The document The Collision Theory Of Bimolecular Gaseous Reaction - Chemical Kinetics Chemistry Notes | EduRev is a part of the Chemistry Course Physical Chemistry.

All you need of Chemistry at this link: Chemistry

**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 → 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 (σ) 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 � 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

∴

let

then …(1)

we know that

then …(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

…(1)

ln k = ln P + ln M + ln …(2)

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

.....(1a)

and

…(2a)

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

…(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

…(1)

We know that

…(1)

then …(2)

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

66 videos|94 docs|32 tests