Determination of stability constants

Notice, particularly, the effect of the change on Kq. The entries included in this table have been chosen to illustrate the variety of formats that are encountered and yet to be internally self-explanatory. As an example, the statement that = 

There are the same number of overall formation constants as stepwise formation constants  

Some typical stability constants are given in Table 5.1. A point to remember is that when values of K , K + etc. are similar then an equilibrium solution will contain mixtures of the complexes (the Pb / case in Table 5.1) when K ,K + values are very different then it is possible to obtain solutions containing, essentially, only a single complex. Generally speaking, K K2 K2 etc. but, as Table 5.1 illustrates, exceptions occur. So, notice in this table the expression of the fact that the common anionic chloro complex of Pd is [PdCU] . 

In order to determine the values of n formation constants, n + 2 independent concentration measurements are needed. These can then be used to obtain the concentrations of the n species ML, ML2. ML and also those of M and L. Two pieces of information are at once available we (should ) know the quantities of M and L (or alternative starting materials) used in the measurement. This means that n additional pieces of information are needed. If it is certain that only one complex, of known empirical formula, is formed, then a measurement of the concentration of the uncomplexed M or L is sufficient to determine the formation constant. This measurement can be made in many ways by polarographic or emf methods (if a suitable reversible electrode exists), by pH measurements (if the acid dissociation constant of HL is known) and by many other techniques, including the whole galaxy of spectroscopic methods. A recent source book for stability constant data (that by Connors, see Further Reading) distinguishes over 30 methods. 

Define n as the average number of ligand molecules bound to M, so [L bound to M] [NaOH] 2 - [NaOH]i [M] 0h[M] 

Our comments on the stability of metal complexes have evolved from the study of stability constant data. The experimental determination of stability constants is an important but often difiBcult task. Perhaps the greatest problem in equilibrium measurements is to determine which species are actually present in solution. EquiUbriinn constants have been measured by many different methods. Usually a solution of the metal ion and ligand is prepared, sufficient time is allowed for the system to come to equilibrium, and the concentrations of the species in solution are then measured. From these equilibrium concentrations one can calculate the equilibrium constant using an expression such as equation (18). 

The measurement of equilibrium concentrations of species is complicated by the fact that the measiuement must not disturb the equilibrium. For example, in reaction (19) one could not measure the Cl concentration in 

Concentrations of species in solution can he measured hy a variety of methods that do not disturb the equilibrium under study the most common are probably spectroscopy and clcctroanalysis. Spectroscopy involves the absorption of light by the species to be studied electroanalysis involves the electrochemistry of the system being investigated. Spectroscopic techniques can he illustrated by studies on the Fe —NCS equilihrium (20). Iron(lll) ion 

The simplest electroanalytical technique for the determination of stability constants is one that makes use of the glass electrode. This device is the fundamental component of the common laboratory pH meter used to determine the activity of H in solution therefore, equilibria studied with the device must involve changes in [H ]. Professor J. Bjemim, of the University of Copenhagen, when a student, determined the stability constants of a variety of NH3 complexes using this technique. 

Many other experimental methods are available. For example, methods that use radioactive isotopes, or employ liquid liquid extraction or ion exchange are fairly common. Virtually any technique that can be used to determine concentration can be, and has been used, to determine stability constants. 

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Janos, R, Determination of stability constants of metal complexes from ion chromatographic measurements, /. Chromatogr., 641, 229, 1993. 

Determination of stability constants towards outer-sphere association reactions for cis-[Ir(phen)2Cl2]X, X = C1 , Oac-, 11 COO, gives the following decreasing order Cl >Oac > HCOO. 50... 

Rossotti, F. J. C., and Rossotti, H. (1961). Determination of Stability Constants. McGraw-Hill, New York. Probably the most respected treatise on stability constants and experimental methods for their determination. 

Values from Refs. (272,646) are derived from measurements of the solubility of calcium sulfate in solutions of the respective sugars (at 298K, 0.2stability constants from solubility measurements has been reviewed - see Ref. (225). 

Rossotti FJC, Rossotti H (1961) The determination of stability constants. McGraw Hill, New York... 

These equilibria have been studied by various methods of which potentiometry and 51V NMR spectroscopy proved to be particularly useful for the identification of species and the determination of stability constants (8-10,13-16,18,20,22,24). Values obtained for stability constants by different research groups under the same conditions usually show good agreement, e.g., for 0.60 M NaCl medium (Table II). In some cases so-called Bronsted (or mixed) constants (25) are... 

Rossotti, F. C. J., Rossotti, V. H. The Determination of Stability Constants. New York McGraw-Hill 1961... 

Hamer, S. 19. London Chapman Hall 1959 — Ion-Association, Buther Worths, Washington 1962. — Rossotti, F. J.C., and H. Rossotti The Determination of Stability Constants and other Equilibrium Constants in Solution. New York McGraw Hill Book Co. 196I. 

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]. 

Gerhard, A., Cobranchi, D. R, Highley, A. M., Huang, Y. H., Konya, G., Zahl, A., Eldik, R. V., Petrucci, S., Eyring, E. M., Li-7-NMR determination of stability constants as a function of temperature for lithium crown-ether complexes in a molten salt mixture, J. Phys. Chem., 98, 7923,1994. 

In practice, the hypersensitive transitions are often used for the determination of stability constants in aqueous solution. Lanthanide absorption bands in solution do not normally change in position on complexation to such an extent that bands due to the complexed and uncomplexed ion can be clearly observed independently, as is often the case for d transition metal ions, but the marked change of intensity of the hypersensitive bands is sufficient to allow determination of K values, for example as demonstrated for various adducts of [Ho(dpm)3].6U... 

Of growing interest is the application of these methods in the field named speciation , that is the study of the kinds of species in which, for example, a metal is present in an environment containing several complexing ligands. This field concerns not only the determination of stability constants of equilibria, but also of the rates of establishment of these equilibria. This means that the simple theories in Sect. 2 have to be extended by accounting for chemical conversions between electroactive (i.e. reducible or oxidizable) and electro-inactive species, occurring in the diffusion layer region. This subject will be treated in more detail in Sect. 7. 

Previous ESR determinations of stability constants for complexes of Mn2+ with commercial fulvic acid preparations (Aldrich) gave log K values... 

A large volume of work64 has been published on the determination of stability constants for complexes of hydroxamic acids, e.g. acetohydroxamic acid.65 The stability of 3d transition metal ions (Mn2+ to Zn2+) with salicylhydroxamic and 5-methyl-, 5-chloro-, 5-bromo-, 5-nitro-, 4-chloro-, 4-bromo- and 3-chloro-salicylhydroxamic acids,66 as well as with methyltolylbenzohydroxamic acid,67 has been studied potentiometrically. Stability constants of iron(III) with a number of hydroxamic acids have been determined by redox potential studies.68... 

Takamatsu, T. and Yoshida, T., 1978. Determination of stability constants of metal-humic-acid complexes by potentiometric titration and ion selective electrodes. Soil Sci., 125 377-386. 

Schnitzer, M., and E. H. Hansen. 1970. Organo-metallic interactions in soils. 8. An evaluation of methods for the determination of stability constants of metal-fulvic acid complexes. Soil Science 109 333-340. 

Hirai et al. [18] found that /LCD forms 1 1 complexes with Methyl Orange and Congo Red in water, whereas y-CD forms 1 2 complex with Methyl Orange and 1 1 complex with Congo Red. Induced circular dichroism of the dyes was studied allowing determination of stability constants. 

Takahashi, Y., Minai, Y., Ambe, S., Makide, Y., Ambe, F. and Tominaga, T. (1997) Simultaneous determination of stability constants of humate complexes with various metal ions using multitracer technique. Sci. Total Environ., 198, 61-71. 

Apart from structural implications (6, 7, 37, 106) attempts have been made to explore a procedure for the quantitative determination of stability constants of metal complexes by means of infrared spectros-copy (47). 

In this section it will be useful to discuss some common experimental methods used in the determination of stability constants of rare earth complexes. Ethylenediamine tetraacetate anion (EDTA) is a hexadentate and forms complexes with trivalent rare earth ion readily. The pioneering studies of Schwarzenbach [4] on the determination of stability constants of rare earth EDTA complexes by potentiometry and polarography can be considered to illustrate the principles involved in the determination of stability constants. 

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