Formalism of the reaction scheme

On the top, the different reactants are written into the first row. The second row (for the reactants) is formed by the stoichiometric coefficients of these reactants (results v ). The first element is the degree of advancement of this reaction Xy The last element is determined by the derivative of this degree of advancement with respect to time used in eq. (2.3). A simple example is the reaction 

Degrees of advancement are formal quantities. However, their use allows us to obtain equations with mass balance by combination of eq. (1.9) and (2.2). In this case, the assumed mechanism is correct and only one single step of a reaction takes place the progress of the reaction can be described by monitoring the concentration of just one properly chosen reactant (e.g. tjiking A ). One obtains accordingly 

the use of the degree of advancement simplifies the equation and the number of components to be monitored during the reaction to one. 

This advantage becomes more obvious in multi-step reactions, since in general a chemical reaction proceeds by more than one step. Furthermore some of the reactants take part in more than one reaction step. Each can be represented by a linear equation as given above. These form a system of r different linear equations of type eq. (1.9). Instead of a single degree of advancement, each step is represented by one. Instead of eq. (2.2) the result is 

The symbol is used if the vector of degrees of advancement is not reduced with respect to linear dependencies between the different steps of the reaction. 

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