Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

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Activated complex Theory of Bimolecular Reaction or Transition state Theory or Eyring Equation

The activated complex forms between reactants as they collide. The difference between the energy of the activated complex and the energy of the reactants is the activation energy, Ea.

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

(a) Exothermic react ion (b) Endothermic reaction According to Eyring the equilibrium is between reactants and the activated complex.
Consider A and B react to form an activated complex that undergoes decay, resulting in product formation.
The activated complex represents the system at the transition state.
This complex is stable.

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

where (AB)# is the act ivated complex and k1 is the equilibrium constant between reactants and activated complex.
If (AB)# one of the vibrat ional degrees of freedo m has become a translat ional degree of freedo m.
From the classical mechanics,
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

kB = Boltzmann constant

from the quantum mechanics,
energy = hv

 than  Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev 

The vibrat ional frequency v is the rate at which the activated complex mo ve across the energ y barrier i.e. the rate constant k2 is ident ified by v.
Then the reaction is
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
⇒ Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
then Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

 for conventional rate

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

i.e. k2 = v × k1
k2 = frequency × k1                                            …(1)

where k1 = equilibrium constant = keq

 

Relation between k1 and ΔG#:
k1 = equilibrium constant = Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
&  ΔG# = ΔH# - TΔS#
where ΔG#, ΔH# & ΔS# are the standard free energy o f act ivat ion, enthalpy o f act ivat ion and entropy of activation. 

k2 = keq × frequency = k1× frequency

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev                                   …(2)
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev                   …(3)
∵ Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
∴ Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev…(4)

and  Δng =  difference is number of mo les between transit ion state and reactant

Relation between ΔE# and Ea

We know that
 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

On taking log

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

On differentiate above equation

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

orActivated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

andActivated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev                          (from arrhanius equation)
thenActivated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

 Ea = ΔE# + RT                                                     …(5)

Relation between E0 & ΔE#

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
E0 = Collision energy

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

Value of A, using above equations From Eyring theory and Arrhenius theory we have

rate constant =  Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev                              …(6)
 

Problem.  Consider the decomposition of

NOCl, 2NOCl(g) → 2NO(g) + Cl2(g)

The Arrhenius parameters for this reaction are A = 1.00 × 1013 M–1 s–1 and Ea = 104 kJ mol–1. Calculate ΔH# and ΔS# for this reaction with T = 300 K.
Sol.
We know that

                     ΔH# = ΔE# + ΔngRT

where Δng = difference in number of moles between act ivated complex and reactant.

                      ΔH# = ΔE# + (-1) RT
                       ΔH# = ΔE# - RT

&                    Ea = ΔE# + RT

then               ΔE# = Ea - RT
∴                    ΔH# = ΔE# + RT = Ea - RT - RT = Ea - RT
                      ΔH# = 104 kJ mol-1 - 2(8.314 J mol-1 K-1) (300 K)
                       = 99.0 kJ mol-1
We know that

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev                           [Δng = -1]
Taking log     Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
                      Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

ΔS# = -12.7 J mol-1 K-1

Note: for unimolecular      Δng = 0

for bimolecular Δng = -1
for trimolecular            Δng = -2
&                                 ΔH# = ΔE# + ΔngRT                                [∵ Ea = ΔE# + RT]4
                                    = Ea - RT + ΔngRT
⇒                                 Ea = ΔH# + RT - ΔngRT
for unimolecular            Ea = ΔH# + RT
for bimolecular              Ea = ΔH# + 2RT
for trimolecular              Ea = ΔH# + 3RT

The Pre-equilibrium Approximation: Consider the following reaction

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

(i) First, equilibrium between the reactants and the intermediate is maintained during the course of the reaction. (ii)  The intermediate undergoes decay to form product.
Then the rate law expression is

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

∵ I is in equilibrium wit h the reactant then

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev   = equilibrium constant

[I] = kC [A][B]

∴ Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev
Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

The Lindemann Mechanism

Lindemann mechanism for unimolecular reactions involves two steps. First reactants acquire sufficient energy to undergo reaction through a bimolecular collision.

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

In this,  A* is the act ivated reactant and undergoes one of two reactions.

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

Then, rate of product formation is

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

& rate of formation of A*

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

Applying the steady-state approximation

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

ThenActivated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev 

It state that the observed order dependence on [A] depends on the relative magnitude of k–1[A] versus k2. At high reactant concentration, k–1[A] > k2 and

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev                                            Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

i.e. the product formation is first order at high pressure. At low reactant concentration k2 > k–1[A] and

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

i.e. at low pressure, the rate of formation product is second order in [A].
Then

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

kuni is the apparent rate constant for the reaction defined as

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

and Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

when k–1[A] >> k2 i.e. at high concentration kuni

 Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

when k–1[A] << k2 i.e. at low concentration kuni = k1[A]

 kuni = k1[A]

Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Chemistry Notes | EduRev

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