Chemical KineticsChemical Kinetics Rates of chemical reactionRates of chemical reaction －－ definition of reaction ratedefinition of reaction rate －－ integrated and differential rate lawintegrated and differential rate law － － determination of rate law determination of rate law Mechanism of chemical reactionMechanism of chemical reaction － － activated complex theoryactivated complex theory －－ model for chemical kineticsmodel for chemical kinetics －－ Arrhenius equationArrhenius equation

2 2

2

2

2 2

[ ]Average Rate

[ ]Instantaneous Rate= -

NO NO O

NO

td NO

dt

Rate LawRate Law

Rate=k[NORate=k[NO22]]nn

The concentration of the products do The concentration of the products do not appear in the rate law.not appear in the rate law.

The value of the exponent n must be The value of the exponent n must be determined by experiment; it cannot determined by experiment; it cannot be written from the balanced be written from the balanced equation.equation.

][][

5252 ONk

dt

ONdR

2N2O5→4NO2+O2

Types of Rate LawsTypes of Rate Laws Integrated Rate Law: how the Integrated Rate Law: how the

concentration of species in the concentration of species in the reaction depend on timereaction depend on time

Differential Rate Law: how the rate of Differential Rate Law: how the rate of a reaction depends on concentrationsa reaction depends on concentrations

Determine the differential rate law for Determine the differential rate law for a given reaction, the form of a given reaction, the form of integrated rate law can be integrated rate law can be automatically known, and vice versaautomatically known, and vice versa

Initial-Rate methodInitial-Rate method

To determine the instantaneous rate To determine the instantaneous rate before the initial concentration of before the initial concentration of reactants have reactants have changed changed significantlysignificantly..

Several experiments are carried out Several experiments are carried out using using different initial concentrationsdifferent initial concentrations..

The initial rate is determined for The initial rate is determined for each run.each run.

4 2 2 2

44 2

2

[ ][ ] [ ]n m

NH NO N H O

d NHk NH NO

dt

Experiments Initial Rate

1 0.1M 0.005M 1.35X10-7

2 0.1M 0.01M 2.70X10-7

2 0.2M 0.01M 5.40X10-7

4NH 2NO

7

7

7

7

4 2

7

4 1 1

2 2.7 10 (0.1) (0.01)(2) 2 1

1 1.35 10 (0.1) (0.005)

3 5.4 10 (0.2) (0.01)(2) 2 1

2 2.7 10 (0.1) (0.01)

[ ][ ]

1.35 10 (0.1)(0.005)

2.7 10

n mm

n m

n mn

n m

Rate km

Rate k

Rate kn

Rate k

Rate k NH NO

k

k Lmol s

Integrated Rate Law － first order

2 5 2 2

2 5 2 52 5 2 5

2 5

2 5

22 5

1 02 5

2 52 5 2 5 0

2 5 0

2 5 2 5 0

2 4

[ ] [ ]1[ ] [ ]

22

[ ]

[ ]

[ ]

[ ]

[ ]ln( ) ln[ ] ln[ ]

[ ]

[ ] [ ] a

a

a

a

t

a

a a

k t

N O NO O

d N O d N ORate k N O k N O

dt dtk k

d N Ok dt

N O

d N Ok dt

N O

N Ok t N O N O k t

N O

N O N O e

][][

law rate aldifferenti

5252 ONk

dt

ONdR a

Plot of NPlot of N22OO55 vs. time vs. time

Half-Life of a First Order Half-Life of a First Order ReactionReaction

The time required for a reaction to The time required for a reaction to reach half of its original reach half of its original concentration is called half-life of a concentration is called half-life of a reaction and id designated by treaction and id designated by t1/21/2..

2 5 2 5 0

2 5 2 5 0

2 5 0 2 5 0 1/ 2

2 5 0 2 5 0 1/ 2

1/ 2

1/ 2

1 [ ] [ ]

2ln[ ] ln[ ]

1ln( [ ] ) ln[ ]

21

ln( ) ln([ ] ) ln([ ] )2

ln 2

ln 2 0.693

a

a

a

a

a a

when N O N O

N O N O k t

N O N O k t

N O N O k t

k t

tk k

Plot of NPlot of N22OO55 vs. time vs. time

Integrated Rate Law － second order

0

2

[ ]

2 2[ ] 00

0

[ ][ ] ( )

[ ] [ ] 1 1

[ ] [ ] [ ] [ ]

1 1

[ ] [ ]

a a

A t

a a aA

a

aA P

d ARate k A k ak

dtd A d A

k dt k dt k tA A A A

k tA A

Plot of CPlot of C44HH66

Integrated Rate Law － zero order

0

0

[ ]

[ ]

0

0

[ ][ ] = ( )

[ ]

[ ] [ ]

[ ] [ ]

a a a

A

aA

a

a

aA P

d ARate k A k k ak

dt

d A k dt

A A k dt

A A k dt

PO2 (torr)1.531.461.331.07

Co

nve

rsio

n (

%) slope=-0.18

PCO (torr)1.531.461.331.07

Co

nv

ers

ion

(%

) slope=1.3

18.03.1

2

OCO PkPr

Pseudo-Order Reaction Law

3 2 2

233

33 0 0 0

0 0 3 0

' ' 233

5 6 3 3

[ ][ ][ ][ ]

[ ] 1.0 10 [ ] 1.0 [ ] 1.0

[ ] [ ] [ ]

[ ][ ] ( [ ][ ] )

BrO Br H Br H O

d BrORate k BrO Br H

dt

BrO M Br M H M

Br H BrO

d BrOk BrO k k Br H

dt

Arrhenius PostulationsArrhenius Postulations

Collisions and RateCollisions and Rate －－ the rate of reaction is much smaller than the rate of reaction is much smaller than calculated collision frequency.calculated collision frequency. A threshold energy (activation energy)A threshold energy (activation energy) －－ This kinetic energy is changed into potential This kinetic energy is changed into potential

energy as the molecules are distorted during a energy as the molecules are distorted during a collision, breaking bonds and rearranging the collision, breaking bonds and rearranging the atoms into product molecules.atoms into product molecules.

Collisions Frequency and Collisions Frequency and Molecular orientationsMolecular orientations

Experiments show that the observed Experiments show that the observed reaction rate is considerably smaller reaction rate is considerably smaller than the rate of collisions with enough than the rate of collisions with enough energy to surmount the barrier.energy to surmount the barrier.

The collision must involve enough The collision must involve enough energy to produce the reaction.energy to produce the reaction.

The relative orientation of the reactants The relative orientation of the reactants must allow formation of any new bonds must allow formation of any new bonds necessary to products.necessary to products.

BrNO collisionBrNO collision

Potential energy graph for Potential energy graph for

2BrNO2BrNO→→2NO+Br2NO+Br22

Temperature Dependence of Temperature Dependence of Rate ConstantsRate Constants

The order of each reactant depends on tThe order of each reactant depends on the detailed reaction mechanism.he detailed reaction mechanism.

Chemical reaction speed up when the teChemical reaction speed up when the temperature is increased.mperature is increased.

－－ molecules must collide to reactmolecules must collide to react －－ an increase in temperature increases an increase in temperature increases the frequency of intermolecular the frequency of intermolecular collisions.collisions.

TT11//TT22 graph graph

TT(K) and (K) and kk

Ea: activation energy

A: pre-exponential factor

Aek

factorp: steric

uencyision freqz:the coll

zpek

RT

E

RT

E

a

a

ln(A))T

1(

R

Eln(k) a

Arrhenius Equation

Plot ln(Plot ln(kk) vs. 1/) vs. 1/TT

Reaction MechanismReaction Mechanism

Most chemical reactions occur by a Most chemical reactions occur by a series of steps called the reaction series of steps called the reaction mechanism.mechanism.

The sum of the elementary steps must The sum of the elementary steps must give the overall balanced equation for give the overall balanced equation for the reaction.the reaction.

The mechanism must agree with the The mechanism must agree with the experimentally determined rate law.experimentally determined rate law.

2 2 3

3 2 2

2 2

3

(1) slow

(2) fast

(1) (2)

:

(1) (2) .

NO NO NO NO

NO CO NO CO

NO CO NO CO

NO intermediate

Step and are called elementary setps

Step (1): rate-determining-step

Activated Complex TheoryActivated Complex Theory

The arrangement of atoms found at The arrangement of atoms found at the top of potential energy hill or the top of potential energy hill or barrier is called the activated barrier is called the activated complex or transition state.complex or transition state.

△△E has no effect on the rate of E has no effect on the rate of reaction.reaction.

The rate depends on the size of the The rate depends on the size of the activation energy Eactivation energy Eaa

CatalysisCatalysis

A substance can speed up a reaction A substance can speed up a reaction without being consumed itself.without being consumed itself.

The catalyst is to provide a new The catalyst is to provide a new pathway for the reaction and to pathway for the reaction and to decrease activation energy.decrease activation energy.

Effect of a Effect of a catalyst catalyst graphgraph

Heterogeneous CatalysisHeterogeneous Catalysis

Adsorption and activation of the reactanAdsorption and activation of the reactantsts

Migration of the adsorbed reactants on tMigration of the adsorbed reactants on the surfacehe surface

Reaction among the adsorbed substancReaction among the adsorbed substanceses

Escape, or desorption, of the products.Escape, or desorption, of the products.

Hydrogenation of ethyleneHydrogenation of ethylene

Exhaust gasesExhaust gases