Stoichiometric stability constants

Originally, the stoichiometric stability constants 6 for the lead and the cadmium complexes with chloride had been determined in NaCl-NaC104 solutions and it had been assumed that the NaCl was completely dissociated. The nominal ionic strength was one molal. The constants were later corrected by replacing the actual free chlorides for the total chlorides in the calculation of... 

Ideally one would wish to measure the activities of all the reacting species in equation (4) but it is not possible to determine activities of single ionic species (at best, mean ionic activities may be determined in some cases) and the determination of activities of uncharged species is fraught with difficulties. However, modem experimental methods (see Section 3) can readily be applied to the determination of concentrations of at least some of the species concerned, leading to stoichiometric stability constants defined by... 

It must be emphasized that such stoichiometric stability constants are dependent, inter alia, upon the ionic strength of the solution, and, in reporting experimental results, the ionic strength of the experimental solutions should always be specified. Further, the numerical value of a stoichiometric constant will depend upon the units used, viz. mole fractions, molar, molal, millimole, and so on, and which is used should always be made clear. 

The stoichiometric stability constants, as defined by Eqs. (2.6) and (2.8), are related through the protolysis constant of water relevant to the experimental conditions (ionic strength and temperature) used to study the stoichiometric reaction. Stability constants that include an asterisk denote conditions where water is used as the reactant and no asterisk is used to denote where hydroxide ion is the reactant (i.e. see Eqs. (2.6) and (2.8)). Equation (2.5) can also be used to denote the reaction for the protolysis of water. In this circumstance, / = 0 and = 1 in the equation, with the right-hand product of the reaction being the hydroxide ion. Stepwise hydrolysis reactions for monomeric species can be written as... 

Numerous investigations have shown the existence of the heptamolybdate, [Mo7024]6 , and octamolybdate, [Mo8026]4, ions in aqueous solution. Potentiometric measurements with computer treatment of the data proved to be one of the best methods to obtain information about these equilibria. Stability constants are calculated for all species in a particular reaction model, which is supposed to give the best fit between calculated and experimental points. In the calculations the species are identified in terms of their stoichiometric coefficients as described by the following general equation for the various equilibria... 

Af is called a formation or stability constant. Note that the formula for the ion pair, NaQ (aq), symbolizes the interaction of 1 atom of Na with 1 atom of Cl, whereas the representation of crystalline halite, NaCl(s), is an empirical formula in which an imspecified number of Na and Cl atoms are present in a 1 1 stoichiometric ratio. 

Average values of complex mobilities obtained using nonlinear curve fitting assuming a 1 1 interaction were used to calculate the stoichiometric coefficients and stability constants through another nonlinear curve fitting [Eq. (3)]. The /x/K7) values were applied because they show a good approach... 

A second possible mathematical approach is to consider the equilibria via complexation or aggregation (21,22). Assuming that a drug compound can bind several tenside molecules in steps (concentration gradient), the brutto equilibria constants or stability constants KA can be given as follows. Normally the aggregation constant is calculated for 1 1 reactions or other known stoichiometric ratios (z) ... 

In an ideal world, crystals would be perfect or stoichiometric with constant composition. But like people crystals are not exempt from imperfections or defects. Crystals with variable composition are termed non-stoichiometric crystals. The defect chemistry of oxides is enormously complex and is extremely vital to their properties. It has involved extensive research in many laboratories and is providing extraordinary insights into structural variations, the stability of structures and the formation of new structures. Here, we first define order-disorder phenomena that are commonly associated with oxides and describe our current understanding of them. The disorder or non-stoichiometry plays a crucial role in oxide applications including catalysis and it is therefore of paramount importance. 

Knowing the stability constants (actually, molarity quotients or stoichiometric constants are more useful here), it is possible to say which... 

La(L4)]3+ isomerisation process on the NMR time scale. Compared to the parent complexes [La(L3)3]3+ which display enantiotopic methylene protons for T > 233 K (see sect. 3.1.3), the introduction of the covalent TREN tripod in [La(L4)]3+ significantly slows down the helical interconversion process. Protonation of the apical nitrogen atom produces the C3-symmetrical podates [R(L4+H)]4+ which display only marginally faster racemisation processes. Although some steric constraints induced by the tripod limit the thermodynamic stability of the podates [f (L4)]3+ and [/J(L4+H)]4+, stability constants confirm their quantitative formation for a total ligand concentration of 0.05 mol dm-3 and a stoichiometric ratio R L4 = 1.0 (Renaud etal., 1999 fig. 17). 

The composition of these complexes and their stability constants have been determined for a large number of metal ions primarily with the use of emf methods (200, 201). The free hydrogen ion concentration and in some cases the free metal ion concentration are determined as functions of the stoichiometric hydrogen ion and metal ion concentrations. From measurements on series of solutions of different concentrations the number of metal atoms in a complex and its charge can be derived, but no information is obtained on the number of water molecules in the complex. Since emf measurements are influenced by changes in activity factors they have usually been done in an inert ionic medium of high concentration (3 M NaC104) and at low metal ion concentrations. The major complexes formed, however, have been found to be stable also in the concentrated solutions needed for X-ray diffraction measurements, and the stability constants determined seem to be... 

If the stability constant of the complex is high (curve A in Figure 22-12), there will be no appreciable dissociation of the complex at or near the stoichiometric point. If the complex is moderately stable (curve B in Figure 22-12), the plot will consist of two straight-line portions with a central curved portion. Extrapolation of the two straight-line portions yields the intersection point. If a complex of low stability is formed, a large excess of ligand will have to be used to drive the... 

Once the stoichiometry of the complex has been established, the stability constant(s) can be calculated, provided the data yields a curve showing some dissociation in the neighborhood of the stoichiometric point (curve B in Figure 22-12). Briefly, for any data point in the region of curvature, complex formation did not proceed to completion, as evidenced from the difference between the measured curve and the "theoretical" one. Here there is obviously an equilibrium between metal ion, ligand and complex, and from each data point a value of the stability constant can be calculated. 

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