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CHM 1046 : General Chemistry and Qualitative Analysis. Unit 15 Chemical Kinetics. Dr. Jorge L. Alonso Miami-Dade College – Kendall Campus Miami, FL. Textbook Reference : Chapter # 16 Module # 4. Thermodynamics vs Kinetics. {Kinetics: paper, Fe, C}. Rusting of Iron : - PowerPoint PPT Presentation
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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
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
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
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ChemicalKinetics
2007 (A)
ChemicalKinetics
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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
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
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
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
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
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 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
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
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ChemicalKinetics
2007 (A)
ChemicalKinetics
ChemicalKinetics
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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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
ChemicalKinetics
2005 A
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2005 B
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2006 (A)
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2007 (A)
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2005 A
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2005 B
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2006 (A)
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2007 (A)
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2005 B
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2006 (A)
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2007 (A)
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2005 B
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
2006 (A)
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
ChemicalKinetics
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