Transition State Theory

Transition State Theory was developed by Henry Eyring in 1935 at the University of Manchester and is a very important factor in the chemical reaction that determines the rates of chemical reaction taking place in an elementary reaction. This theory functions on quasi-equilibrium, which is a chemical equilibrium that is established between the reactants when the reaction started and the complexes that had attained an activated transition state.

Though Transition State Theory cannot determine the absolute reaction rate of a chemical reaction as it will then require a very precise value of potential energy surfaces, it can efficiently calculate the Gibbs free energy or Gibb’s activation energy ( ߡG# or ߡ# GӨ ) and Entropy( Δ#SӨ ) and Enthalpy ( Δ#HӨ )of Activation of a particular reaction whose reaction rate constant is known. 

Thus, transition theory provides a clear understanding of the rate of a chemical reaction and qualitative occurrence of a chemical reaction by assuming equilibrium between the reactants and the activated complex formed at the transition state.

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What is a Transition State?

A transition state of a chemical reaction is basically a configuration attended by reactants during complex formation along with the reaction coordinates where maximum potential energy is attained. Therefore, the meaning of transition state can be simply explained as when two reactants with a defined molecular arrangement undergo a chemical reaction, between the initial and final arrangements of the molecules or atoms an intermediate state of reaction is attained where maximum potential energy is observed. This particular intermediate configuration of atoms or molecules with the maximum value of potential energy is called activated complex and the state is defined as transition state. 

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Now the diagram above shows the transition state of a chemical reaction taking place. It is basically a potential energy graph that shows the minimum energy required to convert reactants into products. From this curve, it is clear that that activation energy is a hurdle that the reactants need to overcome during the chemical reaction to get converted into their corresponding products. Therefore, numerically activation energy is the difference of the potential energy between the intermediate configuration of reaction coordinate and the initial reactants

Activation Energy = P.E. of intermediate configuration - P.E. of initial reactants   

Activated Complex Theory Explained With Formula

Another term for Transition State Theory is Activated Complex Theory which is a qualitative analysis of a chemical reaction and other processes in which the relative positions of the atoms and the molecules of the reactants undergo continuous change resulting in a change of potential energy between the initial and final stage of the reaction.

The Activated Complex Theory is a primary element that helps in determining the value of reaction rate constant symbolized ‘k.'

Now, the reaction can be bimolecular or termolecular. Example,

A + B⟶AB

Thus, the activated intermediate complex will be in equilibrium with A and B.

A + B ⇌ AB# ⟶AB   

Let kbe the rate constant for the reaction. Thus, the formula to determine the rate constant is

k = KBT/h * e-ΔG/RT

Here, KB is Boltzmann constant

             H is Plank’s constant

             T is temperature

             ΔG is Gibbs free energy

  ΔGо# =   ΔHо# -  TΔSо#

  ΔHо# = Ea + (Δղ#g - 1) RT    

Here,  ΔHо#  is Enthalpy

            Ea  is transition energy

Functioning of Active Complex

The two reactants X and Y can react with each other if their molecules collide with one another to form a product XY. Now the rate at which the reaction takes place is called its rate of reaction.  The rate of reaction depends on many factors like temperature, the concentration of the reactants and the use of the catalyst. An increase in the rate of reaction indicates a more effective collision between molecules of reactants. Thus this collision increases with a rise in temperature, use of a catalyst to elevate the potential energy of reactants so that they can easily overcome the barrier of activation energy to form products, and also with the increase in the concentration of the reactants the collision of molecules increases. Therefore it is evident that the activated complex can be formed if the reactant molecules can attend the activation energy. Once the activated complex is formed, it cannot stay in that state as due to high potential energy as compared to the reactants or the products that it forms, it is very unstable in nature and temporary. So if enough activation energy is not present then the complex cannot form a product and eventually breaks back to reactants. If enough energy is present the complex form product.

Basic Concept of Collision Theory

Collision Theory states that the molecules of the reactants need to collide with each other in order for the ratio to take place. Now, if the collision of molecules initiates the reaction that the factors aggravating the collision of the molecules play a very important role in Collision theory.  For instance, if high energy is given to the molecules they will collide with each other more effectively. If the temperature of the reaction increases the molecules will move faster and will collide more with each other.

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So the diagram illustrates that the molecules with higher kinetic energy are colliding faster than the blue sluggish molecules with very low kinetic energy thus the reaction rate will also decrease.

The rate at which the molecules collide with each other is the rate of collision and is also termed as collision rate and is mathematically expressed as Z = NA NBσAB√8кBT/ πμAB

Where NA and NB are the number of molecules of A and B reactants and are directly related to the concentration of the reactants.

√8кBT/ πμAB is the Maxwell-Boltzmann distribution of thermalized gases and determines the mean speed of molecules. 

σAB represents the average sum of collision cross-sections of the molecules where the collision cross-section is defined as the collision region presented by one molecule to the other.

μAB is the reduced mass and is expressed as μAB = mAmB/ mA+mB

The reason that Transition State Theory is preferred over Collision Theory is that Collision Theory is only applicable for gaseous reactants whereas the former is applicable for the reactants in the solution.