The Collision Theory of Bimolecular Gaseous Reaction

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 cm³ between molecules A and B is given by 

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

where E₀ = 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 E₀: 
By between equation; k = Ae^{-E_a / RT}
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^{-E_a / RT}                            [by Arrhenius equation]

[by collision theory]
then 

     ...(1)
We know that

 
...(1)

then                                  ...(2)