COMPUTABILITY OF REACTION RATES FROM DATA

The rate 7 i,tot of a single reaction can thus be determined from a measurement of Rj tot for any species produced or consumed by that reaction. The species production rates are then directly proportional  

Corresponding relations hold for the local rates Rj of Eq. (2.1-7) and also for the macroscopic extents of production = f R Q dt, obtained from overall material balances on transient reactor operations with one reaction. 

For multiple reactions, Eq. (2.1-3) is solvable for the full vector T tot if and only if the matrix n has full rank NR, i.e., if and only if the rows of v are linearly independent. If any species production rates Ri,tot are not measured, the corresponding columns of u must be suppressed when testing for solvability of Eq. (2.1-3). Gaussian elimination (see Section A.4) is convenient for doing this test and for finding a full or partial solution for the reaction rates. 

Consider the three-reaction scheme of Section 2.1. Suppose that an experiment is available with measured values of all the species production rates Rj,tot Therefore, use all columns of the stoichiometric matrix 

Dividing the first row of i/ by its leading nonzero element (thus choosing i/ii as the first pivot) and adding this new row to row 3, we obtain the matrix 

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