Analytical resolution of a parallel second‐order reaction mechanism

The competition among the three different elementary second‐order processes involving the radicals A and B, (1) (2) (3) is frequently established in many combustion and atmospheric chemistry systems. The analytical resolution of the above mechanism for k_AB = 2k_AA and k_AB = 2k_BB, that is, for a cross‐combination ratio ? = k_AB/(k_AAk_BB)^1/2 = 2, is well‐known, but it has been claimed not to exist for ? ≠ 2. In the present paper an analytical resolution of the system (1)–(3), performed under the condition k_AB ≠ 2k_AA and k_AB ≠ 2k_BB, leads to The mathematical procedure leading to this equation and the equation itself are valid independently of the nature of the products of the reactions ( 1 ), ( 2 ) and ( 3 ), that is, recombination or disproportionation products, provided that the reactants and the order of the reactions remain the same. The comparison with numerical integration for exemplary cases is performed. The solutions for the particular cases k_AB ≠ 2k_BB or k_AB ≠ 2k_AA are also presented. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 246–251, 2003