chemical kinetics chapter 16. kinetics reaction rates factors affecting rate quantitative rate...
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Chemical Kinetics
Chapter 16Chapter 16
Kinetics
Reaction RatesReaction RatesFactors affecting rateFactors affecting rate
Quantitative rate expressionsQuantitative rate expressions
DeterminationDetermination
FactorsFactors
Models for RatesModels for Rates
Reaction MechanismsReaction Mechanisms
Effects of catalystsEffects of catalysts
Rates
Change in concentration of a reactant or product Change in concentration of a reactant or product per unit timeper unit time
t
A
t- t
A - A
t time,in Change
A conc, in Change
0t
0t
B A
12_292
.20
.40
.60
.80
1.00
400 800 1200 1600 2000
Rate = 5.4 x 10-4 mol/L.s
Rate = 2.7 x 10-4 mol/L.s
[N2O
5] (m
ol/L
)
Time (s)
Factors affecting rates
Nature of the reactantsNature of the reactants
State of subdivision/surface areaState of subdivision/surface area
ConcentrationConcentration
TemperatureTemperature
CatalystsCatalysts
Reactants
ComplexityComplexity
Bond strengthsBond strengths
Etc.Etc.
242342 O OHC O HC
242342 O OHC O HC
242342 O OHC O HC
Concentrations as functions of time
22 O 2NO 2NO
Time(s) [NO2] [NO] [O2]
0 0.0100 0.0000 0.000050 0.0079 0.0021 0.0011
100 0.0065 0.0035 0.0018150 0.0055 0.0045 0.0023200 0.0048 0.0052 0.0026250 0.0043 0.0057 0.0029300 0.0038 0.0062 0.0031350 0.0034 0.0066 0.0033400 0.0031 0.0069 0.0035
Graph: Concentration vs. time
22 O 2NO 2NO
M10725.1
0 - 400
0.0100 - 0.0031
t- t
NO - NO
t
NO 5
0400
0240022
Average Rate
-[NO2]/t time period(s)
–4.20E-05 0 - 50 –2.80E-05 50 - 100 –2.00E-05 100 - 150 –1.40E-05 150 - 200 –1.00E-05 200 - 250 –1.00E-05 250 - 300 –8.00E-06 300 - 350 –6.00E-06 350 - 400 –1.75E-05 0 - 400
Change of concentration in a time intervalChange of concentration in a time interval
Average Rate
0
0.002
0.004
0.006
0.008
0.01
0.012
0 50 100 150 200 250 300 350 400 450
Time, sec
Con
c.,m
ol/L
[NO2]
[NO]
[O2]
s
M10725.1
0 - 400
0.0100 - 0.0031
t- t
NO - NO
t
NO 5
0400
0240022
Slope of line between two points on the graphSlope of line between two points on the graph
Instantaneous rate
x
y line tangent of slope
t
NO rate 2
s 375
M0.009
t
NO s 100 @ rate 2
s
M10.42 s 100 @ rate 5-
Slope of tangent line at a point on the graphSlope of tangent line at a point on the graph
Instantaneous Rate
0.009 M
375 s
12_291
0.000370s
O2
0.0025
0.005
0.0075
0.0100
0.0006
70s
0.0026
110 s
NO2
NO
50 100 150 200 250 300 350 400
Con
cent
ratio
ns (
mol
/L)
Time (s)
[NO2 ]
t
Initial Rate (t = 0)
Initial rate
x
y line tangent of slope
t
NO rate 2
s 225
M0.010
t
NO s 0 @ rate 2
s
M10.44 s 0 @ rate 5-
Slope of tangent line at time 0 (y intercept)Slope of tangent line at time 0 (y intercept)
Rate Laws
k k == rate constantrate constant
m, n m, n == orderorder
nm BAk rate
22 O 2NO 2NO
rate rate == k[NOk[NO22]]nn
Introduction to Rate Laws
Reversible chemical reactionsReversible chemical reactions
Forward:Forward:
Backward:Backward:
Equilibrium:Equilibrium:
22 O 2NO 2NO
2NO O 2NO 22
22 O 2NO 2NO
Introduction
Dominant Reaction:Dominant Reaction:
Rate Law:Rate Law:
k, k’:k, k’: specific rate constantspecific rate constant
n :n : order of reactantorder of reactant
can be zero, fractional, or negativecan be zero, fractional, or negative
22 O 2NO 2NO
n22 NOk
t
NO rate
-
n22 NOk
t
O erat
Method of Initial Rates
Unknown:Unknown: k, m, nk, m, n
Initial rate:Initial rate: instantaneous rate just after instantaneous rate just after reaction is initiatedreaction is initiated
nm BAk rate
Initial Rates, NO2 decomposition
22 O 2NO 2NO
Experiment
Initial Conc.
[NO2]
Rate [O2]
Formation
1 0.01 7.1 x 10-5
2 0.02 2.8 x 10-4
n22 NOk
t
NO rate
-
Order of Reaction
General:General:
Substituting:Substituting:
Solution:Solution:
n21
n22
NOk-
NOk-
1 rate
2 rate
n1
n2
5-
-4
0.010k-
0.020k-
10 7.1
10 2.8
2 ln n 4ln
2 n(2) 4 n
so
Rate constant
Rate 1Rate 17.1 x 107.1 x 10-5 -5 M sM s-1-1 == -k[0.01 M]-k[0.01 M]22
kk == 0.71 M0.71 M-1-1 s s-1-1
Rate 2Rate 22.8 x 102.8 x 10-4 -4 M sM s-1-1 == -k[0.02 M]-k[0.02 M]22
kk == 0.70 M0.70 M-1-1 s s-1-1
n22 NOk
t
NO rate
-
222 NO70.0
t
NO law rate
You try
Experiment
Initial Conc.
[H2]
Initial Conc.
[I2] Rate
1 0.0113 0.0011 1.9 x 10-23
2 0.0220 0.0033 1.1 x 10-22
3 0.0550 0.0011 9.3 x 10-23
4 0.0220 0.0056 1.9 x 10-22
2HI I H 22
O2 + 2 NO 2NO2
Overall Order
Sum:Sum: 11 ++ 22 ++ 33
== 66
Overall order of reaction:Overall order of reaction: 66
32
32 IHSeOHk rate
Types
Differential:Differential:
RateRate dependence on dependence on concentrationconcentration
Integrated:Integrated:
ConcentrationConcentration dependence on dependence on timetime
n22 NOk
t
NO rate
-
n22 NOk
t
O erat
First Order Reactions
For aA For aA products products
Differential:Differential:
Integrated:Integrated:
Akt
A rate
-
0Alnkt - Aln t
kt A
Aln 0
t
Half-life, first order reactions
Integrated law:Integrated law:
Half-life:Half-life:
Half of initial reactedHalf of initial reacted
[A][A]tt = = ½[A]½[A]00
Independent of Independent of [A][A]00
kt A
Aln 0
t
k
0.693 t
k
ln2 t
21
21
Second Order Reactions
For aA For aA products products
Differential:Differential:
Integrated:Integrated:
2Akt
A rate
-
kt A
1
A
1
0
t
0A
1 kt
A
1
t
Half-life, second order reactions
Integrated law:Integrated law:
Half-life:Half-life:
Half of initial reactedHalf of initial reacted
[A][A]tt = = ½[A]½[A]00
Inversely proportional to Inversely proportional to [A][A]00
kt A
1
A
1
0
t
0Ak
1 t
21
Zero Order Reactions
For aA For aA products products
Differential:Differential:
Integrated:Integrated:
kAkt
A rate 0
-
kt- AA 0 t
0Akt - A t
Graphical Method
First orderFirst order
Second orderSecond order
Zero orderZero order
Straight lineStraight line
0Alnkt - Aln t
0A
1 kt
A
1
t
0Akt - A t
bmx y
First order
Plot:Plot:
ln[A] vs. timeln[A] vs. time
ln[A]
time
ln[A]0
slope = -k
0Alnkt - Aln t
bmx y
Second order
Plot:Plot:
1 1 vs. time vs. time
[A][A]time
1 [A]o
slope = k
bmx y
0A
1 kt
A
1
t
1 [A]
Zero order
Plot:Plot:
[A] vs. time[A] vs. time
[A]
time
[A]0
slope = -kbmx y
0Akt - A t
SummaryConditions set so dominant forward reactionConditions set so dominant forward reaction
Differential Rate LawsDifferential Rate Lawsrate as a function of concentrationrate as a function of concentrationmethod of initial ratesmethod of initial rates
Integrated Rate LawsIntegrated Rate Lawsconcentration as a function of timeconcentration as a function of timegraphical method graphical method
Experimental data collectionExperimental data collectionRate law types can be interconvertedRate law types can be interconverted
Reaction Mechanism
Chemical equation:Chemical equation: SummarySummary
Mechanism:Mechanism: Series of elementary stepsSeries of elementary steps
Elementary Steps:Elementary Steps: Reactions with rate lawsReactions with rate laws
from molecularityfrom molecularity
Molecularity:Molecularity: Number of species that must Number of species that must
collide to produce reactioncollide to produce reaction
Reaction Mechanism
Proposed elementary steps must satisfy conditions:Proposed elementary steps must satisfy conditions:
— reasonable reactionsreasonable reactions
— sum of steps = overall balanced reactionsum of steps = overall balanced reaction
— mechanism rate law = experimental rate mechanism rate law = experimental rate lawlaw
Intermediates
—appear in stepsappear in steps
—produced in one stepproduced in one step
—used in subsequentused in subsequent
—not in overall equationnot in overall equation
Rate-determining step
In a multi-step process:In a multi-step process:
SLOWEST stepSLOWEST step
Determines overall reaction rateDetermines overall reaction rate
““Bottleneck”Bottleneck”
Model for Kinetics
Collision TheoryCollision Theory
rate determined by particle collisionsrate determined by particle collisions
collision frequency and energycollision frequency and energy
Transition State TheoryTransition State Theory
how reactants convert to productshow reactants convert to products
Collision Theory (Bimolecular Collsions)
Z:Z: no. of bimolecular collisions per no. of bimolecular collisions per secondsecond
ffaa:: fraction with Efraction with Eaa
P:P: fraction with correct orientationfraction with correct orientation
EEaa:: activation energyactivation energy
p fZ rate a
Arrhenius Equation
k:k: rate constantrate constant
EEaa:: activation energy (minimum required)activation energy (minimum required)
T:T: absolute temperatureabsolute temperatureR:R: universal gas constantuniversal gas constantA:A: orientation factororientation factor
Energy & orientation requirements for reactionEnergy & orientation requirements for reaction
RT
Ea
Ae k
Hydrolysis of an ester
Transition State Theory
EEaa and internal energy: and internal energy:
Bonds breaking and formingBonds breaking and forming
Atoms rearrangingAtoms rearranging
““Transition State”Transition State”
Unstable intermediateUnstable intermediate
At point of highest energyAt point of highest energy
forward reaction reverse reaction
exothermic reaction
I- + CH3Cl Cl- + CH3I
Catalysts
Speed reactionSpeed reaction
Are not consumedAre not consumed
Alternative pathway for reaction with lower EAlternative pathway for reaction with lower Eaa
TypesTypes
HomogeneousHomogeneous
HeterogeneousHeterogeneous
Enzymes are biological catalystsEnzymes are biological catalysts
12_304
Ea (uncatalyzed )
Effectivecollisions(uncatalyzed)
Effectivecollisions(catalyzed)
Ea (catalyzed )
(a) (b)
Nu
mb
er
of c
olli
sio
ns
with
a g
ive
n e
ne
rgy
Nu
mb
er
of c
olli
sio
ns
with
a g
ive
n e
ne
rgy
Energy Energy
Adsorption, activation, reaction, desorption