Complex Stability and Lability

The formation of a complex [MLé]n+ in solution is part of an equilibrium process that can be represented by a series of steps, each described by its own equilibrium constant (often called formation constant):

(The ligand L has been written as a neutral species for simplicity; it may equally well be an anion.) The overall process is

and the overall equilibrium constant is the product of the stepwise constants:

These equilibria must hold along with ionization or solubility equilibria.

Complex formation changes the solubility of an insoluble metal compound by removing the metal ions from the equilibrium as they are tied up in the complexed form. For example, in the presence of a ligand L, the reaction for the solution of lead carbonate becomes

which is the sum of the solubility equation giving Ksp and the complex formation equation giving Kf. The equilibrium constant is just the product of these two constants,

An increased concentration of L in solution leads to an increase in the concentration of soluble lead. If the ligand also takes part in acid-base equilibria, as many do (e.g., the anions of Bransted acids), the complexation process will be pH dependent:

Of course, [C02—] and [H+] are not mutually independent; they are related by the carbonate equilibria.

A large value for the formation constant means that the formation equilibrium lies far to the right. In the presence of excess ligand, for example, the amount of "free'' metal ion would be small in this case. However, it is important to distinguish between thermodynamically stable systems in the foregoing sense and those that are kinetically inert. Complexes in solution normally undergo continuous breaking and remaking of the metal ligand bonds. (This is true of many other systems also. For example, a weak acid that is largely undissociated according to its ionization constant nevertheless exchanges protons at a very fast rate with solvent water molecules.) If the bond-breaking step is rapid, and consequently ligand exchange reactions are rapid, the complex is called labile. If the ligand exchange reactions are slow, the complex is said to be inert. Lability or inertness has no direct relation to thermodynamic stability, although many inert complexes are thermodynamic-ally stable. Many metal ions complexed by unidentate ligands will undergo complete exchange in a time of fractions of a second: some are much slower, hours or days. These inert complexes are associated with particular electronic configurations of the metal ion. Exchange rates are lower with multidentate ligands. Inert complexes in particular have properties different from both the free metal ion and the ligands. An example is [Fe(CN)6]3", in which the cyanide groups do not exhibit the toxicity of free CN".

Complex stability can be correlated with several properties of the metal ion and the ligand. The following are most important:

Size and oxidation state of the metal. Smaller size and higher positive oxidation state lead to stronger complexing. This can be understood in terms of the stronger bonding that arises with shorter metal-ligand distances and the greater Coulombic contribution from a greater charge.

Chelation. The free energy change upon complex formation depends on both the enthalpy and the entropy changes of the reaction. The enthalpy change is made up largely from the metal-ligand bond energies, while the entropy change involves the change in the degrees of freedom of the system. The number of independent molecules increases when unidentate ligands are replaced by a polydentate one, resulting in a positive contribution to the entropy change and a larger negative free energy change than for a one-to-one exchange. This is a widely accepted explanation for the observed greater stability of chelated systems compared with those of analogous unidentate ligands: the greater the degree of chelation, the greater is the stability. The size of the chelate ring formed is of prime importance. Five-membered rings (including the metal atom) are most favored, with six-membered rings a close second, and other sizes of minor importance.

The electronic configuration of the metal ion. The degeneracy of the d orbitals of a transition metal ion is destroyed when the ion is surrounded by ligands. The d orbitals are said to be split by the ligand field. The splitting pattern depends on the geometry of the complex, while the magnitude of the splitting depends on the nature of the ligand and the metal ion. Occupancy of the lower energy orbitals contributes to the stability of the system (the ligand field stabilization energy) although this is counteracted if the higher energy orbitals are also filled. Thus, this contribution to stability will depend on both the electronic configuration and the magnitude of the d orbital splitting. With a given metal ion, the common ligands usually have the following relative splitting effects: I" < Br" < Cl" < F" < H20 (and most other oxygen donors) < NH3 (and amines) < CN". With octahedral complexes, the electronic configurations leading to a large ligand field stabilization energy involve 3, 6 (with strongly splitting ligands), and 8 d electrons (d3, d6, and d8), while d0, d5 (with weakly splitting ligands), and d10 have no stabilization from this source.10 Trends in the stability of complexes of different metals with a given ligand, for example, Mn(II) < Fe(II) < Co (II) < Ni(II) < Cu(II) > Zn(II), can be traced to the variation of ligand field stabilization energy with elec

10Any intermediate or advanced level textbook on inorganic chemistry will contain a detailed discussion of this topic.

tronic configuration, coupled with the normal trends in bond energies with size.

T^e ¿ard-so/i mafc^ o/ meia/ %a«d, as already discussed.

T^e do«or o/i^e %a«d. One measure of this characteristic is given by the strength of the ligand's conjugate acid. For example, if a ligand is the anion of a strong acid, this implies that the ligand is not an effective donor toward a proton, and in such cases it is generally not a good donor to a metal ion either. The parallelism is rough, because the metal ion acceptor orbitals are quite different from the Is orbital of the proton and there are some notable exceptions (e.g., CO).

The formation of complexes may tie up a metal ion to such an extent that solubility is increased considerably: that is, the concentration of free metal ions required to achieve saturation according to the solubility product requirements is less easily reached. Solids that would otherwise precipitate are thus kept in solution. This is often desirable when waters containing dissolved minerals are employed for industrial or domestic use, and is one reason for the use of phosphates as "builders" in detergent formulations, as discussed in Chapter 7. The calcium and magnesium ions in hard water form insoluble salts with soaps and interfere with the action of most detergents. The soap precipitates have a curd like character and are very difficult to wash away. Hard waters also require larger amounts of the surfactant for adequate cleaning. The Ca(II) and Mg(II) ions can be held in solution by complexing, and certain phosphate ions were widely used for this purpose, most commonly, sodium tripolypho-sphate NasP3Oio. The simplest form of phosphate, orthophosphate PO44, is tetrahedral. Polyphosphates are based on this structure, but with shared oxygens. The tripolyphosphate ion has the following structure:

Unlike orthophosphate, this ion, can form chelates having six-membered rings, and it is potentially tridentate. The extra stability introduced is illustrated by the following equilibrium constants:

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