The theory of reaction rates describes mathematical methods for predicting reaction rates without experiments. The main theories are collision theory, Lindemann theory of unimolecular reactions, and transition state theory. Collision theory postulates that reactions occur when reactant molecules collide with sufficient energy to overcome the activation energy barrier. The rate of reaction is equal to the collision frequency multiplied by the fraction of collisions with sufficient energy. Mathematical treatments of collision theory derive expressions for reaction rates based on Maxwell-Boltzmann distributions and kinetic gas theory.

1. Theory of Reaction Rates :-
The Process or mathematical way by which without performing
experiment, we can find out or predict rate of a reaction is
called theory of reaction rates. These are following ;
A. Collision Theory
B. Lindemann Theory of unimolecular reaction
C. Transition State Theory

2. A. Collision Theory :Collision theory is a particular class of a
reaction rate theory which was first propose
by Max Trautz in 1960 and W Lewis in 1918.
Postulates or basic assumptions of this theory :-
1. The reaction occur when the reacting molecule come very close
to each other and collide with each other, collision between
reactants is the first step of a chemical reaction.
2. Every collision wouldn’t necessarily lead to formation of
product. Only those collision which are effective leads to
formation of product.

3. 3. The collision in which molecule acquire energy equal to or greater
than activation energy called effective collision during. During
collision it was observed that small amount of energy transfer
between reacting molecules involve in collision in most of cases. So
for effective collision molecule must have minimum amount of energy
after which they acquire energy by collision is equal to the activation
energy it’s called Threshold Energy.
The difference between threshold energy and average energy
possesses by the reacting molecule at given temperature is known
as Activation Energy.

4. 4. Molecules are consider rigid hard sphere and during energy
transfer at the time of collision and acquire activation energy only
translational mode of motion is involved.
5. Rate of the reaction=number of effective collision per unit volume,
per unit time i.e collision frequency.
Or, rate= Collision frequency×Fraction of
collision that have sufficient energy≥Ea Or energy factor.
6. The collision must be proper oriented if the reaction is to be takes
place. If molecules are not take part in proper oriented collision,
product formation is not possible. Thus proper oriented effective
collision leads to the formation of product.

5. Mathematical Treatment of Collision Theory :-
First we want to derive reaction rates considering first five postulates
then introduce the six postulates.
In a gaseous system a result of continuous collision there
are inter change of energy between molecules. The distribution of
energy is given by Maxwell-Boltzmann Classical Distribution.
The fraction of molecule acquire energy ≥ activation energy at a
given temperature, will be equal to e-Ea/RT i.e,
Number of activated molecule
Total number of molecule
=
= n/n0 = e–Ea/RT

6. If Z is the number of binary collision per cc per second then effective
number of collision = Z×e–Ea/RT molecule cc-1 s-1
According to assumptions ,
rate of the reaction=number of effective collision
So rate(v) = Z×e–Ea/RT moleculecc-1 s-1
From molecular kinetic theory of gas number of molecule per cc per
second for similar molecule,
Z=1/√2πσ2can’2 [ where, σ = collision diameter, Ca =
velocity, n’= no of molecule present per cc. ]
For dissimilar molecule number of collision per cc per second,
Z= π(
σA + σB
2
)2 √8KT/πμ n‘An’B [where, μ= reduce
mass]

7. Then rate of the reaction,
For similar molecule ; rate(v) = 1/√2πσ 2can’2 × e–Ea/RT
For dissimilar molecule ; rate(v) = π( √8KT/πμ n‘An’B × e–Ea/RT
σA + σB
2
)
Rate(v)
n’2 n’2 =
PN0
RT
=
number
cc
CA =
mol
lit
=
number/N0
cc/103 ×n’
=
103
N0
×n’ mol/lit