Collision theory proposes that for a chemical reaction to occur, reactant molecules must collide with sufficient energy to overcome an activation energy barrier. The rate of reaction is directly proportional to the collision frequency and a fraction of effective collisions. However, collision theory fails to explain several observed reaction rates and does not account for molecular orientations or internal motions. Modifications were made to incorporate effective collision probability but correlations between this factor and reaction characteristics remain unclear.

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3. CONTENTS
Introduction
Main postulates of collision theory
Mathematical treatment of collision theory
Test of simple collision theory
Failure of simple collision theory
Modification of collision theory
General weakness of collision theory
Points to remember

4. INTRODUCTION
• Proposed by Max Trautz & William Lewis.
• Based on the kinetic theory of gases.
• According to this theory, the reactant molecules have to collide in a
certain way with a certain amount of energy in order to form a new
product.
• Since, for the collision at least two molecule are must involve, therefore
this reaction is known as Bimolecular reaction.

5. MAIN POSTULATES OF COLLISION THEORY
• Collision is required between the reactant molecules to convert them
into product.
• Reactant molecules are assumed to be a solid sphere.
• Due to collision, kinetic energy of the reactant molecules increases, & the
molecules which acquire the energy either equal to or more than
activation energy, converts into the product.
• The number of collision between the reactant molecule can be increased
by increasing the temperature of the reactant.
• Thus, Rate of reaction ∝ Temperature.

6. • Not all the molecules of reactant acquire kinetic energy equal to
activation energy, so not all reactant molecules are converted into the
product.
• The activation energy is that minimum additional energy which is required
for effective collision between molecule so that they may got threshold
energy.
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7. MATHEMATICAL TREATMENT OF COLLISION THEORY
A+B Product
According to collision theory,
Rate of reaction ∝ Number of collision between A&B
According to Rate law, Rate of reaction ∝ 𝑨 [𝑩]
So, Number of collision ∝ concentration of reactants
According to Arrhenius law, Rate of reaction= Z𝑒−𝐸𝑎/𝑅𝑇 …(1)
Where, Z= no. of binary collision per unit time, 𝐸𝑎= activation energy
According to kinetic theory, the rate of reaction is related with the no. of
molecule per unit volume i.e. rate ∝ nxn

8. rate ∝ 𝑛2 , rate = k𝑛2 …(2)
Comparing eq. (1) & (2), we get
k𝑛2 = Z𝑒−𝐸𝑎/𝑅𝑇
k= Z 𝑒−𝐸𝑎/𝑅𝑇 /𝑛2 …(3)
From kinetic theory of gases the value of Z is given by-
Z= 4𝑛2
𝜎2 𝜋𝑅𝑇
𝑚
…(4) where, 𝜎 = collision diameters,
m = molar mass of colliding molecule
n= no. of molecules per unit volume (A,B)
Putting eq. (4) into (3) we get,

9. k= 4𝑛2𝜎2 𝜋𝑅𝑇
𝑚
x 𝑒−𝐸𝑎/𝑅𝑇 /𝑛2
After simplifying we’ll get,
k= 4𝜎2 𝜋𝑅𝑇
𝑚
x 𝑒−𝐸𝑎/𝑅𝑇
…(5)
k= z𝑒−𝐸𝑎/𝑅𝑇 , where z= 4𝜎2 𝜋𝑅𝑇
𝑚
is the collision number.
Collision number / collision frequency is the number of collisions per unit
time in per unit volume.
When two molecules of different types are involved in collision, z becomes-
z= 𝜎2[8𝜋𝑅𝑇 (
𝑚1+𝑚2
𝑚1𝑚2
] where, (
𝑚1+𝑚2
𝑚1𝑚2
)= reduced mass

10. TEST OF SIMPLE COLLISION THEORY
• Theory can be tested by comparing values of “z” calculated from the
mathematical eq. derived above & the experimental value of “z”.
• Alternatively theory can be tested by comparing the values of rate
constant (K) obtained from theory & from observed value.
• For e.g. 2HI 𝐻2 + 𝐼2
Experimental value of k= 3.5x10−7 at 550K
Calculated value of k= 5.4x 10−7 at 550K

11. FAILURE OF SIMPLE COLLISION THEORY
1. In polymerization of ethene:- there is vast difference between the
observed & theoretical value of K.
2. Polymerization of 1,3-butadiene :- it occurs at rate which is slower
of 10−4 times than theoretical value.
3. Many chain reactions proceed with much higher rate than theoretical
value.
For e.g. specifically reaction between hydrogen and bromine occurs at a
very high speed than the calculated value.

12. MODIFICATION OF COLLISION THEORY
Collision is the only factor for a chemical reaction in gaseous state then all
reactions must have same rate, which is not same for all reactions.
Thus, some modifications have been suggested in simple theory-
 Collision between all molecules doesn’t bring a chemical reaction. It means
out of total collisions only a fraction of collision is effective to bring a
chemical reaction.
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13. the molecules which comes close to each other for collision must have a
definite or certain orientation so that their collision may be effective.
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14.  Thus the rate constant of reaction depends upon the no. of effective
collision & ‘k’ is given by-
k= P x Z𝑒−𝐸𝑎/𝑅𝑇
or
A= pre-exponential factor
to make allowance for such effect with increase or decrease the rate of
reaction-
The value of ‘P’ reaches- theoretically= 0-1
practically= 1- 10−8

15. GENERAL WEAKNESS OF COLLISION THEORY
Co-relation between ‘P’ & characteristic of reaction molecules have not
been very successful.
Theory doesn’t give any explanation for abnormally high rate of some
reactions for e.g. Chain reactions
Simple collision theory doesn’t give any physical explanation of
relationship between the “P” & “ΔS” (change in entropy)
The theory is unsuccessful for unimolecular reaction until Lindmann’s
theory is considered.

16. Theory is based upon classical mechanics, which needs a lot of
modifications.
There is no consideration have been taken for the internal motion
(rotational motion) of the reactants.
Theory considers molecule as a hard sphere which is not true for the
gaseous molecules specifically.

17. POINTS TO REMEMBER
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18. REFERENCES
• Dalal, Mandeep (2018). A textbook of physical chemistry-Volume-1.
Dalal Institute, Main market, Sector 14, Rohtak, Haryana 124001, India.
• Denise granger (2017). What is collision theory of chemical reactions?
Socratic Q & A, Google search.

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