1. Ch 15 Rates of Chemical Reactions Chemical Kinetics is a study of the rates of chemical reactions. Part 1 macroscopic level what does reaction rate mean? how are reaction rates determined experimentally? how do factors like temp and conc influence rates? Part 2 microscopic level reaction mechanism detailed pathway taken by atoms and molecules in the reaction in order to control the reaction

2. Ch 15 Rates of Chemical Reactions The rate of a chemical reaction is the change of concentration of a substance (reactant) per unit time. The rate of a chemical reaction is the change of concentration of a substance (reactant) per unit time. Generally  conc reactant Generally  conc reactant  time  time Slope of the line changes When Conc is large, Time is small, When Conc is large, Time is small, When Conc is small, Time is long. When Conc is small, Time is long.

3. Ch 15 Rates of Chemical Reactions

4. Reaction Rate Terms Concentration in mol/L [ square brackets ] Concentration in mol/L [ square brackets ] Changes  X = X final - X initial Changes  X = X final - X initial Units for reaction rates mol / L. time Units for reaction rates mol / L. time Rate Expression for this reaction Rate Expression for this reaction 2 N 2 O 5 -> 4 NO 2 + O 2 2 N 2 O 5 -> 4 NO 2 + O 2 1  [N 2 O 5 ]    1  [NO 2 ]    [O 2 ] 1  [N 2 O 5 ]    1  [NO 2 ]    [O 2 ] 4  t 2  t  t 4  t 2  t  t

5. Ch 15 Rates of Chemical Reactions For a chemical reaction to occur, reactants must For a chemical reaction to occur, reactants must physically collide, physically collide, with sufficient energy, with sufficient energy, With appropriate geometry With appropriate geometry For the reaction to occur. Rates are dependent on these variables.

6. Ch 15 Rates of Chemical Reactions Factors that affect the speed of a reaction Factors that affect the speed of a reaction Concentration - greater concentration of reactions results in the faster rate. Concentration - greater concentration of reactions results in the faster rate. Temperature - for endothermic reactions, faster moving molecules react at a faster rate. Temperature - for endothermic reactions, faster moving molecules react at a faster rate. Catalyst - substances that accelerate a chemical reaction, but but are not transformed by the reaction. Catalyst - substances that accelerate a chemical reaction, but but are not transformed by the reaction.

7. Effect of Concentration on Reaction Rate The rate of a reaction is proportional to the concentration of reactants The rate of a reaction is proportional to the concentration of reactants aA + bB -> xX aA + bB -> xX Rate = k [A] m [B] n Rate = k [A] m [B] n k is the proportionality constant called k is the proportionality constant called the rate constant the rate constant [A] and [B] are the concentrations of [A] and [B] are the concentrations of A and B A and B m and n are determined experimentally

8. Effect of Concentration on Reaction Rate Rate = k [A] m [B] n Rate = k [A] m [B] n The order of a reactant is the exponent m or n The order of a reactant is the exponent m or n The order of a reaction is the sum of the exponents The order of a reaction is the sum of the exponents If the exponent is 1, doubling the concentration, doubles the rate If the exponent is 1, doubling the concentration, doubles the rate If the exponent is 2, doubling the concentration, quadruples the rate. If the exponent is 2, doubling the concentration, quadruples the rate. If the exponent is 0, doubling the concentration has no effect on the rate. If the exponent is 0, doubling the concentration has no effect on the rate.

9. Effect of Concentration on Reaction Rate Rate = k [A] m [B] n Rate = k [A] m [B] n The rate constant is k The rate constant is k k is a proportionality constant that relates rate and concentration at a given temperature. k is a proportionality constant that relates rate and concentration at a given temperature.

10. Effect of Concentration on Reaction Rate

11. Determining the Rate Equation for a Reaction. Rate = k [CO] m [NO 2 ] n Rate = k [CO] m [NO 2 ] n

12. Determining the Rate Equation for a Reaction. Rate = k [NO] m [O 2 ] n Rate = k [NO] m [O 2 ] n

13. Determining the Rate Equation for a Reaction.

14. Concentration-Time Relationships: Integrated Rate Law ln [R] t = - kt [R] o [R] o

15. Concentration-Time Relationships: Integrated Rate Law Second-Order Reactions suppose R -> is second order then Second-Order Reactions suppose R -> is second order then -  [R] = k[R] 2 -  [R] = k[R] 2  t  t 1 _ 1 = kt 1 _ 1 = kt [R] t [R] o [R] t [R] o

16. Concentration-Time Relationships: Integrated Rate Law 1 _ 1 = kt 1 _ 1 = kt [R] t [R] o [R] t [R] o

17. Concentration-Time Relationships: Integrated Rate Law 1 _ 1 = kt 1 _ 1 = kt [R] t [R] o [R] t [R] o

18. Concentration-Time Relationships: Integrated Rate Law Zero-Order Reactions suppose R -> is zero order then Zero-Order Reactions suppose R -> is zero order then -  [R] = k[R] 0 -  [R] = k[R] 0  t  t [R] o - [R] t = kt [R] o - [R] t = kt

19. Concentration-Time Relationships: Graphical Analysis Method [R] o - [R] t = kt [R] o - [R] t = kt

20. Concentration-Time Relationships: Graphical Analysis Method ln [R] t = - kt [R] o [R] o

21. Concentration-Time Relationships: Graphical Analysis Method 1 _ 1 = kt 1 _ 1 = kt [R] t [R] o [R] t [R] o

22. Concentration-Time Relationships: Graphical Analysis Method

23. Concentration-Time Relationships: Integrated Rate Law

25. Concentration-Time Relationships: Graphical Analysis Half-Life and First-Order Reactions Half-Life and First-Order Reactions

26. Concentration-Time Relationships: Integrated Rate Law Half-Life and First-Order Reactions Half-Life and First-Order Reactions

27. Concentration-Time Relationships: Integrated Rate Law Half-Life and First-Order Reactions Half-Life and First-Order Reactions ln [R] t = - kt [R] o

28. Concentration-Time Relationships: ln [R] t = - kt [R] o [R] o

29. Particulate View of Reaction Rates Collision Theory The reacting molecules must collide with one another The reacting molecules must collide with one another The reacting molecules must collide with one another with sufficient energy The reacting molecules must collide with one another with sufficient energy The reacting molecules must collide in an orientation that can lead to rearrangement of the atoms. The reacting molecules must collide in an orientation that can lead to rearrangement of the atoms.

30. Particulate View of Reaction Rates Collision Theory The reacting molecules must collide with one another The reacting molecules must collide with one another The rate of reactions is primarily related to the number of collisions which is related to the concentration of molecules. The rate of reactions is primarily related to the number of collisions which is related to the concentration of molecules. The rate of a reaction is related to the concentration of each reactant.

31. Collision Theory: Concentration and Reaction Rate. The rate of molecular reactions is related to the number of collisions Which is related to the concentration. Collisions directly related to Concentrations

32. Collision Theory: Temperature, Reaction Rate and Activation Energy Recall the Boltzman distribution of molecular energies Recall the Boltzman distribution of molecular energies The reacting molecules must collide with one another with sufficient energy The reacting molecules must collide with one another with sufficient energy Activation Energy, E a, minimum energy required for molecules to react. Activation Energy, E a, minimum energy required for molecules to react.

33. Collision Theory: Temperature, Reaction Rate and Activation Energy Increasing the Temperature Increases the number of molecules with sufficient energy to react. Increasing the Temperature Increases the number of molecules with sufficient energy to react.

34. Temperature, Reaction Rate and Activation Energy The reacting molecules must collide in an orientation that can lead to rearrangement of the atoms. A graph of this is described as the reaction pathway. Reactant molecules approach each other with Kinetic energy Kinetic energy decreases, potential increases Kinetic energy decreases, potential increases Reactant Molecules collide and bonds rearrange Highest potential energy Highest potential energy Transition state Transition state Activated complex Activated complex Product molecules convert potential energy to Kinetic energy as they move apart from each other.

35. Temperature, Reaction Rate and Activation Energy

37. Reaction Pathway diagrams

39. Example: The following are the data from an experiment to assess the disinfection of wastewater with a given dose of chlorine. Assuming first-order kinetics, determine the rate constant. Time, min % E. coli remaining 0100 1070 2021 306.3 600.6 Time, min % E. coli remaining 0100 1070 2021 306.3 600.6

41. Effect of temperature on biological reaction rate The effect of temperature on reaction rate is given by the Arrhenius equation: E A = activated energy, J/mol R = Universal gas constant 8.31J/mol-K T = Temperature in Kelvin = ( o C + 273) A = Constant (not significantly affected by small temp. change

42. Arrhenius Equation Arrhenius Equation Describes all variables Arrhenius Equation Describes all variables Describes the dependence of reaction rates on energy, frequency of collisions, temperature and collision geometry Describes the dependence of reaction rates on energy, frequency of collisions, temperature and collision geometry rate constant = k = Ae -Ea/RT rate constant = k = Ae -Ea/RT Where A represents the frequency factor and The rest of the equation represents the fraction of the molecules with minimum energy for collision R = 8.31 x 10 -3 kJ/mol. K

43. Reaction Rates: Arrhenius Equation rate constant = k = Ae -Ea/RT rate constant = k = Ae -Ea/RT R = 8.31 x 10 -3 kJ/mol. K

44. Arrhenius Equation and Activation Energy Graph the data above and calculate The slope. The slope = - E a / R

45. Arrhenius Equation and Activation Energy

46. Effect of Catalysts on Reaction Rate Substances that speed up the rate of a chemical reaction by lowering the reaction barrier (changing the mechanism) Substances that speed up the rate of a chemical reaction by lowering the reaction barrier (changing the mechanism) Heterogeneous catalysts (solid in solution) Heterogeneous catalysts (solid in solution) Homogeneous catalysts -same phase Homogeneous catalysts -same phase

47. Temperature, Reaction Rate and Activation Energy A catalyst effects the rate of reaction by impacting collision geometry http://www.800mainstreet.com/7/0007- 005-rea-t-cat.html http://www.800mainstreet.com/7/0007- 005-rea-t-cat.html

48. Reaction Mechanism Most reactions are bimolecular Most reactions are bimolecular An intermediate molecule is produced and then used in the subsequent reaction(s) An intermediate molecule is produced and then used in the subsequent reaction(s) Each elementary step has its own E a and k which combine to give the overall reaction Each elementary step has its own E a and k which combine to give the overall reaction

49. Reaction Mechanism Mechanisms are postulated from experimental data. Mechanisms are postulated from experimental data. Molecularity unimolecular, bimolecular and termolecular Molecularity unimolecular, bimolecular and termolecular

50. Reaction Mechanism, Molecularity, and Rxn Rate

51. The molecularity of an elementary step and its order are the same The molecularity of an elementary step and its order are the same The rate is determined by the slowest step The rate is determined by the slowest step The rate law included all reactions up to the rate determining step The rate law included all reactions up to the rate determining step

52. Reaction Mechanism, Molecularity, and Rxn Rate The rate is determined by the slowest step The rate is determined by the slowest step Step 1 A + B -> X + M k 1 slow rate E a is large Step 1 A + B -> X + M k 1 slow rate E a is large Step 2 M + A -> Y k 2 fast rate E a is small Step 2 M + A -> Y k 2 fast rate E a is small Overall Reaction 2A + B -> X + Y Overall Reaction 2A + B -> X + Y Rate = k 1 [A] [B] Rate = k 1 [A] [B]

53. Reaction Mechanism, Molecularity, and Rxn Rate

54. The first bimolecular step is the rate-determining step, the Rate equation is Rate = k [NO 2 ] [F 2 ] F is an intermediate, produced in # 1 and used in #2

55. Reaction Mechanism, Molecularity, and Rxn Rate If this were bimolecular, this would be The rate equation

56. Reaction Mechanism, Molecularity, and Rxn Rate

58. Reaction Mechanism and Reaction Rate Equations Experiments determine effect of conc on rate Experiments determine effect of conc on rate Proposed reaction mechanism is used to derive a rate equation (no intermediates) Proposed reaction mechanism is used to derive a rate equation (no intermediates) A rate equation can only be based on elementary steps (not over all rate equations) A rate equation can only be based on elementary steps (not over all rate equations) More than one mechanism can be proposed. More than one mechanism can be proposed.