Phase equilibria complex formation

As with any other chemical reaction, the formation of a metal complex from a metal ion and a set of proligands can be described by an equilibrium constant. In its simplest form, a complexation reaction might involve the reaction of unsolvated metal ions in the gas phase with gas phase proligands to form a complex. In practice it is difficult to study such reactions in the gas phase and complex formation is normally studied in solution, often in water. This introduces the complication that the solvent can also function as a ligand, so that complex formation will involve the displacement of solvent from the metal coordination sphere by the proligand. 

The table summarizes the data up to the end of 1972. For each extractant and Its extractable metal complexes, distribution equilibrium constants, as well as appropriate extraction constants, are recorded. In addition, the homogeneous equilibria involving the acid dissociation of the extractant in the aqueous phase and adduct or mixed ligand complex formation in the organic phase are characterized. Aqueous phase metal complex formation constants however, are not included inasmuch as these are already covered in Stability Constants. 

This 228 page volume summarizes equilibrium constants for liquid-liquid distribution equilibrium constants up to the end of 1972. Each table includes the extractant and its extractable metal complexes, and.the distribution equilibrium constants and extraction constants. The aqueous phase metal complex formation constants are not included and the reader is referred to items and in this bibliography for sources of this type of data. References to the primary literature are included. 

For the supported catalyst it is expected that the ligand does not leach since it is chemically bonded to the carrier. In contrast, the rhodium metal bound to the ligand is subject to leaching due to the reversible nature of the complex formation. The amount will depend on the equilibrium between rhodium dissolved in the organic phase and that bound to the ligand. When an equilibrium concentration of 10 ppb Rh is attained, the yearly loss of Rh for a 100 kton production plant will be about 1 kg Rh per year. Compared to the reactor contents of rhodium (see Table 3.9, 70 kg Rh) this would result in a loss of 1.5% of the inventory per year, which would be acceptable. 

In a typical SPR experiment real-time kinetic study, solution flows over the surface, so desorption of the guest immobilized on the surface due to this flow must be avoided.72 In the first stage of a typical experiment the mobile reactant is introduced at a constant concentration ([H]0) into the buffer flowing above the surface-bound reactant. This favors complex association, and the progress of complex formation at the surface is monitored. The initial phase is then followed by a dissociation phase where the reactant is removed from the solution flowing above the surface, and only buffer is passed over the surface to favor dissociation of the complex.72 74 The obtained binding curves (sensograms) contain information on the equilibrium constant of the interaction and the association and dissociation rate constants for complex formation (Fig. 9). 

The equilibrium constant for reaction 5 depends on the complex formation constant, the association constant of C in the membrane and on the distribution coefficients of H+, and ions between the organic membrane phase and aqueous sample solution, e.g. 

The arrows show the isotherm evolution for continual addition of dissolved Me. The initial isotherm with the slope of 1 (in the double logaritmic plot) corresponds to a Langmuir isotherm (surface complex formation equilibrium). [Me]S0 = solubility concentration of Me for the stable metal oxide [Me]p = solubility concentration of Me for a metastable precursor (e.g., a hydrated Me oxide phase). 

The phenomena of surface precipitation and isomorphic substitutions described above and in Chapters 3.5, 6.5 and 6.6 are hampered because equilibrium is seldom established. The initial surface reaction, e.g., the surface complex formation on the surface of an oxide or carbonate fulfills many criteria of a reversible equilibrium. If we form on the outer layer of the solid phase a coprecipitate (isomorphic substitutions) we may still ideally have a metastable equilibrium. The extent of incipient adsorption, e.g., of HPOjj on FeOOH(s) or of Cd2+ on caicite is certainly dependent on the surface charge of the sorbing solid, and thus on pH of the solution etc. even the kinetics of the reaction will be influenced by the surface charge but the final solid solution, if it were in equilibrium, would not depend on the surface charge and the solution variables which influence the adsorption process i.e., the extent of isomorphic substitution for the ideal solid solution is given by the equilibrium that describes the formation of the solid solution (and not by the rates by which these compositions are formed). Many surface phenomena that are encountered in laboratory studies and in field observations are characterized by partial, or metastable equilibrium or by non-equilibrium relations. Reversibility of the apparent equilibrium or congruence in dissolution or precipitation can often not be assumed. 

The two-state model was used to test whether characteristics of the low-temperature cryosolvent cause the equilibrium constant for complex formation, K(T), to fall precipitously as the temperature is lowered through T ij. In this case, the slow phase that appears below 250 K would correspond to un-complexed ZnCcP. This interpretation fails because within the transition range the fraction, f(T), is unaffected by a ten-fold reduction in the ratio, R = [Cc]/[CcP], whereas use of K(T) calculated from f(T) would predict a larger shift of f(T). Alternatively, the two-state model would apply if a low-temperature form of the complex were created by a change in ligation of either ZnP or FeP. 

The concept sounds attractive, but there is a flaw in the explanation. Assuming an equilibrium situation between the two bulk phases and the interphase, complex formation at the interfacial region requires the same complexes are formed also in the bulk phases. Consequently, in order to produce a considerable amount of the mixed species MA, xBx in the liquid-liquid boundary layer some B must be dissolved in the aqueous, as weU as some A in the organic phase. Since by definition this condition is not met, the relative amount of M present at the interphase region as MAn xBx must be negligible. However, now the metal ion will be distributed between MA in the aqueous phase and MBp in the organic layer (n and p are the... 

The important chromatographic parameter, which can directly be Obtained from the chromatogram, is the retention fiactor k. It is given by the ratio of mass of eluite bound to the stationary phase to the mass in the mobile phase and is conveniently expressed by the corresponding equilibrium concentrations and the phase ratio, When a complex formation in the mobile phase dominates, i.e., the chromatographic process can be represented by the first limiting case, the retention fiactor is obtained by combining Eqs. (SI), (65), (66), and (68) to obtain... 

The third possible mechanism, Ilia, proposed here involves a transfer of solute from the complex formed in the mobile phase to the bound hetaeron and complex formation at the surface. The corresponding equilibrium for this metathetical process, which may be called dynamic complex exchange," can be written as... 

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. 

There are two major factors to be considered in assessing the contribution of potential oxidants for S(IV) to the net aqueous-phase oxidation. The first is the aqueous-phase concentration of the species, and the second is the reaction kinetics, that is, the rate constant and its pH and temperature dependencies. As a first approximation to the aqueous-phase concentrations, Henry s law constants (Table 8.1) can be applied. It must be noted, however, that as discussed earlier for S(IV) this approach may lead to low estimates if complex formation occurs in solution. On the other hand, high estimates may result if equilibrium between the gas and liquid phases is not established, for example, if an organic film inhibits the gas-to-liquid transfer (see Section 9.C.2). 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

Inorganic phosphate ligands are important with respect to the behavior of actinides in the environment and as potential waste forms. There have been a number of experimental studies to determine the equilibrium constants in the actinide-phosphoric acid system, but they have been complicated by the formation of relatively insoluble solid phases and the formation of ternary actinide complexes in solution. 

The use of the equilibrium condition for a fast step can greatly simplify mathematics, as will be seen in various examples in later chapters. Prominent among the fast steps to which the approximation can be applied are dissociation reactions in the gas phase and ionic reactions such as electrolytic dissociation, neutralization, and complex formation, as well as loss, addition, and exchange of... 

The treatment of partition equilibrium was further generalized to the cases in the presence of ion-pair formation [19] and ion-ionophore complex formation [21]. An important corollary of this theory of partition equilibrium based on standard ion transfer potentials of single ions is to give a new interpretation to liquid extraction processes. Kakutani et al. analyzed the extraction of anions with tris(l,10-phenan-throline) iron(II) cation from the aqueous phase to nitrobenzene [22], which demonstrated the effectiveness of the theory and gave a theoretical backbone for ion-pair extraction from an electrochemical point of view. 

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]). 

Example 10.2. Effect of Soluble Ugands and of Particles on the Distribution of Zn(II) Between Particulate and Soluble Phases In order to evaluate the two important variables that—in addition to pH—affect the residual concentrations of a metal ion, we use a simple equilibrium approach to assess the effect of these two variables. We assume a constant pH and characterize the effect of particle ligands, =L, by the surface complex formation equilibrium ... 

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