Collision theory for bimolecular reaction: Postulates and its failure

Collision theory for biomolecular reaction, its assumption, probability factor or orientation factor, energy factor, collision frequency, and limitation have been discussed here.

.In order to explain the mechanism of reactions, various theories have been developed and the most popular theories of reaction rate are given as:

1. Collision theory of reaction rate
2. Transition state theory of reaction rate

What is collision theory?

(collision theory for bimolecular reaction)

According to the collision theory of reaction rate, the collision between the reactant molecules must take place in order to occur a chemical reaction. The rate of reaction will be proportional to the number of collisions per unit time between the reactant molecules. Experimentally it was found that not every collision between reactant molecules results in a chemical reaction but only a small fraction of total collision is effective. There can be the following reasons for such small effective collisions.

1. Energy barrier
2. Orientation factor

Energy barrier in collision theory

During a collision, the reactant molecules may not have sufficient energy to cross the energy barrier or they may have energy less than the activation energy. Thus, these reactant molecules are not capable of undergoing transformation to give a product. This can be explained with the help of an energy profile diagram as shown:

In the above diagram, if sufficient energy which may be equal to or greater than activation energy is supplied to the reactants, molecules can cross the energy barrier and forms an activated complex that yields products. However, if the reactant molecules are not having sufficient energy then their collision will not lead to the formation of the activated complex. Therefore, only those collisions in which reactant molecules have energy greater or equal to the activation energy are useful collisions.

Orientation factor in collision theory

The reactant molecules may not be properly oriented or aligned during the collision. If the reactant molecules are oriented properly, then such collision lead to the bond formation or product formation. The collision between improperly oriented reactant molecules can not lead to bond formation. This can be illustrated as shown below:

In short, the collision theory postulates are as follows:

1. For a reaction to occur, there must be collsion between reactant molecules.
2. Not all collision leads to formation of product, only small fraction of total collision are effective in product formation.
3. For an effective collision, the reactant molecules must collide with sufficient energy and proper orientation.

On the basis of the above discussion, the rate of reaction can be expressed as,

Rate= {collision frequency} ⨉{Energy factor} ⨉ { Orientation factor}

Rate=p z e^{-E_act/ RT} ………………………………………..(i)

Where,

p= orientation factor/ probability factor

z= collision frequency

e^{-E_act/ RT} = energy factor

E_act= activation energy of reaction.

Collision frequency

The total number of collisions between reacting species per unit volume per second is called collision frequency.

When the collision is between two reactants A and B, expression of collision frequency can be given as

where σ_A and σ_B =diameter of reactant A and B respectively

k_b=Boltzmann constant

µ= reduced mass

n_A and n_B =number of molecules per unit volume of gases A and B respectively

If the collision is between molecules of a single reactant, then the above expression is modified as:

Limitations of collision theory

Although the collision theory of reaction rate is satisfactory for a number of reactions, it fails in many cases such as rapid chain reaction, a reaction involving complex molecules, etc. Some of the major failures, weaknesses, or limitations of collision theory are given below:

1. This theory has not attempt to correlate the value of orientation factor with structure and properties of the reacting molecules.
2. Collision theory does not explain the cleavage and formation of bonds in the reaction.
3. The reacting molecules might acquire the energy from translational, potential, vibrational and rotational energies but this theory only considered translation energy with two degree of freedom.
4. The intermolecular distance at which the reaction can occur may also be different from the collision diameter taken in this theory.

Collision theory video

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