Stoichiometric association constant

A comparison of experimental results with those calculated from the Fuoss (2) theory is presented in Table I. The theory 1s only valid approximately so that the order of magnitude agreement is fairly good, except in the cases of MgC03° and CaC03 . Stoichiometric association constants K are then obtained from the activity coefficients, expressions for K, and from equations for the conservation of mass. The latter express the total concentration of a given ion as the sum of the concentrations of the free ion and of the ion-pairs. Values of K and of the activity coefficients of free ions in ionic media depend only upon the effective ionic strength as is shown later. 

A comparison of stoichiometric association constants calculated from the Fuoss (2) model with Debye radii and from the measurements of Johnson and Pytkowicz (2). 

The statistical thermodynamic approach of Pitzer (14), involving specific interaction terms on the basis of the kinetic core effect, has provided coefficients which are a function of the ionic strength. The coefficients, as the stoichiometric association constants in our ion-pairing model, are obtained empirically in simple solutions and are then used to predict the activity coefficients in complex solutions. The Pitzer approach uses, however, a first term akin to the Debye-Huckel one to represent nonspecific effects at all concentrations. This weakens somewhat its theoretical foundation. 

Busch et al. studied the applicability of CZE to the examination of hapten-antibody complex formation (11). The catalytic antibodies examined have been used to accelerate a Diels-Alder reaction. Association constants of two hapten-antibody complexes were investigated and compared to the ELISA method. The samples contained buffer, hapten, and antibody. The constants obtained with CZE are a factor of 3-5 larger than those found with the ELISA method. The free-hapten concentration is measured directly this allows confirmation of the stoichiometric model. Because of the poor concentration sensitivity of UV detection, the application of an extended optical path length such as a bubble cell is necessary to obtain reliable binding parameters. 

Extensive literature has developed related to the preferential interaction of different solvents with proteins or peptides in bulk solution.156-5X1 Similar concepts can be incorporated into descriptions of the RPC behavior of peptides and employed as part of the selection criteria for optimizing the separation of a particular peptide mixture. As noted previously, the dependency of the equilibrium association constant, /CassoCji, of a peptide and the concentration of the solvent required for desorption in RPC can be empirically described1441 in terms of nonmechanistic, stoichiometric solvent displacement or preferential hydration models, whereby the mass distribution of a peptide P, with n nonpolar ligands, each of which is solvated with solvent molecules Da is given by the following ... 

The dichotomy of CV behavior between strongly and weakly interacting anions had been rationalized in the seminal article by Echegoyen s and Kaifer s groups with the square Scheme 1 [61]. When the strength of the interaction between the anion and the reduced redox form (here ferrocenyl) is significant, a new wave appears, and the variation of ferrocenyl potential between the free and bound forms of Scheme 1 is related to the ratio of apparent association constants F e -F ound = A °(V) = 0.059 log (K+/K0) at 25 °C. ound corresponds to the addition of one equiv. anion per ferrocenyl branch or the stoichiometric amount determined from the break points, for instance in Fig. 1. 

The unique TEE framework facilitates -conjugation with pendant aromatic substituents by allowing coplanar orientation throughout the molecular core, as was first witnessed in the X-ray crystal structure of tetrakis(phenylethynyl)ethene 1 determined by Hopf and co-workers [9]. In contrast, coplanarity is prevented by steric interactions in molecules such as cis-stilbenes or tetraphenylethene 2 [10] (Figure 2). The planarity makes it possible for 1 to form highly ordered 1 2 stoichiometric donor-acceptor -complexes in the solid state with electron-deficient molecules such as 2,4,7-trinitrofluoren-9-one and (2,4,7-trinitrofluoren-9-ylidene)malonitrile [11]. In solution, relatively weak 1 1 complexes with each of these two acceptors are formed, with association constants of 7.9 m 1 and 31.5 m 1, respectively, at 300 K in CDCl3. 

The second order dependence In the benzene ME was ascribed to the equilibrium formation of a Cu(II) - quinoline complex, which is also in equilibrium with a "slttlng-atop complex" (SAT) with the porphyrin. The rate controlling step is then the loss of a proton from the SAT. It is also Implicitly assumed that the association constant of the copper-quinollne complex is sufficiently small so that the stoichiometric concentrations of both the metal ion and base may be employed in the rate equation. 

Electrodes sensitive to one of the ion-pair partners in the so-called constant ionic strength cell [95] proved to be valuable to measure the free ion concentration and to determine the stoichiometric equilibrium constant. The latter has a clear thermodynamic meaning if the ionic strength of the medium is indicated, since in this approach, the reference standard state is not the usual infinite dilution of all species dissolved in the solvent (y-> 1, as c -> 0), but is the infinite dilution of the reacting species in the constant ionic medium (7—> 1, as c 0 at 1 = constant) [7]. Even if the constant ionic strength attenuates the variation of liquid junction potentials, the lower the association constant, the lower the consistency of the obtained constant. 

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. 

To obtain accurate estimates of the number of binding sites (n), binding experiments (usually titrations) need to be performed under conditions where the total concentration of A is relatively high, specifically that cAit0, 1 / KAs these conditions define a stoichiometric titration where effectively all of the B added is bound until the sites on A are saturated. Titrations under these conditions are insensitive to the value of the association constant, so to obtain reliable estimates of KAss, data are needed from titrations at much lower concentrations, where cA, toi- V-Kaw It should be clear from this discussion that it is not easy to evaluate both n and accurately, and it is usually necessary to do a global analysis of several data sets, obtained under different concentration conditions. 

The first right-hand expression is written in activities, and this quotient gives the intrinsic dissociation constant. The second right-hand expression is made up of two factors, a quotient of (molar or molal) concentrations that may be called the stoichiometric dissociation constant, and a quotient of activity coefficients. All dissociation constants, association constants K = 1 /ATD), and solubility products in reference books are intrinsic constants. They apply to concentrations only if the solution is extremely dilute for all ionic species. In other cases, one has to know the activity coefficients. y0, i.e., y for a nonionic species, will mostly be close to unity, but y+ and y will generally be < 1, the more so for a higher ion concentration. One may define the free... 

More precise definition of the physicochemical role of the cation, however, requires that three generic issues be addressed (1) the stoichiometry of association complex formation (2) the association constants, Kip, for formation of these complexes and (3) the physicochemical (structural and electronic) properties of different M -Acceptor complexes (i.e., stoichiometrically identical complexes differing only in the nature of Once... 

Do not confuse Ka.-Ka, with the stoichiometric real site association constants in Equation... 

It is, therefore, not necessary to use any excess of binding site monomers in order to saturate the template nearly completely. In order to reach in equimolar concentrations (0.1 molar) during imprinting 90% or better 95% degree of association, association constants of 900 (or better 3800) are necessary. Usual noncovalent interactions show much lower values. Due to this stoichiometric interaction, we have called this type stoichiometric noncovalent interaction [18,26,27]. 

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