Collision Theory of Reaction Rates

According to collision theory, a reaction takes place because the molecules collide with each other. The number of collision that takes place per second per unit volume of the reaction mix is called collision frequency. At ordinary temperature and pressure the value of collision frequency is so high ($\approx {10}^{25}to{10}^{28}$in a gaseous reaction) that if all the collisions were effective, the reaction should be completed in fraction of seconds. However, in actual practice, that is not so. This is explained on the basis of two factors.

(i) Energy factor

For a collisions to be effective, the colliding molecules must have energy more than a particular value. The minimum energy which the colliding molecules must have in order that the collision between them may be effective is called threshold energy. Thus at ordinary temperature and pressure, most of the molecules may not posses energy equal to or greater than threshold value.

A collision between high energy molecules overcomes the repulsion and bring the formation of an unstable molecule cluster, called the activated complex.

Thus, every chemical reaction whether exothermic or endothermic has an energy barrier which has to be overcome before reactants can be transformed into products. If the reactant molecules have sufficient energy, they can reach the peak of the energy barrier after collision and then they change into products. If the activation energy for a reaction is low, the fraction of effective collisions will be large and reaction will be fast. On the other hand, if the activation energy is high, then fraction of effective collisions will be small and the reaction will be slow. When temperature is increased, the number of active molecules increases, i.e., the number of effective collisions will increase and the rate of reaction will increase.

Activation energy E_a = E_{(activated complex)} ^{– E}_{(ground state)}

DH = activation energy of forward reaction - activation energy of backward reaction.

(ii) Orientation factor

In some cases it is found that even if a larger number of colliding molecules have energy more than threshold value, still the reaction is slow. This is because of improper orientation of the colliding molecules at the time of collisions.

Rate of reaction is directly proportional to the number of effective collisions.

Rate = $\frac{dx}{dt}=Collisionfrequency\times fractionofeffectivemolecules$

= z ´ f

According to kinetic theory of gases, the fraction of molecules having energy more than a particular value, E at temperature T is given by

$f=e^{-E_a/RT}$

Rate = $z{e}^{-E_a/RT}$

As rate of reaction is directly related to rate constant K, we can also write

K = $z{e}^{-E_a/RT}$