Collision Theory

In this article, we will learn about collision theory of a chemical reaction.

History Of Collision Theory 

Max Trautz and William Lewis developed the "Collision Theory" for chemical reactions based on the "Kinetic Theory Of Gases" in 1916-18 (because the gas phase reactions are easy to understand compared to liquid and solid phases reactions). Therefore the application of the collision theory is limited to the gas phase reaction only. 

Assumption Made In Collision Theory

We all have heard about the kinetic theory of gases which generally explains the behavior of gases by assuming that the gas consists of molecules or particles or atoms moving rapidly in all directions. All the assumptions made in the kinetic theory of gases are the basis for understanding the collision theory.

Introduction To Collision Theory 

In this theory, we generally assume that the molecules of the reactant are "Hard Spheres".

Collision theory states that "For a reaction to occur, the reacting molecules must collide with one another". The rate of reaction depends upon the frequency of collisions.

Basic Assumptions Made In Collision Theory?? 

........"A basic principle of collision theory is that in order to react, the molecules must collide with each other"........ 

Collision theory predicts the rate of chemical reactions at which they occur, especially for gas phase reactions. This tells us that when a gas molecule collide, a chemical reaction occurs, but not always. This means that only a certain collision causes a chemical reaction and this collision is called an "Effective collision or a successful collision". Whereas "Ineffective collisions (or unsuccessful collisions)" are not responsible for the chemical reaction to occur. The theory also tell us that reacting species (or molecules) often collide without reacting. 

Thus, a chemical reaction takes place when;

1) The collision between the molecules have sufficient energy to breaks the bonds in the reactant and form new bonds of product molecules.

2) molecules collide with proper orientation and collision must be effective.

A chemical reaction doesn't takes place when;

1) The collision between the molecules don't have sufficient energy to breaks the bonds in the reactant and form new bonds of product molecules.

2) molecules are not properly aligned 

Kinetic Theory Of Gases 

The assumptions made by the kinetic theory of gases (generally for the case of ideal gas) which are also applicable in collision theory are as follows;

1. Pressure of a gas is due to the collision of randomly moving molecules with each other. 
2. Says that the kinetic energy of molecules directly proportional to the square root of temperature. 
3. No force of interaction between gas molecules. 
4. The volume of the molecules are generally negligible compared to the total volume of the gas. 
5. Collisions between the gas molecules are completely elastic that means no energy exchange between them. 

These all assumptions are used in the collision theory for clearly understand that, How the chemical reactions occured.

Effective Collision

Let us now understand what is an effective collision and how a collision becomes effective in nature. 

"Effective collision or successful collision means that when the gas molecules collide with each other, they must have a minimum amount of energy called the activation energy to overcome the energy barrier so that the molecules of the product can be formed and at the same time, their collision must be in the proper orientation". Thus, for a collision to be effective the colliding molecules must have energy more than activation energy.

Hence, we can say that for a collision to be effective, the reacting molecules must, 

    (1) Collide with each other. 

    (2) Having sufficient amount of energy. 

    (3) Must collide with proper orientation. 

......."An unsuccessful collision results when the molecules of the reactants do not collide with enough energy"......

According to collision theory, the rate at which a chemical reaction occurs is equal to the frequency of effective collisions (or number of effective collisions per second per unit volume).  

Factors Affecting The Collision Theory

All the factors which affects the number or energy of collisions, they are also affects the collision theory. These factors are the nature of the reactants, the concentration of the reactant molecules, temperatures, surface area of reactant and the presence of the catalyst etc. 

Limitations Of Collision Theory

Besides of so many factors, collision theory also have some limitations. Let's look at some of the limitations of this theory;

1) First limitation, It is only applicable to Gaseous molecules.

2) It can be applied to the spherical molecules only.

3) It can be applied to those reactants that forms activated complexes.

Collision Theory Formula Derivation

☆ Let us consider the reaction to understand that which factors affects the rate of reaction, 

                   A + B ➝ C + D     

                             ------------------(1) 

From kinetic theory of gases, for bimolecular collisions of like molecules of A ( means that A molecule collide with another A molecule), the collision frequency denoted by 'Z',

     ➩ ZAA = σA².nA²√(4πkt/MA) 

                 = σA² (N²/10⁶).CA²√(4πkT/MA)

                                                 -------------------(2) 

Where, 

    σA = Diameter of A molecule (in cm) 

    nA = number of molecule of A 

     N = Avogadro's number

   MA = molecular weight of A

      k = Boltzmann constant (in 1.3×10⁻⁶ erg/K) 

    CA = Concentration of A (in mol/l)

For bimolecular collisions of unlike molecules A&B in the mixture, we have;

 ➩ ZAB = [(σA+σB )/2]².(nA×nB).√[8πkT(1/MA+1/MB)]

            =(σA+σB/2)².(N²/10⁶).CA.CB.

                            √[8πkT(1/MA+1/MB)]

                                     -----------------(3) 

Only those collisions which have energy more than the activation energy 'Eₐ', lead to the chemical reaction. And from Maxwell's distribution law, fractions of all bimolecular collisions that involve energies more than activation energy is given by, 

     ➩ 𝘧 = exp(-Eₐ/RT) , Where, Eₐ>>>RT

                                             -------------------(4) 

Thus, we can say that "The fraction of successful collision (or effective collisions) is a function of activation energy and temperature" in which the fraction of successful collisions are directly proportional to the temperature and inversely proportional to the activation energy. 

From general rate law;

           ➩ -rA = -(1/V) dNA/dt = k.CA.CB

From collision theory;

           ➩ -rA = ZAB×(10³/A) exp(-Eₐ/RT) 

                                                ------------------(5) 

Where, 

          ZAB×(10³/A) – collision frequency   

    exp(-Eₐ/RT) – fraction of successful collisions

                    [∵ZAB = √(T)]

Therefore, 

           ➩ k ∝ √(T). exp(-Eₐ/RT)

           ➩ {k = k₀.√(T).exp(-Eₐ/RT)}

                                          ----------------(6) 

                                 OR

           ➩ {k = k₀.T¹⸍².exp(-Eₐ/RT)}

                                            ---------------(7) 

Where, k₀ is the frequency of correctly oriented collisions between the reacting species 

Equation (7) is a result of collision theory and based on this result, we can say that higher the effective collision rate, higher will be the rate of reaction. And as the temperature of the reacting system increases, the rate of the chemical reaction also increases.

....."Concentration also affects the rate of chemical reaction"........ 

This is because when there is a collision between the reactant molecules for a reaction, and if there are more molecules in less volume means high concentration, then the probability of collision is even higher and the rate of reaction also increases. Thus, the higher the concentration, the higher the rate of the reaction.

Hope you have found this article helpful!!

Let me know what you think about COLLISION THEORY. Feel free to comment if you have any queries.!!