Chemical Kinetics

1. Chemical Kinetics

2. Reaction Rates 01 • Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant  Products aA  bB

3. Reaction Rates 02 • Consider the decomposition of N2O5 to give NO2 and O2: 2 N2O5(g) 4 NO2(g) + O2(g)

4. Reaction Rates 03

5. Rate Law & Reaction Order 01 • 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 Order 02 • Reaction Order: The sum of the powers to which all reactant concentrations appearing in the rate law are raised. • Reaction order is determined experimentally: • By inspection. • From the slope of a log(rate) vs. log[A] plot.

7. Rate Law & Reaction Order 03 • Determination by inspection: aA + bB cC + dD • Rate = R = k[A]x[B]y Use initial rates (t = 0)

8. Rate Law & Reaction Order 04 • 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. E x p e ri m e n t [ NO ] [ H ] I n iti a l Ra t e (M/ s ) 2 – 3 – 3 – 5 1 5 . 0 x 1 0 2 . 0 x 1 0 1 . 3 x 1 0 – 3 – 3 – 5 2 1 0 . 0 x 1 0 2 . 0 x 1 0 5 . 0 x 1 0 – 3 – 3 – 5 3 1 0 . 0 x 1 0 4 . 0 x 1 0 1 0 . 0 x 1 0 Rate Law & Reaction Order 05 • The reaction of nitric oxide with hydrogen at 1280°C is: 2 NO(g) + 2 H2(g) N2(g) + 2 H2O(g) • From the following data determine the rate law and rate constant.

10. - E x p e ri m e n t [I-] I n iti a l Ra t e (M/ s ) [S O ] 2 2 8 - 4 1 0 . 0 8 0 0 . 0 3 4 2 . 2 x 1 0 - 4 2 0 . 0 8 0 0 . 0 1 7 1 . 1 x 1 0 - 4 3 0 . 1 6 0 . 0 1 7 2 . 2 x 1 0 Rate Law & Reaction Order 06 • The reaction of peroxydisulfate ion (S2O82-) with iodide ion (I-) is: • S2O82-(aq) + 3 I-(aq) 2 SO42-(aq) + I3-(aq) • From the following data, determine the rate law and rate constant.

11. Rate Law & Reaction Order 07 • Rate Constant: A constant of proportionality between the reaction rate and the concentration of reactants.rate  [Br2]rate = k[Br2]

12. First-Order Reactions 01 • First Order: Reaction rate depends on the reactant concentration raised to first power. Rate = k[A]

13. First-Order Reactions 02 • 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 Reactions 03 • Identifying First-Order Reactions:

15. First-Order Reactions 04 • Show that the decomposition of N2O5 is first order and calculate the rate constant.

16. First-Order Reactions 06 • Half-Life:Time for reactant concentration to decrease by halfits original value.

17. Second-Order Reactions 01 • 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 Reactions 02 • Half-Life:Time for reactant concentration to decrease by halfits original value.

19. Second-Order Reactions 03 • Iodine atoms combine to form molecular iodine in the gas phase.I(g) + I(g) I2(g) • This reaction follows second-order kinetics and k = 7.0 x 10–1 M–1s–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 Mechanisms 01 • A reaction mechanism is a sequence of molecular events, or reaction steps, that defines the pathway from reactants to products.

21. Reaction Mechanisms 02 • 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 Mechanisms 03 • NO2(g) + CO(g)  NO(g) + CO2(g) Overall • NO2(g) + NO2(g) NO(g) + NO3(g) Elementary • NO3(g) + CO(g) NO2(g) + CO2(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 Mechanisms 04 • Molecularity: is the number of molecules (or atoms) on the reactant side of the chemical equation. • Unimolecular: Single reactant molecule.

24. Reaction Mechanisms 05 • Bimolecular: Two reactant molecules. • Termolecular: Three reactant molecules.

25. Reaction Mechanisms 06 • Determine the overall reaction, the reaction intermediates, and the molecularity of each individual elementary step.

26. Rate Laws and Reaction Mechanisms 01 • Rate law for an overall reactionmust be determined experimentally. • Rate law for elementary stepfollows from its molecularity.

27. Rate Laws and Reaction Mechanisms 02 • Therate lawof 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 thereaction mechanism.

28. Rate Laws and Reaction Mechanisms 03 • Theslowest elementary stepin a multistep reaction is called the rate-determining step. • The overall reaction cannot occur faster than the speed of the rate-determining step. • Therate of the overall reaction is therefore determined by the rate of the rate-determining step.

29. Rate Laws and Reaction Mechanisms 04

30. Rate Laws and Reaction Mechanisms 05 • The following reaction has a second-order rate law: • H2(g) + 2 ICl(g)  I2(g) + 2 HCl(g) Rate = k[H2][ICl] • Devise a possible mechanism. • The following substitution reaction has a first-order rate law: • Co(CN)5(H2O)2–(aq) + I– Co(CN)5I3–(aq) + H2O(l) Rate = k[Co(CN)5(H2O)2–] • Suggest a mechanism in accord with the rate law.

31. The Arrhenius Equation 01 • Collision Theory:A bimolecular reaction occurs when two correctly oriented molecules collide with sufficient energy. • Activation Energy (Ea):The potential energy barrier that must be surmounted before reactants can be converted to products.

32. The Arrhenius Equation 02

33. The Arrhenius Equation 03

34. æ ö E - a ç ÷ k = RT Ae è ø æ æ ö ö E 1 ln k ln A = - + a è ø è ø R T The Arrhenius Equation 04 • This relationship is summarized by the Arrhenius equation. • Taking logs and rearranging, we get:

35. The Arrhenius Equation 05

36. - - 1 1 - - 1 1 t t ( ( ° ° C C ) ) k k (M (M s s ) ) - - 3 3 1 1 .8 .8 7 7 x x 1 1 0 0 6 6 0 0 0 0 0 0 .0 .0 1 1 1 1 3 3 6 6 5 5 0 0 0 0 .0 .0 5 5 6 6 9 9 7 7 0 0 0 0 0 0 .2 .2 4 4 4 4 7 7 5 5 0 0 The Arrhenius Equation 07 The second-order rate constant for the decomposition of nitrous oxide (N2O) into nitrogen molecule and oxygen atom has been measured at different temperatures:Determine graphicallythe activation energyfor the reaction. The second-order rate constant for the decomposition of nitrous oxide (N2O) into nitrogen molecule and oxygen atom has been measured at different temperatures:Determine graphicallythe activation energyfor the reaction.

37. The Arrhenius Equation 09 • 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. Catalysis 01 • A catalyst is a substance that increases the rate of a reaction without being consumed in the reaction.

39. Catalysis 02 • 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. Catalysis 03 • Homogeneous Catalyst: Exists in the same phase as the reactants. • Heterogeneous Catalyst: Exists in different phase to the reactants.

41. Catalysis 04 • Catalytic Hydrogenation:

42. Catalysis 05