B.Sc. (P) Phys Sc. Sem IV | Chemical Kinetics-V | 21-04-2020
Chemical Kinetics-V
Theories of Reaction Rates
The speed of reactions can be understood better by looking into the microscopic picture in terms of
molecular properties such molecular mass and velocities etc. We will study two such theories which
will give us an insight into the microscopic explanation behind reaction speeds, (i) Collision Theory,
and (ii) Transition State Theory (TST) or the Activated Complex Theory (ACT).
Collision Theory

Applicable only to gas phase bimolecular elementary reactions i.e.

Based on kinetic theory of gases.

Molecules are treated as hard spheres (impenetrable).

Products are formed only when the reactant molecules come closer and collide with each
other.

Not every collision leads to product formation. Only those collisions are effective in
converting the reactants to products which result in overcoming the activation energy
barrier and have specific orientation of molecules.
If molecules are considered rigid, hard spheres with no forces of attraction or repulsion, and if every
collision between them leads to product formation, then the rate of reaction will entirely be
determined by collision rate, i.e. the frequency with which the reactant molecules collide. This is the
upper limit or maximum reaction rate that can be observed experimentally.
For a bimolecular elementary reaction;
The number of collisions per unit volume per unit time between
and , i.e. the collision frequency,
is given by:
Where
is the collision cross-section i.e. the area around a molecule in which it can encounter
collisions with other molecules,
is the reduced mass;
where
and
and
Dr. Ruchi Sharma Pandey | Kirori Mal College
and
are the molecular diameters.
are molecular masses.
and
are the number
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B.Sc. (P) Phys Sc. Sem IV | Chemical Kinetics-V | 21-04-2020
of molecules of
and
per unit volume.
is the Boltzmann constant and
is the average
speed of the molecules. The maximum rate of the reaction in terms of collision frequency can then
be written as;
In terms of concentration
and
and
The rate can also be expressed in terms of concentration as;
Where,
comparing the two equations
In reality, only those collisions result in product formation, where the energy acquired by the
molecules after collision, is greater than the threshold energy.
where
Remember
And the fraction of molecules possessing energy equal to
factor
where,
is given by the Maxwell-Boltzmann
is the average kinetic energy of the molecules and hence the rate of
reaction can be written as;
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B.Sc. (P) Phys Sc. Sem IV | Chemical Kinetics-V | 21-04-2020
And we know that;
, on comparison we get;
second order rate constant from collision theory
Collision theory gives good results for simple molecules but the rate constant does not satisfactorily
match exponential results for complex molecules. It was later found that the rate of formation of
products depends not only on
but also on the orientation of molecules at the time of collision.
An additional factor needs to be introduced into the equation for
where
is called the steric factor. It is usually less than 1. So,
Comparing Collision Theory and Arrhenius Equation
According to Arrhenius equation;
k  Ae  Ea / RT
or
 ln k
E
 a2
T
RT
The rate constant from collision theory is written as
natural logarithm of
And if we take
and take its derivative w.r.t , we get
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B.Sc. (P) Phys Sc. Sem IV | Chemical Kinetics-V | 21-04-2020
On comparing the differentials of rate constant from Arrhenius theory and collision theory, we get
Ea   0 
The rate constant can then be written as
RT
2
if we compare the two rate constants, we can obtain the Arrhenius pre-exponential factor as;
Activated Complex Theory, or Transition State Theory
Eyring, Polanyi and Evans proposed that the reactants transform into products via the formation of a
short lived high energy configuration of molecules called as the activated complex (AC) or the
transition state (TS). They postulated;

Reactant molecules must collide;

Molecular collisions must occur with proper orientations;

Collisions must be energetic and lead to the formation of the transition-state complex;

The rate of formation of the transition-state complex is the rate determining step;

The transition-state complex eventually leads to the formation of products
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B.Sc. (P) Phys Sc. Sem IV | Chemical Kinetics-V | 21-04-2020
The transition state or AC, which is formed

is an unstable species that contains partial bonds. It is a transitional species between
reactants and products.

cannot be isolated.

exists at the point of maximum potential energy.

The energy required to form the transition state is the activation energy.

Has two fates:
●
it can either dissociate and return to become the reactants, or
●
rearrangement of bonds in AC can lead to product formation
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B.Sc. (P) Phys Sc. Sem IV | Chemical Kinetics-V | 21-04-2020
For a bimolecular gas phase reaction;
where,
is the second order rate constant of ACT
The mechanism as per the activated complex theory (ACT) is written as;
ACT is based on the assumption that there exists an equilibrium between the reactants and the
activated complex
, and then products are obtained by decomposing the activated complex.
The rate of reaction depends on two things:
a) concentration of the activated complex
b) frequency of decomposition of the activated complex
Where
is the frequency with which the partial bond in the activated complex is broken to give the
products. According to Planck, this frequency is given as
constant and
where
is the Planck’s
is the Avogadro’s number. Also, for the first step of the reaction where the
activated complex is formed,
and
Hence the rate constant for the bi-molecular reaction can be written in terms of the frequency and
as;
Thermodynamics of Activated Complex Theory
We can express
in terms of
, the free energy change in going from the reactants to the
activated complex.
Here,
where
is the standard concentration unit
We know that
Also,
And
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B.Sc. (P) Phys Sc. Sem IV | Chemical Kinetics-V | 21-04-2020
Taking the natural logarithm
Taking a derivative w.r.t temperature
For a bi-molecular reaction
Comparing Activated Complex Theory and Arrhenius Equation
According to Arrhenius equation;
k  Ae  Ea / RT
or
 ln k
E
 a2
T
RT
Comparing the derivative of the rate constants in the two cases;
Putting this expression in the Arrhenius equation for the rate constant;
Comparing with the rate constant obtained from ACT to get the Arrhenius pre-exponential factor
For a bi-molecular reaction
Comparison of Collision Theory and Activated Complex Theory
The key difference between collision theory and transition state theory is that collision theory
relates to the collisions between gas molecules whereas transition state theory relates to the
formation of intermediate compounds in transition states.
If we compare the temperature dependence of the rate constant of the two theories then,
Collision Theory:
Activated Complex Theory:
Equating the two relations;
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B.Sc. (P) Phys Sc. Sem IV | Chemical Kinetics-V | 21-04-2020
Threshold energy:
If we substitute it in the rate constant we got from the collision theory, we get;
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