Reaction Cross Section Relation to the Rate Constant

Reaction Cross Section Relation to the Rate Constant 

To obtain a basis for computing the rate constant for an elementary step consider the simple bimolecular gas-phase transformation 

The A and BC molecules are constantly colliding with one another, but not all such collisions can lead to reaction. If A collides with the C end of BC, AB bond formation is probably much less likely than if collision is with the B end. If the reaction is endothermic, energy must be supplied in order for reaction to take place. The necessary energy is supplied by collision and then redistributed among the reactants. Thus, when molecules collide, we can expect that there is a probability of reaction (less than 1) which depends upon their relative kinetic energy, their relative orientation, and possibly other factors which have not yet been considered. 

The rate of reaction of A atoms per unit volume can be expressed as 

The same arguments which led to (2.21) can be modified to show that the collision frequency per unit volume of A and BC molecules with relative speed between c and c + rfc is 

---