Jouguet s criterion

After s stoichiometric equations have been written, Jouguet s criterion allows us to ensure that the equations are actually independent. Let us assign by S the ith stoichiometry, viz. 

The statement of Jouguet s criterion is, therefore s stoichiometric equations are independent if the rank of the matrix of the stoichiometric coefficients is equal to s. 

Moreover, by combining the Brinkley s [19] criterion, m rt-if/, one can calculate the number of independent stoichiometric equations. In this criterion the number y/ of independent constituents of a chemical system is equal to the rank of the matrix of the indexes of the elements in the formula of the constituents, hence cd = n-y/ = 9-2 = 7. Kinetic considerations have led to write 11 stoichiometric equations. It must be checked by Jouguet s criterion [18] that these 11 stoichiometric equations are independent. In the case of cycohe.xane the stoichiometric equations are 2, 3, 4, 8, 9, 11, and 12. Thus these seven stoichiometric equations are independent and describe the decomposition of cyclohexane. 

In each of these equations r is determined by Jouguet s 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. 

In a recent paper, S. R. Brinkley, J. Chem. Phys., 14, 563, 686 (1946) has proposed another criterion for determining the number of independent components c —c-r starting from the stoichiometric coefficients of the elements in each compound. For a criticism of this method c/. I. Prigogine and R. Defay, J. Chem. Phys., 15, 614 (1947). For a discussion of the relation between Brinkley s criterion and that of Jouguet cf. A. Penecloux, C. R. 228, 1729 (1949). 

---