Chemical Kinetics

Chapter 16Chapter 16

Kinetics

Reaction RatesReaction RatesFactors affecting rateFactors affecting rate

Quantitative rate expressionsQuantitative rate expressions

DeterminationDetermination

FactorsFactors

Models for RatesModels for Rates

Reaction MechanismsReaction Mechanisms

Effects of catalystsEffects of catalysts

Rates

Change in concentration of a reactant or product Change in concentration of a reactant or product per unit timeper unit time

t

A

t- t

A - A

t time,in Change

A conc, in Change

0t

0t

B A

12_292

.20

.40

.60

.80

1.00

400 800 1200 1600 2000

Rate = 5.4 x 10-4 mol/L.s

Rate = 2.7 x 10-4 mol/L.s

[N2O

5] (m

ol/L

)

Time (s)

Factors affecting rates

Nature of the reactantsNature of the reactants

State of subdivision/surface areaState of subdivision/surface area

ConcentrationConcentration

TemperatureTemperature

CatalystsCatalysts

Reactants

ComplexityComplexity

Bond strengthsBond strengths

Etc.Etc.

242342 O OHC O HC

242342 O OHC O HC

242342 O OHC O HC

Concentrations as functions of time

22 O 2NO 2NO

Time(s) [NO2] [NO] [O2]

0 0.0100 0.0000 0.000050 0.0079 0.0021 0.0011

100 0.0065 0.0035 0.0018150 0.0055 0.0045 0.0023200 0.0048 0.0052 0.0026250 0.0043 0.0057 0.0029300 0.0038 0.0062 0.0031350 0.0034 0.0066 0.0033400 0.0031 0.0069 0.0035

Graph: Concentration vs. time

22 O 2NO 2NO

M10725.1

0 - 400

0.0100 - 0.0031

t- t

NO - NO

t

NO 5

0400

0240022

Average Rate

-[NO2]/t time period(s)

–4.20E-05 0 - 50 –2.80E-05 50 - 100 –2.00E-05 100 - 150 –1.40E-05 150 - 200 –1.00E-05 200 - 250 –1.00E-05 250 - 300 –8.00E-06 300 - 350 –6.00E-06 350 - 400 –1.75E-05 0 - 400

Change of concentration in a time intervalChange of concentration in a time interval

Average Rate

0

0.002

0.004

0.006

0.008

0.01

0.012

0 50 100 150 200 250 300 350 400 450

Time, sec

Con

c.,m

ol/L

[NO2]

[NO]

[O2]

s

M10725.1

0 - 400

0.0100 - 0.0031

t- t

NO - NO

t

NO 5

0400

0240022

Slope of line between two points on the graphSlope of line between two points on the graph

Instantaneous rate

x

y line tangent of slope

t

NO rate 2

s 375

M0.009

t

NO s 100 @ rate 2

s

M10.42 s 100 @ rate 5-

Slope of tangent line at a point on the graphSlope of tangent line at a point on the graph

Instantaneous Rate

0.009 M

375 s

12_291

0.000370s

O2

0.0025

0.005

0.0075

0.0100

0.0006

70s

0.0026

110 s

NO2

NO

50 100 150 200 250 300 350 400

Con

cent

ratio

ns (

mol

/L)

Time (s)

[NO2 ]

t

Initial Rate (t = 0)

Initial rate

x

y line tangent of slope

t

NO rate 2

s 225

M0.010

t

NO s 0 @ rate 2

s

M10.44 s 0 @ rate 5-

Slope of tangent line at time 0 (y intercept)Slope of tangent line at time 0 (y intercept)

Rate Laws

k k == rate constantrate constant

m, n m, n == orderorder

nm BAk rate

22 O 2NO 2NO

rate rate == k[NOk[NO22]]nn

Introduction to Rate Laws

Reversible chemical reactionsReversible chemical reactions

Forward:Forward:

Backward:Backward:

Equilibrium:Equilibrium:

22 O 2NO 2NO

2NO O 2NO 22

22 O 2NO 2NO

Introduction

Dominant Reaction:Dominant Reaction:

Rate Law:Rate Law:

k, k’:k, k’: specific rate constantspecific rate constant

n :n : order of reactantorder of reactant

can be zero, fractional, or negativecan be zero, fractional, or negative

22 O 2NO 2NO

n22 NOk

t

NO rate

-

n22 NOk

t

O erat

Method of Initial Rates

Unknown:Unknown: k, m, nk, m, n

Initial rate:Initial rate: instantaneous rate just after instantaneous rate just after reaction is initiatedreaction is initiated

nm BAk rate

Initial Rates, NO2 decomposition

22 O 2NO 2NO

Experiment

Initial Conc.

[NO2]

Rate [O2]

Formation

1 0.01 7.1 x 10-5

2 0.02 2.8 x 10-4

n22 NOk

t

NO rate

-

Order of Reaction

General:General:

Substituting:Substituting:

Solution:Solution:

n21

n22

NOk-

NOk-

1 rate

2 rate

n1

n2

5-

-4

0.010k-

0.020k-

10 7.1

10 2.8

2 ln n 4ln

2 n(2) 4 n

so

Rate constant

Rate 1Rate 17.1 x 107.1 x 10-5 -5 M sM s-1-1 == -k[0.01 M]-k[0.01 M]22

kk == 0.71 M0.71 M-1-1 s s-1-1

Rate 2Rate 22.8 x 102.8 x 10-4 -4 M sM s-1-1 == -k[0.02 M]-k[0.02 M]22

kk == 0.70 M0.70 M-1-1 s s-1-1

n22 NOk

t

NO rate

-

222 NO70.0

t

NO law rate

You try

Experiment

Initial Conc.

[H2]

Initial Conc.

[I2] Rate

1 0.0113 0.0011 1.9 x 10-23

2 0.0220 0.0033 1.1 x 10-22

3 0.0550 0.0011 9.3 x 10-23

4 0.0220 0.0056 1.9 x 10-22

2HI I H 22

O2 + 2 NO 2NO2

Overall Order

Sum:Sum: 11 ++ 22 ++ 33

== 66

Overall order of reaction:Overall order of reaction: 66

32

32 IHSeOHk rate

Types

Differential:Differential:

RateRate dependence on dependence on concentrationconcentration

Integrated:Integrated:

ConcentrationConcentration dependence on dependence on timetime

n22 NOk

t

NO rate

-

n22 NOk

t

O erat

First Order Reactions

For aA For aA products products

Differential:Differential:

Integrated:Integrated:

Akt

A rate

-

0Alnkt - Aln t

kt A

Aln 0

t

Half-life, first order reactions

Integrated law:Integrated law:

Half-life:Half-life:

Half of initial reactedHalf of initial reacted

[A][A]tt = = ½[A]½[A]00

Independent of Independent of [A][A]00

kt A

Aln 0

t

k

0.693 t

k

ln2 t

21

21

Second Order Reactions

For aA For aA products products

Differential:Differential:

Integrated:Integrated:

2Akt

A rate

-

kt A

1

A

1

0

t

0A

1 kt

A

1

t

Half-life, second order reactions

Integrated law:Integrated law:

Half-life:Half-life:

Half of initial reactedHalf of initial reacted

[A][A]tt = = ½[A]½[A]00

Inversely proportional to Inversely proportional to [A][A]00

kt A

1

A

1

0

t

0Ak

1 t

21

Zero Order Reactions

For aA For aA products products

Differential:Differential:

Integrated:Integrated:

kAkt

A rate 0

-

kt- AA 0 t

0Akt - A t

Graphical Method

First orderFirst order

Second orderSecond order

Zero orderZero order

Straight lineStraight line

0Alnkt - Aln t

0A

1 kt

A

1

t

0Akt - A t

bmx y

First order

Plot:Plot:

ln[A] vs. timeln[A] vs. time

ln[A]

time

ln[A]0

slope = -k

0Alnkt - Aln t

bmx y

Second order

Plot:Plot:

1 1 vs. time vs. time

[A][A]time

1 [A]o

slope = k

bmx y

0A

1 kt

A

1

t

1 [A]

Zero order

Plot:Plot:

[A] vs. time[A] vs. time

[A]

time

[A]0

slope = -kbmx y

0Akt - A t

SummaryConditions set so dominant forward reactionConditions set so dominant forward reaction

Differential Rate LawsDifferential Rate Lawsrate as a function of concentrationrate as a function of concentrationmethod of initial ratesmethod of initial rates

Integrated Rate LawsIntegrated Rate Lawsconcentration as a function of timeconcentration as a function of timegraphical method graphical method

Experimental data collectionExperimental data collectionRate law types can be interconvertedRate law types can be interconverted

Reaction Mechanism

Chemical equation:Chemical equation: SummarySummary

Mechanism:Mechanism: Series of elementary stepsSeries of elementary steps

Elementary Steps:Elementary Steps: Reactions with rate lawsReactions with rate laws

from molecularityfrom molecularity

Molecularity:Molecularity: Number of species that must Number of species that must

collide to produce reactioncollide to produce reaction

Reaction Mechanism

Proposed elementary steps must satisfy conditions:Proposed elementary steps must satisfy conditions:

— reasonable reactionsreasonable reactions

— sum of steps = overall balanced reactionsum of steps = overall balanced reaction

— mechanism rate law = experimental rate mechanism rate law = experimental rate lawlaw

Intermediates

—appear in stepsappear in steps

—produced in one stepproduced in one step

—used in subsequentused in subsequent

—not in overall equationnot in overall equation

Rate-determining step

In a multi-step process:In a multi-step process:

SLOWEST stepSLOWEST step

Determines overall reaction rateDetermines overall reaction rate

““Bottleneck”Bottleneck”

Model for Kinetics

Collision TheoryCollision Theory

rate determined by particle collisionsrate determined by particle collisions

collision frequency and energycollision frequency and energy

Transition State TheoryTransition State Theory

how reactants convert to productshow reactants convert to products

Collision Theory (Bimolecular Collsions)

Z:Z: no. of bimolecular collisions per no. of bimolecular collisions per secondsecond

ffaa:: fraction with Efraction with Eaa

P:P: fraction with correct orientationfraction with correct orientation

EEaa:: activation energyactivation energy

p fZ rate a

Arrhenius Equation

k:k: rate constantrate constant

EEaa:: activation energy (minimum required)activation energy (minimum required)

T:T: absolute temperatureabsolute temperatureR:R: universal gas constantuniversal gas constantA:A: orientation factororientation factor

Energy & orientation requirements for reactionEnergy & orientation requirements for reaction

RT

Ea

Ae k

Hydrolysis of an ester

Transition State Theory

EEaa and internal energy: and internal energy:

Bonds breaking and formingBonds breaking and forming

Atoms rearrangingAtoms rearranging

““Transition State”Transition State”

Unstable intermediateUnstable intermediate

At point of highest energyAt point of highest energy

forward reaction reverse reaction

exothermic reaction

I- + CH3Cl Cl- + CH3I

Catalysts

Speed reactionSpeed reaction

Are not consumedAre not consumed

Alternative pathway for reaction with lower EAlternative pathway for reaction with lower Eaa

TypesTypes

HomogeneousHomogeneous

HeterogeneousHeterogeneous

Enzymes are biological catalystsEnzymes are biological catalysts

12_304

Ea (uncatalyzed )

Effectivecollisions(uncatalyzed)

Effectivecollisions(catalyzed)

Ea (catalyzed )

(a) (b)

Nu

mb

er

of c

olli

sio

ns

with

a g

ive

n e

ne

rgy

Nu

mb

er

of c

olli

sio

ns

with

a g

ive

n e

ne

rgy

Energy Energy

Adsorption, activation, reaction, desorption