Average stability constant

The K, values correspond to a given conformation of the solvated ligand (L)solv which may or may not remain the same in the complex in some cases several conformations may be imagined (see Fig. 8). Thus Ks is an average stability constant for the system at thermodynamic equilibrium with respect to both conformation and complexation. 

III. In this way we obtain, with the ion-pair dissociation constant determined from conductance data, a value of 5.3 x 10-5 for the average stability constant of the triple ions (K3 from eqn. 13), This should be compared with 1.24 x lCT M as derived from conductance indicates an important fraction of simple ions over the largest part of the concentration range studied. 

Determination of Conditional Stability Constants for MixedDigands and for Complexes other than 1 1. Schubert s (15) study of complex ions by an ion exchange technique was commented upon by I. Feldman, who mentioned that the method works only for 1 1 complexes. This is inherent to any method, however, which does not vary the ligand concentration. In case of a mixture of ligands, an average stability constant is determined (35). 

Assuming for simplicity a 1 1 stoichiometry for aU ML, complexes, the complexation reaction of a suigle metal ion M with a multiligand system such as HS containing a number of ligands L, can be described by an average stability constant, or, more appropriately, an average concentration quotient (MacCarthy and Perdue, 1991) ... 

The results were interpreted by tbe simultaneous formation of the trimer and tetramer Zx (OH) and Zr4 (OH), with an average stability constant at the two acidities of log 3 = (5.39 0.08) and log, = (8.24 0.07) (errors given by the authors were only for individual values at the two acidities, in case of log, 3 the average value is within the error margin, whereas for log,(, the average is outside this error and the resulting error had to be increased. A more detailed error evaluation is done below). 

Amodiaquine hydrochloride forms 1 1 and 1 2 complexes with ferrous sulphate. The infrared spectra indicate that amodiaquine hydrochloride is bonded to iron via N and O and that water molecules are coordinated to iron (17). It forms a 1 2 complex with silver nitrate in alcoholic solutions. The average stability constant, log K, for the complex is 7.7 and A E is about 10.8 kcal/mol. (18). 

For 3 moll NaClO and at 25 "C, the average stability constant from the data listed in Table 7.4 for Be20H " is log = —3.21 which when combined with the... 

Assuming the two values are independent, the selected value is the weighted average of the two values. The ion interaction parameter data are adjusted accordingly in relation to the selected average stability constant. The selected values are... 

In order to determine the stability constants for a series of complexes in solution, we must determine the concentrations of several species. Moreover, we must then solve a rather complex set of equations to evaluate the stability constants. There are several experimental techniques that are frequently employed for determining the concentrations of the complexes. For example, spectrophotometry, polarography, solubility measurements, or potentiometry may be used, but the choice of experimental method is based on the nature of the complexes being studied. Basically, however, we proceed as follows. A parameter is defined as the average number of bound ligands per metal ion, N, which is expressed as... 

Figure 4. Copper complexation by a pond fulvic acid at pH 8 as a function of the logarithm of [Cu2+]. On the x-axis, complex stability constants and kinetic formation rate constants are given by assuming that the Eigen-Wilkens mechanism is valid at all [M]b/[L]t. The shaded zone represents the range of concentrations that are most often found in natural waters. The + represent experimental data for the complexation of Cu by a soil-derived fulvic acid at various metakligand ratios. An average line, based on equations (26) and (30) is employed to fit the experimental data. Data are from Shuman et al. [2,184]...

Stability constant for rans-[WO(X)(CN)4] n- complexes (50) as defined in Scheme 1. b Average equatorial W —CN distances from crystal structures, see Table I. 

Average values of complex mobilities obtained using nonlinear curve fitting assuming a 1 1 interaction were used to calculate the stoichiometric coefficients and stability constants through another nonlinear curve fitting [Eq. (3)]. The /x/K7) values were applied because they show a good approach... 

Bond distances (average values, in general) are in pm stability constants are in aqueous solutions at 25 °C and at an ionic strength of 0.1 M KN03, unless otherwise stated. 

The characteristic features of parameter estimation in a molecular model of adsorption are illustrated in Table 9.9, taking the simple example of the constant-capacitance model as applied to the acid-base reactions on a hydroxylated mineral surface. (It is instructive to work out the correspondence between equation (9.2) and the two reactions in Table 9.9.) Given the assumption of an average surface hydroxyl, there are just two chemical reactions involved (the background electrolyte is not considered). The constraint equations prescribe mass and charge balance (in terms of mole fractions, x) and two complex stability constants. Parameter estimation then requires the determination of the two equilibrium constants and the capacitance density simultaneously from experimental data on the species mole fractions as functions of pH. 

Obviously one could measure the pH of a known concentration of a weak acid and obtain a value of its hydronium ion activity, which would permit a direct evaluation of its dissociation constant. However, this would be a one-point evaluation and subject to greater errors than by titrating the acid halfway to the equivalence point. The latter approach uses a well-buffered region where the pH measurement represents the average of a large number of data points. Similar arguments can be made for the evaluation of solubility products and stability constants of complex ions. The appropriate expression for the evaluation of solubility products again is based on the half-equivalence point of the titration curve for the particular precipitation reaction [AgI(OH2)2h represents the titrant] ... 

Averaged values of individual separation factors for adjacent pairs of lanthanons being eluted with EDTA and its homologues (calculated from 9 sets of stability constant data) [10],... 

Averaged values for the separation factors for adjacent pairs of lanthanides eluted with EDTA and its homologues are given in Table 1.21. The separation factors are in the range of 1.5 to 3.5 showing considerable improvement in separation factors. In the majority of cases, the separation factors with EDTA as an eluant are greater than the values obtained in methanol-nitric acid medium, which is expected based on the stability constant data for rare earth EDTA complexes. 

Fig. 4.14. Stability constants of Ln(III) coronates versus the ratio D /Dc ratio (assuming an average coordination number of 9) as determined in propylene carbonate at 298 K by potentiometric measurement (counterion CIO ). Redrawn from J.-C.G. Biinzli et al., Inorg. Chem. 28, 2638, 1989.

The order of stabilities derived from Raman spectra appears to be UOi+ > Np02+ > Pu02+. For aqueous solutions of U01+ there is a linear correlation between the frequency of the 0=U=0 symmetric stretch (i cm-1) and the average number of ligands so that the stoichiometries in solutions can be estimated. Complex formation leads to weakening of the U02+ axial bonds in the order OH" > CO " > C2O4" > F" > SO " and this order reflects the corresponding decrease in stability constants (log /3).4 The unstable UO2 ion disproportionates as follows ... 

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