Transition State Theory
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| Transition State Theory |
It is also
called absolute rate theory. or theory of activated complex. In 1985, it was
given by MG Evans, M Polanyi, H. Eyring. It describes or express rate constant
of reaction in thermodynamic parameters K, AG, OH, AS
Postulates:
1. The reaction
between two species leads to the formation of an activated complex.
2. Activated complex is highly unstable energetic
specie that decompose spontaneously to product.
3. Reaction between
reactants and activated complex is a reversible process. There exists a dynamice quilibrium between reactant and activated complex.
4. Formation of
product from activated complex is an irreversible.
Kinetics
of transition state theory
A + B → P
e.q.11.1
K1= rate constant for forward
reaction
K2= rate constant for backward
reaction
K3= formation of product’s rate
constant
Rate of reaction =
e.q.11.2 By
the law of mass action
Rate of
forward reaction = K1 [A][B]
Rate of
backward reaction = K2 [AB]*
At
equilibrium both rates are equal. So,
K1 [A][B] = K2 [AB]*
Keq*: it is the equilibrium constant which is equal to the ratio of rate constant of forward and backward reactions. So equation becomes
[AB]*= Keq* [A][B] e.q.11.3
Put this value of [AB]* in e.q.11.2 we got
e.q.11.4LHS of e.q.11.1 and
11.4 is same so
K [A][B] = K3 Keq* [A] [B]
Simplifying K = K3 Keq*
Here these
rate constant can be expressed in terms of thermodynamics parameters by Von’t
Hoff. We know that Gibbs free energy is
∆G = -RTlnK e.q.11.6
This
equation shows that there is a relation between Gibbs free energy and rate
constant K. we also know that
∆G* = RTlnK eq*
eq.11.7
taking antilog we got, Keq* = e-∆G*/RT
Put this value of Keq* in e.q.11.5 we got K=K3
e-∆G*/RT e.q.11.8
We also know
that ∆G =∆H-T∆S
And ∆G* =∆H*-T∆S*
Put this value of ∆G* in e.q.11.8 we got
K=K3 e-(∆H*-T∆S*/RT)
Or K=K3 e-∆H*/RT. e-∆S*/R e.q.11.9
Eyring
calculation
Eyringcalculated the value of K3 from statistical quantum mechanics as:
e.q.11.10
Here KB= Boltzmann constant and h=Planck’s constant. Putting this value of K3 in e.q.11.9 we got
By taking log this exponential equation can be converted to linear form
e.q.11.11
The e.q.11.11 is the Eyring equation.
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Figure
11.1: Graph for Linear
form of Eyring equation
