New Invariant Expressions in Chemical Kinetics

Abstract

This paper presents a review of our original results obtained during the last decade. These results have been found theoretically for classical mass-action-law models of chemical kinetics and justified experimentally. In contrast with the traditional invariances, they relate to a special battery of kinetic experiments, not a single experiment. Two types of invariances are distinguished and described in detail: thermodynamic invariants, i.e., special combinations of kinetic dependences that yield the equilibrium constants, or simple functions of the equilibrium constants; and "mixed" kinetico-thermodynamic invariances, functions both of equilibrium constants and non-thermodynamic ratios of kinetic coefficients.

Keywords: conservatively perturbed equilibrium; invariant expression; linear complex mechanism; scaled incremental conversion; thermodynamic invariant; two-step mechanism.

Figure 1

Concentration profiles of A (black) and B (blue), starting from pure A (solid) and from pure B (dashed), assuming a single step reversible reaction A ⇄ B with k⁺= 2 s⁻¹, k⁻= 1 s⁻¹. The ratio between B_A(t) (solid blue) and A_B(t) (black dashed) is the equilibrium constant.

Figure 2

From top to bottom, the Scaled Incremental Conversion (SIC) plots of C_B, B_B, B_A and C_A. k₁⁺ = 4.5 s⁻¹, k₁⁻ = 10 s⁻¹, k₂⁺ = 6.5 s⁻¹, k₂⁻ = 12 s⁻¹.

Figure 3

Concentration profiles of A_BC, B_AC and C_AB. The first two, A_BC and B_AC, must be read with the left Y-scale. The last one, C_AB, must be read with the right Y-scale. k₁⁺ = 1.75 s⁻¹, k₁⁻ = 3.00 s⁻¹, k₂⁺ = 1.50 s⁻¹, k₂⁻ = 0.50 s⁻¹.

Figure 4

Corrected concentration profiles of A_BC, B_AC and C_AB. From top to bottom, A_BC − A_eq, B_AC − B_eq and C_AB − C_eq. k₁⁺ = 1.75 s⁻¹, k₁⁻ = 3.00 s⁻¹, k₂⁺ = 1.50 s⁻¹, k₂⁻ = 0.50 s⁻¹.