Most complex formation reactions are usually determined in an aqueous media. However, ligand that are organic soluble are employed too, and their stability constants are often determined in mixed solvent systems such as dioxane - water. For completely organic systems such as acetonitrile, metal complex can be formed quite readily but their stability constants are generally not known. Approximate values have been used for such systems as there is no mathematical expressions that can be relate the equilibrium constants in such systems to the formation constant or stability constant in water or water/organic mixture.
The availability of computers has remarkably facilitates the methods for accurate determining stability constants from big pools of data so that now very complex systems can be handled with ease and approximation previously used has eliminated. The relative ease of measurements and their simple equipments introduced presented a large number of proliferation of stability constant of metal ion complexes reported. The growth of stability data has been extensive and a large number of publications are now available for critical complications. Much of the data published in the literature is rather hastily developed or inaccurately described; also much of the data should be looked upon with considerable doubt.
Stability constant, is a constant describing the equilibrium that exists between a metal ion surrounded by aqueous molecule ligands and the same metal ion surrounded by ligands of another kind in a ligand displacement reaction:
aA + bB ↔ cC + dD
The logarithm of the stability constant is directly related to the Gibbs free energy of the reaction products minus the Gibbs free energy of the reactants in their standard state and it is therefore a measure of the difference in reactivity of the reactants and their products, Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure.
The determination of the activities of the complex ionic species under real conditions is a complex, tedious and time consuming operation which is beyond the interest and/or capabilities of most researchers. However, because concentration closely parallel activities under carefully controlled conditions involving both temperature and ionic strength, it is practical to determine equilibrium concentration constant in place of activities constant.(Martell, A.E., Hancock, R.D, (1996), metal complexes in aqueous solutions)
Researchers would like to determine the activities of all the reactants, but it is not possible to do that for single specie, occasionally it would be only possible to determine the mean ionic activities. However, it is currently possible to do that for at least some of the species of interest through the use of modern experimental techniques.
If and are the total concentrations of a metal and a ligand in a solution respectively, considering [ML], [M], and [L] as the concentrations of individual free species, then we can write (from now and on we shall consider the symbols [X], {X}, and ð›¾X refer to the concentration, the activity, and the activity coefficient, respectively)
= [M] + [ML] = +
= +
Factors affecting Stability of metal complexes
A number of factors contributing to stability constants have been defined, and these factors can be categorized into metal ion depending factors and ligand depending factors.
Metal ion depending factors:
Size and charge: in complexation reactions, positively charged metal ions and anionic or polar neutral ligands carrying high electron density in their lone pair, a purely electrostatic contribution will definitely happen.
Metal class and ligand preference: electro-positively metals (i.e. lighter and/or more highly charged ones such as ) prefer lighter p-block donor from such as N and F donor. While less electropositive netals (i.e heavier and/or lower charged ones such as) prefer heavier p=block donors from the same families such as P, and I donorsto produce higher significantly M - L covalent bond, the second case should be applied. Beside, a grey area of metals and ligand who do sit in either set at, at least not easily, is present.
Natural order of stability for transition metal ions: These ions with incomplete sets of d electron, present a contribution to stability from the crystal field stabilization energy (CFSE), where is ions such as (metal ion with full set of electron) there is no stabilization energy. CFSE of metal ions in metal - ligand complexes has a demonstrated influence on the value of stability constant K of transmission metals and this fact can be noticed in the experimentally determined stabilities for the series of metal ions from to.
Ligand depending factors:
Base strength: since the earlier attempts to determine K, it was obvious the relationship between Brønsted base strength of a ligand and its ability to form a stable complex, which can be explained that base strength is a measure of a capacity to bind a proton. So, substitution of by is reasonable, allowing basicity to define complex stability.
Chelate effect: thermodynamically, the equilibrium constant reports the enthalpy change (∆in the reaction and the entropy change (∆) resulted from a reaction. The greater the amount of energy evolved, the more stable the complex is. Furthermore, the greater the amount of entropy change resulted the greater the stability of the products. Generally, chelating is beneficial for complex stability, and ligands from stronger complexes than comparable monodentate ligand sets.
Chelate ring size: the size of the chelate ring directly influences the size of the stability constants. Since we are restraining the metal ions by binding donor atoms, it is not surprising that there is a correlation between the formed chelate ring size and stability.
Steric strain: Ligands vary much more in size and shape than metal ions, other consequences arise, including simply size effect in terms of fitting around the central atom. These effects of ligand bulk, resulting from molecules being necessarily requires binding different regions of space, and thus required to avoid "bumping" against each other when confined around central metal ions, which is known as steric effect. As a general rule, the bulkier a molecule the weaker the complex formed when there is a set of ligands involved.
Sophisticated effects:
There are some other factors that arise as a result of molecular shape that may add complications. For example, macrocycle effect, which is a large cyclic ligand that carry at least three donor atoms has a hole (i.e. central cavity), so the fir of the metal ions into this hole is an important considerations. As matter of fact, metal ions fitting or missing into predefined shaped ligands is an important aspect of metal coordination chemistry, as it become familiar meeting more sophisticated ligand systems.
Over all stability constants
Since most metal ions usually provide more than one coordination site, they can bind more than only one donor group, or in most cases more than one donor (ligand), the stability constants equation must be extended to take into account the attachment of a set of n ligands. This process occurs in a sequential manner, this is because donor replacement is a result of molecular encounters, within the complex required to make contact with an incoming donor with sufficient velocity and with unit required direction of approach so as to permit a donor exchange to occur. The sequential substation steps for formation of M by a series of equilibrium can be presented in the following equation:
The overall reaction occurring through combination of the previous steps can be expressed as:
And the overall stability constant is:
This constant defines the formation of the overall complex, where all of the donor can be considered replaced by another: it does not infer anything about the mechanism of the process.
Applications
Validated values of stability constants are remarkably useful in many aspects of technology, such as planning analytical methods involving ion-exchange processes, chromatography, separations of metals, complexometric titrations, as well as many aspects of academic, medical, environmental, and industrial research.
In the environment, the toxic effect of some metals becomes increased when derived complexes can be leached by underground water from a mine, waste dump, and land-fill site or waste dumps. On the other hand, highly stable complexes can act as very effective detoxificants and it is important to be able to calculate the effect of defined concentrations of a particular ligand or mixture of ligands on the final composition of elements and compounds in the environment.
In agriculture, the transfer of essential trace elements from the soil to the growing plant and the use of synthetic agents to supplement or control plant nutrients, and many problems of geochemistry, and of a biochemical nature can best be solved with the aid of quantitative data on stability constants.
Determination of the distribution of all the species in a multicomponent systems such as biological fluids (e.g. blood plasma), is known as speciation. Currently, the best used way of performing speciation on a particular system is by making use of reliable stability constant values introduced into appropriate forms of mass action and mass balance equations. A lot of databases have been created and several suitable softwares have been developed for this purpose. For example, a recent version of a blood plasma database incorporates 10 metal ion species, over 100 types of ligand and 10 000 complexation reactions between them. Critically evaluated stability constants are to be found in several modern databases.
Techniques used for stability constant determination:
Potentiometry:
It is an electrochemical technique depends on measuring the potential of an electrode system, usually without the drawing appreciable currency. It allows selective detection of particular ions. In this method, cell potential is governed by the potential of an indicator electrode which in turn responds to changes in the activity of the species of interest. It is the most widely used electrochemically technique, it can be used for quantitative analysis of many species in a solution over a wide range of concentrations (, with relative precision of 0.1 - 5 %. Potentiometric titrations are especially useful for coloured or turbid samples or for mixtures. On the other hand, this kind of titrations is slow and time consuming unless automated.
In the case of using potentiometric titration for stability constants determination, if an electrode reversible to ions of M is introduced into a solution of known and in a medium of constant ionic strength and the solution is combined with a reference electrode through a suitable conducting bridge, the measured e.m.f at a temperature T K is given by the Nernest equation:
E = + ( In [M]
must be determined at the particular ionic strength of the experiment and incorporates the intrinsic electrode parameter as well as relative activity coefficient and liquid junction potentials. Suitable half-cells and various amalgam electrode have beed used to measure [M] and hence to obtain the stability constant of metal complexes of Cu+, Cu2+, Ag+, Au+, Zn2+, Cd2+, Hg2+, Hg22+, Co2+, Ni2+, Sn2+, Pb2+, Bi3+, Fe2+, Pd2+.
Polarograpghy and Stripping voltametry:
Another electrochemical analysis technique based on the measurement of the diffusion - controlled current flowing in an electrolysis cell in which a single electrode is polarized. The current is directly proportional to the concentration of electro-reactive species.
Usually used for both quantitative and qualitative determination of metal traces and organics especially in the range of ( with relative precision of 2 - 3%. The main limitation is that the measurement is too sensitive to solution composition (i.e. dissolved oxygen and/or impurities may remarkably effect sensitivity). The simplicity of the polarograghy instrumentation allows this technique to be widely used in equilibrium chemistry. If the reversible electrode is assured, half-wave electrode potential is given by Heyrorky-lkovic equation:
E = ()s =
Where z is the change in electron number
is the diffusion current
i is the current strength at half - wave potential
A major advantage of this polarograghy is its usefulness as a complement to potentiometry for determining stability constants.
Stripping voltametry can be useful in the determining of the complexation al well. The techniques can be used to determine metal concentration as low as mol/l. Stability constant can be measured in a close way to that used in polarograpghy, and in case the principle involves deposition of a metal ion in reduced form on a mercury electrode followed by reoxidation through reversing polarity so the reoxidation current become directly related to metal ions concentrations in the media.
Cation exchange resins:
It is an insoluble matrix in the form of small beeds. The separation here takes place through the developed structures of pores of the surface of which are sites with easily retained and released ions. Here the trapping of ions takes occur only with simultaneous releasing of other ions, where ions migrate at different rate due to differences in adsorption, solubility, charge or size. The main disadvantage in this techniques is gravity flow separation slow; separated components accompanied by a large excess of eluting electrolyte.
This technique can be used in determining stability constant by partitioning a cationic species Mbetween and aqueous phase and the sodium containing exchange media (ion exchanger) according to the equation:
z(Na+)R + (MLnz+) −−−−−−−− (MLnz+)R + z(Na+)
the stoichiometric partition coefficient for each metal species is given by:
And will be constant as long as k and the ratio of sodium ion concentration are constant.
Nuclear Magnetic Resonance Spectroscopy (NMR):
This developed technique depends on absorption of electromagnetic radiation in the radio frequency region of the spectrum resulting in alteration of the orientation of spinning media in a magnetic field. Used for identification and structural analysis of organic substance. It is remarkably useful for quantitative analysis. The limitations are that expensive and complex instrumentation, moderate to poor sensitivity with continuous wave instrument, finally limited range of solvents for analysing proton spectra unless deuterated.
Using NMR to study metal-ligand equilibrium become of a greater interest and use. Beside its ability to determine stability constant, this technique can also provide sufficient information about the complex structure as well as binding location.
Spectrophotometry methods:
Spectrophotometry is an analytical technique for quantitative measuring the reflection of transmission properties of the substance as a function of wavelength. It involves the use of spectrophotometer, which can measure intensity as a function of a light source length. It is widely used for measuring reflectance or transmittance of solutions, transparent or opaque solids, and gases. Spetcrophtotometer is currently successful in deteriming equilibrium constant. As well known, a lot of the chemical reactions may take place in forward and reverse directions where reactants from products and products break down to reactant. At a certain point, the reaction reaches the equilibrium point at which reactants and products respective concentrations can be determined through testing light transmittance by a spectraphotometer. The amount of light transmitted is a direct indication of the concentration of certain substance.
Drawbacks of using spectrophtotmeter are the complexity of the instrumentations and process, also high cost instrument, and difficult maintenance.
When using spectrophotometer for stability constant determination, the absorbance of specie, M, of concentration c in a cell length d is:
A = εcd
Where: ε is the molar absorption coefficient at a specific wave length.
So: [MLn] = A/εd
One of the terms needed to determine a series of stability constants can be computed provided its spectrum is sufficiently distinguishable.
In the following equilibrium
pM+ qL ↔MpLq
A series of solution can be prepared for which (Mt + Lt) is constant and the ratio x = varies from 0 to 1.
Absorbance in visible spectrometer to E is proportional to [MpLq] and can be measures and plotted against x to give two straight lines intersecting at X = p/q.
Other methods:
Other physical techniques have been used for determining stability constants including polarimetry, Raman spectroscopy, infrared spectroscopy, conductivity, along with depression of the freezing points, and solubility.
