Rates of Chemical Reactions

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1 Rates of Chemical Reactions Jim Birk 12-1

2 Questions for Consideration 1. What conditions affect reaction rates? 2. How do molecular collisions explain chemical reactions? 3. How do concentration, temperature, and catalysts affect molecular collisions and reaction rates? 12-2

3 Outline 1. Reaction Rates definition 2. Collision Theory 3. Conditions That Affect Reaction Rates concentration, temperature, catalysis, surface area 12-3

4 Reaction Rates

5 Reaction Rates Reaction rate is a measure of how fast a reaction occurs. Some reactions are inherently fast and some are slow: 12-5

6 Reaction Rates How do we measure rates in our everyday lives? How do we measure rates of chemical reactions? 12-6

7 Reaction Rates Expressing the Reaction Rate reaction rate - changes in the concentrations of reactants or products per unit time reactant concentrations decrease while product concentrations increase for A B change in concentration of A rate of reaction = - = - change in time conc A 2 -conc A 1 t 2 -t 1 - (conc A) t

8 Reaction Rates Concentration of O 3 at Various Time in its Reaction with C 2 H 4 at 303K C 2 H 4 (g) + O 3 (g) C 2 H 4 O(g) + O 2 (g) Time (s) Concentration of O 3 (mol/l) - (conc A) t x x x x x x x10-5

9 Reaction Rates The concentrations of O 3 vs. time during its reaction with C 2 H 4 C 2 H 4 (g) + O 3 (g) C 2 H 4 O(g) + O 2 (g) rate = - (conc A) t - [C 2 H 4 ] t = - [O 3 ] t

10 Reaction Rates Plots of [C 2 H 4 ] and [O 2 ] vs. time. Tools of the Laboratory

11 Reaction Rates A B - (conc A) t (conc B) t C 2 H 4 (g) + O 3 (g) C 2 H 4 O(g) + O 2 (g) - [C 2 H 4 ] t - [O 3 ] t [O 2 ] t [C 2 H 4 O] t 12-11

12 Reaction Rates H 2 + I 2 2HI - [H 2 ] t - [I 2 ] t 1 [HI] 2 t 12-12

13 Reaction Rates In general, for the reaction aa + bb cc + dd rate = 1 [A] - = - a t 1 b [B] t = + 1 c [C] t = + 1 d [D] t The numerical value of the rate depends upon the substance that serves as the reference. The rest is relative to the balanced chemical equation.

14 Sample Problem Because it has a nonpolluting product (water vapor), hydrogen gas is used for fuel aboard the space shuttle and may be used by Earth-bound engines in the near future. 2H 2 (g) + O 2 (g) 2H 2 O(g) (a) Express the rate in terms of changes in [H 2 ], [O 2 ], and [H 2 O] with time. (b) When [O 2 ] is decreasing at 0.23 mol/l*s, at what rate is [H 2 O] increasing? PLAN: Choose [O 2 ] as a point of reference since its coefficient is 1. For every molecule of O 2 which disappears, 2 molecules of H 2 disappear and 2 molecules of H 2 O appear, so [O 2 ] is disappearing at half the rate of change of H 2 and H 2 O. SOLUTION: (b) (a) - [O 2 ] = - t rate = [H 2 ] t 0.23mol/L*s = = - [O 2 ] t [H 2 O] t = [H 2 O] t [H ; 2 O] = 0.46mol/L*s t

15 Sample Problem How is the rate of disappearance of ozone related to the rate of appearance of oxygen in the following equation: 2O 3 (g) 3 O 2 (g)? If the rate of appearance of oxygen is 6.0 x 10-5 M/s at a particular instant, what is the value of the rate of disappearance of ozone at this same time? 12-15

16 Worksheet # Consider the reaction: 4PH 3 (g) P 4 (g) + 6 H 2 (g) If, in a certain experiment, over a specific time period, mol PH 3 is consumed in a 2.0 L container each second of reaction, what are the rates of production of P 4 and H 2 in this experiment? 2. The decomposition of N 2 O5 proceeds according to the equation: 2N 2 O 5 4NO 2 + O 2 If the rate of decomposition of N 2 O 5 at a particular instant in a reaction vessel is 4.2 x 10-7 M/s, what is the rate of appearance of a) NO 2 b) O

17 Worksheet # 10-1: Answers 1. Consider the reaction: 4PH 3 (g) P 4 (g) + 6 H 2 (g) If, in a certain experiment, over a specific time period, mol PH 3 is consumed in a 2.0 L container each second of reaction, what are the rates of production of P 4 and H 2 in this experiment? P4/ t = M/sec H2/ t = M/sec 2. The decomposition of N 2 O5 proceeds according to the equation: 2N 2 O 5 4NO 2 + O 2 If the rate of decomposition of N 2 O 5 at a particular instant in a reaction vessel is 4.2 x 10-7 M/s, what is the rate of appearance of a) NO x 10-7 M/s b) O x 10-7 M/s 12-17

18 Collision Theory How do you think reactants lead to products? 12-18

19 Collision Theory In order for a reaction to occur, reactant molecules must collide with proper orientation with enough energy Only a small fraction of the collisions that do occur meet these requirements

20 Collision Theory 12-20

21 Collision Theory E a Chemical Equations: Kinetics 21

22 Activation Energy In order for reactants to convert to products, an energy barrier called the activation energy, E a, must be overcome. Collisions that have the proper orientation and have at least the minimum E a can convert to products

23 Activation Energy Reactants must overcome an energy barrier before they can change to products! 12-23

24 Activation Energy Energy is required to break bonds in reactants before the reactants can be converted into products The minimum amount of energy needed to overcome the energy barrier is called the activation energy, E a Reactions with large activation energies tend to be slow because a relatively small fraction of reactants have sufficient energy for an effective collision Reactions with small activation energies tend to be fast because a large fraction of reactants have sufficient energy for an effective collision 12-24

25 Activation Energy: Analogy Activation Energy, n. The useful quantity of energy available in one cup of coffee

26 Activation Energy Each reaction has its own reaction diagram, which shows the amount of energy required to form the activated complex as the reaction progresses

27 Activation Energy Activated complex Short-lived, unstable, high-energy chemical species that must be achieved before products can form Formed from reactant molecules that collide with the proper orientation and sufficient energy Actual structure is unknown 12-27

28 Sample Problem The following reaction is an endothermic reaction: 2NO 2 (g) 2NO(g) + O 2 (g) Draw an energy diagram that shows the relative energies of the reactants, products, and the activated complex. Label the diagram with molecular representations of reactants, products, and a possible structure for the activated complex

29 Sample Problem 2NO 2 (g) 2NO(g) + O 2 (g) 12-29

30 Proper Orientation Consider the following reaction that occurs in smog: NO(g) + O 3 (g) O 2 (g) + NO 2 (g) Which of the following collisions has a proper orientation? 12-30

31 Proper Orientation The importance of molecular orientation to an effective collision. NO + NO 3 2 NO 2

32 Proper Orientation Nature of the transition state in the reaction between CH 3 Br and OH -. CH 3 Br + OH - CH 3 OH + Br - transition state or activated complex

33 Proper Orientation Reaction energy diagram for the reaction of CH 3 Br and OH -.

34 Proper Orientation Reaction energy diagrams and possible transition states.

35 Potential Energy Sample Problem PROBLEM: A key reaction in the upper atmosphere is O 3 (g) + O(g) 2O 2 (g) The E a(fwd) is 19 kj, and the H rxn for the reaction is -392 kj. Draw a reaction energy diagram for this reaction, postulate a transition state, and calculate E a(rev). PLAN: Consider the relationships among the reactants, products and transition state. The reactants are at a higher energy level than the products and the transition state is slightly higher than the reactants. SOLUTION: E a = 19kJ O 3 +O transition state H rxn = -392kJ E a(rev) = ( )kJ = 411kJ Reaction progress 2O 2 O O O forming bond breaking bond O

36 Worksheet # Draw a rough sketch of the energy profile for each of the following cases: a) H = 10 kj/mol, Ea = 25 kj/mol b) H = - 10 kj/mol, Ea = 50 kj/mol c) H = - 50 kj/mol, Ea = 25 kj/mol 2. The activation energy for the reaction: H2 + I2 2HI is 167 kj/mol and the H for the reaction is +28 kj/mol. What is the activation energy for the decomposition of HI? 12-36

37 Worksheet # 10-2: Answers 1. Draw a rough sketch of the energy profile for each of the following cases: a) H = 10 kj/mol, Ea = 25 kj/mol b) H = - 10 kj/mol, Ea = 50 kj/mol c) H = - 50 kj/mol, Ea = 25 kj/mol a) b, c) 2. The activation energy for the reaction: H2 + I2 2HI Is 167 kj/mol and the H for the reaction is +28 kj/mol. What is the activation energy for the decomposition of HI? Ea = 139 kj/mol 12-37

38 Energy of activation Video of energy of activation: (bauer book: chapter 12) 12-38

39 Reaction Rate Conditions that affect reaction rate: Temperature Higher temperatures generally cause reactions to occur faster. Reactant concentration Increasing the concentration of a reactant generally increases the reaction rate. Surface area Increasing the surface area increases the reaction rate if the reactant is a solid. Presence of a catalyst Adding a catalyst increases the rate of the reaction

40 Effect of Concentration Increasing the concentration of reactants or the reaction temperature increases reaction rate by increasing the number of effective collisions

$collisions by increasing the total number of collisions (fraction of collisions that are effective remains the same).$

41 Effect of Concentration Increasing the concentration of one or more reactants increases the number of effective collisions by increasing the total number of collisions (fraction of collisions that are effective remains the same)

42 Effect of Concentration Changing the concentration of a reactant can change the reaction rate: Figure

43 Effect of Concentration How do you express the effect of concentration of a reactant on reaction rate? 12-43

44 Effect of Concentration In math a α x 0 a α x 1 a α x 2 zero order, first order, second order 12-44

45 Effect of Concentration In chemistry rate α x 0 rate α x 1 rate α x 2 Thus, for A B rate α [A] 0 rate α [A] 1 rate α [A] 2 zero order, first order, second order 12-45

46 Effect of Concentration Integrated Rate Laws zero order rate equation rate = - [A] t = k [A] 0 [A] t - [A] 0 = - kt 12-46

47 Effect of Concentration first order rate equation rate = - [A] t = k [A] ln [A] t [A] o = - kt ln [A] t = -kt + ln [A] o

48 Effect of Concentration second order rate equation rate = - [A] t = k [A] = kt [A] t [A] = kt + [A] t [A]

49 Effect of Concentration Units of the Rate Constant k for Several Overall Reaction Orders Overall Reaction Order Units of k (t in seconds) 0 mol/l*s (or mol L -1 s -1 ) 1 1/s (or s -1 ) 2 L/mol*s (or L mol -1 s -1 ) 3 L 2 / mol 2 *s (or L 2 mol -2 s -1 )

50 Effect of Concentration However, the order of a reaction with respect to a particular reactant cannot be determined from the balanced chemical reaction. They can only be obtained from experiments

51 Effect of Concentration The reaction A + 2B products has the rate law, rate = k[a][b] 3. If the concentration of B is doubled while that of A is unchanged, by what factor will the rate of reaction increase? Answer:

52 Effect of Concentration The reaction A + 2B products was found to have the rate law, rate = k[a] [B] 2. Predict by what factor the rate of reaction will increase when the concentration of A is doubled and the concentration of B is also doubled. Answer:

53 Effect of Concentration At 25 C the rate constant for the first-order decomposition of a pesticide solution is min 1. If the starting concentration of pesticide is M, what concentration will remain after 62.0 min at 25 C? Answer: M 12-53

54 Effect of Concentration It takes 42.0 min for the concentration of a reactant in a first-order reaction to drop from 0.45 M to 0.32 M at 25 C. How long will it take for the reaction to be 90% complete? Answer: 284 min 12-54

55 Effect of Concentration Sucrose, C 12 H 22 O 11, reacts slowly with water in the presence of an acid to form two other sugars, glucose and fructose, both of which have the same molecular formulas, but different structures. C 12 H 22 O 11 + H 2 O C 6 H 12 O 6 (glucose) + C 6 H 12 O 6 (fructose) The reaction is first order and has a rate constant of /s at 35 C when the H+ concentration is 0.10 M. Suppose that the initial concentration of sucrose in the solution is 0.40 M. a. What will the sucrose concentration be after 2.0 hours? b. How many minutes will it take for the sucrose concentration to drop to 0.30 M? Answer: a M b. 77 min 12-55

56 Sample Problem At C, cyclobutane (C 4 H 8 ) decomposes in a first-order reaction, with the very high rate constant of 87s -1, to two molecules of ethylene (C 2 H 4 ). (a) If the initial C 4 H 8 concentration is 2.00M, what is the concentration after s? (b) What fraction of C 4 H 8 has decomposed in this time? PLAN: SOLUTION: Find the [C 4 H 8 ] at time, t, using the integrated rate law for a 1st order reaction. Once that value is found, divide the amount decomposed by the initial concentration. (a) ln [C 4H 8 ] 0 [C 4 H 8 ] t = kt ; ln 2.00 [C 4 H 8 ] = (87s -1 )(0.010s) [C 4 H 8 ] = 0.83mol/L (b) [C 4 H 8 ] 0 - [C 4 H 8 ] t [C 4 H 8 ] 0 = 2.00M M 2.00M = 0.58

57 Worksheet # At 700 K, the rate constant for the following reaction is min 1. How many minutes are required for 20% of a sample of cyclopropane to isomerize to propene? C 3 H 6 (cyclopropane) C 3 H 6 (propene) 2. A certain first-order reaction A B is 25% complete in 42 min at 25 C. What is its rate constant? 3. A second - order reaction has a rate constant of s 1. The time required for the reaction to be 75.0% complete is? 12-57

58 Worksheet # 10 3: Answers 1. At 700 K, the rate constant for the following reaction is min 1. How many minutes are required for 20% of a sample of cyclopropane to isomerize to propene? Answer: 360 min C 3 H 6 (cyclopropane) C 3 H 6 (propene) 2. A certain first-order reaction A B is 25% complete in 42 min at 25 C. What is its rate constant? Answer: min 1 3. A second-order reaction has a rate constant of s 1. The time required for the reaction to be 75.0% complete is? Answer: 1000 s 12-58

59 Effect of Concentration A plot of [N 2 O 5 ] vs. time for three half-lives. for a first-order process t 1/2 = ln 2 k = k

60 Effect of Concentration Half- life time required for the concentration of a substance to be reduced to one-half of its original value 12-60

61 Effect of Concentration An Overview of Zero-Order, First-Order, and Simple Second-Order Reactions Zero Order First Order Second Order Rate law rate = k rate = k [A] rate = k [A] 2 Half-life [A] 0 /2k ln 2/k 1/k [A]

62 Effect of Concentration A certain first-order reaction A B is 25% complete in 42 min at 25 C. What is the half-life of the reaction? Answer: 101 min 12-62

63 Sample Problem Cyclopropane is the smallest cyclic hydrocarbon. Because its 60 0 bond angles allow poor orbital overlap, its bonds are weak. As a result, it is thermally unstable and rearranges to propene at C via the following first-order reaction: SOLUTION: CH 2 H 2 C CH 2 (g) H 3 C CH CH 2 (g) The rate constant is 9.2s -1, (a) What is the half-life of the reaction? (b) How long does it take for the concentration of cyclopropane to reach one-quarter of the initial value? PLAN: Use the half-life equation, t 1/2 =, to find the half-life. k One-quarter of the initial value means two half-lives have passed. (a) t 1/2 = 0.693/9.2s -1 = 0.075s (b) 2 t 1/2 = 2(0.075s) = 0.150s

64 Sample Problem A certain first order reaction has a half life of 20.0 minutes. a. Calculate the rate constant for this reaction. b. How much time is required for this reaction to be 75% complete? Answers: a) k = 0.693/t ½ = 0.693/20 = /min b) time = 40.0 minutes 12-64

65 Sample Problem The isomerization of cyclopropane to form propene H 2 C CH 2 \ / CH 3 CH = CH 2 CH 2 is a first-order reaction. At 760 K, 15% of a sample of cyclopropane changes to propene in 6.8 min. What is the half-life of cyclopropane at 760 K? Answer: 29 min 12-65

66 Effect of Concentration An Overview of Zero-Order, First-Order, and Simple Second-Order Reactions Zero Order First Order Second Order Rate law rate = k rate = k [A] rate = k [A] 2 Units for k mol/l*s 1/s L/mol*s Integrated rate law in straight-line form Plot for straight line Slope, y-intercept Half-life [A] t = ln[a] t = 1/[A] t = k t + [A] 0 -k t + ln[a] 0 k t + 1/[A] 0 [A] t vs. t ln[a] t vs. t 1/[A] t = t k, [A] 0 -k, ln[a] 0 k, 1/[A] 0 [A] 0 /2k ln 2/k 1/k [A] 0

67 Worksheet # The rate constant for the first order reaction A B + C is k = 3.3 x 10 2 min 1 at 57 K. What is the half-life for this reaction at 57 K? 2. The half-life of the zero order reactiona B is 0.56 minutes. If the initial concentration of A is 3.4 M, what is the rate constant? 3. The rate constant for the second order reaction 2NO2 N2O4 is 2.79 L/mol min at 48 oc. If the initial concentration of NO2 is 1.05 M, what is the half-life? 4. The decomposition of dimethylether at 504 C is first order with a half-life of seconds. What fraction of an initial amount of dimethylether remains after seconds? 12-67

68 Worksheet # 10-4: Answers 1. The rate constant for the first order reaction A B + C is k = 3.3 x 10 2 min 1 at 57 K. What is the half-life for this reaction at 57 K? Answer: 21 min 2. The half-life of the zero order reactiona B is 0.56 minutes. If the initial concentration of A is 3.4 M, what is the rate constant? Answer: 3.04 mol/l min 3. The rate constant for the second order reaction 2NO2 N2O4 is 2.79 L/mol min at 48 oc. If the initial concentration of NO2 is 1.05 M, what is the half-life? Answer: 0.34 min 4. The decomposition of dimethylether at 504 C is first order with a halflife of seconds. What fraction of an initial amount of dimethylether remains after seconds? Answer: 1/

Chapter 13 Kinetics: Rates and Mechanisms of Chemical Reactions

Chapter 13 Kinetics: Rates and Mechanisms of Chemical Reactions 14.1 Focusing on Reaction Rate 14.2 Expressing the Reaction Rate 14.3 The Rate Law and Its Components 14.4 Integrated Rate Laws: Concentration