Stationary Velocities and Concentrations

Calculation of Stationary Velocities and Concentration 1. The Partition Matrix 

We start with the case of a linear open sequence with a definite number of steps, e.g., four. We do this for the simple reason that the general expressions arrived at are often difficult to write and to read, whereas an example with four steps in the sequence is neither too simple nor too complicated to show the general form of the results obtained. 

We now define a certain number of reaction probabilities, meaning the probability per unit of time that an intermediate or in some cases an ordinary molecule will react according to some prescribed partial reaction. 

In reaction kinetics the order of the partial reactions is relevant, and it is therefore natural to number them 1, 2, 3 . The corresponding reversed reactions may then be numbered — 1, — 2, — 3 . For a linear open or closed sequence this numbering is satisfactory, but when we come to cases of branched sequences the principle fails. In that case it becomes necessary to number substances (states), usually the intermediates, instead of reactions, which then must be characterized by a pair of numbers whose order defines the direction of the reaction. For example, if the states are 1 and 2, the transition from 1 to 2 is symbolized by 12 and the opposite by 21. 

We shall use the two systems alternatively, preferring the former (numbering the reactions) when possible because it is slightly more convenient than the latter, which may be used in nearly all cases. 

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