General Metal-Complex Equilibria

A generalized metal complex formation can be represented as follows (charges have been omitted for convenience)  

If more than one ligand is bound to the metal ion, the stepwise formations and their corresponding equilibrium constants can be represented similarly  

By combining the equations for the individual reaction steps, an overall metal-complex formation reaction and the overall formation constant expression may be written 

The symbol is referred to as the overall formation constant and is also used for all products of stepwise formation constants. When the overall formation equation is used, we must remember that intermediate complexes, although not mentioned, do play a part. If we did, this would be as incorrect as the assumption that in a solution of H2S there are 2 moles of H for every mole of S , that is, without taking HS into account. 

Metal-complex equilibria calculations are accomplished in the same manner as those for polybasic acid equilibria. For this piupose, we have defined a set of fractions to ajyjL to represent the ratios of the concentrations of the metal containing species to the analytical concentration of the metal, Cj. Thus, incorporating the equilibrium constant expression in Equations 5-1 and 5-2 and rearranging, we obtain in (5-3) expressions for the a values that are functions of the equilibrium constants and the free (i.e., not bound to M) ligand concentration. 

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Because of difficulties of this nature, and because of the general lack of usefulness of a noncritical compilation for teaching purposes and for scientists who are not sufficiently expert in the field of equilibrium to carry out their own evaluation, we have decided to concentrate our efforts in this area toward the development of a critical and unique compilation of metal complex equilibrium constants. Although It would seem that decisions between available sets of data must sometimes be arbitrary and therefore possibly unfair, we have found the application of reasonable guidelines leads directly to the elimination of a considerable fraction of the published data of doubtful value. Additional criteria and procedures that were worked out to handle the remaining literature are described in the Introduction of this book. Many of these methods are quite similar to those used in other compilations of critical data. 

It should be noted that dative bonds, like metal complexes and charge transfer species, in general have RHF wave functions which dissociate correctly, and the equilibrium bond lengths in these cases are normally too long. 

Speciation is a dynamic process that depends not only on the ligand-metal concentration but on the properties of the aqueous solution in chemical equilibrium with the surrounding solid phase. As a consequence, the estimation of aqueous speciation of contaminant metals should take into account the ion association, pH, redox status, formation-dissolution of the solid phase, adsorption, and ion-exchange reactions. From the environmental point of view, a complexed metal in the subsurface behaves differently than the original compound, in terms of its solubility, retention, persistence, and transport. In general, a complexed metal is more soluble in a water solution, less retained on the solid phase, and more easily transported through the porous medium. 

The conclusions described in the previous section are inferred from a relatively small number of observations of spin-equilibrium dynamics. Nevertheless, they are internally self-consistent and also compatible with a much wider set of observations derived from studies of electron transfer reactions of metal complexes. For these reasons there is hope that they possess some generality and can be applied to other systems. 

Further experimental and theoretical studies on the rotational barriers of the metal fragment in (cycloheptatriene)Cr(CO)3 complexes195 suggest that (cycloheptatriene)-Cr(CO)3 complexes in general are in equilibrium with their norcaradiene valence isomers and their ground state conformation is controlled by the same electronic factors which effect the cycloheptatriene-norcaradiene equilibrium195. 

The equilibrium in equation (94) is generally defined as a mass-distribution ratio such as that shown above for cation-exchange resins (equation 93), and the position of the equilibrium is determined by the relative Concentration of the counter-ion ML/- and the co-ion X-. The nature of the quaternary amine has little effect on the equilibrium properties of the resin, and the chemistry of metal complex formation in aqueous solution is the dominant factor. 

Since the pioneering studies of Fischer, carbene complexes have become the subjects of very extensive investigations in several laboratories, and they have become known for a large number of the transition metals.100 A fairly general statement about their chemistry is that these compounds usually are neither prepared directly from free carbenes nor are they to be considered as sources of free carbenes, i.e. free carbenes are generally not in equilibrium with the carbene complexes. Instead, they are prepared by indi-... 

The tetrahedral distortions in copper ICC of the type discussed, caused by R1 -substituents with different spatial effects, are strictly proved by x-ray diffraction, as well as confirmed by EPR studies [135,207]. However, a united point of view about the structure of these complexes in solution is still absent (compare Refs. 134, 135, 205 and 206). The existence of a square-pyramidal or distorted tetrahedral configuration, as well as the equilibrium square-tetrahedron, is accepted as possible. We emphasize that, in a series of cases, the nature of metal complex-former is the decisive factor, determining the structures of the examined ICC. Thus, practically independently of the character of the R1 -substituent, palladium chelates are planar, those of beryllium are exclusively tetrahedral, and those of cobalt, zinc, cadmium, and mercury are, in general, also tetrahedral [135]. 

N-Heterocyclic carbenes form intriguingly stable bonds with the majority of metals [12,21,29]. Whereas for saturated and unsaturated N-heterocyclic carbenes of comparable steric demand very similar bond dissociation energies have been observed, phosphines generally form much weaker bonds (Table 2) [21]. As a result, the equilibrium between the free carbene and the carbene metal complex lies far more on the side of the complex than... 

Several directly measured values of AH° for homolytic dissociation of a metal-metal-bonded carbonyl in solution have been obtained (9). This was for the complexes [(n3-C3H5)Fe(CO)2 )2 where L = CO or a number of different P-donor ligands. The low value AH = 56.5 kJ mol-1 when L = CO was not unexpected for such a sterically crowded molecule. The P-donor substituents increased the steric crowding and displaced the equilibria in favor of the monomers but the effect seemed to be controlled more by AS° than AH°. In general metal-metal bond energies, however they may have been estimated, are too large to allow for direct measurement of equilibrium constants in solution in this way. 

The exchange equilibrium discussed above also applies to metal complexes where a generalized re-... 

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