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
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 nA & nB are number of A and B molecules, dAV is the average collision diameter defined as and � is the reduced mass defined as
ZAB = 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 = ZAB e-E0 / RT = no. of collision
where E0 = Energy generated by collision then the rate of relative collision is given by
we know that
The collision theory can be generalized by introducing the steric factor, P, into the equatiohn for the bimolecular rate constant.
Relation between Ea and E0:
By between equation; k = Ae-Ea / RT
By collision theory,
Taking natural log we get ln
ln k = ln P + ln M + ln …(2)
Different iate both equation (1) and (2) with respect to T we get
Comparing equation (1a) & (2a) we get
The expression for Arrhenius pre-exponential factor using collision theory We know that
k = Ae-Ea / RT [by Arrhenius equation]
[by collision theory]
We know that