Module 6 : Reaction Kinetics and Dynamics
Lecture 28 : Elementary Reactions and Reaction Mechanisms
  28.4

Mechanism of unimolecular reactions.

Even for reactions that appear very simple such as A [P] where P refers to products, the mechanism can be fairly involved. This is because for reactions to occur, molecules need to be activated or initiated through collisions (unlike radioactivity which is spontaneous!). Collisions could be with other molecules M that are present in the reaction mixture, which are usually in large amounts. The reaction sequence is

 

A + M A* + M; A* P

(28.33)
If the second step ( A * P ) is slow, this will determine the overall conversion giving first order kinetics. Let us see how this comes about using the steady state approximation for A*


d [ A * ] / d t = k f [ A ] [ M ] - k r [ A * ] [ M ] - k 2 [ A * ] (28.34)
 
[ A * ] = k f [ A ] [ M ] / (k 2 + k r [ M ] ) (28.35)
substituting in d [P] / dt
 
d [P] / dt = k 2 [ A* ] = k 2 k f [ A] [ M ] / (k 2 + k r [ M ] ) (28.36)
This is a general rate expression for the Lindemann - Hinshelwood mechanism outlined above. For low pressures, when [ M ] is small, k 2 >> k r [ M ] and the rate law is of second order
 
d [ P] / d t = (k 2 k f / k 2)[ A ] [ M ] = k f [ A] [ M] (28.37)
 
For high pressures when k r [ M ] >> k 2, the rate law becomes
 
d [ p ] / d t = k 2 k f / k r [ A], (28.38)
which is first order in [ A ]. For many unimolecular reactions such as isomerization of trans CHD = CHD, cis - butadiene, decomposition of N2O5, and so on, the transition from second order at low pressures to first order at high pressures is observed. This also brings out the point that mechanisms for reactions are not ubiquitous but are dependent on reaction conditions and are by no means unique.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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