 9 OH. C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) Rate =  [C 4 H 9 Cl]  t =  [C 4 H 9 OH]  t © 2012 Pearson Education, Inc.

17. Chemical Kinetics Reaction Rates and Stoichiometry What if the ratio is not 1:1? 2 HI(g)  H 2 (g) + I 2 (g) In such a case, Rate =  1212  [HI]  t =  [I 2 ]  t © 2012 Pearson Education, Inc.

18. Chemical Kinetics Reaction Rates and Stoichiometry To generalize, then, for the reaction aA + bBcC + dD Rate =  1a1a  [A]  t =  1b1b  [B]  t = 1c1c  [C]  t 1d1d  [D]  t = © 2012 Pearson Education, Inc.

19. Chemical Kinetics Exercise Relating Rates at Which Products Appear and Reactants Disappear (a) How is the rate at which ozone disappears related to the rate at which oxygen appears in the reaction 2 O 3 (g)  3 O 2 (g)? (b) If the rate at which O 2 appears,  [O 2 ]/  t, is 6.0  10 –5 M/s at a particular instant, at what rate is O 3 disappearing at this same time,  [O 3 ]/  t?

20. Chemical Kinetics Concentration and Rate One can gain information about the rate of a reaction by seeing how the rate changes with changes in concentration. © 2012 Pearson Education, Inc.

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22. Chemical Kinetics Concentration and Rate If we compare Experiments 1 and 2, we see that when [NH 4 + ] doubles, the initial rate doubles. Likewise, when we compare Experiments 5 and 6, we see that when [NO 2  ] doubles, the initial rate doubles. NH 4 + (aq) + NO 2  (aq) N 2 (g) + 2 H 2 O(l) © 2012 Pearson Education, Inc.

23. Chemical Kinetics Concentration and Rate This means Rate  [NH 4 + ] Rate  [NO 2  ] Rate  [NH 4 + ] [NO 2  ] which, when written as an equation, becomes Rate = k [NH 4 + ] [NO 2  ] This equation is called the rate law, and k is the rate constant. Therefore, © 2012 Pearson Education, Inc.

24. Chemical Kinetics Rate Laws A rate law shows the relationship between the reaction rate and the concentrations of reactants. The exponents tell the order of the reaction with respect to each reactant. Since the rate law is Rate = k[NH 4 + ] [NO 2  ] the reaction is First-order in [NH 4 + ] and First-order in [NO 2  ] © 2012 Pearson Education, Inc.

25. Chemical Kinetics Rate Laws Rate = k[NH 4 + ] [NO 2  ] The overall reaction order can be found by adding the exponents on the reactants in the rate law. This reaction is second-order overall. © 2012 Pearson Education, Inc.

26. Chemical Kinetics Exercise Determining a Rate Law from Initial Rate Data The initial rate of a reaction A + B  C was measured for several different starting concentrations of A and B, and the results are as follows: Using these data, determine (a) the rate law for the reaction, (b) the rate constant, (c) the rate of the reaction when [A] = 0.050 M and [B] = 0.100 M.

27. Chemical Kinetics Integrated Rate Laws For First order reaction: Rate = -∆[A]/∆t = -k[A] Using calculus to integrate the rate law for a first- order process gives us ln [A] t [A] 0 =  kt where [A] 0 is the initial concentration of A, and [A] t is the concentration of A at some time, t, during the course of the reaction. © 2012 Pearson Education, Inc.

28. Chemical Kinetics Integrated Rate Laws Manipulating this equation produces ln [A] t [A] 0 =  kt ln [A] t  ln [A] 0 =  kt ln [A] t =  kt + ln [A] 0 which is in the form y = mx + b © 2012 Pearson Education, Inc.

29. Chemical Kinetics First-Order Processes Therefore, if a reaction is first-order, a plot of ln [A] vs. t will yield a straight line, and the slope of the line will be  k. ln [A] t =  kt + ln [A] 0 © 2012 Pearson Education, Inc.

30. Chemical Kinetics Problem The decomposition of a certain insecticide in water at 12  C follows first-order kinetics with a rate constant of 1.45 yr  1. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0  10  7 g/cm 3. Assume that the average temperature of the lake is 12 ºC. (a) What is the concentration of the insecticide on June 1 of the following year? (b) How long will it take for the insecticide concentration to decrease to 3.0  10 –7 g/cm 3 ?

31. Chemical Kinetics First-Order Processes Consider the process in which methyl isonitrile is converted to acetonitrile. CH 3 NCCH 3 CN © 2012 Pearson Education, Inc.

32. Chemical Kinetics First-Order Processes This data were collected for this reaction at 198.9  C. CH 3 NCCH 3 CN © 2012 Pearson Education, Inc.

33. Chemical Kinetics First-Order Processes When ln P is plotted as a function of time, a straight line results. Therefore, –The process is first-order. –k is the negative of the slope: 5.1  10  5 s  1. © 2012 Pearson Education, Inc.

34. Chemical Kinetics Second-Order Processes For Second order reaction: Rate = -∆[A]/∆t = -k[A] 2 Similarly, integrating the rate law for a process that is second-order in reactant A, we get 1 [A] t = kt + 1 [A] 0 also in the form y = mx + b © 2012 Pearson Education, Inc.

35. Chemical Kinetics Second-Order Processes So if a process is second-order in A, a plot of vs. t yields a straight line, and the slope of that line is k. 1 [A] t = kt + 1 [A] 0 1 [A] © 2012 Pearson Education, Inc.

36. Chemical Kinetics Second-Order Processes The decomposition of NO 2 at 300 °C is described by the equation NO 2 (g)NO(g) + O 2 (g) and yields data comparable to this table: Time (s)[NO 2 ], M 0.00.01000 50.00.00787 100.00.00649 200.00.00481 300.00.00380 1212 © 2012 Pearson Education, Inc.

37. Chemical Kinetics Second-Order Processes Plotting ln [NO 2 ] vs. t yields the graph that is not a straight line, so the process is not first- order in [A]. Time (s)[NO 2 ], Mln [NO 2 ] 0.00.01000  4.610 50.00.00787  4.845 100.00.00649  5.038 200.00.00481  5.337 300.00.00380  5.573 © 2012 Pearson Education, Inc.

38. Chemical Kinetics Second-Order Processes Graphing ln vs. t, however, gives this plot Fig. 14.9(b). Time (s)[NO 2 ], M1/[NO 2 ] 0.00.01000100 50.00.00787127 100.00.00649154 200.00.00481208 300.00.00380263 Because this is a straight line, the process is second- order in [A]. 1 [NO 2 ] © 2012 Pearson Education, Inc.

39. Chemical Kinetics Zero Order Reaction

40. Chemical Kinetics Zero Order Reaction Rate = -∆[A]/∆t = k The integrated rate law for zero order reaction is [A] t = -kt + [A] 0

41. Chemical Kinetics Half-Life Half-life is defined as the time required for one-half of a reactant to react. Because [A] at t 1/2 is one-half of the original [A], [A] t = 0.5 [A] 0. © 2012 Pearson Education, Inc.

42. Chemical Kinetics Half-Life For a first-order process, this becomes 0.5 [A] 0 [A] 0 ln =  kt 1/2 ln 0.5 =  kt 1/2  0.693 =  kt 1/2 = t 1/2 0.693 k Note: For a first-order process, then, the half-life does not depend on [A] 0. © 2012 Pearson Education, Inc.

43. Chemical Kinetics Half-Life For a second-order process, 1 0.5 [A] 0 = kt 1/2 + 1 [A] 0 2 [A] 0 = kt 1/2 + 1 [A] 0 2  1 [A] 0 = kt 1/2 1 [A] 0 == t 1/2 1 k[A] 0 © 2012 Pearson Education, Inc.

44. Chemical Kinetics The reaction of C 4 H 9 Cl with water is a first-order reaction. (a) Use Figure 14.4 to estimate the half-life for this reaction. (b) Use the half-life from (a) to calculate the rate constant. Sample Exercise 14.9 Determining the Half-Life of a First-Order Reaction

45. Chemical Kinetics Temperature and Rate Generally, as temperature increases, so does the reaction rate. This is because k is temperature-dependent. © 2012 Pearson Education, Inc.

46. Chemical Kinetics The Collision Model In a chemical reaction, bonds are broken and new bonds are formed. Molecules can only react if they collide with each other. © 2012 Pearson Education, Inc.

47. Chemical Kinetics The Collision Model Furthermore, molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation. © 2012 Pearson Education, Inc.

48. Chemical Kinetics Activation Energy In other words, there is a minimum amount of energy required for reaction: the activation energy, E a. Just as a ball cannot get over a hill if it does not roll up the hill with enough energy, a reaction cannot occur unless the molecules possess sufficient energy to get over the activation-energy barrier. © 2012 Pearson Education, Inc.

49. Chemical Kinetics Reaction Coordinate Diagrams It is helpful to visualize energy changes throughout a process on a reaction coordinate diagram like this one for the rearrangement of methyl isonitrile. © 2012 Pearson Education, Inc.

50. Chemical Kinetics Reaction Coordinate Diagrams The diagram shows the energy of the reactants and products (and, therefore,  E). The high point on the diagram is the transition state. The species present at the transition state is called the activated complex. The energy gap between the reactants and the activated complex is the activation-energy barrier. © 2012 Pearson Education, Inc.

51. Chemical Kinetics Maxwell–Boltzmann Distributions Temperature is defined as a measure of the average kinetic energy of the molecules in a sample. At any temperature there is a wide distribution of kinetic energies. © 2012 Pearson Education, Inc.

52. Chemical Kinetics Maxwell–Boltzmann Distributions As the temperature increases, the curve flattens and broadens. Thus, at higher temperatures, a larger population of molecules has higher energy. © 2012 Pearson Education, Inc.

53. Chemical Kinetics Maxwell–Boltzmann Distributions If the dotted line represents the activation energy, then as the temperature increases, so does the fraction of molecules that can overcome the activation-energy barrier. As a result, the reaction rate increases. © 2012 Pearson Education, Inc.

54. Chemical Kinetics Maxwell–Boltzmann Distributions This fraction of molecules can be found through the expression where R is the gas constant and T is the Kelvin temperature. f = e −E a /RT © 2012 Pearson Education, Inc.

55. Chemical Kinetics Sample Exercise 14.10 Relating Energy Profiles to Activation Energies and Speeds of Reaction Consider a series of reactions having these energy profiles: Rank the reactions from slowest to fastest assuming that they have nearly the same value for the frequency factor A.

56. Chemical Kinetics Arrhenius Equation Svante Arrhenius developed a mathematical relationship between k and E a : k = Ae where A is the frequency factor, a number that represents the likelihood that collisions would occur with the proper orientation for reaction. −E a /RT © 2012 Pearson Education, Inc.

57. Chemical Kinetics Arrhenius Equation Taking the natural logarithm of both sides, the equation becomes ln k =  ( ) + ln A 1T1T y = mx + b Therefore, if k is determined experimentally at several temperatures, E a can be calculated from the slope of a plot of ln k vs.. EaREaR 1T1T © 2012 Pearson Education, Inc.

58. Chemical Kinetics Reaction Mechanisms The sequence of events that describes the actual process by which reactants become products is called the reaction mechanism. © 2012 Pearson Education, Inc.

59. Chemical Kinetics Reaction Mechanisms Reactions may occur all at once or through several discrete steps. Each of these processes is known as an elementary reaction or elementary process. © 2012 Pearson Education, Inc.

60. Chemical Kinetics Reaction Mechanisms The molecularity of a process tells how many molecules are involved in the process. © 2012 Pearson Education, Inc.

61. Chemical Kinetics It has been proposed that the conversion of ozone into O 2 proceeds by a two-step mechanism: O 3 (g)  O 2 (g) + O(g) O 3 (g) + O(g)  2 O 2 (g) (a) Describe the molecularity of each elementary reaction in this mechanism. (b) Write the equation for the overall reaction. (c) Identify the intermediate(s). Exercise Determining Molecularity and Identifying Intermediates

62. Chemical Kinetics Multistep Mechanisms In a multistep process, one of the steps will be slower than all others. The overall reaction cannot occur faster than this slowest, rate- determining step. © 2012 Pearson Education, Inc.

63. Chemical Kinetics Slow Initial Step The rate law for this reaction is found experimentally to be Rate = k[NO 2 ] 2 CO is necessary for this reaction to occur, but the rate of the reaction does not depend on its concentration. This suggests that the reaction occurs in two steps. NO 2 (g) + CO(g)  NO(g) + CO 2 (g) © 2012 Pearson Education, Inc.

64. Chemical Kinetics Slow Initial Step A proposed mechanism for this reaction is Step 1: NO 2 + NO 2  NO 3 + NO (slow) Step 2: NO 3 + CO  NO 2 + CO 2 (fast) The NO 3 intermediate is consumed in the second step. As CO is not involved in the slow, rate- determining step, it does not appear in the rate law. © 2012 Pearson Education, Inc.

65. Chemical Kinetics Exercise Determining the Rate Law for a Multistep Mechanism The decomposition of nitrous oxide, N2O, is believed to occur by a two-step mechanism: N 2 O(g)  N 2 (g) + O(g) (slow) N 2 O(g) + O(g)  N 2 (g) + O 2 (g) (fast) (a) Write the equation for the overall reaction. (b) Write the rate law for the overall reaction.

66. Chemical Kinetics Fast Initial Step The rate law for this reaction is found to be Rate = k[NO] 2 [Br 2 ] Because termolecular processes are rare, this rate law suggests a two-step mechanism. 2 NO(g) + Br 2 (g)  2 NOBr(g) © 2012 Pearson Education, Inc.

67. Chemical Kinetics Fast Initial Step A proposed mechanism is Step 2: NOBr 2 + NO  2 NOBr (slow) Step 1 includes the forward and reverse reactions. Step 1: NO + Br 2 NOBr 2 (fast) © 2012 Pearson Education, Inc.

68. Chemical Kinetics Fast Initial Step The rate of the overall reaction depends upon the rate of the slow step. The rate law for that step would be Rate = k 2 [NOBr 2 ] [NO] But how can we find [NOBr 2 ]? © 2012 Pearson Education, Inc.

69. Chemical Kinetics Fast Initial Step NOBr 2 can react two ways: –With NO to form NOBr. –By decomposition to reform NO and Br 2. The reactants and products of the first step are in equilibrium with each other. Therefore, Rate f = Rate r © 2012 Pearson Education, Inc.

70. Chemical Kinetics Fast Initial Step Because Rate f = Rate r, k 1 [NO] [Br 2 ] = k  1 [NOBr 2 ] Solving for [NOBr 2 ], gives us k1k1k1k1 [NO] [Br 2 ] = [NOBr 2 ] © 2012 Pearson Education, Inc.

71. Chemical Kinetics Fast Initial Step Substituting this expression for [NOBr 2 ] in the rate law for the rate-determining step, gives k2k1k1k2k1k1 Rate =[NO] [Br 2 ] [NO] = k[NO] 2 [Br 2 ] © 2012 Pearson Education, Inc.

72. Chemical Kinetics Sample Exercise 14.15 Deriving the Rate Law for a Mechanism with a Fast Initial Step Show that the following mechanism for Equation 14.24 also produces a rate law consistent with the experimentally observed one:

73. Chemical Kinetics Catalysts Catalysts increase the rate of a reaction by decreasing the activation energy of the reaction.(homogeneous and heterogeneous catalysis) Catalysts change the mechanism by which the process occurs. © 2012 Pearson Education, Inc.

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76. Chemical Kinetics Enzymes Enzymes are catalysts in biological systems. The substrate fits into the active site of the enzyme much like a key fits into a lock. © 2012 Pearson Education, Inc.