1. C h a p t e r 12 Chemical Kinetics

2. Reaction Rates01 Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant  Products aA  bB 

3. Reaction Rates02 Consider the decomposition of N 2 O 5 to give NO 2 and O 2 : 2 N 2 O 5 (g) 4 NO 2 (g) + O 2 (g)

4. Reaction Rates03

5. Rate Law & Reaction Order01 Rate Law: Shows the relationship of the rate of a reaction to the rate constant and the concentration of the reactants raised to some powers. For the general reaction: aA + bB  cC + dD rate = k[A] x [B] y x and y are NOT the stoichiometric coefficients. k = the rate constant

6. Rate Law & Reaction Order02 Reaction Order: The sum of the powers to which all reactant concentrations appearing in the rate law are raised. Reaction order is determined experimentally: 1. By inspection. 2. From the slope of a log(rate) vs. log[A] plot.

7. Rate Law & Reaction Order03 Determination by inspection : aA + bB  cC + dD Rate = R = k[A] x [B] y Use initial rates (t = 0)

8. Rate Law & Reaction Order04 Determination by plot of a log(rate) vs. log[A]: aA + bB  cC + dD Rate = R = k[A] x [B] y Log(R) = log(k) + x·log[A] + y·log[B] = const + x·log[A] if [B] held constant

9. Rate Law & Reaction Order05 The reaction of nitric oxide with hydrogen at 1280°C is: 2 NO (g) + 2 H 2(g)  N 2(g) + 2 H 2 O (g) From the following data determine the rate law and rate constant.

10. Rate Law & Reaction Order06 The reaction of peroxydisulfate ion (S 2 O 8 2- ) with iodide ion (I - ) is: S 2 O 8 2- (aq) + 3 I - (aq)  2 SO 4 2- (aq) + I 3 - (aq) From the following data, determine the rate law and rate constant.

11. Rate Law & Reaction Order07 Rate Constant: A constant of proportionality between the reaction rate and the concentration of reactants. rate  [Br 2 ] rate = k[Br 2 ]

12. First-Order Reactions01 First Order: Reaction rate depends on the reactant concentration raised to first power. Rate = k[A]

13. First-Order Reactions02 Using calculus we obtain the integrated rate equation: Plotting ln[A] t against t gives a straight line of slope –k. An alternate expression is:

14. First-Order Reactions03 Identifying First-Order Reactions:

15. First-Order Reactions04 Show that the decomposition of N 2 O 5 is first order and calculate the rate constant.

16. First-Order Reactions06 Half-Life: Time for reactant concentration to decrease by half its original value.

17. Second-Order Reactions01 Second-Order Reaction: A  Products A + B  Products Rate = k[A] 2 Rate = k[A][B] These can then be integrated to give:

18. Second-Order Reactions02 Half-Life: Time for reactant concentration to decrease by half its original value.

19. Second-Order Reactions03 Iodine atoms combine to form molecular iodine in the gas phase. I (g) + I (g)  I 2(g) This reaction follows second-order kinetics and k = 7.0 x 10 –1 M –1 s –1 at 23°C. (a) If the initial concentration of I was 0.086 M, calculate the concentration after 2.0 min. (b) Calculate the half-life of the reaction if the initial concentration of I is 0.60 M and if it is 0.42 M.

20. Reaction Mechanisms01 A reaction mechanism is a sequence of molecular events, or reaction steps, that defines the pathway from reactants to products.

21. Reaction Mechanisms02 Single steps in a mechanism are called elementary steps (reactions). An elementary step describes the behavior of individual molecules. An overall reaction describes the reaction stoichiometry.

22. Reaction Mechanisms03 NO 2 (g) + CO(g)  NO(g) + CO 2 (g)Overall NO 2 (g) + NO 2 (g)  NO(g) + NO 3 (g)Elementary NO 3 (g) + CO(g)  NO 2 (g) + CO 2 (g) Elementary The chemical equation for an elementary reaction is a description of an individual molecular event that involves the breaking and/or making of chemical bonds.

23. Reaction Mechanisms04 Molecularity: is the number of molecules (or atoms) on the reactant side of the chemical equation. Unimolecular: Single reactant molecule.

24. Reaction Mechanisms05 Bimolecular: Two reactant molecules. Termolecular: Three reactant molecules.

25. Reaction Mechanisms06 Determine the overall reaction, the reaction intermediates, and the molecularity of each individual elementary step.

26. Rate Laws and Reaction Mechanisms01 Rate law for an overall reaction must be determined experimentally. Rate law for elementary step follows from its molecularity.

27. Rate Laws and Reaction Mechanisms02 The rate law of each elementary step follows its molecularity. The overall reaction is a sequence of elementary steps called the reaction mechanism. Therefore, the experimentally observed rate law for an overall reaction must depend on the reaction mechanism.

28. Rate Laws and Reaction Mechanisms03 The slowest elementary step in a multistep reaction is called the rate-determining step. The overall reaction cannot occur faster than the speed of the rate-determining step. The rate of the overall reaction is therefore determined by the rate of the rate-determining step.

29. Rate Laws and Reaction Mechanisms04

30. Rate Laws and Reaction Mechanisms05 The following reaction has a second-order rate law: H 2 (g) + 2 ICl(g)  I 2 (g) + 2 HCl(g) Rate = k[H 2 ][ICl] Devise a possible mechanism. The following substitution reaction has a first-order rate law: Co(CN) 5 (H 2 O) 2– (aq) + I –  Co(CN) 5 I 3– (aq) + H 2 O(l) Rate = k[Co(CN) 5 (H 2 O) 2– ] Suggest a mechanism in accord with the rate law.

31. The Arrhenius Equation01 Collision Theory: A bimolecular reaction occurs when two correctly oriented molecules collide with sufficient energy. Activation Energy (E a ): The potential energy barrier that must be surmounted before reactants can be converted to products.

32. The Arrhenius Equation02

33. The Arrhenius Equation03

34. The Arrhenius Equation04 This relationship is summarized by the Arrhenius equation. Taking logs and rearranging, we get: lnk  E a R     1 T      A k  Ae  E a RT      

35. The Arrhenius Equation05 Temp (°C) k (M -1 s -1 ) 2833.52e-7 3563.02e5 3932.19e-4 4271.16e-3 5083.95e-2

36. The Arrhenius Equation07 The second-order rate constant for the decomposition of nitrous oxide (N 2 O) into nitrogen molecule and oxygen atom has been measured at different temperatures: Determine graphically the activation energy for the reaction.

37. The Arrhenius Equation09 A simpler way to use this is by comparing the rate constant at just two temperatures: If the rate of a reaction doubles by increasing the temperature by 10 ° C from 298.2 K to 308.2 K, what is the activation energy of the reaction?

38. A catalyst is a substance that increases the rate of a reaction without being consumed in the reaction. Catalysis01

39. Catalysis02 The relative rates of the reaction A + B  AB in vessels a–d are 1:2:1:2. Red = A, blue = B, yellow = third substance C. (a) What is the order of reaction in A, B, and C? (b) Write the rate law. (c) Write a mechanism that agrees with the rate law. (d) Why doesn’t C appear in the overall reaction?

40. Catalysis03 Homogeneous Catalyst: Exists in the same phase as the reactants. Heterogeneous Catalyst: Exists in different phase to the reactants.

41. Catalysis04 Catalytic Hydrogenation:

42. Catalysis05