Dr. Paul Charlesworth Michigan Technological University Dr. Paul Charlesworth Michigan Technological University C h a p t e rC h a p t e r C h a p t e rC h a p t e r 12 Chemical Kinetics Chemistry 4th Edition McMurry/Fay Chemistry 4th Edition McMurry/Fay

Prentice Hall ©2004 Chapter 12Slide 2 Reaction Rates01 Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant  Products aA  bB 

Prentice Hall ©2004 Chapter 12Slide 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)

Prentice Hall ©2004 Chapter 12Slide 4 Reaction Rates03

Prentice Hall ©2004 Chapter 12Slide 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

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 7 Rate Law & Reaction Order03 Determination by inspection : aA + bB  cC + dD Rate = R = k[A] x [B] y Use initial rates (t = 0)

Prentice Hall ©2004 Chapter 12Slide 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

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 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 ]

Prentice Hall ©2004 Chapter 12Slide 12 First-Order Reactions01 First Order: Reaction rate depends on the reactant concentration raised to first power. Rate = k[A]

Prentice Hall ©2004 Chapter 12Slide 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:

Prentice Hall ©2004 Chapter 12Slide 14 First-Order Reactions03 Identifying First-Order Reactions:

Prentice Hall ©2004 Chapter 12Slide 15 First-Order Reactions04 Show that the decomposition of N 2 O 5 is first order and calculate the rate constant.

Prentice Hall ©2004 Chapter 12Slide 16 First-Order Reactions06 Half-Life: Time for reactant concentration to decrease by half its original value.

Prentice Hall ©2004 Chapter 12Slide 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:

Prentice Hall ©2004 Chapter 12Slide 18 Second-Order Reactions02 Half-Life: Time for reactant concentration to decrease by half its original value.

Prentice Hall ©2004 Chapter 12Slide 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 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.

Prentice Hall ©2004 Chapter 12Slide 20 Reaction Mechanisms01 A reaction mechanism is a sequence of molecular events, or reaction steps, that defines the pathway from reactants to products.

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 23 Reaction Mechanisms04 Molecularity: is the number of molecules (or atoms) on the reactant side of the chemical equation. Unimolecular: Single reactant molecule.

Prentice Hall ©2004 Chapter 12Slide 24 Reaction Mechanisms05 Bimolecular: Two reactant molecules. Termolecular: Three reactant molecules.

Prentice Hall ©2004 Chapter 12Slide 25 Reaction Mechanisms06 Determine the overall reaction, the reaction intermediates, and the molecularity of each individual elementary step.

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 29 Rate Laws and Reaction Mechanisms04

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 32 The Arrhenius Equation02

Prentice Hall ©2004 Chapter 12Slide 33 The Arrhenius Equation03

Prentice Hall ©2004 Chapter 12Slide 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      

Prentice Hall ©2004 Chapter 12Slide 35 The Arrhenius Equation05 Temp (°C) k (M -1 s -1 ) e e e e e-2

Prentice Hall ©2004 Chapter 12Slide 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.

Prentice Hall ©2004 Chapter 12Slide 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 K to K, what is the activation energy of the reaction?

Prentice Hall ©2004 Chapter 12Slide 38 Catalysis01

Prentice Hall ©2004 Chapter 12Slide 39 A catalyst is a substance that increases the rate of a reaction without being consumed in the reaction. Catalysis01

Prentice Hall ©2004 Chapter 12Slide 40 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?

Prentice Hall ©2004 Chapter 12Slide 41 Catalysis03 Homogeneous Catalyst: Exists in the same phase as the reactants. Heterogeneous Catalyst: Exists in different phase to the reactants.

Prentice Hall ©2004 Chapter 12Slide 42 Catalysis04 Catalytic Hydrogenation:

Prentice Hall ©2004 Chapter 12Slide 43 Catalysis05