Collision Theory of Reaction Rates: Statement & Proof

Collision Theory of Reaction Rates: The collision theory of reaction rates is conceptualized on the basis of the kinetic theory of gases. The kinetic theory is based on the assumption that the molecules of gases are moving continuously and, therefore, colliding with each other.

Since two molecules need to be involved for a collision to take place, the bimolecular reactions are taken as an example to demonstrate and explain collision theory. Let’s learn everything about collision theory in this article.

Learn About the Collision Theory

Collision Theory

Collision theory was formulated and developed by Max Trautz and William Lewis in the year \(1916 – 18.\) Although the Arrhenius equation is applied in several reactions, the collision theory explains the energetic and mechanistic characteristics of a reaction in a comprehensive manner and, therefore, makes it even more relevant in innumerable circumstances.

To explain collision theory, it is essential to understand activation energy and how Arrhenius applied it to the equation to determine reaction rates.

Activation Energy

Every reaction requires some kind of boost for it to kick start. This boost or energy input is required for a reaction to form the intermediate and then the products. An intermediate or the activated complex usually decomposes to give the products of a chemical reaction.

The energy that is consumed or required to form this intermediate or the activated complex is called the activation energy or \({{\text{E}}_{\text{a}}}.\)

Thus, unless the activation energy of the reactant molecules is enough to make them react to form an intermediate complex, the reaction may not occur. With an increase in temperature, the kinetic energy of the reactant molecules will increase, and therefore, the activation energy required will decrease. Arrhenius predicted that a reaction occurs when two or more reactants collide to form the intermediate or an unstable complex.

Arrhenius Equation

Arrhenius equation was proposed by Svante Arrhenius, a Swedish chemist, who was also one of the founders of physical chemistry. Arrhenius provided a physical form and justification of the proposal given by the Dutch chemist, J.H. Vant Hoff, as stated below:

‘When the temperature of a chemical reaction rises by \({10^ \circ }{\text{C}},\) the rate constant of a reaction is doubled.’

Arrhenius equation accurately explains the temperature dependence of the rate of a reaction. It is denoted by:

\(\,{\text{k}} = {\text{Ae}}\frac{{{\text{-}}{{\text{E}}_{\text{a}}}}}{{{\text{RT}}}}\)

Where –
\({\text{A=}}\) Arrhenius factor or frequency factor or pre-exponential factor
The factor is specific to a particular chemical reaction.
\({\text{R=}}\) Gas Constant
\({{\text{E}}_{\text{a}}} = \) Activation energy in Joules/ mole.

While Arrhenius equation gave a physical interpretation for the relationship between temperature and rate constant, theories for rate constants like collision theory gave much clarity and insight on mechanistic and energy-based aspects of a chemical reaction.

Collision Theory of Bimolecular Reactions

In any bimolecular reaction, two participating molecules must follow the three significant points to make an impact.

1. The reactant molecules must collide with each other to reach and form products
2. They need to have enough (sufficient) energy to get the reacting molecules activated
3. They need to collide with sufficient energy

So, unless the energy possessed by the molecules is not sufficient, a collision is not successful. An effective collision can be defined as:

“A collision where the reactant molecules will collide with sufficient energy called threshold energy and also with exact orientation as required to ensure breaking of bonds between reactants and formation of new bonds in the products.”

Thus, not all collisions can be effective. The fraction of effective and successful collisions can be taken as a specific reaction rate. Hence, collision theory assumes reactant molecules as spheres, and accordingly, a reaction occurs when these spheres collide at a particular orientation and with enough energy.

An example of a right collision as against not-so-correctly oriented collisions can be depicted roughly as follows:

‘The collision frequency is defined as the number of collisions per second, per unit volume of any specific reaction mixture.’ It is denoted by \({\text{Z}}{\text{.}}\)

So, taking any bimolecular reaction:

\({\text{X + Y}} \to {\text{Products}}\)

The rate of the reaction can be written as: \(\,{\text{k}} = {{\text{Z}}_{{\text{XY}}}}{\text{e}}\frac{{{\text{-}}{{\text{E}}_{\text{a}}}}}{{{\text{RT}}}}\)

\({{\text{Z}}_{{\text{xy}}}} = \) Collision frequency of reactants
\({{\text{e}}^{ -{\text{Ea}}/{\text{RT}}}} = \) fraction of molecules that have energies equal to or more than the activation energy
Comparing the equation to Arrhenius equation:
\(\,{\text{k}} = {\text{Ae}}\frac{{{\text{-}}{{\text{E}}_{\text{a}}}}}{{{\text{RT}}}}\)

\({\text{Z,}}\) collision frequency is related to A or the Arrhenius factor.

Thus, an effective collision and rate of a chemical reaction depend upon two factors:

1. The activation energy of molecules
2. Correct orientation (for efficient collision) of molecules

Some real-life examples of collision theory include the impact between a golf stick and the ball, wherein the right amount of pressure and the correct orientation will take the ball to its correct destination. The same can also be said with nails and a hammer, where hammering needs to be precise to make it work.

Advantages and Limitations of Collision Theory

The below mentioned are the advantages and limitations of collision theory:

Summary

The collision theory of bimolecular reactions helps in formulating and predicting the rates of reactions of small and simple molecules and is more comprehensive in its approach. It gives a mechanistic and energetic view of the relationship between the rate and temperature of a chemical reaction.

It can be compared with the Arrhenius equation to understand how and why the constant rate values alter with temperature and what does collision frequency and effective collision implies to the rate of a chemical reaction. While it is comprehensive and predicts reactions accurately, it comes with its limitations too.

Molecularity of Elementary & Complex Reactions

FAQs on Collision Theory of Reaction Rates

Q.1. What are the 3 points of collision theory?
Ans: According to collision theory:
a. The reactant molecules must collide with one another.
b. They must collide with sufficient energy to make an impact.
c. The collisions must happen at a particular orientation for the molecules to break old bonds and form new bonds.

Q.2. What is the collision theory of reaction rate?
Ans: Collision theory of bimolecular reaction is based upon the kinetic theory of gases and gives a comprehensive knowledge about the relationship between temperature and rate constant. According to collision theory, an effective collision at an appropriate orientation between the interactive molecules is required for the reaction to be successful.

Q.3. What does the collision theory state in terms of chemical reactions?
Ans: Collision theory states that for a reaction to occur, the molecules need to collide with each other with effective energy and correct orientation. And, not all collisions are successful since many do not occur as prescribed, with the correct amount of energy and right orientation of the molecules.

Q.4. What is the example of collision theory?
Ans: A bimolecular reaction where two reactants react to form products is an example of collision theory. Real-life examples include golf ball and golf club, hammer and nail, etc.

Q.5. What are the limitations of collision theory?
Ans: The limitations of collision theory include:
a. Collision theory cannot be applied to larger molecules such as polymers and polymerization reactions.
b. The results of reaction rates obtained from collision theory for chain reactions are not accurate.