Stoichiometric numbers constant derivation

Biochemical reactions balance the atoms of all elements except for hydrogen, or of metals when they are bound reversibly and their ionic concentrations are held constant. Thus a system of biochemical reactions can be represented by an apparent conservation matrix or an apparent stoichiometric number matrix. The adjective apparent is used because hydrogen ions are omitted in the apparent conservation matrix since they are not conserved. Hydrogen ions are also omitted in the apparent stoichiometric number matrix since they do not appear in biochemical reactions. The conservation and stoichiometric number matrices for a system of biochemical reactions can be derived from the conservation matrix... 

The composition of these complexes and their stability constants have been determined for a large number of metal ions primarily with the use of emf methods (200, 201). The free hydrogen ion concentration and in some cases the free metal ion concentration are determined as functions of the stoichiometric hydrogen ion and metal ion concentrations. From measurements on series of solutions of different concentrations the number of metal atoms in a complex and its charge can be derived, but no information is obtained on the number of water molecules in the complex. Since emf measurements are influenced by changes in activity factors they have usually been done in an inert ionic medium of high concentration (3 M NaC104) and at low metal ion concentrations. The major complexes formed, however, have been found to be stable also in the concentrated solutions needed for X-ray diffraction measurements, and the stability constants determined seem to be... 

Let us assume that it has been shown analytically that the reaction is pure and let us further assume that it has been shown by kinetical experiments that the reaction does not follow the kinetics derived from its stoichiometrical equation in the well-known way. Obviously then we have to split up the overall reaction in a number of steps, each represented by a chemical equation, and thus we must assume n > 1. If for the time being we exclude the addition of foreign substances acting as catalysts, the number of elements is obviously constant. We must therefore increase the number of molecules occurring in the system by 1 for each added step and are thus compelled to destroy the stoichiometrical simplicity. To justify the addition of such reactions which are not evident from the stoichiometrical scheme a new theory was introduced in 1913. This may be called the theory of intermediates in stationary concentrations (or even better the theory of intermediates in quasi-stationary concentrations) and has since then shown to be of the greatest importance in reaction kinetics. 

Equation (21) is not strictly valid for calculating the heat of micellization because certain assumptions made in its derivation do not hold here. The equation implies that the micelle is at equilibrium near cmc in a standard state [27,54]. However, micelles are not definite stoichiometric entities but aggregates of different sizes that are in dynamic equilibrium with themselves and surfactant monomers. The aggregation number may vary with temperature. An extended mass action model describes micellization as a multiple equilibrium characterized by a series of equilibrium constants (see Section 6.2). Because these equilibrium constants cannot be determined, the micellar equilibrium is usually described by... 

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