Sem 1 Jyotsana Panwar

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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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