Chemical Engineering Science, Vol.184, 25-32, 2018
New invariances for chemical reactions from Scaled Incremental Conversion (SIC)
For the two-step chemical reaction A reversible arrow B reversible arrow C, invariant dependences of a new type have been found. These invariants relate concentration dependences which are started from the single component (single-component-dependences). For constructing the invariants, a three-stage procedure is used:& para;& para;1. Scaled Incremental Conversion (SIC), chi, is determined for any substance as chi = X(t)-X-0/X-eq-X-0, where X-eq and X-0 are equilibrium and initial concentrations for any substance, A, B, or C, respectively; X(t) is the concentration at any moment of time.& para;& para;2. Differences of SIC terms Delta chi are determined for different pairs of substances. SIC terms are calculated in experiments with symmetrical initial conditions.& para;& para;3. A generating function of invariants is constructed which produces invariants as ratios of different Delta chi. These ratios remain constant at any time during the non-steady-state reaction.& para;& para;It is demonstrated that the variety of invariants obtained depends on the initial conditions used in the procedure. Explicit analytical expressions have been found assuming the same initial conditions, two, and three different initial conditions, respectively.& para;& para;All invariants are functions of three independent parameters which are ratios of kinetic coefficients. Two of them are equilibrium reaction constants, and the third one is the ratio of kinetic coefficients belonging to different reactions. (C) 2018 Elsevier Ltd. All rights reserved.