John C. Kotz State University of New York, College at Oneonta John C. Kotz Paul M. Treichel John Townsend Chapter 15 Principles of Reactivity: Chemical Kinetics

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3 © 2009 Brooks/Cole - Cengage Chemical Kinetics Chapter 15 H 2 O 2 decomposition in an insect H 2 O 2 decomposition catalyzed by MnO 2 PLAY MOVIE

4 © 2009 Brooks/Cole - Cengage We can use thermodynamics to tell if a reaction is product- or reactant- favored.We can use thermodynamics to tell if a reaction is product- or reactant- favored. But this gives us no info on HOW FAST reaction goes from reactants to products.But this gives us no info on HOW FAST reaction goes from reactants to products. KINETICS — the study of REACTION RATES and their relation to the way the reaction proceeds, i.e., its MECHANISM.KINETICS — the study of REACTION RATES and their relation to the way the reaction proceeds, i.e., its MECHANISM. The reaction mechanism is our goal!The reaction mechanism is our goal! Chemical Kinetics

5 © 2009 Brooks/Cole - Cengage Reaction Mechanisms The sequence of events at the molecular level that control the speed and outcome of a reaction. Br from biomass burning destroys stratospheric ozone. (See R.J. Cicerone, Science, volume 263, page 1243, 1994.) Step 1:Br + O 3 f BrO + O 2 Step 2:Cl + O 3 f ClO + O 2 Step 3:BrO + ClO + light f Br + Cl + O 2 NET: 2 O 3 f 3 O 2

6 © 2009 Brooks/Cole - Cengage Reaction rate = change in concentration of a reactant or product with time.Reaction rate = change in concentration of a reactant or product with time. Three “types” of ratesThree “types” of rates –initial rate –average rate –instantaneous rate Reaction Rates Section 15.1

7 © 2009 Brooks/Cole - Cengage Determining a Reaction Rate Blue dye is oxidized with bleach. Its concentration decreases with time. The rate — the change in dye conc with time — can be determined from the plot. Blue dye is oxidized with bleach. Its concentration decreases with time. The rate — the change in dye conc with time — can be determined from the plot. See Chemistry Now, Chapter 15 Dye Conc Time PLAY MOVIE

8 © 2009 Brooks/Cole - Cengage Determining a Reaction Rate See Active Figure 15.2

9 © 2009 Brooks/Cole - Cengage ConcentrationsConcentrations and physical state of reactants and productsand physical state of reactants and products TemperatureTemperature CatalystsCatalysts Factors Affecting Rates

10 © 2009 Brooks/Cole - Cengage Concentrations & Rates Section M HCl6 M HCl Mg(s) + 2 HCl(aq) f MgCl 2 (aq) + H 2 (g) PLAY MOVIE

11 © 2009 Brooks/Cole - Cengage Physical state of reactantsPhysical state of reactants Factors Affecting Rates PLAY MOVIE

12 © 2009 Brooks/Cole - Cengage Catalysts: catalyzed decomp of H 2 O 2 2 H 2 O 2 f 2 H 2 O + O 2 2 H 2 O 2 f 2 H 2 O + O 2 Factors Affecting Rates PLAY MOVIE

13 © 2009 Brooks/Cole - Cengage Catalysts 1. CO 2 (g) e CO 2 (aq) 2. CO 2 (aq) + H 2 O(liq) e H 2 CO 3 (aq) 3. H 2 CO 3 (aq) e H + (aq) + HCO 3 – (aq) Adding trace of NaOH uses up H +. Equilibrium shifts to produce more H 2 CO 3. Enzyme in blood (above) speeds up reactions 1 and 2 See Page 702

14 © 2009 Brooks/Cole - Cengage TemperatureTemperature Factors Affecting Rates Bleach at 54 ˚CBleach at 22 ˚C PLAY MOVIE

15 © 2009 Brooks/Cole - Cengage Iodine Clock Reaction 1. Iodide is oxidized to iodine H 2 O I H + f 2 H 2 O + I 2 2. I 2 reduced to I - with vitamin C I 2 + C 6 H 8 O 6 f C 6 H 6 O H I - When all vitamin C is depleted, the I 2 interacts with starch to give a blue complex.

16 © 2009 Brooks/Cole - Cengage Iodine Clock Reaction

17 © 2009 Brooks/Cole - Cengage Concentrations and Rates To postulate a reaction mechanism, we study reaction rate andreaction rate and its concentration dependenceits concentration dependence

18 © 2009 Brooks/Cole - Cengage Concentrations and Rates Take reaction where Cl - in cisplatin [Pt(NH 3 ) 2 Cl 3 ] is replaced by H 2 O

19 © 2009 Brooks/Cole - Cengage Concentrations & Rates Rate of reaction is proportional to [Pt(NH 3 ) 2 Cl 2 ] We express this as a RATE LAW Rate of reaction = k [Pt(NH 3 ) 2 Cl 2 ] where k = rate constant k is independent of conc. but increases with T

20 © 2009 Brooks/Cole - Cengage Concentrations, Rates, & Rate Laws In general, for a A + b B f x X with a catalyst C Rate = k [A] m [B] n [C] p The exponents m, n, and p are the reaction orderare the reaction order can be 0, 1, 2 or fractionscan be 0, 1, 2 or fractions must be determined by experiment!must be determined by experiment!

21 © 2009 Brooks/Cole - Cengage Interpreting Rate Laws Rate = k [A] m [B] n [C] p If m = 1, rxn. is 1st order in AIf m = 1, rxn. is 1st order in A Rate = k [A] 1 If [A] doubles, then rate goes up by factor of __ If [A] doubles, then rate goes up by factor of __ If m = 2, rxn. is 2nd order in A.If m = 2, rxn. is 2nd order in A. Rate = k [A] 2 Rate = k [A] 2 Doubling [A] increases rate by ________ If m = 0, rxn. is zero order.If m = 0, rxn. is zero order. Rate = k [A] 0 Rate = k [A] 0 If [A] doubles, rate ________

22 © 2009 Brooks/Cole - Cengage Deriving Rate Laws Expt. [CH 3 CHO]Disappear of CH 3 CHO (mol/L)(mol/Lsec) Derive rate law and k for CH 3 CHO(g) f CH 4 (g) + CO(g) from experimental data for rate of disappearance of CH 3 CHO

23 © 2009 Brooks/Cole - Cengage Deriving Rate Laws Rate of rxn = k [CH 3 CHO] 2 Here the rate goes up by ______ when initial conc. doubles. Therefore, we say this reaction is _________________ order. Now determine the value of k. Use expt. #3 data— mol/Ls = k (0.30 mol/L) 2 k = 2.0 (L / mols) k = 2.0 (L / mols) Using k you can calc. rate at other values of [CH 3 CHO] at same T.

24 © 2009 Brooks/Cole - Cengage Concentration/Time Relations What is concentration of reactant as function of time? Consider FIRST ORDER REACTIONS The rate law is

25 © 2009 Brooks/Cole - Cengage Concentration/Time Relations Integrating - (∆ [A] / ∆ time) = k [A], we get ln is natural logarithm [A] at time = 0 [A] / [A] 0 =fraction remaining after time t has elapsed. Called the integrated first-order rate law.

26 © 2009 Brooks/Cole - Cengage Concentration/Time Relations Sucrose decomposes to simpler sugars Rate of disappearance of sucrose = k [sucrose] Glucose If k = 0.21 hr -1 and [sucrose] = M How long to drop 90% (to M)?

27 © 2009 Brooks/Cole - Cengage Concentration/Time Relations Rate of disappear of sucrose = k [sucrose], k = 0.21 hr -1. If initial [sucrose] = M, how long to drop 90% or to M? Use the first order integrated rate law ln (0.100) = = - (0.21 hr -1 )(time) time = 11 hours

28 © 2009 Brooks/Cole - Cengage Using the Integrated Rate Law The integrated rate law suggests a way to tell the order based on experiment. 2 N 2 O 5 (g) f 4 NO 2 (g) + O 2 (g) Time (min)[N 2 O 5 ] 0 (M) ln [N 2 O 5 ] Rate = k [N 2 O 5 ]

29 © 2009 Brooks/Cole - Cengage Using the Integrated Rate Law 2 N 2 O 5 (g) f 4 NO 2 (g) + O 2 (g) Rate = k [N 2 O 5 ] Data of conc. vs. time plot do not fit straight line. Plot of ln [N 2 O 5 ] vs. time is a straight line!

30 © 2009 Brooks/Cole - Cengage Using the Integrated Rate Law All 1st order reactions have straight line plot for ln [A] vs. time. (2nd order gives straight line for plot of 1/[A] vs. time) Plot of ln [N 2 O 5 ] vs. time is a straight line! Eqn. for straight line: y = mx + b y = mx + b Plot of ln [N 2 O 5 ] vs. time is a straight line! Eqn. for straight line: y = mx + b y = mx + b

31 © 2009 Brooks/Cole - Cengage Properties of Reactions

32 © 2009 Brooks/Cole - Cengage Half-Life HALF-LIFE is the time it takes for 1/2 a sample is disappear. For 1st order reactions, the concept of HALF-LIFE is especially useful. See Active Figure 15.9

33 © 2009 Brooks/Cole - Cengage Reaction is 1st order decomposition of H 2 O 2.Reaction is 1st order decomposition of H 2 O 2. Half-Life

34 © 2009 Brooks/Cole - Cengage Half-Life Reaction after 1 half-life.Reaction after 1 half-life. 1/2 of the reactant has been consumed and 1/2 remains.1/2 of the reactant has been consumed and 1/2 remains.

35 © 2009 Brooks/Cole - Cengage Half-Life After 2 half-lives 1/4 of the reactant remains.After 2 half-lives 1/4 of the reactant remains.

36 © 2009 Brooks/Cole - Cengage Half-Life A 3 half-lives 1/8 of the reactant remains.A 3 half-lives 1/8 of the reactant remains.

37 © 2009 Brooks/Cole - Cengage Half-Life After 4 half-lives 1/16 of the reactant remains.After 4 half-lives 1/16 of the reactant remains.

38 © 2009 Brooks/Cole - Cengage Half-Life Sugar is fermented in a 1st order process (using an enzyme as a catalyst). Sugar is fermented in a 1st order process (using an enzyme as a catalyst). sugar + enzyme f products sugar + enzyme f products Rate of disappear of sugar = k[sugar] k = 3.3 x sec -1 What is the half-life of this reaction?

39 © 2009 Brooks/Cole - Cengage Half-Life Solution [A] / [A] 0 = fraction remaining when t = t 1/2 then fraction remaining = _________ Therefore, ln (1/2) = - k · t 1/ = - k · t 1/2 t 1/2 = / k t 1/2 = / k So, for sugar, t 1/2 = / k = 2100 sec = 35 min Rate = k[sugar] and k = 3.3 x sec -1. What is the half- life of this reaction?

40 © 2009 Brooks/Cole - Cengage Half-Life Solution 2 hr and 20 min = 4 half-lives Half-life Time ElapsedMass Left 1st35 min2.50 g 2nd g 3rd g 4th g Rate = k[sugar] and k = 3.3 x sec -1. Half-life is 35 min. Start with 5.00 g sugar. How much is left after 2 hr and 20 min (140 min)?

41 © 2009 Brooks/Cole - Cengage Half-Life Radioactive decay is a first order process. Tritium f electron + helium Tritium f electron + helium 3 H 0 -1 e 3 He 3 H 0 -1 e 3 He t 1/2 = 12.3 years If you have 1.50 mg of tritium, how much is left after 49.2 years?

42 © 2009 Brooks/Cole - Cengage Half-Life Solution ln [A] / [A] 0 = -kt [A] = ?[A] 0 = 1.50 mgt = 49.2 y Need k, so we calc k from: k = / t 1/2 Obtain k = y -1 Now ln [A] / [A] 0 = -kt = - ( y -1 )(49.2 y) = = Take antilog: [A] / [A] 0 = e = = fraction remaining Start with 1.50 mg of tritium, how much is left after 49.2 years? t 1/2 = 12.3 years

43 © 2009 Brooks/Cole - Cengage Half-Life Solution [A] / [A] 0 = is the fraction remaining! Because [A] 0 = 1.50 mg, [A] = mg But notice that 49.2 y = 4.00 half-lives 1.50 mg f mg after 1 half-life 1.50 mg f mg after 1 half-life f mg after 2 f mg after 2 f mg after 3 f mg after 3 f mg after 4 f mg after 4 Start with 1.50 mg of tritium, how much is left after 49.2 years? t 1/2 = 12.3 years

44 © 2009 Brooks/Cole - Cengage Half-Lives of Radioactive Elements Rate of decay of radioactive isotopes given in terms of 1/2-life. 238 U f 234 Th + He4.5 x 10 9 y 14 C f 14 N + beta5730 y 131 I f 131 Xe + beta8.05 d Element seaborgium Sg 0.9 s

45 © 2009 Brooks/Cole - Cengage MECHANISMS A Microscopic View of Reactions Mechanism: how reactants are converted to products at the molecular level. RATE LAW f MECHANISM experiment ftheory PLAY MOVIE

46 © 2009 Brooks/Cole - Cengage Activation Energy Molecules need a minimum amount of energy to react. Visualized as an energy barrier - activation energy, E a. Reaction coordinate diagram PLAY MOVIE

47 © 2009 Brooks/Cole - Cengage MECHANISMS & Activation Energy Conversion of cis to trans-2-butene requires twisting around the C=C bond. Rate = k [trans-2-butene]

48 © 2009 Brooks/Cole - Cengage MECHANISMS Activation energy barrier CisTrans Transition state

49 © 2009 Brooks/Cole - Cengage Energy involved in conversion of trans to cis butene trans cis energy Activated Complex +262 kJ -266 kJ MECHANISMS 4 kJ/mol

50 © 2009 Brooks/Cole - Cengage Mechanisms Reaction passes thru a TRANSITION STATE where there is an activated complex that has sufficient energy to become a product.Reaction passes thru a TRANSITION STATE where there is an activated complex that has sufficient energy to become a product. ACTIVATION ENERGY, E a = energy req’d to form activated complex. Here E a = 262 kJ/mol

51 © 2009 Brooks/Cole - Cengage Also note that trans-butene is MORE STABLE than cis-butene by about 4 kJ/mol. Therefore, cis f trans is EXOTHERMIC This is the connection between thermo- dynamics and kinetics. MECHANISMS

52 © 2009 Brooks/Cole - Cengage Effect of Temperature Reactions generally occur slower at lower T.Reactions generally occur slower at lower T. Iodine clock reaction. See Chemistry Now, Ch. 15 f H 2 O I H + f 2 H 2 O + I 2 Room temperature In ice at 0 o C PLAY MOVIE

53 © 2009 Brooks/Cole - Cengage Activation Energy and Temperature Reactions are faster at higher T because a larger fraction of reactant molecules have enough energy to convert to product molecules. In general, differences in activation energy cause reactions to vary from fast to slow.

54 © 2009 Brooks/Cole - Cengage Mechanisms 1.Why is trans-butene cis-butene reaction observed to be 1st order? 1.Why is trans-butene e cis-butene reaction observed to be 1st order? As [trans] doubles, number of molecules with enough E also doubles. As [trans] doubles, number of molecules with enough E also doubles. 2.Why is the trans cis reaction faster at higher temperature? 2.Why is the trans e cis reaction faster at higher temperature? Fraction of molecules with sufficient activation energy increases with T. Fraction of molecules with sufficient activation energy increases with T.

55 © 2009 Brooks/Cole - Cengage More About Activation Energy Arrhenius equation — Rate constant Temp (K) 8.31 x kJ/Kmol Activation energy Frequency factor Frequency factor related to frequency of collisions with correct geometry. Plot ln k vs. 1/T straight line. slope = -E a /R Plot ln k vs. 1/T f straight line. slope = -E a /R

56 © 2009 Brooks/Cole - Cengage More on Mechanisms Reaction of trans-butene f cis-butene is UNIMOLECULAR - only one reactant is involved. BIMOLECULAR — two different molecules must collide f products A bimolecular reaction Exo- or endothermic? PLAY MOVIE

57 © 2009 Brooks/Cole - Cengage Collision Theory Reactions require (a) activation energy and (b) correct geometry. O 3 (g) + NO(g) f O 2 (g) + NO 2 (g) O 3 (g) + NO(g) f O 2 (g) + NO 2 (g) 2. Activation energy and geometry 1. Activation energy PLAY MOVIE

58 © 2009 Brooks/Cole - Cengage Mechanisms O 3 + NO reaction occurs in a single ELEMENTARY step. Most others involve a sequence of elementary steps. Adding elementary steps gives NET reaction. PLAY MOVIE

59 © 2009 Brooks/Cole - Cengage Mechanisms Most rxns. involve a sequence of elementary steps. 2 I - + H 2 O H + f I H 2 O 2 I - + H 2 O H + f I H 2 O Rate = k [I - ] [H 2 O 2 ] Rate = k [I - ] [H 2 O 2 ]NOTE 1.Rate law comes from experiment 2.Order and stoichiometric coefficients not necessarily the same! 3.Rate law reflects all chemistry down to and including the slowest step in multistep reaction.

60 © 2009 Brooks/Cole - Cengage Mechanisms Proposed Mechanism Step 1 — slowHOOH + I - f HOI + OH - Step 2 — fastHOI + I - f I 2 + OH - Step 3 — fast2 OH H + f 2 H 2 O Rate of the reaction controlled by slow step — RATE DETERMINING STEP, rds. RATE DETERMINING STEP, rds. Rate can be no faster than rds! Most rxns. involve a sequence of elementary steps. 2 I - + H 2 O H + f I H 2 O 2 I - + H 2 O H + f I H 2 O Rate = k [I - ] [H 2 O 2 ] Rate = k [I - ] [H 2 O 2 ]

61 © 2009 Brooks/Cole - Cengage Mechanisms Elementary Step 1 is bimolecular and involves I - and HOOH. Therefore, this predicts the rate law should be Rate  [I - ] [H 2 O 2 ] — as observed!! The species HOI and OH - are reaction intermediates. 2 I - + H 2 O H + f I H 2 O Rate = k [I - ] [H 2 O 2 ] Rate = k [I - ] [H 2 O 2 ] Step 1 — slowHOOH + I - f HOI + OH - Step 2 — fastHOI + I - f I 2 + OH - Step 3 — fast2 OH H + f 2 H 2 O

62 © 2009 Brooks/Cole - Cengage Rate Laws and Mechanisms NO 2 + CO reaction: Rate = k[NO 2 ] 2 Single step Two possible mechanisms Two steps: step 1 Two steps: step 2 PLAY MOVIE

63 © 2009 Brooks/Cole - Cengage Ozone Decomposition over Antarctica 2 O 3 (g) f 3 O 2 (g)

64 © 2009 Brooks/Cole - Cengage Ozone Decomposition Mechanism Proposed mechanism Step 1: fast, equilibrium O 3 (g) e O 2 (g) + O (g) Step 2: slowO 3 (g) + O (g) f 2 O 2 (g) 2 O 3 (g) f 3 O 2 (g)

65 © 2009 Brooks/Cole - Cengage CATALYSISCATALYSIS Catalysts speed up reactions by altering the mechanism to lower the activation energy barrier. Dr. James Cusumano, Catalytica Inc. What is a catalyst? Catalysts and society Catalysts and the environment See Chemistry Now, Ch 15 PLAY MOVIE

66 © 2009 Brooks/Cole - Cengage CATALYSIS In auto exhaust systems — Pt, NiO 2 CO + O 2 f 2 CO 2 2 NO f N 2 + O 2 PLAY MOVIE

67 © 2009 Brooks/Cole - Cengage CATALYSIS 2.Polymers: H 2 C=CH 2 ---> polyethylene 3.Acetic acid: CH 3 OH + CO f CH 3 CO 2 H 4. Enzymes — biological catalysts

68 © 2009 Brooks/Cole - Cengage CATALYSIS Catalysis and activation energy Uncatalyzed reaction Catalyzed reaction MnO 2 catalyzes decomposition of H 2 O 2 2 H 2 O 2 f 2 H 2 O + O 2 PLAY MOVIE

69 © 2009 Brooks/Cole - Cengage Iodine-Catalyzed Isomerization of cis-2-Butene See Figure 15.15

70 © 2009 Brooks/Cole - Cengage Iodine-Catalyzed Isomerization of cis-2-Butene