Lindemann Theory of Unimolecular Reactions

Lindemann Theory of Unimolecular Reactions

For a reaction to occur, the reactant molecules must come in close contact for collision. For a collision, there must be at least two molecules so the reaction can not be truly unimolecular and hence collision theory can not be applied to unimolecular reaction.
For the occurrence of such reactions, Lindermann proposed that there is a time-lag between activation by collision and subsequent reaction. During which the activated molecules may lose the excess energy and then they will not react and if they do not lose the excess energy they will react. Applying Lindermann theory of time-lag unimolecular reaction-
A   →   Products
Possible mechanism of the reaction is given below-

We see that the reactant molecules (A) combine firstly to form few activated molecules (A*). Then there is a time-lag during which the activated molecules may revert to original state by losing the excess energy or the activated molecules may react to form product.
Rate of formation of
A* = k₁[A]²
Rate of disappearance of
A* = k₂[A*][A] + k₃[A*]
or, A* = [A*](k₂[A] + k₃)
According to steady state principle, whenever a short lived reaction intermediate is formed, its rate of formation can be taken as its rate of disappearance i.e.
k₁[A]² = [A*](k₂[A] + k₃)
A* = k₁[A]² / (k₂[A] + k₃)
Since the rate of reaction is proportional to the concentration of activated molecules. Hence-

Limitations of Lindemann Theory

Lindemann approach breaks down for two reasons-
1. The bimolecular step takes no account of the energy dependence of activation, the internal degrees of freedom of the molecule are completely ignored and the theory underestimates the rate of activation.
2. The unimolecular step fails to take into account that a unimolecular reaction specifically involves one particular form of molecular motion (for example rotation around a double bond).

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