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**The Collision Theory of Bimolecular Gaseous Reaction.**

The reaction between two species takes place only when they are in contact i.e. the reactant species must be collide before they react.

Consider the bimolecular elementary reaction.

A + B â†’ P

rate

The rate of reaction to be proportional to the rate of collision i.e. the mean sped of the molecules, their collision cross-section (Ïƒ) and the number of densities of A and B. Using kinetic theory of gases, the rate of bimolecular collisions per second per cm^{-3} between unlike molecule is given by

Where n_{A} & n_{B }are number of A and B molecules, d_{AV} is the average collision diameter defined as and ï¿½ is the reduced mass defined as

Z_{AB} = collision frequency The detailed analysis of the bimolecular collisions leads to the result that the number of collision per second per cm^{3} between molecules A and B is given by

rate = Z_{AB} e^{-E0 / RT} = no. of collision

where E_{0} = Energy generated by collision then the rate of relative collision is given by

âˆ´

let

then â€¦(1)

we know that

then â€¦(2)

The collision theory can be generalized by introducing the steric factor, P, into the equatiohn for the bimolecular rate constant.

Then

**Relation between E _{a} and E_{0}: **

By between equation; k = Ae

By collision theory,

Taking natural log we get ln

â€¦(1)

ln k = ln P + ln M + ln â€¦(2)

Different iate both equation (1) and (2) with respect to T we get

.....(1a)

and

â€¦(2a)

Comparing equation (1a) & (2a) we get

â€¦(3)

The expression for Arrhenius pre-exponential factor using collision theory We know that

k = Ae^{-Ea / RT} [by Arrhenius equation]

[by collision theory]

then

â€¦(1)

We know that

â€¦(1)

then â€¦(2)

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