CHEMICAL KINETICS CHAPTER 13 I Introduction A Definition

CHEMICAL KINETICS CHAPTER 13

I. Introduction A. Definition of Chemical Kinetics “The study of the speed or rate of reactions and the nanoscale pathways or processes by which reactants are transformed into products. B. Examples of Reactions and Rates Rusting of Iron Combustion Reaction C. Significance of Studying Kinetics

D. Factors Affecting Reaction Rate 1. Concentration of Reactants 2. Temperature 3. Presence of a Catalyst 4. Surface Area of a Solid Reactant or Catalyst 5. Properties of Reactants and Products

II. Understanding Reaction Rates A. Kinetic Molecular Theory Matter composed of particles in constant motion. Increase in temperature increases particle’s kinetic energy. B. Collision Theory For a reaction to occur , reactant molecules must collide with the proper orientation and with an energy greater than some minimum value. Activation Energy (Ea) – minimum energy required for reaction to occur.

Importance of Orientation One hydrogen atom can approach another from any direction … Effective collision; the I atom can bond to the C atom to form CH 3 I … and reaction will still occur; the spherical symmetry of the atoms means that orientation does not matter. Ineffective collision; orientation is important in this reaction.

Distribution of Kinetic Energies At higher temperature (red), more molecules have the necessary activation energy.

C. Transition State Theory 1. Note Reaction Profile: CO(g) + NO 2(g) CO 2(g) + NO(g)

2. Note Ea for either forward or reverse reaction. “At a given temperature, the higher the energy barrier, the slower the reaction. ” 3. Transition State or “Activated Complex” “Transition structure (between reactants and products) which is always found on top of the energy hill (energy of activation). 4. Is reaction, exothermic or endothermic as written from left to right?

Reconsideration of Factors Affecting Reaction Rate!! 1. Concentration 2. Temperature 3. Catalyst

III. Rates of Reactions A. Definition 1. Reaction rate: expresses how much product is appearing or how much reactant in disappearing per unit time. 2. Units for reaction rates: (Examples) Ms-1 or M/s or mol L-1 s-1

For Reaction: A → P Rate of Disappearance of “A” = - ΔA / Δt Rate of Formation of “P” = + ΔP / Δt

B. Example Average Rate Determination For Rxn of Cisplatin and Water: H 2 O + Pt(NH 3)2 Cl 2 Pt(NH 3)2 Cl(H 2 O) + Cl. Cisplatin Time (min) 0 200 400 [Cisplatin] (mol/L) 0. 01000 0. 00747 0. 00558 What is average rate of disappearance of cisplatin (in mol L-1 min-1) for the first 200 min? What is average rate of disappearance of cisplatin (in mol L-1 min-1) for the next 200 min?

C. Instantaneous Rate Determination Significance of Measuring Instantaneous Rates!!

D. Reaction Rates and Stoichiometry Given the reaction: 2 N 2 O 5(g) 4 NO 2(g) + O 2 (g) If the rate of NO 2 formation is 0. 060 mol L-1 s-1: 1. What is the rate of disappearance of N 2 O 5? 2. What is the rate of formation of O 2?

IV. Concentration and Rxn Rate A. Rate Law Equation: 1. An equation that relates the rate of a reaction to the concentrations of reactants (and catalyst) raised to various powers. 2. Must be experimentally determined!!

3. For reaction: A + B C Rate is proportional to reactant concentrations Rate = k[A]m [B]n k = rate constant (exponents “m” and “n” must be experimentally determined). 4. For reaction: 2 NO 2(g) + F 2(g) 2 NO 2 F(g) (experimentally determined Rate Law is: ) Rate = k [NO 2]1[F 2]1 = k [NO 2][F 2] Exponents not necessarily same as rxn coefficients!!

4. For hypothetical reaction: 2 A(g) + B 2(g) 2 AB(g) (experimentally determined Rate Law is: ) Rate = k [A]2 Not all reactants necessarily show up in the rate law equation!!

B. Reaction Order For the general equation: a. A + b. B p. P The rate equation is: Rate = k [A]m [B]n m and n are experimentally determined and are usually integers (0, 1, 2, 3, …). They may be fractions.

This reaction is said to m th order with respect to A and n th order with respect to B. The overall reaction order is the sum of the individual orders, or Overall Reaction Order = m + n

Example: For the following reaction: 2 NO(g) + Cl 2(g) 2 NOCl(g) The observed rate law is: Rate = k [NO]2 [Cl 2] What is the reaction order with respect to NO? What is the reaction order with respect to Cl 2? What is the overall reaction order? How would the rate of the reaction be affected by doubling the concentration of both NO and Cl 2?

C. Determination of Rate Law Exponents Done experimentally by measuring initial rates for several different known concentrations of reactants. Consider the reaction: 2 NO(g) + 2 H 2(g) N 2(g) + 2 H 2 O(g) Given the information on the next slide: 1. Determine the rate law. 2. What is the order of the reaction? 3. What is the value of the rate constant? “units”

Experiment Initial Concentration (M) Rate [NO] [H 2] mol / L. s 1 0. 100 1. 23 x 10 -3 2 0. 100 0. 200 2. 45 x 10 -3 3 0. 200 0. 100 4. 93 x 10 -3 4 0. 300 0. 100 1. 11 x 10 -2

1. Determine the rate law. a. Determine general form of rate law. rate = k [NO]m[H 2]n b. Determine exponents. For each reactant, compare two experiments or trials where its concentration is changing and all other reactant concentrations are held constant.

Methods For Determining Rate Law Exponents Method 1 – solve analytically Substitute data into rate law and compare Divide equation with larger rate by eq. with smaller rate. Cancel terms and solve. or simplifying Method 2 - solve by inspection How does changing conc. affect rate?

2. Determine order of the reaction. 3. Determine rate constant (include units). Use rate law and either set of data. 4. What is the rate of the reaction when [NO] = [H 2] = 0. 200 M ?

V. Integrated Rate Law Equations derived from rate law (by using calculus) which are convenient for solving concentration versus time problems. For: 1. First Order Rxns – only one covered 2. Second Order Rxns 3. Zero Order Rxns

A. Integrated First Order Rate Law For reaction: a. A Product rate = - Δ[A] / Δt = k[A] and using calculus: where [A]o is the concentration of A at time zero (t = 0) and [A]t is the concentration at time t. *** A and A 0 may be replaced by quantities that are proportional to concentration !!!!

B. Problem The sugar, sucrose, will undergo the following (first order) hydrolysis reaction C 12 H 22 O 11 + H 2 O C 6 H 12 O 6 + C 6 H 12 O 6 sucrose glucose fructose with a rate constant of 6. 2 x 10 -5 s-1 at 35 o. C. A sample of 0. 20 mol of sucrose was initially dissolved in a total volume of 500 m. L. 1. What is the sucrose conc. after 2 hours?

2. What will be the glucose concentration after the 2 hours have elapsed? 3. How many minutes will it take for the sucrose concentration to drop to 0. 30 M?

C. Half-Life and First Order Reactions 1. Definition (t 1/2) – the time required for the concentration of a reactant to fall to one half its initial value. 2. Significance: Useful in describing radioactive decay rates Useful in describing rates of 1 st order reactions 3. Equation derived from Integrated Rate Law

4. Problem - Radioactive Iodine-131 has t 1/2 of 8 days. If you had a sample of 10, 000 I-131 atoms initially, how many I-131 atoms would remain after 32 days?

5. Problem – The first order hydrolysis reaction of sucrose C 12 H 22 O 11 + H 2 O C 6 H 12 O 6 + C 6 H 12 O 6 sucrose glucose fructose has a rate constant of 6. 17 x 10 -4 s-1 under experimental conditions. a. What is the half-life for the hydrolysis of sucrose? b. How many minutes are required for 75% of the initial sucrose to react?

VI. Temperature and Rxn Rate A. Nanoscale Explanation as to why increasing temperature increase reaction rate. B. Mathematical Relationship Arrhenius Equation (not responsible for problem solving)

VII. Reaction Mechanisms A. Introduction Reaction mechanism is a series of elementary reactions or simple steps whose overall effect is given by the net chemical reaction (equation). 1. It is a theory of how the reaction occurs which is based on experimental data. 2. Cannot be absolutely proven. 3. Steps must be elementary reactions.

B. Elementary Reaction 1. Definition- the simplest step in what is often a multi-step mechanism for an observed chemical reaction. a. The equation for an elementary reaction shows exactly which molecules, atoms, or ions take part in the elementary reaction. b. For an elementary reaction, the rate law is directly determined from the elementary reaction.

2. Elementary Reactions in Mechanisms Types a. Unimolecular Reaction – structure of a single particle (atom, molecule, or ion) rearranges to produce a different particle or particles. b. Bimolecular Reaction - two particles (atoms, ions, or molecules) collide and rearrange into products. c. Termolecular Reaction – (less likely)

3. Problems Identify the type of elementary reaction and give the rate law for the following elementary reactions: a. Cl + Cl 2 b. N 2 O 5 NO 2 + NO 3

C. Properties of Valid Mechanisms 1. Must consist of only unimolecular, bimolecular, or termolecular elementary reactions. (True for any mechanisms given to you. ) ***2. Sum of the elementary reactions should be equal to the overall reaction equation. ***3. Should predict the experimentally observed rate law. The overall rate of the reaction is dependent on the slowest step in the mechanism - the rate-limiting step.

D. Example Mechanism Problems 1. For the overall reaction: 2 NO 2 Cl 2 NO 2 + Cl 2 the following mechanism is proposed. NO 2 Cl NO 2 + Cl (slow) NO 2 Cl + Cl NO 2 + Cl 2 (fast) a. Does the sum of the elementary processes equal the overall reaction? b. What is the rate law for the overall rxn? c. Identify any reaction intermediates.

2. For the overall reaction: (CH 3)3 CCl + OH- (CH 3)3 COH + Clthere are two proposed mechanisms. 1) Concerted mechanism (CH 3)3 CCl + OH- (CH 3)3 COH + Cl 2) Two Step Mechanism (CH 3)3 CCl (CH 3)3 C + + Cl (CH 3)3 C+ + OH - (CH 3)3 COH (slow) (fast)

From kinetic data, the correct rate law for the overall reaction is: rate = k[(CH 3)3 CCl] Questions: 1. Which is the correct mechanism? Why? 2. What is the order of the overall reaction? 3. Identify reaction intermediates in each proposed mechanism.

VIII. Catalysts A. Definition Catalyst – a species that increases the rate of an overall reaction but is not consumed in the reaction. Not shown in overall reaction. Will show up in rate law for catalyzed reaction.

B. How Do They Increase Reaction Rate? 1. Catalysts alter / participate in rxn mechanism. 2. Lower activation energy. Speeds reaction. 3. See Fig 13. 17 (next slide) 4. Catalyst changes kinetics, but not thermodynamics of reaction. Increases speed of reaction. Does not change net energy of reaction, type of product produced, or direction of reaction.

C. Homogeneous vs. Heterogeneous Catalysts Heterogeneous Catalyst- catalyst in different phase from reacting substance. (hydrogenation of vegetable oils – next slide) (catalytic converters in autos) Homogeneous Catalyst – catalyst in same phase as reacting substance. (enzymes)

Heterogeneous Catalysis Hydrogen is adsorbed onto the surface of a nickel catalyst. A C=C approaches … … and is adsorbed. Hydrogen atoms attach to the carbon atoms, and the molecule is desorbed.

D. Enzymes (Homogeneous Catalysts) 1. Protein that catalyzes reaction. 2. Most efficient catalysts known to man. 3. Specifically binds to reactants (substrates), holding them in correct position for reaction to occur. 4. Lower activation energy by stabilizing transition state or altering mechanism. 5. Examples: Lysozyme Next slide