2. Copyright 1999, PRENTICE HALLChapter 141 Chemical Kinetics Chapter 14 David P. White University of North Carolina, Wilmington

3. Copyright 1999, PRENTICE HALLChapter 142 Chemical Kinetics Kinetics is the study of how fast chemical reactions occur. There are 4 important factors which affect rates of reactions: –reactant concentration, –temperature, –action of catalysts, and –surface area. Goal: to understand chemical reactions at the molecular level.

4. Copyright 1999, PRENTICE HALLChapter 143 Chemical Kinetics Reaction Rates Speed of a reaction is measured by the change in concentration with time. For a reaction A  B Suppose A reacts to form B. Let us begin with 1.00 mol A.

5. Copyright 1999, PRENTICE HALLChapter 144 Chemical Kinetics Reaction Rates

6. Copyright 1999, PRENTICE HALLChapter 145 Chemical Kinetics Reaction Rates –At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present. –At t = 20 min, there is 0.54 mol A and 0.46 mol B. –At t = 40 min, there is 0.30 mol A and 0.70 mol B. –Calculating,

7. Copyright 1999, PRENTICE HALLChapter 146 Chemical Kinetics Reaction Rates For the reaction A  B there are two ways of measuring rate: –the speed at which the products appear (i.e. change in moles of B per unit time), or –the speed at which the reactants disappear (i.e. the change in moles of A per unit time). A plot of number of moles versus time shows that as the reactants (red A) disappear, the products (blue B) appear.

8. Copyright 1999, PRENTICE HALLChapter 147 Chemical Kinetics Reaction Rates

9. Copyright 1999, PRENTICE HALLChapter 148 Chemical Kinetics Rates in Terms of Concentrations For the reaction A  B there are two ways of Most useful units for rates are to look at molarity. Since volume is constant, molarity and moles are directly proportional. Consider: C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq)

10. Copyright 1999, PRENTICE HALLChapter 149 Chemical Kinetics Rates in Terms of Concentrations C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq)

11. Copyright 1999, PRENTICE HALLChapter 1410 Chemical Kinetics Rates in Terms of Concentrations C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) –We can calculate the average rate in terms of the disappearance of C 4 H 9 Cl. –The units for average rate are mol/Ls or M/s. –The average rate decreases with time. –We plot [C 4 H 9 Cl] versus time. –The rate at any instant in time (instantaneous rate) is the slope of the tangent to the curve. –Instantaneous rate is different from average rate. –We usually call the instantaneous rate the rate.

12. Copyright 1999, PRENTICE HALLChapter 1411 Chemical Kinetics Rates in Terms of Concentrations

13. Copyright 1999, PRENTICE HALLChapter 1412 Chemical Kinetics Reaction Rates and Stoichiometry For the reaction C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) we know In general for aA + bB  cC + dD

14. Copyright 1999, PRENTICE HALLChapter 1413 The Dependence of Rate on Concentration In general rates increase as concentrations increase. NH 4 + (aq) + NO 2 - (aq)  N 2 (g) + 2H 2 O(l)

15. Copyright 1999, PRENTICE HALLChapter 1414 The Dependence of Rate on Concentration For the reaction NH 4 + (aq) + NO 2 - (aq)  N 2 (g) + 2H 2 O(l) we note –as [NH 4 + ] doubles with [NO 2 - ] constant the rate doubles, –as [NO 2 - ] doubles with [NH 4 + ] constant, the rate doubles, –We conclude rate  [NH 4 + ][NO 2 - ]. Rate law: Rate = k[NH 4 + ][ NO 2 - ]. The constant k is the rate constant.

16. Copyright 1999, PRENTICE HALLChapter 1415 The Dependence of Rate on Concentration For a general reaction with rate law Rate = k[reactant 1] m [reactant 2] n, we say the reaction is mth order in reactant 1 and nth order in reactant 2. The overall order of reaction is m + n + …. A reaction can be zeroth order if m, n, … are zero. Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry.

17. Copyright 1999, PRENTICE HALLChapter 1416 The Dependence of Rate on Concentration Using Initial Rates to Determine Rate Laws A reaction is zero order in a reactant if the change in concentration of that reactant produces no effect. A reaction is first order if doubling the concentration causes the rate to double. A reaction is second order if doubling the concentration results in a 2 2 increase in rate. A reacting is nth order if doubling the concentration causes an 2 n increase in rate. Note that the rate constant does not depend on concentration.

18. Copyright 1999, PRENTICE HALLChapter 1417 The Change of Concentration with Time First-Order Reactions Goal: convert rate law into a convenient equation to give concentrations as a function of time. For a first order reaction, the rate doubles as the concentration of a reactant doubles. We can show that A plot of ln[A] t versus t is a straight line with slope -k and intercept ln[A] 0. In the above we use the natural logarithm, ln, which is log to the base e.

19. Copyright 1999, PRENTICE HALLChapter 1418 The Change of Concentration with Time First-Order Reactions

20. Copyright 1999, PRENTICE HALLChapter 1419 The Change of Concentration with Time Half-Life Half-life is the time taken for the concentration of a reactant to drop to half its original value. That is, half life, t 1/2 is the time taken for [A] 0 to reach ½[A] 0. Mathematically,

21. Copyright 1999, PRENTICE HALLChapter 1420 The Change of Concentration with Time Half-Life

22. Copyright 1999, PRENTICE HALLChapter 1421 The Change of Concentration with Time Second-Order Reactions For a second order reaction with just one reactant A plot of 1/[A] t versus t is a straight line with slope k and intercept 1/[A] 0 For a second order reaction, a plot of ln[A] t vs. t is not linear.

23. Copyright 1999, PRENTICE HALLChapter 1422 The Change of Concentration with Time Second-Order Reactions

24. Copyright 1999, PRENTICE HALLChapter 1423 The Change of Concentration with Time Second-Order Reactions We can show that the half life A reaction can have rate constant expression of the form rate = k[A][B], i.e., is second order overall, but has first order dependence on A and B.

25. Copyright 1999, PRENTICE HALLChapter 1424 Temperature and Rate Most reactions speed up as temperature increases. (E.g. food spoils when not refrigerated.) When two light sticks are placed in water: one at room temperature and one in ice, the one at room temperature is brighter than the one in ice. The chemical reaction responsible for chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light. As temperature increases, the rate increases.

26. Copyright 1999, PRENTICE HALLChapter 1425 Temperature and Rate

27. Copyright 1999, PRENTICE HALLChapter 1426 Temperature and Rate As temperature increases, the rate increases. Since the rate law has no temperature term in it, the rate constant must depend on temperature. Consider the first order reaction CH 3 NC  CH 3 CN. –As temperature increases from 190  C to 250  C the rate constant increases from 2.52  10 -5 s -1 to 3.16  10 -3 s -1. The temperature effect is quite dramatic. Why?

28. Copyright 1999, PRENTICE HALLChapter 1427 Temperature and Rate The Collision Model Observations: rates of reactions are affected by concentration and temperature. Goal: develop a model that explains why rates of reactions increase as concentration and temperature increases. The collision model: in order for molecules to react they must collide. The greater the number of collisions the faster the rate.

29. Copyright 1999, PRENTICE HALLChapter 1428 Temperature and Rate The Collision Model

30. Copyright 1999, PRENTICE HALLChapter 1429 Temperature and Rate The Collision Model The more molecules present, the greater the probability of collision and the faster the rate. The higher the temperature, the more energy available to the molecules and the faster the rate. Complication: not all collisions lead to products. In fact, only a small fraction of collisions lead to product. In order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products.

31. Copyright 1999, PRENTICE HALLChapter 1430 Temperature and Rate Activation Energy Arrhenius: molecules must posses a minimum amount of energy to react. Why? –In order to form products, bonds must be broken in the reactants. –Bond breakage requires energy. Activation energy, E a, is the minimum energy required to initiate a chemical reaction.

32. Copyright 1999, PRENTICE HALLChapter 1431 Temperature and Rate Activation Energy

33. Copyright 1999, PRENTICE HALLChapter 1432 Temperature and Rate Activation Energy Consider the rearrangement of acetonitrile: –In H 3 C-N  C, the C-N  C bond bends until the C-N bond breaks and the N  C portion is perpendicular to the H 3 C portion. This structure is called the activated complex or transition state. –The energy required for the above twist and break is the activation energy, E a. –Once the C-N bond is broken, the N  C portion can continue to rotate forming a C-C  N bond.

34. Copyright 1999, PRENTICE HALLChapter 1433 Temperature and Rate Activation Energy

35. Copyright 1999, PRENTICE HALLChapter 1434 Temperature and Rate Activation Energy The change in energy for the reaction is the difference in energy between CH 3 NC and CH 3 CN. The activation energy is the difference in energy between reactants, CH 3 NC and transition state. The rate depends on E a. Notice that if a forward reaction is exothermic (CH 3 NC  CH 3 CN), then the reverse reaction is endothermic (CH 3 CN  CH 3 NC).

36. Copyright 1999, PRENTICE HALLChapter 1435 Temperature and Rate Activation Energy Consider the reaction between Cl and NOCl: –If the Cl collides with the Cl of NOCl then the products are Cl 2 and NO. –If the Cl collided with the O of NOCl then no products are formed. We need to quantify this effect.

37. Copyright 1999, PRENTICE HALLChapter 1436 Temperature and Rate Activation Energy

38. Copyright 1999, PRENTICE HALLChapter 1437 Temperature and Rate The Arrhenius Equation Arrhenius discovered most reaction-rate data obeyed the Arrhenius equation: –k is the rate constant, E a is the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K. –A is called the frequency factor. –A is a measure of the probability of a favorable collision. –Both A and E a are specific to a given reaction. If we have a lot of data, we can determine E a and A graphically by rearranging the Arrhenius equation: If we do not have a lot of data, then we can use

39. Copyright 1999, PRENTICE HALLChapter 1438 Temperature and Rate The Arrhenius Equation If we have a lot of data, we can determine E a and A graphically by rearranging the Arrhenius equation: If we do not have a lot of data, then we can use

40. Copyright 1999, PRENTICE HALLChapter 1439 Reaction Mechanisms The balanced chemical equation provides information about the beginning and end of reaction. The reaction mechanism gives the path of the reaction. Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction.

41. Copyright 1999, PRENTICE HALLChapter 1440 Reaction Mechanisms Elementary Steps Elementary step: any process that occurs in a single step. Molecularity: the number of molecules present in an elementary step. –Unimolecular: one molecule in the elementary step, –Bimolecular: two molecules in the elementary step, and –Termolecular: three molecules in the elementary step. It is not common to see termolecular processes (statistically improbable).

42. Copyright 1999, PRENTICE HALLChapter 1441 Reaction Mechanisms Elementary Steps Elementary steps must add to give the balanced chemical equation. Intermediate: a species which appears in an elementary step which is not a reactant or product. Rate Laws of Elementary Steps The rate law of an elementary step is determined by its molecularity: –Unimolecular processes are first order, –Bimolecular processes are second order, and –Termolecular processes are third order.

43. Copyright 1999, PRENTICE HALLChapter 1442 Reaction Mechanisms Rate Laws of Multistep Mechanisms Rate-determining step: is the slowest of the elementary steps. Therefore, the rate-determining step governs the overall rate law for the reaction. Mechanisms with an Initial Fast Step It is possible for an intermediate to be a reactant. Consider 2NO(g) + Br 2 (g)  2NOBr(g)

44. Copyright 1999, PRENTICE HALLChapter 1443 Reaction Mechanisms Mechanisms with an Initial Fast Step 2NO(g) + Br 2 (g)  2NOBr(g) The experimentally determined rate law is Rate = k[NO] 2 [Br 2 ] Consider the following mechanism for which the rate law is (based on Step 2):

45. Copyright 1999, PRENTICE HALLChapter 1444 Reaction Mechanisms Mechanisms with an Initial Fast Step The rate law is (based on Step 2): Rate = k 2 [NOBr 2 ][NO] The rate law should not depend on the concentration of an intermediate because intermediates are usually unstable. Assume NOBr 2 is unstable, so we express the concentration of NOBr 2 in terms of NOBr and Br 2 assuming there is an equilibrium in step 1 we have

46. Copyright 1999, PRENTICE HALLChapter 1445 Reaction Mechanisms Mechanisms with an Initial Fast Step By definition of equilibrium: k 1 [NO][Br 2 ] = k -1 [NOBr 2 ] Therefore, the overall rate law becomes Note the final rate law is consistent with the experimentally observed rate law.

47. Copyright 1999, PRENTICE HALLChapter 1446 Catalysis A catalyst changes the rate of a chemical reaction. There are two types of catalyst: –homogeneous, and –heterogeneous. Chlorine atoms are catalysts for the destruction of ozone. Homogeneous Catalysis The catalyst and reaction is in one phase. Hydrogen peroxide decomposes very slowly: 2H 2 O 2 (aq)  2H 2 O(l) + O 2 (g).

48. Copyright 1999, PRENTICE HALLChapter 1447 Catalysis Homogeneous Catalysis 2H 2 O 2 (aq)  2H 2 O(l) + O 2 (g). In the presence of the bromide ion, the decomposition occurs rapidly: –2Br - (aq) + H 2 O 2 (aq) + 2H + (aq)  Br 2 (aq) + 2H 2 O(l). –Br 2 (aq) is brown. –Br 2 (aq) + H 2 O 2 (aq)  2Br - (aq) + 2H + (aq) + O 2 (g). –Br - is a catalyst because it can be recovered at the end of the reaction. Generally, catalysts operate by lowering the activation energy for a reaction.

49. Copyright 1999, PRENTICE HALLChapter 1448 Catalysis Homogeneous Catalysis

50. Copyright 1999, PRENTICE HALLChapter 1449 Catalysis Homogeneous Catalysis Catalysts can operate by increasing the number of effective collisions. That is, from the Arrhenius equation: catalysts increase k be increasing A or decreasing E a. A catalyst may add intermediates to the reaction. Example: In the presence of Br -, Br 2 (aq) is generated as an intermediate in the decomposition of H 2 O 2. When a catalyst adds an intermediate, the activation energies for both steps must be lower than the activation energy for the uncatalyzed reaction.

51. Copyright 1999, PRENTICE HALLChapter 1450 Catalysis Heterogeneous Catalysis The catalyst is in a different phase than the reactants and products. Typical example: solid catalyst, gaseous reactants and products (catalytic converters in cars). Most industrial catalysts are heterogeneous. First step is adsorption (the binding of reactant molecules to the catalyst surface). Adsorbed species (atoms or ions) are very reactive. Molecules are adsorbed onto active sites (red spheres) on the catalyst surface.

52. Copyright 1999, PRENTICE HALLChapter 1451 Catalysis Heterogeneous Catalysis

53. Copyright 1999, PRENTICE HALLChapter 1452 Catalysis Heterogeneous Catalysis Consider the hydrogenation of ethylene: C 2 H 4 (g) + H 2 (g)  C 2 H 6 (g),  H = -136 kJ/mol. –The reaction is slow in the absence of a catalyst. –In the presence of a metal catalyst (Ni, Pt or Pd) the reaction occurs quickly at room temperature. –First the ethylene and hydrogen molecules are adsorbed onto active sites on the metal surface. –The H-H bond breaks and the H atoms migrate about the metal surface.

54. Copyright 1999, PRENTICE HALLChapter 1453 Catalysis Heterogeneous Catalysis Consider the hydrogenation of ethylene: C 2 H 4 (g) + H 2 (g)  C 2 H 6 (g),  H = -136 kJ/mol. –When an H atom collides with an ethylene molecule on the surface, the C-C  bond breaks and a C-H  bond forms. –When C 2 H 6 forms it desorbs from the surface. –When ethylene and hydrogen are adsorbed onto a surface, less energy is required to break the bonds and the activation energy for the reaction is lowered.

55. Copyright 1999, PRENTICE HALLChapter 1454 Catalysis Enzymes Enzymes are biological catalysts. Most enzymes are protein molecules with large molecular masses (10,000 to 10 6 amu). Enzymes have very specific shapes. Most enzymes catalyze very specific reactions. Substrates undergo reaction at the active site of an enzyme. A substrate locks into an enzyme and a fast reaction occurs.

56. Copyright 1999, PRENTICE HALLChapter 1455 Catalysis Enzymes

57. Copyright 1999, PRENTICE HALLChapter 1456 Catalysis Enzymes The products then move away from the enzyme. Only substrates that fit into the enzyme lock can be involved in the reaction. If a molecule binds tightly to an enzyme so that another substrate cannot displace it, then the active site is blocked and the catalyst is inhibited (enzyme inhibitors). The number of events (turnover number) catalyzed is large for enzymes (10 3 - 10 7 per second).

58. Copyright 1999, PRENTICE HALLChapter 1457 Catalysis Nitrogen Fixation and Nitrogenase Nitrogen gas cannot be used in the soil for plants or animals. Nitrogen compounds, NO 3, NO 2 -, and NO 3 - are used in the soil. The conversion between N 2 and NH 3 is a process with a high activation energy (the N  N triple bond needs to be broken). An enzyme, nitrogenase, in bacteria which live in root nodules of legumes, clover and alfalfa, catalyses the reduction of nitrogen to ammonia.

59. Copyright 1999, PRENTICE HALLChapter 1458 Catalysis Nitrogen Fixation and Nitrogenase

60. Copyright 1999, PRENTICE HALLChapter 1459 Catalysis Nitrogen Fixation and Nitrogenase The fixed nitrogen (NO 3, NO 2 -, and NO 3 - ) is consumed by plants and then eaten by animals. Animal waste and dead plants are attacked by bacteria that break down the fixed nitrogen and produce N 2 gas for the atmosphere.

61. Copyright 1999, PRENTICE HALLChapter 1460 End of Chapter 14 Chemical Kinetics