One general gaseous reaction in which A is the reactant, R is a reactive chain carrier, P is the product, and α is the number of chain carriers produced by one carrier in the propagation step so that we can write it as,
The chain carrier is destroyed by collision with other molecules or collision against the walls of the vessels. The rate of formation of chain carrier is given by,
The steady-state approximation for the chain carrier, i.e.
Here, k3 = constant for considered equal to the sum of two terms, kw for the wall reaction and kg for the gas phase reaction, so, equation (2) we can write as,
According to equation (3), consider the following cases;
Case:1: when α =1
Each propagation step of the reaction results in the formation of a product molecule with the regeneration of only one chain carrier, a reaction known as non- branched or stationary chain reaction.
In these reactions, the radical concentration α ratio of its formation rate to the decomposition rate.
An example of this reaction is the Pyrolysis of several organic compounds.
Case:2: when α>1
More than on-chain carriers are produced in the propagation sequences of the reaction called non-stationary chains or Branched chains reaction.
Case:3: when α>>1
Many chain carriers are produced in the propagation sequence; the concentration carrier [R] is almost infinite. The reaction rate also becomes almost infinite, resulting in explosions called isothermal explosions.
