Chapter 12 Chemical Kinetics Chapter 12 Table of Contents 12.1 12.2 12.3 12.4 12.5 12.6 12.7 Reaction Rates Rate Laws: An Introduction Determining the Form of the Rate Law The Integrated Rate Law Reaction Mechanisms A Model for Chemical Kinetics Catalysis Copyright © Cengage Learning. All rights reserved 2 Section 12.1 Reaction Rates Objectives • To define Chemical Kinetics • To define Reaction Rate and illustrate how it is determined • To illustrate that the Instantaneous Rate is calculated by determining the slope of the tangent line at a given point on a curve. Return to TOC Copyright © Cengage Learning. All rights reserved 3 Section 12.1 Reaction Rates Chemical Kinetics • Chemical Kinetics – the area of chemistry that studies the rate at which a chemical reaction takes place. • The following reaction is considered spontaneous (favorable) and will release energy: N2 (g) + 3H2 (g) 2NH3(g) + energy • However, the two gas reactants may coexist indefinitely under normal conditions. • Not so good if you are in the fertilizer business! Return to TOC Copyright © Cengage Learning. All rights reserved 4 Section 12.1 Reaction Rates Reaction Rate • Change in concentration of a reactant or product per unit time. Rate = = concentration of A at time t2 concentration of A at time t1 t2 t1 A t [A] means concentration of A in mol/L; A is the reactant or product being considered. Return to TOC Copyright © Cengage Learning. All rights reserved 5 Section 12.1 Reaction Rates The Decomposition of Nitrogen Dioxide 2NO2(g) 2NO(g) + O2(g) (@ 300OC) Return to TOC Copyright © Cengage Learning. All rights reserved 6 Section 12.1 Reaction Rates The Decomposition of Nitrogen Dioxide 2NO2 2 NO + O2 Rate = [NO2]/ t Slope! Average if you use the data points or instantaneous if you use the tangent line at a given point for a given time. Return to TOC Copyright © Cengage Learning. All rights reserved 7 Section 12.1 Reaction Rates Objectives Review • To define Chemical Kinetics • To define Reaction Rate and illustrate how it is determined using a slope calculation • To illustrate that the Instantaneous Rate is calculated by determining the slope of the tangent line at a given point on a curve. • Work Session: page 566 #7, 19, 21 Return to TOC Copyright © Cengage Learning. All rights reserved 8 Section 12.2 Atomic Rate Laws: Masses An Introduction Objectives • To define the Rate Law Equation and its variables • To determine the form (order) of the rate law experimentally Return to TOC Copyright © Cengage Learning. All rights reserved 9 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Law • The Rate Law shows how the rate depends on the [concentrations] of reactants . [Reactant] units of M 2NO2(g) → 2NO(g) + O2(g) Rate = k[NO2]n k = rate constant (coefficient of parabola or m if linear) [NO2] = Concentration of reactant (M = mol/L) n = order of the reactant (form) This form of the rate law allows you to model the continuous curve regardless of the order (exponent). Return to TOC Copyright © Cengage Learning. All rights reserved 10 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Law Rate = k[NO2]n • The concentrations of the products do not appear in the rate law because the reaction rate is being studied under conditions where the reverse reaction does not contribute to the overall rate. • 2NO2(g) 2NO(g) + O2(g) • The value of the exponent n must be determined by experiment; it cannot be written from the balanced equation. Return to TOC Copyright © Cengage Learning. All rights reserved 11 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Law Rate = k[NO2]n Rate = [NO2]/ t Return to TOC Copyright © Cengage Learning. All rights reserved 12 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Law Rate = k[NO2]n (How to Calculate n experimentally) • Experiment Initial [NO2] Initial Rate(mol/L*s) • 1 0.450 M 1.25 X 10-5 • 2 0.90 M 2.50 X 10-5 • Rate = k[NO2]n write the expression for both exp’ts the bigger value in the numerator…. • Rate 2 = k[0.9]n = 2.50 X 10-5 • Rate1 = k[0.45]n = 1.25 X 10-5 • Simplify and solve for n • [2]n = 2 Return to TOC Copyright © Cengage Learning. All rights reserved 13 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Law • • • • • • Rate 2 = k[0.9]n = 2.50 X 10-5 Rate1 = k[0.45]n = 1.25 X 10-5 Simplify and solve for n [2]n = 2 n = 1 or in other words, The rate law for this reaction is first order with respect to the reactant NO2. (Important to define) • 2NO2(g) 2NO(g) + O2(g) Return to TOC Copyright © Cengage Learning. All rights reserved 14 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Laws: A Summary • Experimental convenience usually dictates which type of rate law is determined experimentally. • Knowing the rate law for a reaction is important mainly because we can usually infer the individual steps involved in the reaction from the specific form of the rate law. We are usually looking for the slow step in a process. Return to TOC Copyright © Cengage Learning. All rights reserved 15 Section 12.2 Atomic Rate Laws: Masses An Introduction Objectives Review • To define the Rate Law Equation and its variables • To determine the form (order) of the rate law experimentally Return to TOC Copyright © Cengage Learning. All rights reserved 16 Section 12.3 The Mole Determining the Form of the Rate Law Objectives • To determine the overall reaction order of the rate law experimentally using data from several reactants Return to TOC Copyright © Cengage Learning. All rights reserved 17 Section 12.3 The Mole Determining the Form of the Rate Law Overall Reaction Order • The sum of the exponents in the reaction rate equation. aA + bB cC + …? Rate = k[A]n[B]m Overall reaction order = n + m k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B Copyright © Cengage Learning. All rights reserved Return to TOC 18 Section 12.3 The Mole Determining the Form of the Rate Law • Let’s use the following EXPERIMENTAL data to determine the order (form) for each reactant. • NH4+ + NO2- N2 + 2H2O • First, write the general rate law……Rate = ?? • Exp’t Initial Initial Initial Rate • [NH4+ ] [NO2- ] (mol/L*s) • 1 0.100 M 0.0050 M 1.35 X 10-7 • 2 0.100 M 0.010 M 2.70 X 10-7 • 3 0.200 M 0.010 M 5.40 X 10-7 • Remember the trick to find rate order = bigger numerator • For order w/respect to [NH4+ ], [other] must stay constant Return to TOC Copyright © Cengage Learning. All rights reserved 19 Section 12.3 The Mole Determining the Form of the Rate Law • • • • • • • • • • Overall Reaction Order Remember bigger numerator! NH4+ + NO2- N2 + 2H2O Exp’t Initial Initial [NH4+ ] [NO2- ] Initial Rate (mol/L*s) 1 0.100 M 0.0050 M 1.35 X 10-7 2 0.100 M 0.010 M 2.70 X 10-7 3 0.200 M 0.010 M 5.40 X 10-7 Rate 2 = k[0.100]n [0.010]m = 2.70 X 10-7 Rate1 = k[0.100]n [0.0050]m = 1.35 X 10-7 Simplify and solve for m Copyright © Cengage Learning. All rights reserved Return to TOC 20 Section 12.3 The Mole Determining the Form of the Rate Law • • • • • • • • • • NH4+ + NO2- N2 + 2H2O Exp’t Initial Initial [NH4+ ] [NO2- ] Initial Rate (mol/L*s) 1 0.100 M 0.0050 M 1.35 X 10-7 2 0.100 M 0.010 M 2.70 X 10-7 3 0.200 M 0.010 M 5.40 X 10-7 Rate 2 = k[0.100]n [0.010]m = 2.70 X 10-7 Rate1 = k[0.100]n [0.0050]m = 1.35 X 10-7 Simplify and solve for m [2]m = 2 The rate law for this reaction is first order in the reactant NO2-. What about the other reactant? Copyright © Cengage Learning. All rights reserved Return to TOC 21 Section 12.3 The Mole Determining the Form of the Rate Law • • • • • • • • • • • With respect to NH4+ (keep other [conc] same) NH4+ + NO2- N2 + 2H2O Exp’t Initial Initial Initial Rate [NH4+ ] [NO2- ] (mol/L*s) 1 0.100 M 0.0050 M 1.35 X 10-7 2 0.100 M 0.010 M 2.70 X 10-7 3 0.200 M 0.010 M 5.40 X 10-7 Rate 3 = k[0.200]n [0.010]m = 5.40 X 10-7 Rate2 = k[0.100]n [0.010]m = 2.70 X 10-7 Simplify and solve for n Also first order with respect to NH4+ Copyright © Cengage Learning. All rights reserved Return to TOC 22 Section 12.3 The Mole Determining the Form of the Rate Law Overall Reaction Order • The sum of the exponents in the reaction rate equation. aA + bB cC + …? Rate = k[A]n[B]m Overall reaction order = n + m m=1,n=1 Overall Reaction order =2 Copyright © Cengage Learning. All rights reserved Return to TOC 23 Section 12.3 The Mole Determining the Form of the Rate Law • Turn to page 567 and work on #25. Return to TOC Copyright © Cengage Learning. All rights reserved 24 Section 12.3 The Mole Determining the Form of the Rate Law Concept Check How do exponents (orders) in rate laws compare to coefficients in balanced equations? Why? Return to TOC Copyright © Cengage Learning. All rights reserved 25 Section 12.3 The Mole Determining the Form of the Rate Law Objectives Review • To determine the overall reaction order of the rate law experimentally using data from several reactants • Work Session: # 26, 27, 28 (just find the order) • CLICK to Slide 43 to skip Integrated Rate Law Return to TOC Copyright © Cengage Learning. All rights reserved 26 Section 12.4 The Integrated Rate Law Half-Life of Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 27 Section 12.4 The Integrated Rate Law First-Order • Rate = k[A] • Integrated: ln[A] = –kt + ln[A]o [A] = concentration of A at time t k = rate constant t = time [A]o = initial concentration of A Return to TOC Copyright © Cengage Learning. All rights reserved 28 Section 12.4 The Integrated Rate Law Plot of ln[N2O5] vs Time Return to TOC Copyright © Cengage Learning. All rights reserved 29 Section 12.4 The Integrated Rate Law First-Order • Half–Life: t1 2 0.693 = k k = rate constant • Half–life does not depend on the concentration of reactants. Return to TOC Copyright © Cengage Learning. All rights reserved 30 Section 12.4 The Integrated Rate Law Exercise A first order reaction is 35% complete at the end of 55 minutes. What is the value of k? k = 7.8 x 10–3 min–1 Return to TOC Copyright © Cengage Learning. All rights reserved 31 Section 12.4 The Integrated Rate Law Second-Order • Rate = k[A]2 • Integrated: 1 1 = kt + A A 0 [A] = concentration of A at time t k = rate constant t = time [A]o = initial concentration of A Copyright © Cengage Learning. All rights reserved Return to TOC 32 Section 12.4 The Integrated Rate Law Plot of ln[C4H6] vs Time and Plot of 1/[C4H6] vs Time Return to TOC Copyright © Cengage Learning. All rights reserved 33 Section 12.4 The Integrated Rate Law Second-Order • Half–Life: t1 2 1 = k A 0 k = rate constant [A]o = initial concentration of A • Half–life gets longer as the reaction progresses and the concentration of reactants decrease. • Each successive half–life is double the preceding one. Return to TOC Copyright © Cengage Learning. All rights reserved 34 Section 12.4 The Integrated Rate Law Exercise For a reaction aA Products, [A]0 = 5.0 M, and the first two half-lives are 25 and 50 minutes, respectively. a) Write the rate law for this reaction. rate = k[A]2 b) Calculate k. k = 8.0 x 10-3 M–1min–1 c) Calculate [A] at t = 525 minutes. [A] = 0.23 M Copyright © Cengage Learning. All rights reserved Return to TOC 35 Section 12.4 The Integrated Rate Law Zero-Order • Rate = k[A]0 = k • Integrated: [A] = –kt + [A]o [A] = concentration of A at time t k = rate constant t = time [A]o = initial concentration of A Return to TOC Copyright © Cengage Learning. All rights reserved 36 Section 12.4 The Integrated Rate Law Plot of [A] vs Time Return to TOC Copyright © Cengage Learning. All rights reserved 37 Section 12.4 The Integrated Rate Law Zero-Order • Half–Life: t1 = 2 A 0 2k k = rate constant [A]o = initial concentration of A • Half–life gets shorter as the reaction progresses and the concentration of reactants decrease. Copyright © Cengage Learning. All rights reserved Return to TOC 38 Section 12.4 The Integrated Rate Law Concept Check How can you tell the difference among 0th, 1st, and 2nd order rate laws from their graphs? Return to TOC Copyright © Cengage Learning. All rights reserved 39 Section 12.4 The Integrated Rate Law Rate Laws Return to TOC Copyright © Cengage Learning. All rights reserved 40 Section 12.4 The Integrated Rate Law Summary of the Rate Laws Return to TOC Copyright © Cengage Learning. All rights reserved 41 Section 12.4 The Integrated Rate Law Exercise Consider the reaction aA Products. [A]0 = 5.0 M and k = 1.0 x 10–2 (assume the units are appropriate for each case). Calculate [A] after 30.0 seconds have passed, assuming the reaction is: a) Zero order b) First order c) Second order 4.7 M 3.7 M 2.0 M Return to TOC Copyright © Cengage Learning. All rights reserved 42 Section 12.6 Reaction Mechanisms Objectives • To define reaction mechanism • To determine if a mechanism is a possible explanation of observed behavior Return to TOC Copyright © Cengage Learning. All rights reserved 43 Section 12.6 Reaction Mechanisms Reaction Mechanism • Most chemical reactions occur by a series of elementary steps. • An intermediate is formed in one step and used up in a subsequent step and thus is never seen as a reactant or product in the overall balanced reaction. Return to TOC Copyright © Cengage Learning. All rights reserved 44 Section 12.6 Reaction Mechanisms A Molecular Representation of the Elementary Steps in the Reaction of NO2 and CO NO2(g) + CO(g) → NO(g) + CO2(g) . --------------------------------------------------------------------NO2(g) + NO2(g) → NO(g) + NO3(g) . NO3(g) + CO(g) → NO2(g) + CO2(g) intermediate? Return to TOC Copyright © Cengage Learning. All rights reserved 45 Section 12.6 Reaction Mechanisms Elementary Steps (Molecularity) Page 550 • Molecularity – the number of species that must collide to produce the reaction in that step. • Unimolecular – reaction involving one molecule; first order. • A products Rate = k[A] • Bimolecular – reaction involving the collision of two species; second order. • A + A products Rate = k[A]2 • A + B products Rate=k[A][B] Return to TOC Copyright © Cengage Learning. All rights reserved 46 Section 12.6 Reaction Mechanisms Elementary Steps (Molecularity) Page 550 • Termolecular – reaction involving the collision of three species; third order. • A + A + B products Rate = [ ][ ][ ] = [ ] [ ] • A + B + C products Rate = Return to TOC Copyright © Cengage Learning. All rights reserved 47 Section 12.6 Reaction Mechanisms Rate-Determining Step • A reaction is only as fast as its slowest step. • The rate-determining step (slowest step) determines the rate law and the molecularity of the overall reaction. • Focus on the slow step….. Return to TOC Copyright © Cengage Learning. All rights reserved 48 Section 12.6 Reaction Mechanisms Reaction Mechanism Criteria (must meet All 3) • The sum of the elementary steps must give the overall balanced equation for the reaction. (Like Hess’s Law) • The mechanism must agree with the experimentally determined rate law. (Given) • If these two conditions are met, the mechanism is possibly correct as a mechanism can never be proved absolutely correct. Return to TOC Copyright © Cengage Learning. All rights reserved 49 Section 12.6 Reaction Mechanisms A Molecular Representation of the Elementary Steps in the Reaction of NO2 and CO NO2(g) + CO(g) → NO(g) + CO2(g) --------------------------------------------------------------------NO2(g) + NO2(g) → NO(g) + NO3(g) (slow) NO3(g) + CO(g) → NO2(g) + CO2(g) (fast) • • • • Does the sum of the elementary steps give the overall balanced equation for the reaction? Does the mechanism agree with the experimentally determined rate law given as Rate = k[NO2]2 ? Is this a possible mechanism for this reaction? The overall rate can not be faster than the slow step. Copyright © Cengage Learning. All rights reserved Return to TOC 50 Section 12.6 Reaction Mechanisms Decomposition of N2O5 Return to TOC Copyright © Cengage Learning. All rights reserved 51 Section 12.6 Reaction Mechanisms Decomposition of N2O5 Is this a possible Mechanism? 1?2? 2N2O5(g) 4NO2(g) + O2(g) Step 1: 2(N2O5 NO2 + NO3 ) (fast) Step 2: NO2 + NO3 → NO + O2 + NO2 (slow) Step 3: NO3 + NO → 2NO2 (fast) • • • Does the sum of the elementary steps give the overall balanced equation for the reaction? Does the mechanism agree with the experimentally determined rate law?? Is this a possible mechanism for this reaction? Return to TOC Copyright © Cengage Learning. All rights reserved 52 Section 12.6 Reaction Mechanisms Write the balanced reaction for the synthesis of gases nitrogen dioxide and fluorine that forms 1 product. ____NO2 + ____F2 ____ NO2F The experimentally determined rate law is: Rate = k[NO2][F2] A suggested mechanism is: NO2 + F2 NO2F + F (slow) F + NO2 NO2F (fast) Is this an acceptable mechanism? Return to TOC Copyright © Cengage Learning. All rights reserved 53 Section 12.6 Reaction Mechanisms The experimentally determined rate law is: Rate = k[NO2][F2] A suggested mechanism is: NO2 + F2 NO2F + F (slow) F + NO2 NO2F (fast) Is this an acceptable mechanism? • Does the sum of the elementary steps give the overall balanced equation for the reaction? • Does the mechanism agree with the experimentally determined rate law?? Return to TOC Copyright © Cengage Learning. All rights reserved 54 Section 12.6 Reaction Mechanisms Concept Check (sometimes the Rate Law Looks Tricky.. The reaction A + 2B C has the following proposed mechanism: A+B D (fast equilibrium) D+BC (slow) Does this rate law make sense? rate = k[A][B]2 A has to collide with B, then with another B Why wouldn’t rate = [B] work? Slow step. D is really A + B Copyright © Cengage Learning. All rights reserved Return to TOC 55 Section 12.6 Reaction Mechanisms Objectives Review • To define reaction mechanism • To determine if a mechanism is a possible explanation of observed behavior • Work Session: 49, 51 Return to TOC Copyright © Cengage Learning. All rights reserved 56 Section 12.7 A Model for Chemical Kinetics Objectives • To define activation energy EA • To understand EA on a Potential Energy Graph Return to TOC Copyright © Cengage Learning. All rights reserved 57 Section 12.7 A Model for Chemical Kinetics Arrhenius Equation • Molecules must collide to react. • Main Factors: k = Ae k = A = Ea = R = T = Ea / RT rate law constant frequency factor (Molecular Orientations) activation energy gas constant (8.3145 J/K·mol) temperature (in K) Return to TOC Copyright © Cengage Learning. All rights reserved 58 Section 12.7 A Model for Chemical Kinetics Activation Energy, Ea • Energy that must be overcome to produce a chemical reaction. Return to TOC Copyright © Cengage Learning. All rights reserved 59 Section 12.7 A Model for Chemical Kinetics Transition States and Activation Energy Return to TOC Copyright © Cengage Learning. All rights reserved 60 Section 12.7 A Model for Chemical Kinetics Change in Potential Energy Return to TOC Copyright © Cengage Learning. All rights reserved 61 Section 12.7 A Model for Chemical Kinetics For Reactants to Form Products • Collision must involve enough energy to produce the reaction (must equal or exceed the activation energy). • Relative orientation of the reactants must allow formation of any new bonds necessary to produce products. Return to TOC Copyright © Cengage Learning. All rights reserved 62 Section 12.7 A Model for Chemical Kinetics The Gas Phase Reaction of NO and Cl2 Return to TOC Copyright © Cengage Learning. All rights reserved 63 Section 12.7 A Model for Chemical Kinetics Objectives Review • To define activation energy EA • To understand EA on a Potential Energy Graph • Work Session: Page 571 #53 Return to TOC Copyright © Cengage Learning. All rights reserved 64 Section 12.8 Catalysis Objectives • To define a catalyst • To identify catalysis on a Potential Energy Graph Return to TOC Copyright © Cengage Learning. All rights reserved 65 Section 12.8 Catalysis Catalyst • A substance that speeds up a reaction without being consumed itself. • Provides a new pathway for the reaction with a lower activation energy. Return to TOC Copyright © Cengage Learning. All rights reserved 66 Section 12.8 Catalysis Energy Plots for a Catalyzed and an Uncatalyzed Pathway for a Given Reaction Return to TOC Copyright © Cengage Learning. All rights reserved 67 Section 12.8 Catalysis Effect of a Catalyst on the Number of Reaction-Producing Collisions Return to TOC Copyright © Cengage Learning. All rights reserved 68 Section 12.8 Catalysis Heterogeneous Catalysis Return to TOC Copyright © Cengage Learning. All rights reserved 69 Section 12.8 Catalysis Homogeneous Catalysis Return to TOC Copyright © Cengage Learning. All rights reserved 70 Section 12.8 Catalysis Objectives Review • To define a catalyst • To identify catalysis on a Potential Energy Graph • Work Session Page 572 # 65(a, b) #68a • Catalyst Video 1:40 • End of Chapter 12! Return to TOC Copyright © Cengage Learning. All rights reserved 71 Section 12.8 Catalysis Heterogeneous Catalyst • Most often involves gaseous reactants being adsorbed on the surface of a solid catalyst. • Adsorption – collection of one substance on the surface of another substance. Return to TOC Copyright © Cengage Learning. All rights reserved 72 Section 12.8 Catalysis Heterogeneous Catalyst 1. Adsorption and activation of the reactants. 2. Migration of the adsorbed reactants on the surface. 3. Reaction of the adsorbed substances. 4. Escape, or desorption, of the products. Return to TOC Copyright © Cengage Learning. All rights reserved 73 Section 12.8 Catalysis Homogeneous Catalyst • Exists in the same phase as the reacting molecules. • Enzymes are nature’s catalysts. Return to TOC Copyright © Cengage Learning. All rights reserved 74 Section 12.2 Atomic Rate Laws: Masses An Introduction Types of Rate Laws • Differential Rate Law (rate law) – shows how the rate of a reaction depends on concentrations. • Integrated Rate Law – shows how the concentrations of species in the reaction depend on time. Return to TOC Copyright © Cengage Learning. All rights reserved 75 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Laws: A Summary • Because we typically consider reactions only under conditions where the reverse reaction is unimportant, our rate laws will involve only concentrations of reactants. • Because the differential and integrated rate laws for a given reaction are related in a well– defined way, the experimental determination of either of the rate laws is sufficient. Return to TOC Copyright © Cengage Learning. All rights reserved 76 Section 12.3 The Mole Determining the Form of the Rate Law • Determine experimentally the power to which each reactant concentration must be raised in the rate law. Return to TOC Copyright © Cengage Learning. All rights reserved 77 Section 12.3 The Mole Determining the Form of the Rate Law Method of Initial Rates • The value of the initial rate is determined for each experiment at the same value of t as close to t = 0 as possible. • Several experiments are carried out using different initial concentrations of each of the reactants, and the initial rate is determined for each run. • The results are then compared to see how the initial rate depends on the initial concentrations of each of the reactants. Return to TOC Copyright © Cengage Learning. All rights reserved 78 Section 12.7 A Model for Chemical Kinetics Linear Form of Arrhenius Equation Return to TOC Copyright © Cengage Learning. All rights reserved 79 Section 12.7 A Model for Chemical Kinetics Exercise Chemists commonly use a rule of thumb that an increase of 10 K in temperature doubles the rate of a reaction. What must the activation energy be for this statement to be true for a temperature increase from 25°C to 35°C? Ea = 53 kJ Return to TOC Copyright © Cengage Learning. All rights reserved 80 Section 12.7 A Model for Chemical Kinetics Linear Form of Arrhenius Equation Ea 1 ln(k ) = + ln A R T Return to TOC Copyright © Cengage Learning. All rights reserved 81 Section 12.7 A Model for Chemical Kinetics Collision Model • Molecules must collide to react. • Main Factors: Activation energy, Ea Temperature Molecular orientations Return to TOC Copyright © Cengage Learning. All rights reserved 82