2.7 Exercises 55 2.7 Exercises Exercise 2.1: Finding independent sets of reactions Consider the following set of chemical reactions, 2N205=2N204 + O2 N205 = NO2 + NO3 NO2 + NO3 = N205 NO2 + NO3 = NO2 + O2 + NO NO + N2O5 = 3NO2 NO2 + NO2 = N204 (2.61) (2.62) (2.63) (2.64) (2.65) (2.66) (a) Determine the stoichiometric matrix, v, and the species list, A, for this reaction system so the reaction network is summarized by VA = 0 (b) Use Octave, MATLAB, or your favorite software package to determine the rank of the stoichiometric matrix. How many of the reactions are linearly independent? (c) Now that you have found the number of independent reactions, ni, which n; of the original set of 6 reactions can be chosen as an independent set? Try guess- ing some set of n; reactions and determine the rank of the new stoichiometric matrix. Stop when you have determined successfully one or more sets of ni independent reactions. Hint: you want to examine the rank of sub-matrices obtained by deleting rows (i.e., reactions) from the original stoichiometric matrix. In Octave, if you assign the original stoichiometric matrix to a name, stoi, then you can obtain the rank of the stoichiometric matrix associated with deleting the fifth reaction, for ex- ample, by stoi2 = (stoi(1:4,:); stoi(6,:)] rank(stoi2) Do you see how the indices in forming stoi 2 work out? Notice we do not have to enter any more matrices after we build the original stoichiometric matrix to test the ranks of various reaction networks. (d) What do you think of a colleague's answer that contains Reactions 2.62 and 2.63 in the final set. Can this be correct? Why or why not? Exercise 2.2: The stoichiometric matrix 1212 By