Chapter 13 b: Chemical Kinetics
Sections 13.5-13.7
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
40
The Effect of Temperature on
reaction Rate
Rate of reaction depends on the temperature
can by explained by collision theory.
Rate constant k vary with the temperature
Arrhenius equation:(Svante Arrhenius 1889)
where T is the temperature in Kelvins
R is gas constant in energy units, 8.314 J/(mol·K)
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
41
Arrhenius equation
Frequency factor, A (pre-exponential factor) - # of times that
reactants approach the activation barrier per unit time
is a number between 0 and 1
Activation energy, Ea -The energy barrier, or the hump that
must be surmounted by the reactants to be transformed to
products
Exponential factor- The fraction of approaches that are
successful in crossing the activation barrier and forming
products
The exponential factor increases with increasing T but
decreases with an increasing value of activation energy
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
42
Activation energy
•Activation energy, Ea-
The minimum energy of collision
required for two molecules to
react is called the activation
energy, Ea.
•Higher the Ea slower is the rate
of a reaction
Chapter 13: Chemical Kinetics
A. Ghumman
Chem 1011
43
Transition-state theory
Transition-state theory explains the reaction resulting from
the collision of two molecules in terms of an activated
complex.
e.g. A reaction in which methyl isonitrile(CH3NC) rearranges to
isonitrile(CH3CN)
In order for the reaction to occur, the
H3C-N bond must break, and a new
H3C-C bond form.
Chapter 13: Chemical Kinetics
A. Ghumman
Chem 1011
44
Activated complex
An activated
complex (transition
state) is an unstable
grouping of atoms
that can break up to
form products.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
45
Potential-Energy Diagrams for
Reactions
To illustrate graphically the formation of a transition
state, we can plot the potential energy of a
reaction versus time.
Figure illustrates the endothermic reaction of nitric
oxide and chlorine gas.
Note that the activation energy is the energy
necessary to form the activated complex.
The ∆H of the reaction is the net change in energy
between reactants and products
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
46
Potential-energy curve for the endothermic
reactions
Chem 1011
reaction of nitric
and chlorine
Chapter 13: Chemical Kineticsoxide
A. Ghumman
47
Potential-energy curve for the exothermic
reactions
Products are at lower energy than the reactants.
For the reverse reaction we have to supply enough activation
energy to form the activated complex.
Ea(forward)-Ea(reverse) = ∆H
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
48
Reaction Rate and Temperature
The higher the energy barrier (larger activation energy), the
fewer molecules that have sufficient energy to overcome it.
That extra energy comes from converting the kinetic energy of
motion to potential energy in the molecule when the molecules
collide.
Increasing the temperature increases the average kinetic
energy of the molecules.
• will increase the number of molecules with sufficient
energy to overcome the energy barrier.
Therefore, increasing the temperature will increase the
reaction rate.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
49
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
50
Experimental Measurements of the
frequency factor, A and Ea
Taking the natural logarithm of both sides of the Arrhenius
equation, we get
ln k = ln A -
Ea
RT
Rearrange
y =
mx
+
b
Arrhenius plot-A graph of ln(k) vs. (1/T) is a straight line with a
slope of –Ea/R
(−8.314 J/mol·K)(slope of the line) = Ea (in Joules)
ey-intercept = A, (unit is the same as k)
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
51
Determine the activation energy and frequency
factor for the reaction given the following data.
O3(g) → O2(g) + O(g)
Temp,
K
600
700
800
900
1000
1100
1200
∙
3.37 × 10
4.83 × 10
3.58 × 10
1.70 × 10
5.90 × 10
1.63 × 10
3.81 × 10
k, M–1 s–1
Chem 1011
Temp,
K
3
1300
4
1400
5
1500
6
1600
6
1700
7
1800
7
1900
∙
7.83 × 10
1.45 × 10
2.46 × 10
3.93 × 10
5.93 × 10
8.55 × 10
1.19 × 10
k, M–1 s–1
7
8
8
8
8
8
9
Chapter 13: Chemical Kinetics
A. Ghumman
52
Arrhenius Equation:
Two-Point Form
If you have only two (T,k) data points, the following forms of
the Arrhenius equation can be used:
Ea 1
1
R T1
ln k = ln A -
and
ln k 2 = ln A -
( )
Ea
R
( T1 )
2
– With this form of the equation, given the activation energy
and the rate constant k1 at a given temperature T1, we can
find the rate constant k2 at any other temperature, T2.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
53
Sample Problem 13.8
The reaction given below has a rate constant k of
2.57 M–1∙s–1 at 701 K and 567 M–1∙s–1 at 895 K. Find
the activation energy in kJ/mol.
NO2(g) + CO(g) → CO2(g) + NO(g)
It is often said that the rate of a reaction doubles for
every 10 °C rise in temperature. Calculate the
activation energy for such a reaction.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
54
Collision Theory of Kinetics
For most reactions, in order for a reaction to take
place, the reacting molecules must collide with each
other.
Once molecules collide they may react together or
they may not, depending on two factors:
1. whether the collision has enough energy (Ea) to
“break the bonds holding reactant molecules
together”;
2. whether the reacting molecules collide in the proper
orientation for new bonds to form.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
55
Collision Theory
•Frequency factor A can be separated into two separate parts
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
56
Collision Theory
Collision theory maintains that the rate constant for
a reaction is the product of these factors.
1. Collision frequency Z-# of collisions that
occur per unit time
– Under typical conditions a single molecule
undergoes 109 collision/sec
2. Steric factor p, the fraction of collisions with
the proper orientation to react.
– In this theory the rate constant for a reaction is
given by
k = ZPf where
Chem 1011
f =e
Chapter 13: Chemical Kinetics
A. Ghumman
-E a
RT
57
Collision Model
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
58
Reaction Mechanisms
Elementary Reaction-is a single molecular event
such as collision of molecules, resulting in a reaction.
Reaction Mechanism-The set of elementary
reaction whose overall effect is given by the net
chemical equation.
Reaction Intermediate-A species produced during
a reaction that does not appear in the net equation
because it reacts quickly in a subsequent step in the
mechanism.
Often it cannot be isolated.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
59
Reaction Mechanisms
Balanced chemical equation is a description of overall result of a
reaction.
The Actual reaction may involve several steps called as
elementary steps. Consider the following reaction
NO2(g) + CO(g) →NO (g) +CO2 (g) (overall reaction)
At temperature below 500K this gas –phase reaction take place
in two steps
1.
NO2+ NO2 →NO3 + NO
(elementary step)
2.
NO3 + CO →NO2 (g) +CO2 (elementary step)
NO2(g) + CO(g) →NO (g) +CO2 (g)
• Which species is the reaction intermediate?
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
60
Molecularity
Molecularity: It is the number of molecules on the
reactant side of an elementary reaction.
Unimolecular reaction:It is an elementary reaction
that involves one reactant molecule e.g.
Decomposition reaction (previously excited species)
Bimolecular reaction: It is an elementary reaction
that involves two reactant molecules, most common
Termolecular reaction: It is an elementary
reaction that involves three reactant molecules e.g.
gas phase reactions
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
61
Writing the Overall Chemical
Equation From a mechanism
The Decomposition of ozone is believed to occur in
two steps
O3 O2 + O
O3 + O → 2O2
Identify any reaction intermediate. What is the overall
reaction?
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
62
Rate Law For an Elementary
Reaction
For an elementary reaction , the rate is proportional to the
product of the concentration of each reactant molecule.
For unimolecular reaction
A →B
Rate = k[A]
Bimolecular reaction
A+B→C+D
Rate = k[A][B]
Termolecular reaction
A+B+C→D+ E
Rate = k[A][B][C]
Since a chemical reaction may occur in several steps, there is no
easily stated relationship between its overall reaction and its
rate law.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
63
Rate Laws for Elementary steps
Chapter 13: Chemical Kinetics
A. Ghumman
Chem 1011
64
Rate-Determining Step
In most mechanisms, one step occurs more slowly
than the other steps.
Rate-determining step- the slowest step in the
mechanism
The slowest step has the largest activation
energy.
It determines the rate of the overall reaction
As a result product formation cannot occur any
faster than the slowest step.
The rate law of the rate-determining step determines
the rate law of the overall reaction
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
65
Overall NO2(g) + CO(g) → NO(g) + CO2(g) Rateobs = k[NO2]2
1)
NO2(g) + NO2(g) → NO3(g) + NO(g) Rate = k1[NO2]2 slow
2)
NO3(g) + CO(g) → NO2(g) + CO2(g) Rate = k2[NO3][CO] fast
•The first step is slower than
the second step because its
Ea is larger.
•The first step is rate-determining
step.
•The rate law of the first step is
the same as the rate law of the
overall reaction.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
66
Validating a Mechanism
In order to validate (not prove) a mechanism, two
conditions must be met:
1. The elementary steps must sum to the overall
reaction;
2. the rate law predicted by the mechanism must be
consistent with the experimentally observed rate law.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
67
Practice Problem
Determine the overall reaction, the rate-determining
step, and the rate law, and identify all intermediates
of the following mechanism.
1. A + B2 → AB + B
slow
2. A + B → AB
fast
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
68
Catalysis
Catalyst: A substance that has power to speed up a reaction
without being consumed by the reaction
Catalysts are of enormous importance to chemical industry
Catalysts work by providing an alternative mechanism for
the reaction with lower activation energy
They increase the rate of a reaction at lower temperature
but not the others
They are often quite specific; increase the rate of only
certain reaction.
Catalysts regenerate themselves at the end of reaction for
reuse
Usually metals or metal oxides are good catalysts
Enzymes are biological catalysts
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
69
Catalysis: Ozone Depletion by Cl
atoms
mechanism without catalyst
O3(g) + O(g) → 2 O2(g) v.slow
mechanism with catalyst
Cl(g) + O3(g) ⇔ O2(g) + ClO(g) Fast
ClO(g) + O(g) → O2(g) + Cl(g) Slow
Chapter 13: Chemical Kinetics
A. Ghumman
Chem 1011
70
Catalysis
Homogeneous catalysts are in the same phase as the
reactant particles.
The catalytic destruction of O3 by Cl in gas phase.
Cl(g) + O3(g) →ClO(g) + O2(g)
ClO(g) + O(g) → Cl(g) + O2(g)
O3(g) +O(g) → 2O2(g)
Heterogeneous catalysts are in a different phase than the
reactant particles.
solid catalytic converter in a car’s exhaust system
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
71
Heterogeneous catalysis
Chemisorption; is the binding of a species to a
surface by chemical bonding
Surface catalysis is thought to occur by chemical
adsorption of the reactants onto the surface of the
catalyst e.g. Catalytic Hydrogenation of C2H4
Adsorption is the attraction of molecules to a
surface.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
72
Surface Science
Understanding the chemical processes that occur at surfaces
Surface Techiques: XPS (X-ray photoelectron spectroscopy
and scanning tunnling microscopy
• Important steps.
– Diffusion
– Adsorption of the reactant molecules to the catalyst
surface
– Conversion of the reactants to products
•
Active sites
– Desorption of the products, regenerating the active sites
• Advantages: You can recover the catalysts (Pt, Pd, Rh,
Ru)for reuse.
• Disadvantages:deactivation of catalyst
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
73
Enzymes: Biological Catalysts
Most biological reactions require a catalyst to proceed
at a reasonable rate
Protein molecules that catalyze biological reactions
are called enzymes.
Enzymes work by adsorbing the substrate reactant
onto an active site that orients it for reaction.
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
74
Enzyme–Substrate Binding
Lock and Key Mechanism
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
75
Operational Skills
Relating the different ways of expressing reaction rates
Calculating the average reaction rate
Determining the order of reaction from the rate law
Determining the rate law from initial rates
Using the Arrhenius equation
Writing the overall chemical equation from a mechanism
Determining the molecularity of an elementary reaction
Writing the rate equation for an elementary reaction
Determining the rate law from a mechanism
Chem 1011
Chapter 13: Chemical Kinetics
A. Ghumman
76