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Chapter 13Chemical Kinetics

Read Study Chapter 13 View the videos in the

Science Learning Center (SLC), N-604. One is

entitled, Catalysis Technology for a Clean

Environment and the other is Reaction Rates.

Chapter Overview

1. Introduction - Background and Key

Definitions 2. Factors Influencing the Rates of

Reactions 3. Rate Laws 4. Activation

Energies 5. Reaction Mechanisms - The

Paragraphs of the Chemical Language 6.

Effects of Catalysts

Introduction

1. Chemical Kinetics - The study of how fast

chemi- cal reactions take place a study of the

RATE of a reaction. 2. Chemical Reaction Rate

- A change in the amount or concentration of a

reactant or product in a given period of

time. Rate - DReactant

DProduct D time D time

3. Kinetics vs. thermodynamics - Factors to be

con- sidered when predicting whether or not a

change will take place 1) Energy (Enthalpy)

Change 2) The Change in disorder (Entropy) 3)

The RATE of the change

Thermodynamics

Kinetics

4. Reaction Mechanism - A detailed molecular-,

atomic-, or ionic-level picture or model of

how a reaction takes place.

How does NO (g) react with O2 (g) in the

atmosphere to form NO2 (g), a major contributor

to smog?

2 NO (g) O2 (g) 2 NO2 (g)

R1

Step 1 NO (g) O2 (g) NO3 (g)

Fast

R2

Step 2 NO3 (g) NO (g) O2 (g)

Fast

R3

Step 3 NO3 (g) NO (g) NO2 (g)

Slow

By measuring the rates of reactions under

various conditions, rate laws can be deduced.

The chemist, then, designs reaction mechanisms to

explain the observed rate laws.

5. Factors affecting the rates of reactions -

1) The Nature of the Reactants 2) The

Reactants Concentrations 3) The Reactants

Total Surface Area 4) The Temperature 5) The

presence or absence of catalysts

Memorize!!

Memorize!!

Memorize!!

Memorize!!

Memorize!!

FACTORS AFFECTING REACTION RATES

- 1) The Nature of the Reactants -
- Ions in solution tend to react very quickly.
- Covalent molecules tend to react more slowly.
- Large covalent molecules tend to react more
- slowly than small covalent molecules.
- Molecules with strong covalent bonds tend to
- react more slowly than those with weak bonds.

- 2) The Concentrations of the Reactants -
- For a reaction to occur, three things must happen

- - The reacting molecules, atoms, or ions, must
- collide.
- They must be properly oriented with respect to

one - another.
- The must have sufficient energy.
- The probability of these three factors being

present is - increased as the concentration of the reactants

is - increased.

Proper Orientation is Necessary

Suffcient Energy is Necessary

Bounces Off!

Reacts!

Homogeneous Reactions - Reactions that take

place in a single solution (phase). Cu2 4

NH3 (aq) Cu(NH3)42

NaOH (aq) HCl (aq) NaCl (aq) H2O (l)

3) The Reactants State of Subdivision

- Heterogeneous Reactions - Reactions in which

reactants are in different phases. The

reactions take place at the interface between the

phases. The larger the surface area of the

interface, the higher the rate of reaction.

V 1 m3 A 6 m2

V 1 m3 A 8 m2

V 1 m3 A 12 m2

V 1 m3 A 36 m2

V 1 m3 A 20 m2

V 1 m3 A ?? m2

Powder

http//blog.wired.com/wiredscience/2008/03/top-10-

amazing.html

http//pubs.acs.org/cen/government/86/8608gov1.htm

l

Examples of Heterogenous Reactions - C (s)

O2 (g) CO2 (g) Zn (s) 2 HCl (aq) ZnCl2

(aq) H2 (g) AgCl (s) 2 NH3

(aq) Ag(NH3)2 Cl -

4) The Temperature - Reaction rates are

increased by increases in temperature. Rule of

Thumb A 10oC rise in temperature will double

the rate of the reaction.

Practice Exercise The temperature at which a

reaction is run is raised from 0oC to 40oC. How

much is the rate of the reaction

increased? toC Rate 0 R1 10 2R1 20 4R1 30

8R1 40 16R1 R2

R2 2(t2 - t1)/10R1

If you want to slow down the reaction that causes

your milk to sour, you put the milk in the

refrigerator to lower its temperature.

What about the Thermite Reaction and temperature?

http//blog.wired.com/wiredscience/2008/03/top-10-

amazing.html

5) Catalysis - How can a catalyst change the

rate of a reaction and yet NOT be

consumed? Thermodynamic Answer By changing the

energy pathway.

Activation Energy

Reactants

Energy

Products

With a catalyst, the energy hump is lowered

-- the energy pathway is changed.

Kinetic Answer The catalyst is a reactant in

one step of the reaction mechanism and a product

in a subsequent step.

Homogeneous Catalysis - Reactions wherein the

catalyst is present in the same phase as the

reactants. 2 SO2 (g) O2 (g) 2 SO3 (g)

NO (g)

Catalyst

Heterogeneous Catalysis - Reactions wherein the

cat- alyst is present in a separate phase from

the reactants.

Pt (s)

2 H2 (g) O2 (g) 2 H2O (g)

Catalyst

Heterogeneous Catalysis

Hydrogen reacts very exothermically with oxygen.

Even so, they can be held in the same container

together for years without reacting unless a

catalyst or source of energy, such as a spark,

are introduced into the mixture.

Rate Laws

Rate Law - A mathematical equation that shows how

the rate of a reaction is affected by the

concentration of re- actants or products in a

reaction.

Measuring the Rate of a Reaction - Follow the

disap- pearance of a reactant or the appearance

of a product.

2 N2O5 (g) ? 2 N2O4 (g) O2 (g)

Rate DO2/Dt (1/2)(DN2O4/Dt)

- (1/2)(DN2O5/Dt)

Decomposition of N2O5 (g)

Reaction of Ethylene w/ O3 (g)

Another Case!

Measuring the Rate of a Reaction

- Method of Initial Rates A method that involves

running - A reaction several times starting with different

initial - Concentrations of reactants.
- Hold the temperature constant.
- If Present, keep the solvent constant.
- Vary (change) only one concentration at a
- time.

Method of Initial Rates

2 NO (g) 2 H2 (g) ? N2 (g) 2 H2O (g)

866oC

Run Reactant Rate of Number Concentration de

crease in NO H2 NO

1 0.10 0.010 0.062 2 0.10 0.040 0.24

6 3 0.30 0.010 0.558

Method of Initial Rates

Effect of H2 on the Rate 0.040 M 0.246

M/s 0.010 M 0.062 M/s

4.0

4.0

As the H2 is raised by a factor of 4.0, the

rate of decrease in NO (the rate of the

reaction) is raised by a factor of 4.0. ? Rate

? H2

Effect of NO on the Rate 0.30 M 0.558

M/s 0.10 M 0.062 M/s

? Rate ? NO2

3.0

9.0

Method of Initial Rates

Rate ? H2NO2 Rate k H2NO2 This is

the RATE LAW!

where k is called the Reaction Rate

Constant! k is independent of reactant

concentrations but IS dependent on temperature.

The Rate Law exponents are usually NOT the same

as the coefficients in the balanced chemical

equation. Therefore, the rate law cannot be

predicted. It MUST be experimentally determined.

k

aA bB ? cC dD

Rate k AmBn

Run Reactant Initial Number Concentration R

ate A B 1 0.030 0.010 1.7

x 10-8 2 0.060 0.010 6.8 x 10-8

3 0.030 0.020 4.9 x 10-8

rate 1 k(0.030)m(0.010)n 1.7 x 10-8 M/s rate

2 k(0.060)m(0.010)n 6.8 x 10-8 M/s

rate 1 1.7 x 10-8 (0.030)m

0.030 m rate 2 6.8 x 10-8 (0.060)m

0.060

0.25 (0.50)m Log (0.25) Log (0.50)m

m Log (0.50) Log (0.25) m 2.0 Log (0.50)

rate 1 k(0.030)m(0.010)n 1.7 x 10-8 M/s rate

3 k(0.030)m(0.020)n 4.9 x 10-8 M/s

rate 1 1.7 x 10-8 (0.010)n

0.010 n rate 3 4.9 x 10-8 (0.020)n

0.020

0.35 (0.50)m Log (0.35) Log (0.50)n

n Log (0.50) Log (0.35) n 1.5 Log (0.50)

Rate k A2B3/2

2 I- S2O82- I2 (aq) 2 SO42-

Run I- S2O82- Initial Rate

1 0.15 0.45 2.6 x 10 - 4

2 0.15 0.25 1.4 x 10 - 4

3 0.50 0.45 8.6 x 10 - 4

Find the Rate Law Rate k I-mS2O82- n

rate 1 k(0.15)m(0.45)n 2.6 x 10 -4 M/s rate

3 k(0.50)m(0.45)n 8.6 x 10 -4 M/s

rate 1 2.6 x 10-4 (0.15)m 0.15

m rate 3 8.6 x 10-4 (0.50)m 0.50

0.30

0.30 (0.30)m Log (0.30) Log (0.30)m

m Log (0.30) Log (0.30) m 1.0 Log (0.30)

rate 1 k(0.15)m(0.45)n 2.6 x 10 -4 M/s rate

2 k(0.15)m(0.25)n 1.4 x 10 -4 M/s

rate 1 2.6 x 10-4 (0.45)n 0.45

n rate 2 1.4 x 10-4 (0.25)n 0.25

1.86

1.86 (1.80)n Log (1.86) Log (1.80)n n

Log (1.80) Log (1.86) n 1.0 Log (1.80)

? Rate k I-S2O82-

Rate Laws

The Order of a Reaction The sum of the

exponents in the Rate Law for the reaction

866oC 2 NO (g) 2 H2 (g) ? N2 (g) 2 H2O

(g) k1

Rate k1 H2NO2

Determined by Experiment

First Order with respect to H2 Second Order

with respect to NO Third order OVERALL

Rate Laws

a A b B ? c C d D k2

Determined by Experiment

Rate k2 A2B3/2

Second Order with respect to A 1.5 Order with

respect to B 3.5 order OVERALL

2 I- S2O82- ? I2 (aq) 2 SO42-

Rate k I-S2O82-

First Order with respect to both I- and

S2O82- and second order OVERALL

Rate Laws

a A b B c C ? d D e E k4

Rate k4 AmBn

Subtances involved in a reaction that have NO

concentration effect on the rate of the reaction

are said to have a zeroth order effect. The

reaction above is zeroth order with respect to

C.

REMEMBER The rate law for a reaction CANNOT

be predicted from the chemical equation! It MUST

be experimentally determined!

Rate Laws

Class Exercise The following reaction is second

order with respect to acetaldehyde. Write the

Rate Law for this reaction.

CH3-C H (g) ? CH4 (g) CO (g)

k O

Rate k CH3-C H2 O

Rate Constants The value of the rate constant,

k, for a given reaction depends on the NATURE of

the reactants and the TEMPERATURE, but NOT on the

concentration of reactants.

Rate Constants

Class Exercise A 2 B ? C Rate k B

0.012 molL-1s-1

When B0 0.60 M and A0 0.020 M, Find k.

k rate/B0 (0.012 molL-1s-1)/(0.60

molL-1) 0.020 s-1

Find the rate of the reaction when A0 B0

0.010 M

rate k B (0.020 s-1)(0.010 M) 2.0 x

10-4 Ms-1

Rate Law Characteristics

Zero Order Reactions Reactions with rates that

are not dependent on the concentration of

reactants.

Reactant

Reaction Rate

Time

Time

The rate of metabolism of alcohol in the body is

indepen- dent of alcohol. The RATE is constant!

Rate Law Characteristics

First Order Reactions 2 N2O5 (g) ? 4 NO (g)

O2 (g) Rate kN2O5

In General Rate kA

A

ln A

Time

Time

Rate Law Characteristics

A Ao e-kt Integrated Rate Law (1st

Order)

ln A ln Ao (-kt) ln A - kt

ln Ao y mx b

Half-Life The time required for one-half of a

reactant to disappear in a reaction. For FIRST

ORDER reactions, The half-life is INDEPENDENT of

reactant concentration.

O.K. Lets Prove That!

Rate Law Characteristics

ln A ln Ao (-kt)

A Ao

ln

-kt

ButA ½ Ao at time t1/2

Ao 2Ao

ln

ln (1/2)

-kt1/2

kt1/2 - ln (1/2) ln 2 0.693 t1/2

0.693/k CONSTANT

The Half-Life (t1/2) of a First Order process is

inversely proportional to the rate constant, k,

and is independent of the reactant concentration.

2nd Order Reactions Rate kA2

Simplest Type Rate kAB Also 2nd Order

k 2 NO2 (g) ? 2 NO (g) O2 (g)

Rate kNO22

Integrated Rate Law (2nd Order)

1/A kt 1/Ao y mx b

At time t1/2, A 1/2Ao . Therefore

2/Ao kt1/2 1/Ao 2/Ao - 1/Ao

kt1/2

1 Ao

kt1/2 ? t1/2 1/kAo

How can you tell 1st order reactions from 2nd

order?

1st Order

2nd Order

ln A

1/A

time

time

Temperature Effects on Reaction Rates

k Ae-Ea/RT

Arrhenius Plot

Take log of both sides ln k ln A ln e

-Ea/RT ln k ln A - Ea/RT ln k

-(Ea/R)(1/T) ln A

y mx b

Slope - Ea/R Ea -R(Slope)

Temperature Effects on Reaction Rates

If you know the k at one temperature, you can

find k for a different temperature with the

Arrhenius Equation.

ln k1 -(Ea/R)(1/T1) ln A ln k2

-(Ea/R)(1/T2) ln A ln k1 Ea/RT1 ln

A ln k2 Ea/RT2 ln A ln k1 Ea/RT1

ln k2 Ea/RT2

Temperature Effects on Reaction Rates

ln k1 Ea/RT1 ln k2 Ea/RT2 ln k1 - ln k2

Ea/R(1/T2)-(1/T1) ln (k1/k2)

Class Exercise Ea 18.7 kJ/mol k1 0.0400

s-1 T1 273 K T2 298 K k2

??

ln k2 ln k1 - Ea/R(1/T2)-(1/T1) ln k2

-2.538 k2 0.0798 s-1

Activation Energy The minimum energy

necessary for a reaction to occur.

Temperature Effects on Reaction Rates

Arrhenius Plot

k Ae-Ea/RT

Reaction Mechanisms

Reaction Mechanism A series of consecutive

molecular- level events or steps that lead from

reactants to products. They can be disproven but

never proven.

For a mechanism to be valid, it must account for

every- thing that is known about the reaction,

including the rate law for the reaction and its

stoichiometry.

Elementary Process A single reaction step in a

reaction mechanism.