TRANSITION STATE THEORY

Transition state theory or theory of absolute reaction rate was developed by Eyring considering statistical mechanics. It is known as theory of absolute reaction rate, because it was fundamental properties such as vibrational frequency of the reactant molecules to calculate the rate of reaction.

According to this theory---

(1) In order for only chemical reaction to take place the reactant molecules possessing sufficient energy must approach each other, to form a lose association known as activated complex. This complex is in equilibrium with the reactant molecules. The configuration of this complex is such that energetically it corresponds to the top of energy barrier separating the reactants from the product.

(2) The activated complex is an aggregate of atoms, it may be thought of being similar to a molecule except that it has one special vibration with respect to which it is unstable. This vibration leads to dissociation of the complex into products. If the frequency of this vibration is v then rate in molecules per unit volume per second at which products are formed as---

Rate = v x concentration of activated complex

Now let us consider the following reaction---

A + B <=====> [ AB] ^#

Where is [AB]^# activated complex.

Since reactant molecules and activated complex are in equilibrium, the equilibrium constant---

K^# = [AB]^# / [A][B]

Or, conc of activated complex, [AB]^# = K^# [A][B]

Now, if v is the frequency of the vibration of the unstable degree of freedom, then vibrational energy is hv, but from statistical mechanics, vibrational energy per degree of freedom is KT, so ---

hv = KT

Or, v = KT / h 

[where K= Boltzmann’s constant]

Hence the rate of reaction---

Rate = v [AB]^#

Rate = (KT / h) K^# [A][B] ------ (a)

Now simple kinetic study for the reaction---

A + B ------> Products states 

Rate = K_r [A][B] ------ (b)

where K_r is rate constant

Comparing (a) and (b), we get---

K_r = (KT / h) K^# ------ (1)

Now from Vant Hoff’s isotherm---

-ΔG^# = RT lnK^#

(Where, ΔG^# = free energy change during an activated formation)

Or, K^# = e^{- ΔG#/RT}

Or, K^# = e^-ΔH#/RT . e^ΔS#/R

ΔS^# and ΔH^# are entropy and enthalpy of activation.

So, from equation (1) ---

K_r = (KT / h) e^-ΔH#/RT . e^ΔS#/R ------ (2)

Thus, experimentally measuring rate constant (K_r) at two different temperature, enthalpy and entropy of activation can be known. This is the most important success of transition state theory, because with the knowledge of ΔH^# and ΔS^# for a reaction, knowledge about its mechanism can be obtained.