Equilibrium dissociation constant dimensions

Figure 3 Dependence of the equilibrium concentration [A] of the analyte on the initial concentration [B0] (indicated by (B) in the text) of ligand added to the reaction mixture before CZE analysis. The curves are calculated for different values of the dissociation constants (between 1CT5- and 103-fold of the initial concentration of A). Reaction between analyte and ligand is according to A + B = AB. The initial concentration (A) is kept constant, and increasing initial concentrations (B) are added to the reaction mixture. All concentrations are given in arbitrary units (including the dimension of KD). (Reprinted from Ref. 22.)...

This equilibrium constant is expressed as the association constant which has dimensions (concentration)-1, in molar terms M-1. The dissociation constant KDiss is the reciprocal of and has dimensions of concentration (M). The objective of the following derivation is to obtain an equation of the form cAB = f(cA tot, cBjtot, fCA ), in which ci tot are the total or stoichiometric concentrations of the components i (which are known), in contrast to the quantity c in Eqn. 9.19, which are the free concentrations of the species in solution, which are not known. An equation of this form will enable us to calculate theoretical data. 

In spite of these thermodynamic requirements, most papers report equilibrium constants with dimensions for convenience (e.g. dm mol for the stability constant of a 1 1 complex or mol dm for its dissociation constant). 

This describes a first order reaction with the observed rate constant cat/ M- Remembering that has the dimensions of a dissociation constant, we can compare the above equation to that derived for two step ligand binding, when the second step is preceded by a rapid pre-equilibrium (see p. 66). The constant k JK can be determined from the analysis of the record as a first order reaction. Although, even at such low initial substrate concentrations, the effects of reversibility or product inhibition may perturb the later parts of the reaction. The more usual procedure found in the literature is to plot v/ce(0) against Cs(0) from a set of initial rate measurements and to take k JK as the initial slope. As pointed out in section 3.2, one obtains an apparent second order rate constant. 

Confinement of water into regions with dimensions of only a few nanometers, such as typically those found in PEMs, accompanied by a strong electrostatic field due to the anions, will result in a significantly lower dielectric constant for the water than that observed in bulk water. Measurement of this structural ordering of the water has not been accomplished experimentally to date, and this was the motivation to the recent calculation of the dielectric saturation of the water in PEMs with an equilibrium thermodynamical formulation. " In addition to information concerning the state of the water this modeling has provided information concerning the distribution of the dissociation protons in sulfonic acid-based PEMs. 

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