The principle of linear independent reactions

Some multi-step reactions have been discussed above in the examples. In all cases the different partial steps were elementary reactions. None of the rate equations of these steps had any dependence on one another. It is obvious that this number of linearly independent steps of reaction (partial reactions) plays an essential part in the process to set up the rate equations. 

This number has to be known for the calculation of the yields as well as for a kinetic analysis of the reaction system. Linear dependencies exist between different rows of the stoichiometric matrix v, if its rank is smaller than the number r of all the partial reactions possible. Under such circumstances the advancement of the reaction can be described by a reduced number s r of degrees of advancement or concentrations (j defines the rank of the stoichiometric matrix). In the following, two examples are given to demonstrate the problems, which arise by this restriction. They are chosen to give information about various aspects of linear dependence. 

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