Geometry of Titration Systems An Application of Horn's Theory to the Determination of />K-Values

Recently the work by Horn, Jackson, and Feinberg 1 5 has led to a reformulation of polynomial kinetics under the name of general mass-action kinetics. An essential step in this direction was an ingenious new notation which allowed to write down all differential equations in a certain matrix form, called the Horn-equation (by Müller-Herold6). The equation allows to discuss all chemical reaction systems of the well-stirred type, no matter whether closed or open, and whether exhibiting exotic phenomena or not. An important subnotion in Horn's theory is that of a reaction simplex, at first introduced into the theory of monomolecular reactions by Wei and Prater 7. As an example for the practical applicability of the Horn-equation (and as a first step toward the solution of the problem of how to determine all rate constants in an arbitrary reaction network), the determination of px-values of an n-step titration may be chosen. This is a sequence of reactions which may be considered in isolation (so that the equilibrium point of each can be determined separately). Nonetheless, the potential use of Horn's theory for experimentalists in more general cases will become apparent. At first, some of the results of Horn, Jackson, and Feinberg are to be reproduced for later use. Then we will briefly describe the titration process in terms of Horn's theory. The main part will be devoted to the description of a method for determining PK-values of an n-step titration, followed by an ap-