Collision Theory: Definition, Reaction Rates, and Postulates

Collision Theory: This theory helps explain how particles interact for a cause of the reaction and the formation of new products. The Arrhenius equation significantly explains the effect of temperature on the reaction rate and hence the rate constant, \({\rm{k}}\). It is because it considers the frequency factor \({\rm{A}}\) and the activation energy \({{\rm{E}}_{\rm{a}}}\) of the reaction. However, a much better explanation about the rate reaction. The rate is given by collision theory put forward by Max Trautz and William Lewis in \(1916 – 18.\) It is based upon the kinetic theory of gases. According to this theory, it is assumed that the reactant molecules are hard spheres and reaction between them occurs when they collide with each other.

Collision Theory Definition

A chemical reaction takes place due to collisions between reacting molecules. For a bimolecular reaction, Rate \({\rm{ = }}{{\rm{Z}}_{{\rm{AB}}}}{\rm{.}}{{\rm{e}}^{{\rm{ – Ea/RT}}}}\) Here \({\rm{Z}}\)is collision frequency and \({{\rm{e}}^{{\rm{ – Ea/RT}}}}\) fraction of molecules with energy equal to or greater than \({{\rm{E}}_{\rm{a}}}\).

Collision Theory of Reaction Rates

For a chemical reaction to occur, the reacting molecules must approach each other and collide. As a result of these collisions, the bonds existing in the reacting molecules are cleaved, and the product with new bonds are formed.

But suppose all the collisions of the reactant molecules lead to the product of the reaction. In that case, the reaction rate at any given temperature is expected to be proportional to the number of collisions taking place between the reacting molecules in unit time at that temperature.

However, the actual rate of reaction is much smaller than the rate calculated from the number of binary collisions of the reacting molecules taking place in unit time.

For example, the number of collisions taking place in one second in one litre of an equimolar mixture of \({{\rm{H}}_{\rm{2}}}{\rm{(g)}}\) and \({{\rm{I}}_{\rm{2}}}{\rm{(g)}}\) at \({\rm{STP}}\) is around \({\rm{1}}{{\rm{0}}^{30}}.\) Therefore, if all these collisions lead to the formation of \({\rm{HI}}({\rm{g}})\) as per the equation \({{\rm{H}}_2}({\rm{g}}) + {{\rm{I}}_{\rm{2}}}{\rm{(g)}} \to 2{\rm{HI(g)}}\) the reaction must be completed within a fraction of a second. But this is not true. Such discrepancies are found in respect of many gases reactions.

Therefore, Arrhenius proposed a simple collision theory to explain the observed reaction rates in the gaseous state. The theory is known as Kinetic molecular theory or collision theory of reaction rates.

Main Postulates of Collision Theory

1. A collision must occur between the molecules of reacting gases for a reaction to occur.
2. But all collisions do not lead to the formation of the products.
3. The colliding molecules must possess minimum energy so that their collisions lead to the formation of the products (reaction to occur). It is referred to as threshold energy.
4. Most of the molecules at \({\rm{STP}}\) generally possess energy less than this threshold energy. Such molecules are referred to as normal molecules. The difference in the energy between the threshold energy and the energy of the normal colliding molecules is referred to as activation energy.
   Activation energy = threshold energy – the energy of normal colliding molecules
5. Every reaction under the given experimental conditions will have its characteristic or specific value of the activation energy. For example, the activation energy for the \({\rm{HI}}\) decomposition reaction is \(52.8\,{\rm{kJ/mol}}{\rm{.}}\,{\rm{For}}\,{\rm{2N}}{{\rm{O}}_2}({\rm{g}}) \to 2{\rm{NO(g) + }}{{\rm{O}}_2}{\rm{(g)}}\) the activation energy is \(111\,{\rm{kJ/mol}}\).

Activation Energy

When two billiard balls collide, they bounce off of one other. It is also the most likely outcome when two molecules, A and B, come into contact: they bounce off one another, wholly unchanged and unaffected. For a collision to be successful by resulting in a chemical reaction, A and B must collide with sufficient energy to break chemical bonds. The chemical bonds in the reactants are broken in any chemical reaction, and new bonds in the products are formed.

Therefore, to effectively initiate a reaction, the reactants must be moving fast enough (with enough kinetic energy) so that they collide with sufficient force for bonds to break. This minimum energy with which molecules must be moving for a collision to result in a chemical reaction is known as the activation energy.

Arrhenius Equation

The Arrhenius equation is \({\rm{k}}\,{\rm{ = }}\,{\rm{A}}{{\rm{e}}^{{\rm{ – Ea/RT}}}}\) where \({\rm{A}}\) is the frequency or pre-exponential factor, and \({{\rm{e}}^{{\rm{ – Ea/RT}}}}\) represents the fraction of collisions that have enough energy to overcome the activation barrier (i.e., have energy greater than or equal to the activation energy \({{\rm{E}}_{\rm{a}}}\)) at temperature \({\rm{T}}\). This equation can be used to understand how the rate of a chemical reaction depends on temperature.

Expression for the Rate Constant of a Bimolecular Reaction

For an elementary bimolecular reaction, \({\rm{A + B}} \to \) if \({{\rm{Z}}_{{\rm{AB}}}}\) Products, if \({{\rm{Z}}_{{\rm{AB}}}}\) is the collision frequency and \(‘{\rm{f}}’\) is the fraction of molecules whose collisions are effective, then evidently,

Rate of reaction \({\rm{ = }}\frac{{{\rm{dx}}}}{{{\rm{dt}}}}{\rm{ = }}{{\rm{Z}}_{{\rm{AB}}}}{\rm{ \times f}}\,……..{\rm{(i)}}\)

Further, according to the kinetic theory of gases, the fraction of molecules having energy more than a particular value, \({\rm{E}}\) at temperature  \({\rm{T}}\), is given by Boltzmann factor, viz.,

\({\rm{f}}\,{\rm{ = }}\,{{\rm{e}}^{{\rm{ – E/RT}}}}\,……..{\rm{(ii)}}\)

Now, as the rate of a chemical reaction depends upon the activation energy, \({{\rm{E}}_{\rm{a}}}\)equation \({\rm{(ii)}}\) may be written as \({\rm{f}}\,{\rm{ = }}\,{{\rm{e}}^{{\rm{ – Ea/RT}}}}\)

Substituting this value in equation \({\rm{(i)}}\), we get Rate \({\rm{ = }}\,{{\rm{Z}}_{{\rm{AB}}}}.\,{{\rm{e}}^{{\rm{ – Ea/RT}}}}\,\)

As rate of reaction is directly related to rate constant, \({\rm{k}}\) we can also write \({\rm{k}}\,{\rm{ = }}\,\,{{\rm{Z}}_{{\rm{AB}}}}.\,{{\rm{e}}^{{\rm{ – Ea/RT}}}}\)

This equation predicts the values of rate constant fairly accurately for reactions involving atomic species or simple molecules. However, if reactant molecules are complex, significant deviations are observed. Even if the colliding molecules have energy greater than threshold energy, they may not have proper orientation at the time of the collision. This may lead to no bonds breaking in the reactant molecules and no new bonds forming to form product molecules.

Thus, for a collision to be effective, the colliding molecules must have energy greater than threshold energy and must have the proper orientation. For example, the reaction between bromomethane and alkali may or may not lead to the formation of methanol depending upon whether they have a proper orientation or not at the time of the collision, as shown below.

It may be further illustrated by taking the example of the following reaction.

\({\rm{N}}{{\rm{O}}_2}\left( {\rm{g}} \right){\rm{ + N}}{{\rm{O}}_2}\left( {\rm{g}} \right) \to {{\rm{N}}_2}{{\rm{O}}_4}\left( {\rm{g}} \right)\)

Figure \({\rm{(a)}}\) represents a proper orientation of the colliding molecules resulting in the formation of \({{\rm{N}}_{\rm{2}}}{{\rm{O}}_{\rm{4}}}\) Figure \({\rm{(b)}}\) represents improper orientation at the time of the collision, and hence no new product is formed.

To account for the orientation factor for the collision to be effective, another factor, \({\rm{P}}\),called orientation factor or steric factor or probability factor, has to be taken into consideration, and the equation is modified to the form: \({\rm{k}}\,{\rm{ = }}\,{\rm{P}}{{\rm{Z}}_{{\rm{AB}}}}{\rm{.}}{{\rm{e}}^{{\rm{ – Ea/RT}}}}\)

Thus, according to collision theory, the rate of a reaction depends upon the number of effective collisions, which depends upon the following two factors:

\({\rm{(i)}}\) Energy factor, i.e., the colliding molecules must have energy greater than the threshold energy.
\({\rm{(ii)}}\) The orientation factor, i.e., the colliding molecules, must have proper orientation at the time of the collision.

Comparing the above equation with Arrhenius equation \({\rm{k}}\,{\rm{ = }}\,{\rm{P}}{{\rm{Z}}_{{\rm{AB}}}}{\rm{.}}{{\rm{e}}^{{\rm{ – Ea/RT}}}}\). We observe that the Arrhenius parameter A is also called frequency factor, is mathematically given as

\({\rm{A = P \times }}{{\rm{Z}}_{{\rm{AB}}}}\)

Effect of Catalyst on Reaction Rate

The action of a catalyst on the rate of reaction is explained through the concept of activation energy. Higher the activation energy or higher the threshold energy, the slower is the reaction rate. Therefore, a new reaction path with a lower energy barrier (or threshold energy) is provided in the presence of a catalyst.

Since the energy barrier is decreased, many molecules can attain this value in the collisions; hence the rate increases. The energy barrier of the reverse reaction is also naturally lowered. Therefore, a good catalyst for a forward reaction is also a good catalyst for the backward reaction in a reversible reaction. Thus, a catalyst speeds up both the forward and the reverse reactions to the same extent. Hence it does not alter the position of the equilibrium in a reversible reaction.

It only hastens the attainment of equilibrium.

Effect of Temperature on Rate of Reaction

Collision theory proposed that the reaction takes place between the activated molecules. The rise of temperature increases the fraction of the activated molecules and the fraction of the activated collisions. Thus, the rate of reaction increases.

The same conclusion can be arrived at by applying the Arrhenius equation to two different temperatures \({\rm{(}}{{\rm{T}}_{\rm{1}}}\,{\rm{and}}\,{{\rm{T}}_{\rm{2}}}{\rm{)}}\)

\({\rm{log}}\frac{{{{\rm{k}}_{\rm{2}}}}}{{{{\rm{k}}_{\rm{1}}}}}{\rm{ = }}\frac{{{{\rm{E}}_{\rm{a}}}}}{{{\rm{2}}{\rm{.303R}}}}\left( {\frac{{{{\rm{T}}_{\rm{2}}}{\rm{ – }}{{\rm{T}}_{\rm{1}}}}}{{{{\rm{T}}_{\rm{1}}}{{\rm{T}}_{\rm{2}}}}}} \right)\)

Where \({{\rm{k}}_1} = \) specific rate at \({{\rm{T}}_{\rm{1}}}\)

\({{\rm{k}}_2} = \) specific rate at \({{\rm{T}}_{\rm{2}}}\)

\({{\rm{E}}_{\rm{a}}} = \) activation energy

\({\rm{R}} = \) gas constant

Drawbacks/Disadvantages of Collision Theory

The main drawback of the Collision theory is that it considers atoms and molecules to be hard spheres and ignores their structures. It does not provide any prediction of p, the “steric factor”, calculated values for the rate constant are usually too high compared with measured values. As outlined above, the theory does not account for the orientation of the collision, front to back and along the line-of-centres. That is, molecules need to collide in the correct direction for reaction to occur.

Collision theory does not explain activation barriers. Activation barriers occur because bonds need to be stretched or distorted to react, and these processes require energy. Molecules must overcome electron-electron repulsion to come close together. The collision theory does not explain the observed temperature dependence given by the Arrhenius equation.

\({\rm{k}}\,{\rm{ = }}\,\,{\rm{A}}{{\rm{e}}^{{\rm{ – Ea/RT}}}}\)

Summary

Chemical reactions require collisions between reactant species. These reactant collisions must be of proper orientation and sufficient energy to result in product formation. Collision theory provides a simple but effective explanation for the effect of many experimental parameters on reaction rates. The Arrhenius equation describes the relationship between a reaction’s rate constant and its activation energy, temperature, and dependence on collision orientation.

For the chemical reaction to occur, reactant particles need to collide with one another. Not every collision results in the formation of products. For products to be formed, the collision has to have a certain minimum amount of energy associated with it.

FAQs on Collision Theory

Q.1. What is the collision theory of reaction rates?
Ans: This theory is used to predict the rates of chemical reactions, particularly for gases. The rate of a chemical reaction is proportional to the number of collisions between reactant molecules. Thus, the more often reactant molecules collide, the more often they react with one another, and the faster will be the reaction rate. 

Q.2. What are the four points of collision theory?
Ans: The four points of Collision theory are as follows:
1. The collision frequency must be greater than the frequency factor for the reaction.
2. The collision energy must be greater than the activation energy for the reaction.
3. The collision must occur in the proper orientation. 
4. The orientation probability factor must be 1.

Q.3. How does temperature affect the rate of reaction?
Ans: Collision theory proposed that the reaction takes place between the activated molecules. The rise of temperature increases the fraction of the activated molecules and the fraction of the activated collisions. Thus, the rate of reaction increases.
The same conclusion can be arrived at by applying the Arrhenius equation to two different temperatures \(({T_1}\,and\,{T_2})\)
\({\rm{log}}\frac{{{{\rm{k}}_2}}}{{{{\rm{k}}_1}}}{\rm{ = }}\frac{{{{\rm{E}}_{\rm{a}}}}}{{{\rm{2}}.{\rm{303R}}}}\left( {\frac{{{{\rm{T}}_{\rm{2}}}{\rm{ – }}{{\rm{T}}_{\rm{1}}}}}{{{{\rm{T}}_{\rm{1}}}{{\rm{T}}_{\rm{2}}}}}} \right)\)
Where \({{\rm{k}}_1} = \) specific rate at \({{\rm{T}}_{\rm{1}}}\)
\({{\rm{k}}_2} = \) specific rate at \({{\rm{T}}_{\rm{2}}}\)
\({{\rm{E}}_{\rm{a}}}=\) activation energy
\({\rm{R}}=\) gas constant.

Q.4. In some cases, it is found that a large number of colliding molecules have energy more than the threshold value, yet the reaction value is slow. Why?
Ans: This is because of the improper orientation of the colliding molecules at the time of the collision. 

Q.5. What is the collision theory based on?
Ans: It is based on the assumption that when a reaction occurs, the reacting particles must collide. All collisions will not bring about chemical change.

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