Contributions to the spectroscopic–kinetic analysis of linear reaction systems: Systems with three linearly independent reactions using the concept of parallel projection

Linear reaction systems consist by definition of first-order reaction steps. Linearly independent reactions are independent of reaction order. Each reaction mechanism consists of a distinct number (s) of linearly independent reaction steps. Thus, the mechanism ABCD can be described by three linearly independent reactions as it is also true for A→B→C→D (s=3). In the following, a procedure for the analysis of linear reaction systems consisting of three linearly independent reaction steps is described which is based on absorbance (A) as well as absorbance difference quotient (ADQ) diagrams (two graphs of the ‘Mauser diagrams') and the concept of parallel projection. In this way it is possible to determine the ratio of eigenvalues describing the reaction mechanism. Furthermore, the reaction system (s=3) can be reduced to a system which is described only by two linearly independent concentration variables (s=2). The kinetic equations of evaluation are simplified by the concept of parallel projection. This can be helpful, for example, when one independent reaction step shows poor spectroscopic properties. The method can be extended to the analysis of quasilinear photoreactions. The method is demonstrated using a practical example (A′→B′, C′→D′, E′→F′).