Stability constants calculation methods

Martell, A. E., and Motekaitis, R. J. (1992). Determination and Use of Stability Constants, 2nd ed. Wiley, New York. An excellent treatment of stability constants including methods of calculation and computer programs. 

The binding of several RuCp compounds to HSA was studied as a first approach to outline its pharmacokinetics and had been investigated by spectroscopic methods (absorption and fluorescence) and ultraflltration-UV-vis. as weU. It was found that TM34 binds to HSA forming a 1 1 adduct the stability constant calculated for this HSA-TM34 adduct was log Kb = 4. This value is similar to that found for KP1019 and shows that the complex can be transported in the blood by HSA [11],... 

Some suggested calculation procedures and the variation in results obtained from different calculation methods for evaluation of concentration stability constants of metal ion complexes in aqueous solution. A. M. Bond, Coord. Chem. Rev., 1971,6, 377-405 (43),... 

Mapsi et al. [16] reported the use of a potentiometric method for the determination of the stability constants of miconazole complexes with iron(II), iron(III), cobalt(II), nickel(II), copper(II), and zinc(II) ions. The interaction of miconazole with the ions was determined potentiometrically in methanol-water (90 10) at an ionic force of 0.16 and at 20 °C. The coordination number of iron, cobalt, and nickel was 6 copper and zinc show a coordination number of 4. The values of the respected log jSn of these complexes were calculated by an improved Scatchard (1949) method and they are in agreement with the Irving-Williams (1953) series of Fe2+ < Co2+ < Ni2 < Cu2+ < Zn2+. 

Numerous investigations have shown the existence of the heptamolybdate, [Mo7024]6 , and octamolybdate, [Mo8026]4, ions in aqueous solution. Potentiometric measurements with computer treatment of the data proved to be one of the best methods to obtain information about these equilibria. Stability constants are calculated for all species in a particular reaction model, which is supposed to give the best fit between calculated and experimental points. In the calculations the species are identified in terms of their stoichiometric coefficients as described by the following general equation for the various equilibria... 

Stability constant too large to be reliably calculated using curve-fitting method. No evidence of binding was seen. 

The study of molecular complexation was then extended to other aromatic nitro derivatives125. Although, as was described before, one of the more frequent methods of studying the formation of molecular complexes is by UV-visible spectrophotometry, the author did not observe detectable differences in the UV-visible absorbance spectra between the 2-hydroxypyridine-l-fluoro-2,4-dinitrobenzene (FDNB) mixtures and the sum of their separate components. The author observed that the signals of the 1II NMR spectra of FDNB in apolar solvents were shifted downward by the addition of 2-hydroxypyridine from solutions where [2-hydroxypyridine] [FDNB] he calculated the apparent stability constants, which are shown in Table 13. 

The preceding section summarized basicity results obtained from the stability constants of 7r-complexes and EDA-complexes. These results can only reflect a qualitative gradation of the basicity. If one moves from these complexes to u-complexes, then exact values for the basicity of unsaturated compounds can be obtained by measuring the formation equilibria of the proton addition complexes in strongly acid solutions. The experimental methods and the calculations have been described in Sections III, A-C. 

The free energy is calculated from the stability constant, which can be determined by a number of experimental methods that measure some quantity sensitive to a change in concentration of one of the reactants. Measurement of pH, spectroscopic absorption, redox potential, and distribution coefficient in a solvent extraction system are all common techniques. 

KP and v can, in contrast to kp, not be determined via the concentration gradient for binary and ternary mixed micelles, because for the calculation of the Nemstian distribution a constant CMC and an almost constant partial molar volume must be assumed. The calculation of aggregation constants of simple bile salt systems based on Eq. (4) yields similar results (Fig. 8b). Assuming the formation of several concurrent complexes, a brutto stability constant can be calculated. For each application of any tenside, suitable markers have to be found. The completeness of dissolution in the micellar phase is, among other parameters, dependent on the pH value and the ionic strength of the counterions. Therefore, the displacement method should be used, which is not dependent on the chemical solubilization properties of markers. For electrophoretic MACE studies, it is advantageous for the micellar constitution (structure of micelle, type of phase micellar or lamellar) to be known for the relevant range of concentrations (surfactant, lipids). 

Thus, as shown earlier, CE represents a suitable technique for the determination of enantioselective binding constants between chiral drugs and cyclodextrins. The results obtained under appropriate conditions are reasonable and can be applied for optimization purposes as well as for a better understanding of the fine nuances of chiral CE separations. On the other hand, some care must be taken for the proper application of CE methods for the determination of the binding constants as well as when applying these data. A critical review of the calculation of stability constants for the chiral selector-enantiomer interactions from electrophoretic mobilities has been published by Vespalec and Bocek (40). 

Stability constants, from which AG° values are calculated, provide a direct measure of the extent of complexing in solution, and these values have been used to determine cation selectivity by macrocyclic compounds. Several of the methods commonly used to determine log K values cannot be used with many of these systems. Thus, procedures based on change in hydrogen ion concentration (pH titration, hydrogen electrode, etc.) cannot be used in those cases where the ligand is uncharged and its concentration is not pH dependent. Spectral methods generally have not been used because of the usual lack of favorable absorption characteristics by the compounds, cations or cation-complexes in the cases studied. 

The polarographic experimental and calculated curves of complex formation with the following ligands N, Ai -bis(2-pyridyl methyl)- ,2-diaminoethane [118], picolinic acid [119], Ai-(2-hydroxyethyl)ethylenedi-amine [120], 1-hydroxyethylenediphospho-nic acid [121], and Ai-(2-hydroxyethyl)imi-nodiacetic acid [122] was used for modeling the Cd(II)-Kgand systems. The stoichiometry and stability constants of formed complexes were evaluated. The same method was used for determinations of stability constants of Cd(II) complexes with monoaza-12-crown-4 ether in aqueous solution in the presence of an excess of sodium ions [123]. 

For multistep complexation reactions and for ligands that are themselves weak acids, extremely involved calculations are necessary for the evaluation of the equilibrium expression from the individual species involved in the competing equilibria. These normally have to be solved by a graphical method or by computer techniques.26,27 Discussion of these calculations at this point is beyond the scope of this book. However, those who are interested will find adequate discussions in the many books on coordination chemistry, chelate chemistry, and the study and evaluation of the stability constants of complex ions.20,21,28-30 The general approach is the same as outlined here namely, that a titration curve is performed in which the concentration or activity of the substituent species is monitored by potentiometric measurement. 

Literature values for stability constants (153) have usually been determined for solutions much less concentrated than those needed for diffraction measurements, and the values for these solutions have to be checked by other methods. For the thallium(III) bromide complexes the stability constants for the concentrated solutions used [1-2.6 M in Tl(III)], were derived from Tl-205 NMR shift measurements. The fraction of Tl(III), bonded in each of the complexes calculated from these constants as a function of the chloride concentration (Fig. 17), shows... 

They also proposed the method as a means of measuring stability constants for the complexes. As well, they analyzed the thermodynamics of the desorption process and were able to calculate the localized temperature which must be created in a small volume around the... 

If the equilibrium constant of the chemical reaction (such as complex stability constant, hydration-dehydration equilibrium constant, or the piCa of the investigated acid-base reaction) is known, limiting currents can be used to calculate the rate constant of the chemical reaction, generating the electroactive species. Such rate constants are of the order from 104 to 1010 Lmols-1. The use of kinetic currents for the determination of rate constants of fast chemical reactions preceded even the use of relaxation methods. In numerous instances a good agreement was found for data obtained by these two independent techniques. 

Equations 2.46 and 2.47 can be substituted into Equation 2.48 or other expressions characteristic of ion exchange, and the stability constants or their ratios can be calculated. Schubert s method is also based on similar principles (Marcus and Kertes 1969 Chapter 1, Section 1.2.2). His method to determine the stability constants, however, is not widely used, most likely because it is strongly affected by experimental conditions. 

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