The BRINKLEY criterion

This criterion stipulates the number I of stoichiometric equations which are necessary to describe the chemical change  

J is equal to the rank of the matrix of the indices of the elements in the formulae for the constituents. The rank of a matrix is the order of the determinant of the highest order, which can be extracted from the matrix, which is not equal to zero. 

Consider the reaction for the decomposition of neopentane stirred flow 

Starting by determining the number of independent constituents, the formula matrix can be written as follows  

It is possible to extract a non-zero determinant of order 2 from this matrix. It is deduced that J = 2. As J = 5, then 1 = 3. Three stoichiometric equations must therefore be written, for example  

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Very often, it happens that some , are nearly zero (or even weakly negative) and, therefore, the corresponding stoichiometric equations can be considered as of negligible importance. Thus, the reacting system is described by a number, s, of stoichiometric equations less than the number, s = c — c, given by the Brinkley criterion. 

Using the Brinkley criterion, there are three equations for the reaction ... 

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