Opposing Reactions of First Order

The transition probabilities of opposing reactions of first order can be summarized in a scheme given as 

[A] refers to the concentration of the reacting species and [Aq] to the initial concentration of the species at the beginning of the reaction. 

After the preceding comments, the generalization of the scheme should not cause problems. Consider a reaction scheme as given in Eq. (18.12). 

We have designated the individual compounds in place of A, B, C,. ..with (1), (2), (3),— Further, the individual components are numbered in such a way that only compounds with successive numbers can be converted into one another. The 

Into this transition matrix now the individual transition probabilities are inserted. There are a lot of zeros in the transition matrix. For example, pu = 0. This arises from the kinetic scheme. It is not allowed that a species is directly transformed from (1) into (3). Rather the reaction runs via the intermediate compound (2). Therefore, the matrix is a tridiagonal one. 

---