Parallel second order reactions

A similar situation applies if parallel second-order reactions yield different products ... 

ILLUSTRATION 5.3 DETERMINATION OF RELATIVE RATE CONSTANTS FOR COMPETITIVE PARALLEL SECOND-ORDER REACTIONS (FIRST-ORDER IN EACH SPECIES)... 

Here c(x, t)dx is the concentration of material with index in the slice (x, x + dx) whose rate constant is k(x) K(x, z) describes the interaction of the species. The authors obtain some striking results for uniform systems, as they call those for which K is independent of x (Astarita and Ocone, 1988 Astarita, 1989). Their second-order reaction would imply that each slice reacted with every other, K being a stoichiometric coefficient function. Only if K = S(z -x) would we have a continuum of independent parallel second-order reactions. In spite of the physical objections, the mathematical challenge of setting this up properly remains. Ho and Aris (1987) have shown how not to do it. Astarita and Ocone have shown how to do something a little different and probably more sensible physically. We shall see that it can be done quite generally by having a double-indexed mixture with parallel first-order reactions. The first-order kinetics ensures the individuality of the reactions and the distribution... 

This corresponds to parallel first-order decompositions of H2S+ and HS, or to parallel second-order reactions of HS and S with H30+. In the example of 4-aminosalicylic acid, fen2s [H2S+] represents a relatively small correction term [250]. In the cases of 4-aminobenzoic acid [78] and anthranilic acid [77], however, feH2s [H2S+] is the more important term at pH values below 4. Equation (68) is equivalent to the following equation for the dependence of the first-order rate coefficient on... 

Parallel second-order reactions occurring in two different zones of polymeric solids without mutual interference ... 

Van de Vusse and Voetter [1961] also considered the parallel second-order reactions... 

Oxidation of As(III) by the silver(III) ion [Ag(OH)4] in alkaline solution occurs by parallel, second-order reactions of the three arsenite... 

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