Hinshel wood theory

Hinshelwood modified theory

1. HINSHELWOOD THEORY K.LOGANATHAN

2. Sir Cyril Hinshelwood The Nobel Prize in Chemistry 1956 was awarded jointly to Sir Cyril Norman Hinshelwood and Nikolaevich "for their researches into the mechanism of chemical reactions."

3. The first successful explanation of unimolecular reactions was provided by Lindemann in 1921 and then elaborated by Cyril Hinshelwood. In the Lindemann –Hinshelwood mechanism it is supposed that a reactant molecule A becomes energetically excited by collision with another A molecule in a bimolecular step

4. Effective Rate constant (Lindemann–Hinshelwood mechanism) A test of this theory is to plot 1/ k r against 1/[A], and to expect a straight line . This behaviour is observed often at low concentrations but deviations are common at high concentrations

5. Lindemann theory breaks down for two main reasons: The bimolecular step takes no account of the energy dependence of activation; the internal degrees of freedom of the molecule are completely neglected, and the theory consequently underestimates the rate of activation . ii ) The unimolecular step fails to take into account that a unimolecular reaction specifically involves one particular form of molecular motion (e.g. rotation around a double bond for cis -trans isomerization ). iii) The First-order rates are maintained down to the lower concentration than the theory appeared to permit.

6. Hinshelwood modification Hinshelwood modified Lindemann Mechanism by stating that “every energized molecule will not enter into product formation but will go into activated molecule. And these activated molecules will lead to product formation” 𝐴 + 𝐴→ 𝐴 ∗ + 𝐴 (𝐸𝑛𝑒𝑟𝑔𝑖𝑧𝑎𝑡𝑖𝑜𝑛 ) 𝐴 ∗ + 𝐴 → 𝐴 + 𝐴 (𝐷𝑒 − 𝑒𝑛𝑒𝑟𝑔𝑖𝑧𝑎𝑡𝑖𝑜𝑛 ) 𝐴 ∗ → 𝐴 # (𝐴𝑐𝑡𝑖𝑣𝑎𝑡𝑖𝑜𝑛) 𝐴 # → 𝑃 (𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛) 𝑘 1 𝑘 −1 𝑘 2 𝑘 3

7. Hinshelwood’s idea was that the energy acquired in a collision can be stored in any of the bonds in a molecule, and that this therefore introduces a statistical factor into the calculation of the rate constant He suggested that the expression z 1 exp(- E/RT) applied only if the energy is distributed among two degrees of freedom .However, some unimolecular reactions, s is very large. The activation energy is distributed initially among these degree of freedom; it would affects in many ways. Once the energy in the molecule, distributed in a way among s vibrational degrees of freedom, the molecule is in a position eventually to react.

8. After a number of vibrations of the energized molecule A* which may be a very large number – the energy may find its way into the appropriate degrees of freedom. So that A* can immediately pass into the products .Hinshelwood derived the following formula for the fraction of molecules having energy in excess of ε *:where s is the degree of freedom f * = He then expressed the rate constant k 1 as instead of simply as z 1 exp ( ε o * / kT ). Thus, an additional 1/(s-1)![ ε o * / kT ] has appeared and if s is sufficiently large, this may be greater than unity by many powers of 10. k 1 =z 1 1 (s-1)! ε o * kT e xp ( ε o * / kT ) 1 (s-1)! ε o * kT e xp ( ε o * / kT ) S-1 S-1 1 2 S-1

9. Equation (1) can give much high rates of activation and theorefore , much higher k 1 /k -1 values than those given by the simple collision theory . It can be shown that the experimental activation energy per molecule ε a is related to ε * as ε * = ε a +(s-3/2) kT

10. Schematic plot of 1/k 1 versus 1/[A]

11. Criticism to Hinshelwood theory. 1)The number of degree of freedom required to give agreement with experiment based Hinshelwood theory is about one-half of the total number of the vibrational modes. there is no satisfactory explanation for this. 2)This approach provided a better fit to observed kinetics in the region of low pressure. 3)A/c to this theory , k ∞ =k 1 k 2 /k -1 =k 2 .1/(s-1)! ( ε o * / kT ). exp ( ε o * / kT ) Thus one would expect a strong temperature dependence of the pre-exponential factor, only larger value of s. No experimental evidence for this. 4)The Hinshelwood treatment cannot account for the lack of linearity found experimentally for the plot of 1/k 1 vs 1/[A] S-1

12. Reference: Chemical Kinetics. By Keith J. Laidler Principles of Chemical Kinetics by James E.House Atkins' Physical Chemistry  Principles of Physical Chemistry by B.R . Puri , L.R. Sharma