POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULAR REACTION

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 → A 2

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 = k 1 [A] 2 Rate of deactivation = k 2 [A*][A] Rate of decomposition = k 3 [A*] k 1 k 2 k 3 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 k 1 [A] 2 = k 2 [A*][A] + k 3 [A*] [A*] =   Rate of reaction =  [A*] = k 3 [A*] = --------(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 : k 3 >> = = [A] 2   High pressure : = = = [A]  

13. THEORIES OF UNIMOLECULAR GASEOUS REACTIONS Limitations: We know that the rate of uni molecular reaction is = k[A] Equating this equation with equation (1) we get k[A]= Rearranging this equation resulted equation (2) + + ----------(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  * 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  * 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 = *-  * /KT , b =  * /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 K 2 (  *) is Where l # is the statistical factor is the number of vibration-rotational quantum states of the activated molecule F r 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 q i 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 C 2 H 6 2CH 3 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,

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