Page - 11 - in Advanced Chemical Kinetics

While the overall reaction evolves no intermediates, i.e.,A2þ2BÐ kþ k� 2AB, the stoichiometric matrix (10)andmolecularmatrix (11) infer S¼ �1 �2 2 0 0 0 0 �1 0 �1 1 0 0 2 �1 0 �1 1 0 1 �1 �1 0 1 2664 3775, M¼ A Z B 2 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0BBBBBBBB@ 1CCCCCCCCA A2 Z AZ B BZ AB 8>>>>>>>><>>>>>>>>: (19) Notethat therelationbetweenthemisorthogonal, i.e.,Eqs. (15)and(18)hold.Whilethestoichio- metricmatrixof intermediatesandHoriutimatrixareNs=4, Nint =3(Z,AZ,BZ),Nas=1(Z), Nint¼ �2 2 0 �1 0 1 2 �1 �1 1 �1 0 26664 37775,σ¼ �1 0 0 1 �2 �1 0 1 26664 37775 AtomicbalanceconstraintsaregivenbyEq. (11) ηt,A¼2ηc1þηc3þηc6, ηt,Z¼2ηc2þηc3þηc5, ηt,B¼2ηc4þηc5þηc6: (20) whereas,nt,A,nt,Z, andnt,Bare the totalnumberofmolesofA,Z, andBatoms, respectively. ThekeycomponentsNkcandreactionrouteNrrof thesystemaregivenbyEqs. (16)and(17) Nkc=Nc�rank(M)=6�3=3, Figure3. Four-stepreversible reactionhaving tworoutes. Complex Reactions and Dynamics http://dx.doi.org/10.5772/intechopen.70502 11