CHEMICAL KINETICSCHAPTER 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 Rate1. 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 TheoryFor 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 OrientationOne hydrogen atom

can approach another from any direction …

… and reaction will still occur; the spherical symmetry of the atoms means

that orientation does not matter.

Effective collision; the I atom can bond to the C atom to form CH3I

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) + NO2(g) CO2(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-1s-1

For Reaction: A → P

Rate of Disappearance of “A” = - ΔA / Δt

Rate of Formation of “P” = + ΔP / Δt

t

A

t

A

t

A

B. Example Average Rate Determination For Rxn of Cisplatin and Water: H2O + Pt(NH3)2Cl2 Pt(NH3)2Cl(H2O) + Cl-

Cisplatin Time (min) [Cisplatin] (mol/L) 0 0.01000 200 0.00747 400 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 N2O5(g) 4 NO2(g) + O2 (g)

If the rate of NO2 formation is 0.060 mol L-1 s-1:

1. What is the rate of disappearance of N2O5?

2. What is the rate of formation of O2?

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 NO2(g) + F2(g) 2 NO2F(g) (experimentally determined Rate Law is:)

Rate = k [NO2]1[F2]1 = k [NO2][F2]

Exponents not necessarily same as rxn coefficients!!

4. For hypothetical reaction:

2 A(g) + B2(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: aA + bB pP

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) + Cl2(g) 2 NOCl(g)

The observed rate law is:

Rate = k [NO]2 [Cl2]

What is the reaction order with respect to NO? What is the reaction order with respect to Cl2? What is the overall reaction order?

How would the rate of the reaction be affected by doubling the concentration of both NO and Cl2?

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 H2(g) N2(g) + 2 H2O(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”

Initial Concentration (M) Rate

Experiment [NO] [H2] mol / L.s

1 0.100 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[H2]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] = [H2] = 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:

aA 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 A0 may be replaced by quantities that are proportional to concentration !!!!

[ ]ln

[ ]

t

o

Akt

A

B. Problem The sugar, sucrose, will undergo the following

(first order) hydrolysis reaction

C12H22O11 + H2O C6H12O6 + C6H12O6

sucrose glucose fructose

with a rate constant of 6.2 x 10-5 s-1 at 35oC. A sample of 0.20 mol of sucrose was initially

dissolved in a total volume of 500 mL.

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 0.30M?

C. Half-Life and First Order Reactions

1. Definition (t1/2) – 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 1st order reactions

3. Equation derived from Integrated Rate Law

1

2

.693t

k

4. Problem - Radioactive Iodine-131 has t1/2 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

C12H22O11 + H2O C6H12O6 + C6H12O6

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)

/Ea RTk Ae

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 Cl2

b. N2O5 NO2 + NO3

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 NO2Cl 2 NO2 + Cl2 the following mechanism is proposed.

NO2Cl NO2 + Cl (slow)

NO2Cl + Cl NO2 + Cl2 (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:

(CH3)3CCl + OH- (CH3)3COH + Cl-

there are two proposed mechanisms.

1) Concerted mechanism

(CH3)3CCl + OH- (CH3)3COH + Cl-

2) Two Step Mechanism

(CH3)3CCl (CH3)3C + + Cl - (slow)

(CH3)3C+ + OH - (CH3)3COH (fast)

From kinetic data, the correct rate law for the overall reaction is:

rate = k[(CH3)3CCl] Questions:

1. Which is the correct mechanism? Why?

2. What is the order of the overall reaction?

3. Identify reaction intermediates in eachproposed 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