Peter Atkins • Julio de Paula
Atkins’ Physical Chemistry
Eighth Edition
Chapter 22 – Lecture 3
The Rates of Chemical Reactions
Copyright © 2006 by Peter Atkins and Julio de Paula
Rate Law:
An experimentally determined law of nature
Mechanism: A theory of the sequence of events that may
be occurring at the molecular level
The mechanism must agree with the rate law!!
Example of a mechanism once believed to be correct
H2 (g) + I2 (g) ⇌ 2 HI (g)
Rate law proposed in 1894:
ratef = kf [H2] [I2]
rater = kr [HI]2
Mechanism:
appears to be a simple
bimolecular mechanism
Step (1)
H2 + I2 ⇌ H2I2
Step (2)
H2I2 → 2 HI
Rate law proposed in 1967:
rate 
1
2
k[H2 ][I2 ]
k' [HI]
1
[I2 ]
Reaction Mechanisms
The overall progress of a chemical reaction can be represented
at the molecular level by a series of simple elementary steps
or elementary reactions
The sequence of elementary steps that leads to product
formation is the reaction mechanism.
2NO (g) + O2 (g)
2NO2 (g)
N2O2 is detected during the reaction!
Elementary step:
NO + NO
N 2O 2
+ Elementary step:
N2O2 + O2
2NO2
Overall reaction:
2NO + O2
2NO2
Intermediates - species that appear in a reaction mechanism
but not in the overall balanced equation
An intermediate is always formed in an early elementary step
and consumed in a later elementary step.
Elementary step:
NO + NO
N 2O 2
+ Elementary step:
N2O2 + O2
2NO2
Overall reaction:
2NO + O2
2NO2
Molecularity of a reaction - the number of molecules reacting
in an elementary step.
•
Unimolecular reaction – elementary step with 1 molecule
•
Bimolecular reaction – elementary step with 2 molecules
•
Termolecular reaction – elementary step with 3 molecules
Rate Laws and Elementary Steps
Unimolecular reaction
A
products
rate = k [A]
Bimolecular reaction
A+B
products
rate = k [A][B]
Bimolecular reaction
A+A
products
rate = k [A]2
Writing plausible reaction mechanisms:
•
The sum of the elementary steps must give the overall
balanced equation for the reaction.
•
The rate-determining step should predict the same rate
law that is determined experimentally.
Rate-determining step - the slowest step in the
sequence of steps leading to product formation.
Fig. 22.16 Diagrams of possible reaction schemes
Fig. 22.17 Reaction profile when 1st step is RDS
The experimental rate law for the reaction between NO2
and CO to produce NO and CO2 is rate = k[NO2]2. The
reaction is believed to occur via two steps:
Step 1:
NO2 + NO2
NO + NO3
Step 2:
NO3 + CO
NO2 + CO2
What is the equation for the overall reaction?
NO2+ CO
NO + CO2
What is the intermediate?
NO3
What can you say about the relative rates of steps 1 and 2?
rate = k[NO2]2 is the rate law for step 1 so
step 1 must be slower than step 2
Fig. 22.8 Approach of concentrations to their equilibrium values
For the reaction: A ⇌ B
• In practice, most kinetic
studies are on reactions
far from equilibrium
• ∴ Reverse reactions
are unimportant
Fig. 22.13 Concentrations of A, I and P with time
A→I→P
Consumption of A is ordinary
1st-order decay:
[ A]  [ A]o e k a t
Note that the concentration of I
rises to a maximum
then falls to zero...
Fig. 22.14 Basis of steady-state approximation
A→I→P
Assumption:
d[I]
0
dt
[I] remains negligibly small
Fig. 22.15 Comparison of the exact result for the concentrations
of a reaction and concentrations from steady-state approximation
How do we postulate a plausible mechanism?
• Common approach is to use the kinetic isotope effect
• Process facilitates identification of bond-breaking events
• Decrease in reaction rate is observed when an atom is
replaced with a heavier isotope
• Primary kinetic isotope effect – the RDS requires scission
of a bond involving that isotope
• Secondary kinetic isotope effect – bond scission occurs
in a bond NOT involving that isotope
How do we postulate a plausible mechanism?
• Effect arises from change in activation energy when atom
is replaced with a heavier isotope
• Change is in zero-point vibrational energy of bond
E vib  (v 
1 )hν
2
Fig. 22.18 Changes in reaction profile when a C−H
bond is replaced with C−D
Fig. 22.19 Protons can tunnel through the activation barrier
• Effective barrier
height is reduced
• Important only at
low temperatures
when most of the
reactant molecules
are left of the barrier
• More important in
electron transfer
reactions even at room
temperature
Fig. 22.20 Difference in zero-point vibrational energies to
describe the secondary kinetic isotope effect
k(D)
 eλ
k(H)
where λ is an
experimentally
determined parameter
• If λ > 1 then the deuterated
form reacts more slowly
• If λ < 1 then the undeuterated
form reacts more slowly