Constant Stability

The stability constant (K) of an equilibrium as shown in scheme (XIII) can be determined from the changes in r3 with solute concentrations. 

The condition for this is that Ps should react with, at least, one of the compounds involved A, B or AB. For instance, in case of Ps oxidation, Eq. (14) can be extended as  

Each compound has its own reaction rate constant, k j, and effective concentration, C . The latter depend on the nominal (selected) concentrations of A and B, and on K. The unknown parameters, k j and K, can thus be determined by studying mixtures of A and B of various nominal concentrations k A and k B are conveniently measured separately, by using pure solutions of either A or B, respectively. 

Equation (23) shows that the measured parameter, X3, is a linear function of the concentrations of the solutes. This is similar to what one has with, e.g., spectrophotometry. In PALS however there is no such means as to change the excitation wavelength to enrich information deriving reliable stability constants through PAT requires the study of a large number of solute concentrations. Quantitative information is difficult to obtain when too many equilibria are present [110]. 

One advantage of PALS is that, as far as 13 is concerned, the medium appears transparent to Ps even at high concentrations of some solutes (e.g. CIO, CL, alkali cations). A promising application would be then to measure stability constants in concentrated solutions, to assess the validity of equations for the activity coefficients at high ionic strengths [111]. 

6 Stability Constants There are certain cases in which the equilibrium constant for a reaction of the sample with some substance can be easily measured and yields valuable structural information. Useful structural information is forthcoming only when there have been previous studies of related equilibria, as is the case with acids and bases. 

The necessary equipment is a good pH meter, a burette, and a jacketed titration cell (Fig. 3-6). The carefully weighed sample is added to the titration cell and a known volume of pure solvent is added, the mixture is stirred magnetically until the add (or base) has dissolved completely, and a slow stream of nitrogen is passed through the solution. The glass electrode is then standardized in a buffer solution and placed in the cell. When the solution has come to thermal equilibrium with the cell, the addition of increments of carbonate-free base is begun and the pH is recorded as soon as equilibrium is attained after each addition. The exact value of the p C should be 

The thermodynamic stabilities of coordination compounds are typically measured using stability or formation constants, as shown in Equations(l5.l)-(l5.4) for Cu(NH3)4+. The tetraaquacopper(ll) cation is used as the starting material in Equation (15.1) because the hydration enthalpy Is so negative that most metal ions cannot exist as naked cations in aqueous solution. It is not always possible for the stepwise constants to be measured individually, so typically only the overall formation constant is reported, where n is the number of ligands attached to the metal ion. If the stepwise stability constants do happen to be known, then the overall constant can be determined from the product of each individual formation constant. The stepwise formation constants for coordination compounds usually decrease in magnitude as the value of n increases. This is an entropic effect that has to do with the number of available substitutions. Thus, for example, addition of NH3 to [Cu(H20)4] in Equation (15.1) has four possible positions available for substitution, whereas addition of NH3 to [Cu(NH3)3(H20)] in Equation (15.4) has only one possible position available for substitution. 

TABLE 15.4 Selected stability constants for transition metal compounds, reported as the logarithm of the overall stability constant at 298 K. 

Solution. The two formation constants are simply multiplied together fi2 = K,K2 = IJx 10. The reason why K2 K in this case has to do with the different geometries of the two coordination compounds. The actual stepwise chemical equations are as follows  

Because of the greater number of products, the second equilibrium is strongly favored by entropy. 

Example 15-3. Which of the following would be expected to have the largest overall formation constant [Ni(en)3] +, [Ni(edta)] , or [Ni(NH3)J Explain your answer. 

The best place to start is with a measure of the ability to chelate individual metal ions. This is expressed by the stability constants, that is, equilibrium constants for the reaction of chelant with metal, as shown in Equation 10.1  

The stability constant is normally shown as the logarithmic value, logK, and so the larger the value of logic, the further to the right the equilibrium is and the stronger the chelate is and the less free metal ion is in solution. These are equilibrium constants and so give no information on the kinetics of the reaction [31]. 

Stability constants for common chelants and some key metal ions are given in Table 10.3. Based on this table, using Fe3+ as an example, the order of binding 

However, this is not the whole story, as in most applications there is a mixture of hardness ions (50-200 ppm) that compete for chelant with a small amount of transition metal ions (0.1-5 ppm). This is where selectivity of chelants becomes important. A simple way to analyze this is shown in Table 10.4, where the selectivity for different metal ions in the presence of the most common hardness metal ion Ca2 + has been calculated. Selectivity is calculated as the ratio of the stability constant for a metal ion divided by the stability constant for Ca2+ (Equation 10.2)  

Here a different pattern emerges and demonstrates the unusual selectivity of EDDS for transition metal ions in the presence of Ca2 +, where it is now more selective than EDTA, particularly for iron and copper. The order of selectivity for Fe3 + is EDDS DTPMP EDTA IDS HEDP NTA = MGDA EDTMP EDG GLDA. However, Table 10.4 is only an illustration in that it only considers one metal and calcium at a time and does not consider all the metal ions, pH, temperature, concentrations, and so on. 

The equilibrium constant for the formation of a metal complex is known as its stability constant. (Some authors, however, present the datum as its reciprocal, the instability constant of the complex, by analogy with the dissociation of a weak acid.) There are two kinds of stability constants stepwise Ki, K2, K3. Kn) and overall 0n). We will assume that there are six aqua ligands to be replaced by some other unidentate ligand X , in an aqueous solution of M  

In principle, this continues until we reach MXe. Alternatively, we can consider the formation of MXe as a single step 

If a sexidentate ligand were to coordinate to M +, /3 would just be 3x = with units L moF. Consequently, we cannot compare /3i for formation of a sexidentate ligand with the overall stability constant /3e for six comparable unidentate ligands because the units are incompatible. 

The stability constants are defined here in terms of concentrations and hence have dimensions. True thermodynamic stability constants K° and P° would be expressed in terms of activities (Section 2.2), and these constants can be obtained experimentally by extrapolation of the (real) measurements to (hypothetical) infinite dilution. Such data are of limited value, however, as we cannot restrict our work to extremely dilute solutions. At practical concentrations, the activities and concentrations of ions in solution differ significantly, that is, the activity coefficients are not close to unity worse still, there is no thermodynamically rigorous means of separating anion and cation properties for solutions of electrolytes. Thus, single-ion activity coefficients are not experimentally accessible, and hence, strictly speaking, one cannot convert equations such as 13.6 or 13.8 to thermodynamically exact versions. 

Tabulations of stability constants usually list log K values for various M and X x may be zero, of course) at specified ionic strengths, often including extrapolated values for J = 0. The temperature is also noted, since AH° for complex formation, though rarely large, cannot normally be disregarded. 

It has been found that in a reaction mixture at equilibrium at a certain temperature the product of the activities of the products divided by the 

The activity of a species A is the product of its concentration and an activity coefficient 7a- 

The activity coefficient has a value of unity in very dilute solutions, so that under such conditions, concentrations and activities are numerically equal. In the 0.01 to 5 M solutions most commonly used in the laboratory, activity coefficients are less than 1, and hence activities are lower than concentrations. 

That the activity of a species in solution is less than its concentration is interpreted as indicating that the species cannot act independently but is under the influence of other solute particles hence its effective concentration is decreased. In subsequent discussions of equilibrium constants, we shall firequently replace activities with concentrations. Note that this involves the assumption of unit activity coefficients, and thus will be quantitatively accurate only in very dilute solution. 

Metal complexes are formed in solution by stepwise reaction, and equilibrium constants can be written for each step, equations (6), (7). 

The simplest and probably the most fundamental reaction, since it initiates all oligomerization reactions, is the condensation of two appropriate metal ions to give a dinuclear monohydroxo-bridged 

This equation shows that not only a high metal-ion concentration, but also a high pH, often favors the formation of higher polynuclear species, since y generally increases more rapidly than x. For many aqua metal ions, however, the precipitation of insoluble hydroxides sets an upper pH limit, so that in practice it is possible to study the oligomerization reactions only within a narrow pH region defined by the magnitude of the first acid dissociation constant of the monomeric aqua ion and the pH at which insoluble hydroxide formation occurs. 

A wide variety of methods has been used in studies of oligomerization reactions. The most important quantitative method is potentiometric measurement of pH as a function of the total metal concentration and of the concentration of the analytical excess of acid or base. Other quantitative methods which are often used are potentiometric determination of metal ion concentration, calorimetry, spectrophotometry, and ion exchange. These, together with a number of other techniques, have recently been discussed thoroughly by Baes (22). 

One way to overcome the above problem would be to suppress hydrolysis of the amine ligands by working with an appropriate amine buffer medium. This strategy has been used with great success by Andersen et al. to obtain quantitative equilibrium data for the formation of mononuclear amine complexes (195, 196). Andersen et al. have also studied the formation of polynuclear complexes under similar conditions, but equilibrium was not attained with respect to these species (40, 42, 60, 87). The fact, however, that both thermal hydrolysis and charcoal/chromium(II)-catalyzed hydrolysis in such an amine buffer medium give the same polynuclear species in almost identical ratios would seem to indicate that some degree of equilibration had been achieved. It therefore seems likely that these methods could, in principle, be modified so as to also be applicable for equilibrium studies. Quite a different approach would be to study complexes with macrocy-clic amines such as cyclam, which are known to have a reduced tendency to hydrolysis. However, such systems have not as yet been studied in detail. 

Condensation to monohydroxo-bridged complexes is often described by Eq. (28), for which the equilibrium constants Kd are related to those defined by Eq. (27) by Kd = Q2i/Qh, where is the first acid dissociation constant of the mononuclear aqua ion. 

In general, the equilibrium constant for the formation of the complex ML from ML i will be 

The equilibrium constants K2, K are known as stepwise formation constants. Alternatively, one may consider the equilibrium constant for the overall reaction 

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MA( , ) + A. MA n-[MA( , )][A] Ky, Kfy being called the step-wise stability constants. Overall stability constants, designated may be evaluated by multiplication of the individual stability constants, e.g. 

Good to excellent Hammett plots were obtained using substituent constants (see Figure 2.6). Surprisingly, literature examples of good Hammett correlations of stability constants are rare The p-values are shown in Table 2.7. 

NMR signals of the amino acid ligand that are induced by the ring current of the diamine ligand" ". From the temperature dependence of the stability constants of a number of ternary palladium complexes involving dipeptides and aromatic amines, the arene - arene interaction enthalpies and entropies have been determined" ". It turned out that the interaction is generally enthalpy-driven and counteracted by entropy. Yamauchi et al. hold a charge transfer interaction responsible for this effect. 

Martell, A. E. Stability Constants of Metal-Ion Complexes, Chemical Society London, 1971... 

The data refer to various temperatures between 18 and 25°C, and were compiled from values cited by Bjerrum, Schwarzenbach, and Sillen, Stability Constants of Metal Complexes, part II, Chemical Society, London, 1958, and values taken from publications of the lUPAC Solubility Data Project Solubility Data Series, International Union of Pure and Applied Chemistry, Pergamon Press, Oxford, 1979-1992 H. L. Clever, and F. J. Johnston, J. Phys. Chem. Ref Data, 9 751 (1980) Y. Marcus, Ibid. 9 1307 (1980) H. L. Clever, S. A. Johnson, and M. E. Derrick, Ibid. 14 631 (1985), and 21 941 (1992). 

Marin, D. Mendicuti, F. Polarographic Determination of Composition and Thermodynamic Stability Constant of a Complex Metal Ion, /. Chem. Educ. 1988, 65, 916-918. 

Source All values are from Martell, A. E. Smith, R. M. Critical Stability Constants, Vol. 4. Plenum Press New York, 1976. I Unless otherwise stated, values... 

A. E. MarteU and R. M. Smith, Critical Stability Constants, Plenum Press, New York, 1974. 

Table 3. Thermodynamic and Stability Constant Data for Selected Aqueous Cadmium Complexes ...

The ligand pATa values and transition metal chelate stability constants of arylisoxazoles were detected photometrically and the stability of the complexes studied (79JlCi25i). 

A significant achievement of Anatoly K. Babko was in the area of systematic physicochemical research of complex compounds in solution based on their photometric properties. Anatoly K. Babko showed the stability constants of complexes to be highly important, and demonstrated the relevance of the stepwise character of the dissociation of complex compounds. 

In metal chelate adsorption chromatography a metal is immobilised by partial chelation on a column which contains bi- or tri- dentate ligands. Its application is in the separation of substances which can complex with the bound metals and depends on the stability constants of the various ligands (Porath, Carlsson, Olsson and Belfrage Nature 258 598 I975 Loennerdal, Carlsson and Porath FEES Lett 75 89 1977). 

Chaput, Jeminet and Juillard measured the association constants of several simple polyethylene glycols with Na", K", Cs", and Tl". Phase transfer catalytic processes and most biological processes are more likely to involve the first two cations rather than the latter two, so we will confine the discussion to these. Stability constants for the dimethyl ethers of tetra-, penta-, hexa-, and heptaethylene glycols were determined poten-tiometrically in anhydrous methanol solution and are shown in Table 7.1. In the third column of the table, the ratio of binding constants (Ks/K s) is calculated. Note that Simon and his coworkers have referred to this ratio as the selectivity constant. ... 

Table 7.1. Stability constants for several open-chained polyethers in anhydrous methanol at 25...

Thus, a can be calculated (it is sometimes negligible), and the rate constants are evaluated graphically or by least-squares analysis the estimates of k and k must be consistent with the known stability constant. 

L. G. SiLLfiN and A. E. Martell, Stability Constants of Metal-ion Complexes, The Chemical Society, London, Special Publications No. 17, 1964, 754 pp., and No. 25, 1971, 865 pp. Stability Constants of Metal-lon Complexes, Part A. Inorganic Ligands (E. Hcigfeldt, ed.), 1982, pp. 310, Part B. Organic Ligands (D. Perrin, ed.), 1979, pp. 1263. Pergamon Press, Oxford. A continually updated database is now provided by L. D. Pettit and K. J. Powell (eds.), IVPAC Stability Constants Database, lUPAC and Academic Software. 

Table 19.1 Stability constants and thermodynamic functions for some complexes of Cd at 25°C...

Compared to later elements in their respective transition series, scandium, yttrium and lanthanum have rather poorly developed coordination chemistries and form weaker coordinate bonds, lanthanum generally being even less inclined to form strong coordinate bonds than scandium. This is reflected in the stability constants of a number of relevant 1 1 metal-edta complexes ... 

The redox behaviour of Th, Pa and U is of the kind expected for d-transition elements which is why, prior to the 1940s, these elements were commonly placed respectively in groups 4, 5 and 6 of the periodic table. Behaviour obviously like that of the lanthanides is not evident until the second half of the series. However, even the early actinides resemble the lanthanides in showing close similarities with each other and gradual variations in properties, providing comparisons are restricted to those properties which do not entail a change in oxidation state. The smooth variation with atomic number found for stability constants, for instance, is like that of the lanthanides rather than the d-transition elements, as is the smooth variation in ionic radii noted in Fig. 31.4. This last factor is responsible for the close similarity in the structures of many actinide and lanthanide compounds especially noticeable in the 4-3 oxidation state for which... 

In view of the magnitude of crystal-field effects it is not surprising that the spectra of actinide ions are sensitive to the latter s environment and, in contrast to the lanthanides, may change drastically from one compound to another. Unfortunately, because of the complexity of the spectra and the low symmetry of many of the complexes, spectra are not easily used as a means of deducing stereochemistry except when used as fingerprints for comparison with spectra of previously characterized compounds. However, the dependence on ligand concentration of the positions and intensities, especially of the charge-transfer bands, can profitably be used to estimate stability constants. 

The stability constant for the nickel chelate of pyrido[2,3-d]-pyrimidine-4(3 r)-one has been measured. ... 

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