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 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 3 Section 12.1 Reaction Rates The Decomposition of Nitrogen Dioxide Return to TOC Copyright © Cengage Learning. All rights reserved 4 Section 12.1 Reaction Rates The Decomposition of Nitrogen Dioxide Return to TOC Copyright © Cengage Learning. All rights reserved 5 Section 12.1 Reaction Rates Instantaneous Rate • Value of the rate at a particular time. • Can be obtained by computing the slope of a line tangent to the curve at that point. Return to TOC Copyright © Cengage Learning. All rights reserved 6 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Law • Shows how the rate depends on the concentrations of reactants. • For the decomposition of nitrogen dioxide: 2NO2(g) → 2NO(g) + O2(g) Rate = k[NO2]n: k = rate constant n = order of the reactant Return to TOC Copyright © Cengage Learning. All rights reserved 7 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. Return to TOC Copyright © Cengage Learning. All rights reserved 8 Section 12.2 Atomic Rate Laws: Masses An Introduction Rate Law Rate = k[NO2]n • 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 9 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 10 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 11 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. Return to TOC Copyright © Cengage Learning. All rights reserved 12 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 13 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 14 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. 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 15 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 16 Section 12.4 The Integrated Rate Law Half-Life of Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 17 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 18 Section 12.4 The Integrated Rate Law Plot of ln[N2O5] vs Time Return to TOC Copyright © Cengage Learning. All rights reserved 19 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 20 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 21 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 22 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 23 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 24 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 25 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 26 Section 12.4 The Integrated Rate Law Plot of [A] vs Time Return to TOC Copyright © Cengage Learning. All rights reserved 27 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 28 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 29 Section 12.4 The Integrated Rate Law Rate Laws Return to TOC Copyright © Cengage Learning. All rights reserved 30 Section 12.4 The Integrated Rate Law Summary of the Rate Laws Return to TOC Copyright © Cengage Learning. All rights reserved 31 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 32 Section 12.5 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 product in the overall balanced reaction. Return to TOC Copyright © Cengage Learning. All rights reserved 33 Section 12.5 Reaction Mechanisms A Molecular Representation of the Elementary Steps in the Reaction of NO2 and CO NO2(g) + CO(g) → NO(g) + CO2(g) Return to TOC Copyright © Cengage Learning. All rights reserved 34 Section 12.5 Reaction Mechanisms Elementary Steps (Molecularity) • Unimolecular – reaction involving one molecule; first order. • Bimolecular – reaction involving the collision of two species; second order. • Termolecular – reaction involving the collision of three species; third order. Return to TOC Copyright © Cengage Learning. All rights reserved 35 Section 12.5 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. Return to TOC Copyright © Cengage Learning. All rights reserved 36 Section 12.5 Reaction Mechanisms Reaction Mechanism Requirements • The sum of the elementary steps must give the overall balanced equation for the reaction. • The mechanism must agree with the experimentally determined rate law. Return to TOC Copyright © Cengage Learning. All rights reserved 37 Section 12.5 Reaction Mechanisms Decomposition of N2O5 Return to TOC Copyright © Cengage Learning. All rights reserved 38 Section 12.5 Reaction Mechanisms Decomposition of N2O5 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) Return to TOC Copyright © Cengage Learning. All rights reserved 39 Section 12.5 Reaction Mechanisms Concept Check The reaction A + 2B C has the following proposed mechanism: A+B D (fast equilibrium) D+BC (slow) Write the rate law for this mechanism. rate = k[A][B]2 Return to TOC Copyright © Cengage Learning. All rights reserved 40 Section 12.6 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 41 Section 12.6 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 42 Section 12.6 A Model for Chemical Kinetics Transition States and Activation Energy Return to TOC Copyright © Cengage Learning. All rights reserved 43 Section 12.6 A Model for Chemical Kinetics Change in Potential Energy Return to TOC Copyright © Cengage Learning. All rights reserved 44 Section 12.6 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 45 Section 12.6 A Model for Chemical Kinetics The Gas Phase Reaction of NO and Cl2 Return to TOC Copyright © Cengage Learning. All rights reserved 46 Section 12.6 A Model for Chemical Kinetics Arrhenius Equation k = Ae Ea / RT A Ea R T = = = = frequency factor activation energy gas constant (8.3145 J/K·mol) temperature (in K) Return to TOC Copyright © Cengage Learning. All rights reserved 47 Section 12.6 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 48 Section 12.6 A Model for Chemical Kinetics Linear Form of Arrhenius Equation Return to TOC Copyright © Cengage Learning. All rights reserved 49 Section 12.6 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 50 Section 12.7 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 51 Section 12.7 Catalysis Energy Plots for a Catalyzed and an Uncatalyzed Pathway for a Given Reaction Return to TOC Copyright © Cengage Learning. All rights reserved 52 Section 12.7 Catalysis Effect of a Catalyst on the Number of Reaction-Producing Collisions Return to TOC Copyright © Cengage Learning. All rights reserved 53 Section 12.7 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 54 Section 12.7 Catalysis Heterogeneous Catalysis Return to TOC Copyright © Cengage Learning. All rights reserved 55 Section 12.7 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 56 Section 12.7 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 57 Section 12.7 Catalysis Homogeneous Catalysis Return to TOC Copyright © Cengage Learning. All rights reserved 58