The JOUGUET criterion

Each linear combination of stoichiometric equations is itself a stoichiometric equation. This is the reason why the number of stoichiometric equations is fixed, but not their nature. The writing of a complex stoichiometric system is therefore likely to lead to equations which are not independent. One must make certain that this is not the case. JOUGUET s criterion indicates that the equations are independent if the rank of the matrix of the stoichiometric coefficients is equal to I. 

The matrix of the generalized stoichiometric coefficients can be written as follows  

This matrix is of rank 3 and the equations are actually independent. 

Consider a bateh reactor containing nj moles of constituent Cj. The law of definite proportions stipulates that the variation (dnj)j in the quantity of Cj due to the reaction i is proportional to the stoiehiometrie coefficient Vy. d j represents the proportionality coefficient, is a Jouguet-de Bonder chemical variable. The total variation dnj due to the I reactions (39) can be written as follows  

The transposition to a continuous reactor operating under steady-state conditions leads to the following expression  

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In order for all the balance equations to be independent, no rows of the above matrix should be obtainable by a linear combination of other rows. This means that this matrix must contain at least one determinant of a nonnull rank R. This condition is called the Jouguet criterion or criterion of independence of the reactions. 

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