ChemicalKinetics

Unit 15Chemical Kinetics

Dr Jorge L AlonsoMiami-Dade College ndash

Kendall CampusMiami FL

Textbook Reference bullChapter 16bullModule 4

CHM 1046 General Chemistry and Qualitative Analysis

ChemicalKinetics

Thermodynamics vs Kinetics

Rusting of Iron

2Fe (s) + O2 (g) + 2H2O (l) rarr 2Fe(OH)2 (s)

Fe2O3 (s) + 2 Al (s)

Al2O3 (s) + 2 Fe (l)

Horxn = -8476 kJ

Thermite Reaction

(with limited O2 magnetite Fe3O4 is formed FeOmiddotFe2O3)

ThermiteRxnHo

rxn = -8846 kJ

Mg ignition

Kinetics paper Fe C

FSH2FSH1

ChemicalKinetics

Kineticsbull Studies the rate (speed) at which a chemical

process occurs

bull Kinetics also sheds light on the reaction mechanism (exactly how the reaction occurs)

Factors That Affect Reaction Ratesbull Physical State of the Reactantsbull Concentration of Reactants

bull Temperaturebull Presence of a Catalyst

ChemicalKinetics

Factors That Affect Reaction Rates

1 Physical State of the Reactants (surface area) In order to react molecules must come in

contact with each other

The more homogeneous the mixture of reactants the faster the molecules can react

bull Finely ground substances have more surface areas and react faster than chunk pieces

bull Gases liquids or solutions react faster than solids (Higher pressure and concentration also affects rate)

(1) Gases Liquids Solutions (High P amp Conc)

(2) Solids

RxRateLicopodiumPowder

Which will react faster

ChemicalKinetics

Thermodynamics vs Kinetics

Rusting of Iron

2Fe (s) + O2 (g) + 2H2O (l) rarr 2Fe(OH)2 (s)

Fe2O3 (s) + 2 Al (s)

Al2O3 (s) + 2 Fe (l)

Horxn = -8476 kJ

Thermite Reaction

(with limited O2 magnetite Fe3O4 is formed FeOmiddotFe2O3)

ThermiteRxnHo

rxn = -8846 kJ

Mg ignition

Kinetics paper Fe C

FSH2FSH1

ChemicalKinetics

Kineticsbull Studies the rate (speed) at which a chemical

process occurs

bull Kinetics also sheds light on the reaction mechanism (exactly how the reaction occurs)

Factors That Affect Reaction Ratesbull Physical State of the Reactantsbull Concentration of Reactants

bull Temperaturebull Presence of a Catalyst

ChemicalKinetics

Factors That Affect Reaction Rates

1 Physical State of the Reactants (surface area) In order to react molecules must come in

contact with each other

The more homogeneous the mixture of reactants the faster the molecules can react

bull Finely ground substances have more surface areas and react faster than chunk pieces

bull Gases liquids or solutions react faster than solids (Higher pressure and concentration also affects rate)

(1) Gases Liquids Solutions (High P amp Conc)

(2) Solids

RxRateLicopodiumPowder

Which will react faster

ChemicalKinetics

Kineticsbull Studies the rate (speed) at which a chemical

process occurs

bull Kinetics also sheds light on the reaction mechanism (exactly how the reaction occurs)

Factors That Affect Reaction Ratesbull Physical State of the Reactantsbull Concentration of Reactants

bull Temperaturebull Presence of a Catalyst

ChemicalKinetics

Factors That Affect Reaction Rates

1 Physical State of the Reactants (surface area) In order to react molecules must come in

contact with each other

The more homogeneous the mixture of reactants the faster the molecules can react

bull Finely ground substances have more surface areas and react faster than chunk pieces

bull Gases liquids or solutions react faster than solids (Higher pressure and concentration also affects rate)

(1) Gases Liquids Solutions (High P amp Conc)

(2) Solids

RxRateLicopodiumPowder

Which will react faster

ChemicalKinetics

Factors That Affect Reaction Rates

1 Physical State of the Reactants (surface area) In order to react molecules must come in

contact with each other

The more homogeneous the mixture of reactants the faster the molecules can react

bull Finely ground substances have more surface areas and react faster than chunk pieces

bull Gases liquids or solutions react faster than solids (Higher pressure and concentration also affects rate)

(1) Gases Liquids Solutions (High P amp Conc)

(2) Solids

RxRateLicopodiumPowder

Which will react faster

ChemicalKinetics

Factors That Affect Reaction Rates

2 Concentration of Reactants As the concentration of

reactants increases so does the likelihood that reactant molecules will collide

RxRateampConcMg+HCl

RxnwithConcOxy

RxRateampConcMg+HClGraph

03 M 6 M

ChemicalKinetics

Reaction Rates

determined by monitoring the change in

concentration of either reactants or products as

a function of time

-[A] t

[B] tRate = =

[A]amp [B] [B][A]

A B

Spectrometer

RxRateIntro

ChemicalKinetics

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Reaction Rates

butyl chloride butanol

Rate = =-[A] t

[B] t

-[A]

-[A]

t

t

ChemicalKinetics

Reaction Rates

The average rate of the reaction over each interval is the change in concentration divided by the change in time Ave rate =

[C4H9Cl]t

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull Note that the average rate decreases as the reaction proceeds

bull This is because as the reaction goes forward there are fewer collisions between reactant molecules

ChemicalKinetics

Reaction Rates

bull The slope of a line tangent to the curve at any point is the instantaneous rate at that time

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull All reactions slow down over time

bull Therefore the best indicator of the rate of a reaction is the instantaneous rate near the beginning

Concentration vs Time Graph

ChemicalKinetics

Reaction Rates and Stoichiometry

bull In this reaction the ratio of C4H9Cl to C4H9OH is 11

bull Thus the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Rate =-[C4H9Cl]

t=

[C4H9OH]t

ChemicalKinetics

Reaction Rates and Stoichiometry

bull To generalize then for the reaction

a A + b B c C + d D

bull What if the ratio is not 112 HI(g) H2(g) + I2(g)

Rate = minus 12

[HI]t

= [I2]t

t

D

d

1

t

C

c

1

t

B

b

1

t

A

a

1Rate

Rate = minus [HI]t

=[I2]t

Rate1 = minus[HI]t

Rate2 =[I2]t

How do rates compare ne

ChemicalKinetics

Practice Problems

52 10x 81t

O

s100

00350

2

1Rate

t

O

bt

NO

aRate

22 11

t

B

2

1

t

A

3

1Rate

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

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ChemicalKinetics

Additional Practice Problems

Where are the answers

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2000

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c)

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2004 A

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2004 B

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2005 A

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2005 B

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2006 (A)

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2007 (A)

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Reaction Rates

determined by monitoring the change in

concentration of either reactants or products as

a function of time

-[A] t

[B] tRate = =

[A]amp [B] [B][A]

A B

Spectrometer

RxRateIntro

ChemicalKinetics

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Reaction Rates

butyl chloride butanol

Rate = =-[A] t

[B] t

-[A]

-[A]

t

t

ChemicalKinetics

Reaction Rates

The average rate of the reaction over each interval is the change in concentration divided by the change in time Ave rate =

[C4H9Cl]t

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull Note that the average rate decreases as the reaction proceeds

bull This is because as the reaction goes forward there are fewer collisions between reactant molecules

ChemicalKinetics

Reaction Rates

bull The slope of a line tangent to the curve at any point is the instantaneous rate at that time

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull All reactions slow down over time

bull Therefore the best indicator of the rate of a reaction is the instantaneous rate near the beginning

Concentration vs Time Graph

ChemicalKinetics

Reaction Rates and Stoichiometry

bull In this reaction the ratio of C4H9Cl to C4H9OH is 11

bull Thus the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Rate =-[C4H9Cl]

t=

[C4H9OH]t

ChemicalKinetics

Reaction Rates and Stoichiometry

bull To generalize then for the reaction

a A + b B c C + d D

bull What if the ratio is not 112 HI(g) H2(g) + I2(g)

Rate = minus 12

[HI]t

= [I2]t

t

D

d

1

t

C

c

1

t

B

b

1

t

A

a

1Rate

Rate = minus [HI]t

=[I2]t

Rate1 = minus[HI]t

Rate2 =[I2]t

How do rates compare ne

ChemicalKinetics

Practice Problems

52 10x 81t

O

s100

00350

2

1Rate

t

O

bt

NO

aRate

22 11

t

B

2

1

t

A

3

1Rate

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Reaction Rates

butyl chloride butanol

Rate = =-[A] t

[B] t

-[A]

-[A]

t

t

ChemicalKinetics

Reaction Rates

The average rate of the reaction over each interval is the change in concentration divided by the change in time Ave rate =

[C4H9Cl]t

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull Note that the average rate decreases as the reaction proceeds

bull This is because as the reaction goes forward there are fewer collisions between reactant molecules

ChemicalKinetics

Reaction Rates

bull The slope of a line tangent to the curve at any point is the instantaneous rate at that time

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull All reactions slow down over time

bull Therefore the best indicator of the rate of a reaction is the instantaneous rate near the beginning

Concentration vs Time Graph

ChemicalKinetics

Reaction Rates and Stoichiometry

bull In this reaction the ratio of C4H9Cl to C4H9OH is 11

bull Thus the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Rate =-[C4H9Cl]

t=

[C4H9OH]t

ChemicalKinetics

Reaction Rates and Stoichiometry

bull To generalize then for the reaction

a A + b B c C + d D

bull What if the ratio is not 112 HI(g) H2(g) + I2(g)

Rate = minus 12

[HI]t

= [I2]t

t

D

d

1

t

C

c

1

t

B

b

1

t

A

a

1Rate

Rate = minus [HI]t

=[I2]t

Rate1 = minus[HI]t

Rate2 =[I2]t

How do rates compare ne

ChemicalKinetics

Practice Problems

52 10x 81t

O

s100

00350

2

1Rate

t

O

bt

NO

aRate

22 11

t

B

2

1

t

A

3

1Rate

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Reaction Rates

The average rate of the reaction over each interval is the change in concentration divided by the change in time Ave rate =

[C4H9Cl]t

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull Note that the average rate decreases as the reaction proceeds

bull This is because as the reaction goes forward there are fewer collisions between reactant molecules

ChemicalKinetics

Reaction Rates

bull The slope of a line tangent to the curve at any point is the instantaneous rate at that time

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull All reactions slow down over time

bull Therefore the best indicator of the rate of a reaction is the instantaneous rate near the beginning

Concentration vs Time Graph

ChemicalKinetics

Reaction Rates and Stoichiometry

bull In this reaction the ratio of C4H9Cl to C4H9OH is 11

bull Thus the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Rate =-[C4H9Cl]

t=

[C4H9OH]t

ChemicalKinetics

Reaction Rates and Stoichiometry

bull To generalize then for the reaction

a A + b B c C + d D

bull What if the ratio is not 112 HI(g) H2(g) + I2(g)

Rate = minus 12

[HI]t

= [I2]t

t

D

d

1

t

C

c

1

t

B

b

1

t

A

a

1Rate

Rate = minus [HI]t

=[I2]t

Rate1 = minus[HI]t

Rate2 =[I2]t

How do rates compare ne

ChemicalKinetics

Practice Problems

52 10x 81t

O

s100

00350

2

1Rate

t

O

bt

NO

aRate

22 11

t

B

2

1

t

A

3

1Rate

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Reaction Rates

bull The slope of a line tangent to the curve at any point is the instantaneous rate at that time

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

bull All reactions slow down over time

bull Therefore the best indicator of the rate of a reaction is the instantaneous rate near the beginning

Concentration vs Time Graph

ChemicalKinetics

Reaction Rates and Stoichiometry

bull In this reaction the ratio of C4H9Cl to C4H9OH is 11

bull Thus the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Rate =-[C4H9Cl]

t=

[C4H9OH]t

ChemicalKinetics

Reaction Rates and Stoichiometry

bull To generalize then for the reaction

a A + b B c C + d D

bull What if the ratio is not 112 HI(g) H2(g) + I2(g)

Rate = minus 12

[HI]t

= [I2]t

t

D

d

1

t

C

c

1

t

B

b

1

t

A

a

1Rate

Rate = minus [HI]t

=[I2]t

Rate1 = minus[HI]t

Rate2 =[I2]t

How do rates compare ne

ChemicalKinetics

Practice Problems

52 10x 81t

O

s100

00350

2

1Rate

t

O

bt

NO

aRate

22 11

t

B

2

1

t

A

3

1Rate

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Reaction Rates and Stoichiometry

bull In this reaction the ratio of C4H9Cl to C4H9OH is 11

bull Thus the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Rate =-[C4H9Cl]

t=

[C4H9OH]t

ChemicalKinetics

Reaction Rates and Stoichiometry

bull To generalize then for the reaction

a A + b B c C + d D

bull What if the ratio is not 112 HI(g) H2(g) + I2(g)

Rate = minus 12

[HI]t

= [I2]t

t

D

d

1

t

C

c

1

t

B

b

1

t

A

a

1Rate

Rate = minus [HI]t

=[I2]t

Rate1 = minus[HI]t

Rate2 =[I2]t

How do rates compare ne

ChemicalKinetics

Practice Problems

52 10x 81t

O

s100

00350

2

1Rate

t

O

bt

NO

aRate

22 11

t

B

2

1

t

A

3

1Rate

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Reaction Rates and Stoichiometry

bull To generalize then for the reaction

a A + b B c C + d D

bull What if the ratio is not 112 HI(g) H2(g) + I2(g)

Rate = minus 12

[HI]t

= [I2]t

t

D

d

1

t

C

c

1

t

B

b

1

t

A

a

1Rate

Rate = minus [HI]t

=[I2]t

Rate1 = minus[HI]t

Rate2 =[I2]t

How do rates compare ne

ChemicalKinetics

Practice Problems

52 10x 81t

O

s100

00350

2

1Rate

t

O

bt

NO

aRate

22 11

t

B

2

1

t

A

3

1Rate

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Practice Problems

52 10x 81t

O

s100

00350

2

1Rate

t

O

bt

NO

aRate

22 11

t

B

2

1

t

A

3

1Rate

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

0510)07301240(

secmol10 x 22

10

022A 3-

st

rateave

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Data shows the relationship between the reaction rate and the conc of reactants

How does Concentration affect Rate

NH4+(aq) + NO2

minus(aq) N2(g) + 2 H2O(l)

bull The data demonstrates

Rate [NH4+]

Rate [NO2minus]

Rate [NH4+] [NO2

minus]or

Rate = k [NH4+] [NO2

minus]This equation is the rate law and k is the rate constant particular temp

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Generalized Rate Laws

bull The exponents x and y express the order of reaction and bear no necessary relationship to the coefficients of the balanced equation ndash they must be determined experimentally

bull This reaction is x - order in [A] y - order in [B]

Overall rate = x + y

Rate = k [A]x [B]y

a A + b B c C

Only if reaction occurs in one step mechanism will x and y equal coefficients of balanced equation

tctbta

C1B1A1

bull The overall reaction order can be found by adding the exponents on the reactants in the rate law

The previous reaction is second-order overall

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Rate = k [A]2 [B]0 = k [A]2

Experiment Number [A] (M) [B] (M)

Initial Rate (Ms)

1 0100 0100 40 x 10-5

2 0100 0200 40 x 10-5

3 0200 0100 160 x 10-5

Determination of Rate Law from Reaction Rate Data

If rate not affected by [A] then order with respect to [A] is x = 0 [2A] rate= k [3A] rate= k etchellip the same applies to [B]

Rate = k [A]x [B]y

If the rate affected by [A] in linear fashion then order [A] is x = 1 [2A]1 rate= 2x [3A]1 rate= 3xetchellip the same applies to [B]

If rate affected by [A] in exponential fashion order [A] is x = 2 [2A]2 rate =4x [3A]2 rate =9x etchellip the same applies to [B]

What are the possible values for x and y

Possibilities for x and y Zero order = no effect1st order = linear effect2nd order = exponential

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Integrated Rate Laws

Rate = = k [A]x

For reaction a A Products

Reaction rate can be defined in two mathematical ways (1) empirically as change in conc over time or (2) as a function of concentration (rate law)

-[A]

t

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

y = mx + b y = mx + by = mx + b

Using calculus we can integrate the rate law equation to gives us a mathematical relationship that shows us how the concentration varies over a period of time Rate expressions are then rearranged into linear equations

= k

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

[A]t = minus kt + [A]0ln [A]t = minus kt + ln [A]0

For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

1[A]t

= kt +1

[A]0

IntegrateIntegrate IntegrateIntegrate IntegrateIntegrate

Integrated Rate Laws

[A]

[A]

ln[A] 1

[A]

[A]ln[A]

= k

y = mx + b

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

How many moles of X were initially in the flask

How many molecules of Y were produced in the first 20 minutes of the reaction

What is the order of this reaction with respect to X Justify your answer

Write the rate law for this reaction

X(g) 2 Y(g) + Z (g)

1]X[]X[

1

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Calculate the specific rate constant for this reaction Specify units

Calculate the concentration of X in the flask after a total of 150 minutes of reaction

X(g) 2 Y(g) + Z (g)

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Practice Problems

0][

1

][

1

Akt

A t

ktAA t

0][

1

][

1)100(

]01000[

1

]00650[

1

0

skt

k

100

100154

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Half-Life

t12 =

0693k

1k[A]0

[A]0

2k

t12 =

t12 =

For a zero-order process

For a first-order process

For a second-order process

1stOrderampfrac12Life

bull Half-life is defined as the time required for one-half of a reactant to react

[A]0

[A]frac12

bull Because [A] at t12 is one-half of the original [A] [A]t = 05 [A]0

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Half-LifeFor a first-order process

05 [A]0

[A]0

ln = minuskt12

ln 05 = minuskt12

minus0693 = minuskt12

= t12

0693k

NOTE For a first-order process the half-life does not depend on [A]0

For a second-order process

105 [A]0

= kt12 + 1

[A]0

2[A]0

= kt12 + 1

[A]0

2 [A]0

= kt12

1[A]0

-

= t12

1k[A]0

1[A]t

= kt +1

[A]0ln [A]t = minus kt + ln [A]0

ln 05[A]0 = minus kt12 + ln [A]0

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Practice Problems

11 ss

k

= k [A]0-[A]

t= k [A]2

-[A]

t= k [A]1

-[A]

t

For each of the following rate expression determine the units of the rate constant k

= k [M]0-[M]

t= k [M]1

-[M]

t= k [M]2

-[M]

t

= t12

0693k

1sMs

M k 11sMMs

1k

ln 05[A]0 = minus ktfrac12 + ln [A]0ln [A]t = minus kt + ln [A]0

03850k

07502

0150 1500

2

3000 3000

2

6000

min183

min54

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Kinetics

Factors That Affect Reaction Rates1 Physical State of the Reactants

2 Concentration of Reactants

3 Temperaturebull Activation Energy (Transition State

Theory)bull Reaction Mechanisms4 Presence of a Catalyst

Rate = = k [A]x -[A]

t

Rate(s) (l ) (g)

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Factors That Affect Reaction Rates3 Temperature

At higher temperatures reactant molecules have more kinetic energy move faster and collide more often and with greater energy

RxRateampTemp

bull Generally as temperature increases so does the reaction rate

bull This is because k is temperature dependent

bull k is also dependent on activation energy

ln [A]t = minus kt + ln [A]0

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Activation Energy The Collision Model

bull In a chemical reaction bonds are broken and new bonds are formedbull Molecules can only react if they collide with each other with sufficient

(activation) energy (Ea)

Furthermore molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation

O3 + NO O2 + NO2

EaCollisionEnergy

EaOrientation

EaEner+Orient

( )Activated Complex

+

Reactants

+

Products

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Transition State Theory

PotentialEnergy

Reaction Coordinate

Reactants

Products

H

Transition state (Energy Level))

Energy Reaction Coordinate Diagrams

Ea = Activation Energy

EaampTransS tate

X3-YZ Activated Complex (the molecule)

( )Activated Complex

+

Reactants

+

Products

H

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

MaxwellndashBoltzmann Distributionsbull Temperature is defined as a measure of the average kinetic energy of the

molecules in a sample

bull At any temperature there is a wide distribution of kinetic energies

bull As the temperature increases the curve flattens and broadens

bull Thus at higher temperatures a larger population of molecules has higher energy

bull If the dotted line represents the activation energy as the temperature increases so does the fraction of molecules that can overcome the activation energy barrier

bull As a result the reaction rate increases

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

MaxwellndashBoltzmann Distributions

This fraction of molecules can be found through the expression

where R is the gas constant and T is the Kelvin temperature f = eminusEaRT

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Arrhenius EquationSvante Arrhenius developed a mathematical relationship between the rate constant k the temperature (T) at which the reaction occurs and the activation energy Ea

k = A eminusEaRT

where A is the frequency factor a number that represents the likelihood that collisions would occur with the proper orientation for reaction

21 T

1

T

1

R

Ea

1

2

kk

ln

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Arrhenius Equation

R

Eslope a RslopeEa x

Therefore if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs 1T

ln k = -Ea ( ) + ln A1T

y = m x + b

Problem Calculate the activation energy (in Jmol) for the reaction in plot above R= 831 JmolK

R

)KmolJ318(001950002150

)76()410(Ea

x

molJ10x81)KmolJ318(K00020

73E 4

1a x

k = A eminusEaRT

Taking the natural logarithm of both sides the equation becomes

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Reaction Mechanisms

The detailed sequence of events that describes the actual pathway by which reactants become products

OH- (aq) + CH3Cl (g) CH3OH (aq) + Cl- (aq)

RxMechaBimolecularIntro

Activated Complex ProductsReactants

Transition State

Methyl chloride Methyl alcohol

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2000

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

c)

ChemicalKinetics

2004 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2004 B

ChemicalKinetics

ChemicalKinetics

2005 A

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Reaction MechanismsConsider the following reaction

bull A proposed mechanism for this reaction is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

Movie1

RxMechanismNO2+COProp1

Movie 2

Experimental Evidence reaction rate is second order in [NO2] amp does not depend on [CO] at all even though CO is required for reaction to occur

Rate = k [NO2]2

NO3 = intermediate reactant

Bimolecular mechanism conc of both reactants affects rate

bull The overall reaction cannot occur faster than this slowest rate-determining step

ChemicalKinetics

Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

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Additional Practice Problems

Where are the answers

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Determining Rx MechanismsUsing radioactive isotope labeling can help us to experimentally determine the reaction mechanism

bull Better proposed mechanism is

Step 1 NO2 + NO2 NO3 + NO (slow)

Step 2 NO3 + CO NO2 + CO2 (fast)

NO2 (g) + CO (g) NO (g) + CO2 (g)

DeterRxMechanismIsotopLabel1NO2+CO

DeterRxMechanismIsotopLabel2NO2+CO

The simplest proposed mechanism is

frac12 labeled

ChemicalKinetics

Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

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Where are the answers

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Factors That Affect Reaction Rates

4 Presence of a Catalyst Catalysts speed up reactions Catalysts are not consumed during

the course of the reaction

Catalyst of SO2 + H2S

Catalysis of H2O2 by MnO22 H2O2 (l) 2 H2O (l) + O2 (g)

MnO2

H2OSO2 + 2 H2S 2 H2O(l) + 3 S(aq)

ChemicalKinetics

CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

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CatalystsIncrease the reaction rate by changing the

mechanism thus also changing (decreasing) the activation energy by which the process occurs

Add catalystEa

Ea

ChemicalKinetics

NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

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NO NO N2 O2

Some Reactions an in Internal Combustion Engine

2 C8H18 (l) + 25 O2 (g) 16 CO2 (g) + 18 H2O (g) (+heat)

N2 (g) + O2 (g) 2 NO (g) (causes acid rain amp ozone depletion))Pt Catalytic Converter 2 NO(g) O2(g) + N2(g)

Surface Catalysis

Pt

Pt Surface

Pt

Reactant molecules attach to Catalytic Surface

Bonds of attached molecules are Broken

Atoms recombine to form product which are then released from surface

ChemicalKinetics

The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

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The catalyst (in the form of platinum and palladium) is coated onto a ceramic honeycomb or ceramic beads that are housed in a muffler-like package attached to the exhaust pipe

Catalytic Converters

The catalyst helps to convert carbon monoxide into carbon dioxide It converts the hydrocarbons into carbon dioxide and water It also converts the nitrogen oxides back into nitrogen and oxygen

ChemicalKinetics

Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

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Catalysis

One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break

H2 + H2C=CH2 H3C-CH3

Ethylene Ethane

Ni

SurfaceCatalysisHydrogenation

ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

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ChemicalKinetics

Enzymes biological catalysts

bull Lock and Key Theory the substrate (reactant) fits into the active site of the enzyme much like a key fits into a lock

substrate

enzyme

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

Additional Practice Problems

Where are the answers

ChemicalKinetics

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2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2005 B

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2006 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

2007 (A)

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics

ChemicalKinetics