The analytical resolution of parallel first- and second-order reaction mechanisms.

Given the species A₁ and A₂, the competition among the three different elementary processes <EQN><NUMBER>1</NUMBER></EQN><EQN><NUMBER>2</NUMBER></EQN><EQN><NUMBER>3</NUMBER></EQN> is frequently found in thermal and photochemical reaction systems. In the present paper, an analytical resolution of the system (1)–(3), performed under plausible contour conditions, namely, finite initial molar concentrations for both reactants, [A₂]₀ and [A₁]₀, and nonzero reaction rate coefficients k₁, k₂, and k₃, leads to the equation [A₁] = ((δ[A₂]^γ - [A₂])/β) - α, where α = k₁/2k₃, γ = β + 1 = 2k₃/k₂, and δ = ([A₂]₀ + β[A₁]₀ + β α))/[A₂]₀^γ. The comparison with a numerical integration employing the fourth-order Runge–Kutta algorithm for the well-known case of the oxidation of organic compounds by ferrate ion is performed. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 562–566, 2010 [ABSTRACT FROM AUTHOR]