Transition State Theory and Thermodynamic Treatment

Transition State Theory

This theory was proposed by Eyring and Polanyl and is also known as the theory of absolute reaction rates or activated complex theory.
According to this theory, chemical reaction is simply a continuous series of changes in bond length and other rearrangement of atoms in reactant molecules as soon as the reactant, molecules with sufficient energy begin to approach each other. Some bonds start getting longer and ultimately break while new bonds start forming. Reactant molecules thus lead to the formation of a particular configuration of atoms.
This critical configuration corresponds to maximum energy of the reacting system and is called 'transition state' which is always in equilibrium with the reactant molecules. The transition state is assumed to have properties of a ordinary reactant molecules but it has only transient existence. Once it is formed, it decomposes to products and hence the rate of reaction is the rate of decomposition of transition state. The entire energy changes from reactant to products can be shown with the help of potential energy diagram-

The transition state theory is superior to collision theory because the transition state theory can explain the reactions involving molecules having a large number of atoms.

Thermodynamic Treatment of Transition State Theory

Let us consider a following bimolecular reaction-
A   +   B   ⇌   [AB*]  →  Product
If an activated complex is in equilibrium with reactants then the equilibrium constant for the formation of complex is given by-
K*   =   [AB*] / [A][B]
[AB*]  = K* [A][B]
According to this theory, the rate of raction is the number of activated complexes which pass over the potential energy barrier in a unit time. Hence-
− d[A]/dt = [AB*] x rate of decomposition of complex.
The complex, however should decompose only if enough vibrational energy is given to the system so as to cause the atoms to vibrate with certain critical frequency leading to the bond cleavage. The frequency is given by-
𝜈 = E_vib./h
Where E_vib. is the average energy of the vibration leading to decomposition and is given by-
E_vib. = k.T
Where k = Boltzamann Constant.
so, 𝜈 = kT/h
or, − d[A]/dt = K* [A][B](kT/h)
Since, the rate of reaction is K[A][B], hence, the rate constant-
K = (kT/h)K*
We know that-
ΔG* = − RTlnK*
ΔG* = free energy in standard state
or, K* = e^−ΔG*/RT
Since, ΔG* = ΔH* −TΔS. Hence the rate constant is given as-
or, K = (kT/h) e^−ΔG*/RT
or, K = (kT/h) e^ΔS*/R . e^−ΔH*/RT
Where, ΔH* and ΔS* are the change in enthalpy and change in entropy in standard state respectively.

Collision Theory

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