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Lindemann Mechanism For The First-Order Reactions

It was stated in section 6.4 that the products are formed only when reaction molecular come close and collide together at one and the same time. During the collision, molecular rearrangement takes place which leads to the formation of products. For example, a second –order reaction of the types









May by traced to a bimolecular collision process involving A and B, and A, respectively. However, the first-order reactions in the gas phase cannot be accounted for by the above collision theory. The first successful explanation of first-order reactions was provided by Lindemann. The mechanism is.

(i) A + A ⟺ A* + A                  (rapd equillibrium)
(ii) A* ⟶ Products


Step (i) involves a rapid equilibrium reaction where in the forward reaction, a molecular A is activated by colliding with another A molecular with a rate constant k1 and in the backward reaction, the excited molecule A is deactivated by colliding with another A molecule with rate constant k-1. Step (ii) represents another possibility of deactivation where the excited molecule is decomposed to give the products with rate constant k2. Since the step (ii) is slow and rate determining, the rate at which products are formed will be determined by the unimolecular decay and hence first order kinetics will be observed.

The lindemann scheme is similar to the general scheme a given by where a molecule of M is replaced by a molecule of A. The general rate low in the present case, will become.


 



From it is obvious that the lindemann mechamsm will follow a complicated rate law if the rate constants k2 k1and k-1 have comparable values. However, the first –order kinetics will emerge only under the condition that k2 < k-1 [A]. As state earlier, this condition will be observed only when the reaction is carried out at high gaseous pressures.

At low pressures where k-1[A] < k2 , the lindemann mechanism will follow the rate law







That’s second-order kinetics.

The rate of reaction is proportional to [A*], which is assumed to be constant. The rate of the reaction is a function of [A]  which is steadily decreasing as the reaction proceeds.

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