Equilibria of complex formation

Martell, A. E., Ed. (1971). Coordination Chemistry, Vol. 1. Van Nostrand-Reinhold, New York. This is one of the American Chemical Society Monograph Series. Chapter 7 by Hindeman and Sullivan and Chapter 8 by Anderegg deal with equilibria of complex formation. 

Rossotti, H. (1978). The Study of Ionic Equilibria in Aqueous Solutions. Longmans, New York. A wealth of information on the equilibria of complex formation. 

Murakami. S., Ogura, K., and Yoshino, T.. Equilibria of complex formation between bivalent metal ions and 3,3 -bis(N,N -bisfcarboxymethyl) aminomethyl -o-cresol-sulfonphthalein. Bull. Chem. Soc. Jpn., 53. 2228, 1980. 

As noted earlier, the substitution of organometallic ions or pseudometal ions for a central metal ion has applications which are of interest to the physical-inorganic chemist. These applications are best indicated by looking at examples from three representative areas (1) the equilibria of complex formation (2) studies of reaction mechanisms and (3) problems of stereochemistry and chemical bonding. 

According to R. Brdicka and K. Vesely the carbonyl form of formaldehyde is reduced and the limiting kinetic current is given by the rate of the chemical volume reaction of dehydration. An analogous situation occurs for the equilibria among complexes, metal ions and complexing agents if the rates of complex formation and decomposition are insufficient to preserve the equilibrium. A simple example is the deposition of cadmium at a mercury electrode from its complex with nitrilotriacetic COO"... 

Classical methods for the investigation of complex formation equilibria in solution (UV/Vis spectrometry, thermochemical and electrochemical techniques) are still in use (for an appraisal of these and other methods see, e.g., ref. 22). Examples for the determination of the ratio of metal to ligand in an Hg-protein complex by UV spectrometry are given in ref. 23, for the study of distributions of complex species of Cd in equilibria by combined UV spectrometry and potentio-metry in ref. 24 and by potentiometry alone in ref. 25, and for the combination of calorimetry and potentiometry to obtain thermodynamic data in ref. 26. 

Such equilibria are known to consist of a number of consecutive complex equilibria. The formation constant / represents the free enthalpy of complex formation in the gas phase. This quantity can not be determined by experiment. 

The relaxation approach has played an important role in our understanding of the mechanisms of complex formation in solution (Chap. 4) 39,i4o -pjjg qj computer programs has now eased the study of multiple equilibria. For example, four separate relaxation effects with t s ranging from 100 xs to 35 ms are observed in a temperature-jump study of the reactions of Ni with flavin adenine dinucleotide (fad) (Eqn. (8.121)). The complex relaxation... 

Using a nonequilibrium approach, strong binding can be studied (ligand-receptor complex) (43). However, of particular interest in ACE and MACE is the characterization of weak interactions, since the rate of complex formation and the exchange of solute between aqueous and micellar phase could be too fast to be studied with conventional structure determination methods (MS, NMR). The alternative to those methods, namely, to measure in an equilibrium state, makes MACE highly attractive. Thus, weak bond strengths (acid-base and complex/partition equilibria) are measurable. 

The equilibria considered up to now have all involved inner sphere complexes. There is the possibility that an inner sphere complex may react with free ligands in solution this includes the solvent itself, to give an outer sphere complex where the ligand enters the secondary solvation shell of the inner sphere complex. If the two species involved in this type of interaction are of opposite sign, which is the situation where this type of complex formation is expected to be most effective, the outer sphere complex is called an ion pair. Fuoss65 has derived an expression (equation 38) for the ion pair formation constant, XIP, from electrostatic arguments ... 

Chapters 7 to 12 deal with factors affecting conformational equilibria and complex formation. Angyal explains the effect of calcium chloride on the anomeric equilibria of certain sugars by formation of especially stable complexes. These involve an axial-equatorial-axial sequence of three hydroxyl groups on a six-membered ring or a cis-cis sequence on a five-membered ring. Lemieux and Brewer use model compounds to study solvation effects on the orientation of the hydroxymethyl... 

The value of the equilibrium constant for an encounter is certainly of prime importance in the discussion of interchange pathways of complex formation. This was first suggested, in fact by Werner [4] as early as in 1912. Most of the work on ligand substitution in complexes is based on the assumption that encounter equilibria could be calculated from the ion-pairing equation of Fuoss [5] which was derived in turn from a consideration of diffusion-controlled reactions by Eigen [6]. At zero ionic strength, the encounter equilibrium constant, Kp is given as... 

Enthalpy changes encountered in ion-exchange processes carried out with resins of a conventional type are usually small (see, e.g., [97,102]) when covalent bond formation, association, or complex formation are absent. In systems where association equilibria (or complex formation) prevail in either the solution or the resin phase, the equilibrium is, as a rule, shifted markedly, as a result of the decrease in selectivity with increased temperature (see, e.g., [103-106]). 

Ingri N. and Sillen L. G. (1962) High-speed computers as a supplement to graphical methods II. Some computer programs for studies of complex formation equilibria. Acta Chem. Scand. 16, I73-I9I. 

Of course, the problems of hydrolysis can be obviated by using non-aqueous solvents, and pseudo-metal ions have the necessary solubilities. For example, spectrophotometric studies (18) of complex formation equilibria between 2,2 -bipyridine (bipy) and dialkyltin dichloride have been reported. The log K values for complexes R2SnCl2-bipy are 3.19 (R, n-C4H9), 3.36 (R, CH3), and 6.7 (R, Cl) in acetonitrile. There is surprisingly little difference between the constants for dimethyl- and the dibutyltin dichloride complexes. The equilibrium constant for the dibutyl-tin dichloride complex increases with increasing dielectric constant of an alcohol solvent. 

However, the case in which the solubility of a solid can be calculated from the known analytical concentration of added components and from the solubility product alone is very seldom encountered. Ions that have dissolved from a crystalline lattice frequently undergo chemical reactions in solution, and therefore other equilibria in addition to the solubility product have to be considered. The reaction of the salt cation or anion with water to undergo acid-base reactions is very common. Furthermore, complex formation of salt cation and salt anion with each other and with one of the constituents of the solution has to be considered. For example, the solubility of FeS(s) in a sulfide-containing aqueous solution depends on, in addition to the solubility equilibrium, acid-base equilibria of the cation (e.g., Fe + H2O = FeOH + H ) and of the anion (e.g., S + HjO = HS + OH, and HS" + H2O = H2S + OH ), as well as on equilibria describing complex formation (e.g., formation of FeHS" or FeSi ). 

The related extraction equilibrium is represented by Eq. (4.2) and the accompanying extraction constant Kex by Eq. (4.3). The three individual equilibria for complex formation and partitioning of ligand and metal complex are given by ... 

The applicability of donicities to cation-solvent interactions is most convincingly demonstrated by the polarographic reduction of various metal ions in solvents of different donicity. The observed variation of half-wave potentials with solvent donicity can be explained neither in terms of the Born equation nor by simple microscopic electrostatic models in view of the magnitude of the dipole moments of solvent molecules. The concept also provides the basis for an interpretation of complex formation reactions and the behaviour of electrolytes (ion pair equilibria) in a large number of EPD solvents. 

In standard treatments of complex formation equilibria, instead of individual, or step-wise, Ks defined as above, overall equilibrium constants are commonly used. The symbol is used for such equilibrium constants. In the present context, the sequence of reactions are defined as ... 

These are not the only equilibria which may have to be considered. There is the possibility that there may also be present complexes of the type M2L (aq), M3L (aq). There is also the possibility that protonation/deprotonation of the ligand has to be considered. The chemistry of complex formation is an extensive field of study, and reference to specialist inorganic texts is necessary. The following only indicates some of the typical equilibrium calculations which are involved. 

Appendix C shows the formation constants (/ff) of several complex ions note that all are 10 or greater, which means that the equilibria of the formation reactions lie far to the right. 

A method using variation of solvent composition to study the formation equilibria of complexes and its application to the nickel(ll)-chloride system is reported. In pure acetone the formation of the complex NiCl " was detected, and this species readily decomposed with increasing water content. The extrapolation of experimental results, determined between 0 and 0.05 mole fraction of water, to pure water, resulted in a value of logiQ / (NiCl ") — 14 as a rough approximation. 

In organic solvents, the possibility of complex formation appears to be enhanced over that in aqueous solutions. Such equilibria are conveniently studied by means of potentiometric titrations. Although most of the published data for organic systems involve silver halides, the method is quite general and is applicable to any system providing that the concentration of at least one ion can be independently monitored, say by e.m.f. measurements. (Since a detailed analysis of this method has been given by Butler only an outline will be given here.)... 

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