Chemical Kinetics
Chapter 16
Kinetics
Reaction Rates
Factors affecting rate
Quantitative rate expressions
Determination
Factors
Models for Rates
Reaction Mechanisms
Effects of catalysts
Rates
Change in concentration of a reactant or product
per unit time
A B
Change in conc, A At - A 0 A


Change in time, t
tt - t0
t
12_292
1.00
Rate = 5.4 x 10-4 mol/L.s
[N2O5] (mol/L)
.80
Rate = 2.7 x 10-4 mol/L.s
.60
.40
.20
400
800
1200
Time (s)
1600
2000
Factors affecting rates
Nature of the reactants
State of subdivision/surface area
Concentration
Temperature
Catalysts
Reactants
Complexity
Bond strengths
Etc.
C2 H 4  O3  C2 H 4 O  O 2
C2 H 4  O3  C2 H 4 O  O 2
C2 H 4  O3  C2 H 4 O  O 2
Concentrations as functions of time
2NO2
Time(s)
0
50
100
150
200
250
300
350
400
[NO2]
0.0100
0.0079
0.0065
0.0055
0.0048
0.0043
0.0038
0.0034
0.0031
2NO  O2
[NO]
0.0000
0.0021
0.0035
0.0045
0.0052
0.0057
0.0062
0.0066
0.0069
[O2 ]
0.0000
0.0011
0.0018
0.0023
0.0026
0.0029
0.0031
0.0033
0.0035
Graph: Concentration vs. time
NO2  NO2 400 - NO2 0 0.0031 - 0.0100


 1.725  10 5 M
t
t 400 - t 0
400 - 0
Concentration vs Time
0.012
Conc.,mol/L
2NO  O2
2NO2
[NO2]
0.01
0.008
[NO]
0.006
[O2]
0.004
0.002
0
0
50
100
150
200
250
Time, sec
300
350
400
450
Average Rate
Change of concentration in a time interval
-[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
Average Rate
Slope of line between two points on the graph
NO2  NO2 400 - NO2 0 0.0031 - 0.0100
5 M

 Concentration vs Time
 1.725  10
t
t 400 - t 0
400 - 0
s
0.012
[NO2]
0.01
Conc.,mol/L
0.008
[NO]
0.006
[O2]
0.004
0.002
0
0
50
100
150
200
250
Time, sec
300
350
400
450
Instantaneous rate
Slope of tangent line at a point on the graph
y
slope of tangent line 
x
NO2 
rate 
t
NO2   0.009 M
rate @ 100 s 

t
375 s
M
rate @ 100 s  2.4  10
s
-5
Instantaneous
Rate
Concentration vs Time
0.012
[NO2]
Conc.,mol/L
0.01
0.009 M
0.008
[NO]
0.006
[O2]
0.004
0.002
0
0
50
100
150
200
250
Time, sec
300
350
400
450
375 s
12_291
0.0100
NO2
Concentrations (mol/L)
0.0075
0.0026 [NO 2 ]
0.0006
70s
t
110 s
0.005
NO
0.0003
70s
0.0025
O2
50
100
150
200
Time (s)
250
300
350
400
Initial Rate (t = 0)
Concentration vs Time
0.012
[NO2]
Conc.,mol/L
0.01
0.008
[NO]
0.006
[O2]
0.004
0.002
0
0
50
100
150
200
250
Time, sec
300
350
400
450
Initial rate
Slope of tangent line at time 0 (y intercept)
y
slope of tangent line 
x
NO2 
rate 
t
NO2   0.010 M
rate @ 0 s 

t
225 s
M
rate @ 0 s  4.4  10
s
-5
Rate Laws
rate  kA B
m
k
=
m, n =
2NO2
rate =
n
rate constant
order
2NO  O2
k[NO2]n
Introduction to Rate Laws
Reversible chemical reactions
Forward:
2NO2
Backward:
2NO  O2
Equilibrium: 2NO2
2NO  O2
2NO2
2NO  O2
Introduction
Dominant Reaction:
Rate Law:
k, k’:
n:
2NO2
2NO  O2
NO 2 
n
rate   kNO 2 
t
O 2 
n
rate 
 k NO2 
t
specific rate constant
order of reactant
can be zero, fractional, or negative
Method of Initial Rates
rate  kA B
m
n
Unknown:
k, m, n
Initial rate:
instantaneous rate just after
reaction is initiated
Initial Rates, NO2 decomposition
2NO2
2NO  O2
NO 2 
n
rate   kNO 2 
t
Experiment
1
2
Initial Conc.
[NO2]
0.01
0.02
Rate [O2]
Formation
7.1 x 10
-5
2.8 x 10
-4
Order of Reaction
General:
rate 2 - k 2 NO2 

n
rate 1 - k1 NO2 
n
Substituting: 2.8  10
-4
7.1  10
-5
Solution:
4  (2)
n
ln 4  n

- k 2 0.020
n
- k1 0.010
n
so
ln 2
n2
Rate constant
NO 2 
n
rate   kNO 2 
t
Rate 1
7.1 x 10-5 M s-1
k
Rate 2
2.8 x 10-4 M s-1
k
=
=
-k[0.01 M]2
0.71 M-1 s-1
=
=
-k[0.02 M]2
0.70 M-1 s-1
NO2 
2
rate law 
 0.70NO2 
t
You try
H 2  I 2  2HI
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
O2 + 2 NO  2NO2
Overall Order
  I 
rate  kH 2SeO3  H
Sum:
1
=
+
6
2
Overall order of reaction:
+
6
 2
3
 3
Types
Differential:
Rate dependence on concentration
NO 2 
n
rate   kNO 2 
t
O 2 
n


rate 
 k NO2 
t
Integrated:
Concentration dependence on time
First Order Reactions
For aA  products
Differential:
A 
rate   kA 
t
Integrated:
ln At  - kt  ln A0

A 0
ln
A t
 kt
Half-life, first order reactions
Integrated law:

A 0
ln
A t
Half-life:
Half of initial reacted
[A]t = ½[A]0
Independent of [A]0
t1
t1
2
2
 kt
ln2

k
0.693

k
Second Order Reactions
For aA  products
Differential:
Integrated:
A 
2
rate   kA 
t
1
1
 kt 
At
A0
1
1

 kt
At A0
Half-life, second order reactions
Integrated law:
1
1

 kt
At A0
Half-life:
Half of initial reacted
[A]t = ½[A]0
Inversely proportional to [A]0
t1
2
1

kA0
Zero Order Reactions
For aA  products
Differential:
A
0
rate   kA  k
t
At  - kt  A0
Integrated:
At  A0  - kt
Graphical Method
First order
ln At  - kt  ln A0
Second order
1
1
 kt 
At
A0
Zero order
At
Straight line
 - kt  A0
y  mx  b
First order
ln[A]0
ln At  - kt  ln A0
y  mx  b
slope = -k
ln[A]
Plot:
ln[A] vs. time
time
Second order
1
1
 kt 
At
A0
y  mx  b
Plot:
1 vs. time
[A]
slope = k
1
[A]
1
[A]o
time
Zero order
At
 - kt  A0
y  mx  b
[A]0
slope = -k
[A]
Plot:
[A] vs. time
time
Summary
Conditions set so dominant forward reaction
Differential Rate Laws
rate as a function of concentration
method of initial rates
Integrated Rate Laws
concentration as a function of time
graphical method
Experimental data collection
Rate law types can be interconverted
Reaction Mechanism
Chemical equation:
Summary
Mechanism:
Series of elementary steps
Elementary Steps:
Reactions with rate laws
from molecularity
Molecularity:
Number of species that must
collide to produce reaction
Reaction Mechanism
Proposed elementary steps must satisfy conditions:
—
reasonable reactions
—
sum of steps = overall balanced reaction
—
mechanism rate law = experimental rate law
Intermediates
—
appear in steps
—
produced in one step
—
used in subsequent
—
not in overall equation
Rate-determining step
In a multi-step process:
SLOWEST step
Determines overall reaction rate
“Bottleneck”
Model for Kinetics
Collision Theory
rate determined by particle collisions
collision frequency and energy
Transition State Theory
how reactants convert to products
Collision Theory (Bimolecular Collsions)
rate  Z  f a  p
Z:
fa :
P:
no. of bimolecular collisions per second
fraction with Ea
fraction with correct orientation
Ea: activation energy
Arrhenius Equation
k
Ea

RT
Ae
k: rate constant
Ea: activation energy (minimum required)
T:absolute temperature
R: universal gas constant
A: orientation factor
Energy & orientation requirements for reaction
Hydrolysis of an ester
Transition State Theory
Ea and internal energy:
Bonds breaking and forming
Atoms rearranging
“Transition State”
Unstable intermediate
At point of highest energy
forward reaction
reverse reaction
exothermic reaction
I- + CH3Cl  Cl- + CH3I
Catalysts
Speed reaction
Are not consumed
Alternative pathway for reaction with lower Ea
Types
Homogeneous
Heterogeneous
Enzymes are biological catalysts
Number of collisions
with a given energy
Effective
collisions
(uncatalyzed)
Number of collisions
with a given energy
12_304
Ea (catalyzed )
E a (uncatalyzed )
Energy
(a)
Effective
collisions
(catalyzed)
Energy
(b)
Adsorption, activation, reaction, desorption