Stabilities of complexes

The thermodynamic stability of a species is a measure of the extent to which this species will be formed from other species under certain conditions, provided that the system is allowed to reach equilibrium. Consider a metal ion M in solution together with a monodentate ligand L, then the system may be described by the following stepwise equilibria, in which, for convenience, coordinated water molecules are not shown  

The equilibrium constants Kl,K2.Kn are referred to as stepwise stability constants. 

The equilibrium constants pi,p2.p are called the overall stability constants and are related to the stepwise stability constants by the general expression 

In the above equilibria it has been assumed that no insoluble products are formed nor any polynuclear species. 

A knowledge of stability constant values is of considerable importance in analytical chemistry, since they provide information about the concentrations of the various complexes formed by a metal in specified equilibrium mixtures this is invaluable in the study of complexometry, and of various analytical separation procedures such as solvent extraction, ion exchange, and chromatography.2,3 

The square brackets denotes the concentrations. The equilibrium constants K, K2,.Km are referred to as stepwise equilibrium constants. 

Coordinate bonds between metals and ligands result in the formation of complexes under many different types of conditions. In some cases, complexes form in the gas phase, and the number of known solid complexes is enormous. However, it is in solutions that many of the effects of complex formation are so important. For example, in qualitative analysis, AgCl precipitates when a solution of HC1 is added to one containing Ag+. When aqueous ammonia is added, the precipitate dissolves as a result of the formation of a complex, 

It is possible to determine the concentration of certain metal ions by performing a titration in which the complexation of the metal is the essential reaction. Typically, a chelating agent such as EDTA is used because the complexes formed are so stable. The specific composition of complexes formed in solutions often depends on the concentrations of the reactants. As a part of the study of the chemistry of coordination compounds, some attention must be given to the systematic treatment of topics related to the composition and stability of complexes in solution. This chapter is devoted to these topics. 

Lanthanide and Actinide Chemistry S. Cotton 2006 John Wiley Sons, Ltd. 

In a graph of log K against Z (the atomic number), there is a smooth increase expected as the ionic radius decreases as the greater charge density of the smaller ions leads to more stable complexes. There are inflections, particularly around Gd, possibly due to the change in coordination number of the aqua ion. 

For these complexation reactions, A//has small values, either exothermic or endothermic the main driving force for complex formation, particularly where multidentate ligands are involved, is the large positive entropy change. Thus for  

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TABLE 6.2 Stabilities of complexes of alkylbenzenes and rates of substitutions ... 

The values of constants of stability of complexes AuBr Thio, AuBiyr/rio AuBrThio, AuBrThio have been calculate. They equal 8,90-lO " 2,81-10" 2,23-10"" 5,60-10"". 

Fig. 5.4. The stability of complex systems is determined by changes in the free work Wf. Note the minus sign - systems try to move so that they produce the maximum work.

The stability of complex ions varies within very wide limits. It is quantitatively expressed by means of the stability constant. The more stable the complex, the greater is the stability constant, i.e. the smaller is the tendency of the complex ion to dissociate into its constituent ions. When the complex ion is very stable, e.g. the hexacyanoferrate(II) ion [Fe(CN)6]4", the ordinary ionic reactions of the components are not shown. 

Schwerdtfeger, P. (1989) Relativistic effects in gold chemistry. II. The stability of complex halides of Au(III). Journal of the American Chemical Society, 111, 7261-7262. 

Ahrland et al. (1958) classified a number of Lewis acids as of (a) or (b) type based on the relative affinities for various ions of the ligand atoms. The sequence of stability of complexes is different for classes (a) and (b). With acceptor metal ions of class (a), the affinities of the halide ions lie in the sequence F > Cl > Br > I , whereas with class (b), the sequence is F < Cl" < Br < I . Pearson (1963, 1968) classified acids and bases as hard (class (a)), soft (class (b)) and borderline (Table 1.23). Class (a) acids prefer to link with hard bases, whereas class (b) acids prefer soft bases. Yamada and Tanaka (1975) proposed a softness parameter of metal ions, on the basis of the parameters En (electron donor constant) and H (basicity constant) given by Edwards (1954) (Table 1.24). The softness parameter a is given by a/ a - - P), where a and p are constants characteristic of metal ions. 

Effect of Chelate Ring Size on Complex Stability Comparison of Stabilities of Complexes of EDTA (Chelate Ring Size Five Involving the Two Nitrogens) and TMDTA (Analogous Chelate Ring Size Six ) ... 

Stability of Complexes of Imidazole with Metal Ions of Biological and Biomedical Interest ... 

Merdan T, Kunath K, Petersen H, Bakowsky U, Voigt KH, Kopecek J, Kissel T (2005) PEGylation of poly(ethylene imine) affects stability of complexes with plasmid DNA under in vivo conditions in a dose-dependent manner after intravenous injection into mice. Bioconjug Chem 16 785-792... 

The decrease in size of the +3 ions of the lanthanides is also a factor in stability of complexes of these ions, and complexes with a given ligand usually show an increase in stability in progressing through... 

Although the subject of stability of complexes will be discussed in greater detail in Chapter 19 it is appropriate to note here some of the general characteristics of the metal-ligand bond. One of the most relevant principles in this consideration is the hard-soft interaction principle. Metal-ligand bonds are acid-base interactions in the Lewis sense, so the principles discussed in Sections 9.6 and 9.8 apply to these interactions. Soft electron donors in which the donor atom is sulfur or phosphorus form more stable complexes with soft metal ions such as Pt2+ or Ag+, or with metal atoms. Hard electron donors such as H20, NH3( or F generally form stable complexes with hard metal ions like Cr3+ or Co3+. 

The orbital energies are useful when comparing the stability of complexes in different structures. As usual, electrons are placed in the orbitals starting with the orbitals of lowest energy. We will have opportunity to make use of the orbital energies when we consider reactions of complexes in which the transition state has a different structure than that of the starting complex (see Chapter 20). 

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