Analysis of linear reaction systems with two linearly independent steps on the basis of the absorbance triangle and the formal integration

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 A→B→C can be described by two linearly independent reactions as is also true for A→B, C→D (s=2). Subsequently, a general method is described for the spectrometric kinetic evaluation of linear reactions (s=2). The differential geometric analysis of the space spread out of the absorbances at two different wavelengths leads to the so-called ‘absorbance triangle’. The application of the concept of parallel projection on this absorbance triangle provides quantities (zi) which are formal in close connection to the concentration equations describing the reaction system. The evaluation of differential equations which can be established by zi leads to the searched eigenvalues of the system in combination with the method of formal integration. The results obtained are in accordance with theorem 2 of kinetics (two strictly linear reaction systems having the same number of linearly independent reaction steps cannot be distinguished from each other by purely spectroscopic means). The procedure and precision of evaluation are demonstrated by the investigation of the spontaneous hydrolysis of Boc-gly-ONP (N-tert-butoxycarbonyl acetate) and o-NPA (o-nitrophenyl acetate) in borax buffer (pH=8.7, temperature 25.0°C).