POTENTIAL ENERGY SURFACE - KINETIC ISOTOPE EFFECT - LINDEMANN THEORY - HINSHELWOOD THEORY - RRK TREATMENT- RRKM TREATMENT - SLATER'S TREATMENT

1. Dr.P.GOVINDARAJ
Associate Professor & Head , Department of Chemistry
SAIVA BHANU KSHATRIYA COLLEGE
ARUPPUKOTTAI - 626101
Virudhunagar District, Tamil Nadu, India
POTENTIAL ENERGY SURFACE, KINETIC ISOTOPE EFFECT &
THEORIES OF UNIMOLECULAR REACTION

2. POTENTIAL ENERGY SURFACE
Definition
• The three dimensional graphical representation of the progress of the reaction obtained
by plotting potential energy and bond length of the reactant and product is called potential
energy surface for a chemical reaction
• A potential energy surface show how the potential energy of a chemical system changes with
the (relative) position of the atom
• For a chemical reaction , A + BC → AB + C the PES diagram is shown below

3. POTENTIAL ENERGY SURFACE
• Consider formation of a diatomic molecule from two atoms
• The Potential energy diagram for the above reaction is
A + A → A2

4. POTENTIAL ENERGY SURFACE
• Consider the following reaction sequence
A + BC → AB + C
• Mechanism
A + B - C → A ---- B ---- C → A- B + C
• The potential energy diagram for the formation of BC from B and C is
B C
B C

5. POTENTIAL ENERGY SURFACE
• The potential energy diagram for the formation of AB from A and B is
• By joining the above two graphical representation resulted potential energy surface
for the formation of AB from BC by the following reaction
A +BC →AB + C
B
A
B
A

6. POTENTIAL ENERGY SURFACE
• Between any two minima (Valley points) the lowest energy path will pass through
a maxima at a saddle point which we also that saddle point a transition state structure
Saddle point in chemical kinetics

7. KINETIC ISOTOPE EFFECT
Types
• The change in rate of a reaction on substituting an atom of a bond, which is broken
in the course of the reaction by its heavier isotope is called kinetic isotope effect
• Primary kinetic isotope effect (bonds which are broken in rate determining step)
• Secondary kinetic isotope effect (bonds which are not broken in rate determining step)
Definition

8. KINETIC ISOTOPE EFFECT

9. KINETIC ISOTOPE EFFECT

10. THEORIES OF UNIMOLECULAR GASEOUS REACTIONS
LINDEMANN THEORY
• First step : A + A ⇌ A* + A
• Second step : A* → Product
Rate of activation = k1[A] 2
Rate of deactivation = k2[A*][A]
Rate of decomposition = k3 [A*]
k1
k2
k3
• Consider a unimolecular reaction
A → P
• According to this theory, a unimolecular reaction proceeds with a following mechanism
• According to Lindemann mechanism, a time lag exist between the activation of A to A*
and the decomposition of A* to products. During this time lag, A* can be deactivated
back to A

11. THEORIES OF UNIMOLECULAR GASEOUS REACTIONS
k1[A] 2 = k2[A*][A] + k3 [A*]
[A*] =
k1[A] 2
k2[A] + k3
Rate of reaction =
−𝑑[𝐴]
𝑑𝑡
 [A*] = k3[A*]
−𝑑[𝐴]
𝑑𝑡
=
k1 k3[A]2
k2[A] + k3
--------(1)
• According to Steady state approximation, the rate of formation of A* is equal to rate of
disappearance of A*
i.e.,

12. THEORIES OF UNIMOLECULAR GASEOUS REACTIONS
2. Low pressure : k3 >> k2[A]
−𝑑[𝐴]
𝑑𝑡
=
k1k3[A]2
k3
= 𝑘1[A]2
1. High pressure : k2[A] >> k3
−𝑑[𝐴]
𝑑𝑡
=
k1k3[A]2
k2[A]
=
k1k3[A]
k2
= 𝑘′[A]

13. THEORIES OF UNIMOLECULAR GASEOUS REACTIONS
Limitations:
• We know that the rate of uni molecular reaction is
−𝑑[𝐴]
𝑑𝑡
= k[A]
• Equating this equation with equation (1) we get
k[A]=
k1 k3[A]2
k2[A] + k3
• Rearranging this equation resulted equation (2)
1
𝑘[𝐴]
=
k2[A] + k3
k1 k3[A]2
1
𝑘
=
k2[A]2
k1 k3[A]2
+
k3[A]
k1 k3[A]2
1
𝑘
=
k2
k1 k3
+
1
k1 [A]
----------(2)

14. THEORIES OF UNIMOLECULAR GASEOUS REACTIONS
• The plot of 1/k Vs 1/[A] gives straight line as per the equation (2) but deviation
from linearity have been found with the experimental results shown in the diagram

15. HINSHELWOOD’S TREATEMNT
According to Hinshelwood,
• For uni molecular reactions, the number of vibrational degrees of freedom “s” is
considerable i.e., the activation energy is distributed initially among these degrees of
freedom
• Since the energy is in the molecule, distributed in any way among “s” vibrational
degrees of freedom, the molecule is in a position to react
• After a number of vibrations of the energized molecule A* , which may be a very
considerable number than the energy may find its way into appropriate degrees of
freedom so that A* can pass at once into products

16. • The rate constant for the uni molecular reaction is expressed as
• Where
s is the vibrational degrees of freedom
0* is the energy possessed by the energized molecule A*
HINSHELWOOD’S TREATEMNT

17. RRK TREATMENT
According to RRK treatment,
• The mechanism for uni molecular reaction is
• Where M is any molecule, including another A
A* is energized molecule
A# is activated molecule
• Activated molecule is passing directly through the dividing surface of the potential
energy surface
• An energy molecule A* has acquired all the energy it needs to become an activated
molecule

18. RRK TREATMENT
• In the energized molecule A* an amount of energy * is distributed among the
normal modes of vibration. Since the molecular system are coupled loosely by the
normal modes of vibration, the energy can flow between them and after a sufficient
number of vibrations the critical amount of energy 0* may be in a particular normal
mode and reaction can occur
• The energized molecule A* have random lifetimes. i.e., the energy is distributed
randomly among the various normal modes. So that the process depends entirely on
statistical factors

19. RRK TREATMENT
• RRK treatment expressed the first order rate co-efficient ‘K’ as
• Where
x = *- 0* /KT , b = 0* /KT
s is the vibrational degrees of freedom

20. RRKM TREATMENT
• The total energy contained in the energized molecule is classified as either active or
inactive
• The inactive energy is energy that remains in the same quantum state during the
course of reaction and therefore cannot contribute to the breaking of bonds
• The zero-point energy is inactive, as is the energy of overall translation and rotation
• Vibrational energy and the energy of internal rotations are active
• The distribution function f(*) is expressed as
According to RRKM treatment,

21. RRKM TREATMENT
• Where N(*) is the density of states having energy between  * and  *+ d *
The denominator is the partition function relating to the active – energy contribution
• The expression for K2 (*) is
• Where
l# is the statistical factor
𝑃( ∗ 𝑎𝑐𝑡𝑖𝑣𝑒) is the number of vibration-rotational quantum states of the activated
molecule
Fr is the correction factor to correct that rotations may not be the same in the
activated molecule as in the energized molecule

22. RRKM TREATMENT
• The first order rate constant is expressed as
• Where
q# is the partition functions for activated states
qi is the partition functions for initial states

23. SLATER’S TREATEMENT
• In a uni molecular reaction, the breaks take place as a result of a number of normal –mode
vibrations coming into phase
• For example, In the dissociation of ethane into methyl radical
C2H6 2CH3
• When the ethane molecule is energized as a result of collisions, the energy is distributed
among the 18 normal modes of vibration
• As it vibrates the C-C bond expands and contracts in a complicated way and the normal –
mode of vibrations coming into phase then the C-C bond becomes extended by a critical
amount
According to slater’s theory,