Stoichiometric saturation solubilities

There are currently insufficient data to determine the exact conditions for which each of these assumptions may apply, especially in field situations. In many instances, neither one of these assumptions will explain the observed solubility of a solid-solution, which may lie between the "maximum" stoichiometric saturation solubility and the "minimum" primary saturation solubility. Nonetheless, these solubility limits can often be estimated. 

By examining the compositional dependence of the equilibrium constant, the thermodynamic properties of the solid solution can be determined if the final solution is either at equilibrium or stoichiometric saturation. That is, the provisional activities and activity coefficients will be valid if either equilibrium or stoichiometric saturation is attained in the solubility data. 

These activities can be verified if It can he shown that the solubility data of (8) are at stoichiometric saturation, but as mentioned above, this requires independent thermodynamic definition of K(x). 

Most thermodynamic data for solid solutions derived from relatively low-temperature solubility (equilibration) studies have depended on the assumption that equilibrium was experimentally established. Thorstenson and Plummer (10) pointed out that if the experimental data are at equilibrium they are also at stoichiometric saturation. Therefore, through an application of the Gibbs-Duhem equation to the compositional dependence of the equilibrium constant, it is possible to determine independently if equilibrium has been established. No other compositional property of experimental solid solution-aqueous solution equilibria provides an independent test for equilibrium. If equilibrium is demonstrated, the thermodynamic properties of the solid solution are also... 

The effect of substitutional impurities on the stability and aqueous solubility of a variety of solids is investigated. Stoichiometric saturation, primary saturation and thermodynamic equilibrium solubilities are compared to pure phase solubilities. Contour plots of pure phase saturation indices (SI) are drawn at minimum stoichiometric saturation, as a function of the amount of substitution and of the excess-free-energy of the substitution. SI plots drawn for the major component of a binary solid-solution generally show little deviation from pure phase solubility except at trace component fractions greater than 1%. In contrast, trace component SI plots reveal that aqueous solutions at minimum stoichiometric saturation can achieve considerable supersaturation with respect to the pure trace-component end-member solid, in cases where the major component is more soluble than the trace. 

Stoichiometric saturation states can be represented on Lippmann phase diagrams (figure 1) by relating the total solubility product variable Ellgg (defined specifically at stoichiometric saturation with respect to a solid Ex. CxA) to the Kgg constant (equation 12) and to the aqueous activity fractions and c,aq-... 

In predicting solid-solution solubilities, one of two possible hypotheses must be chosen. In the first, the solid-solution is treated as a one-component or pure-phase solid, given that the equilibration time is sufficiently short, the solid to aqueous-solution ratio is sufficiently high and the solid is relatively insoluble. These requirements are needed to ensure that no significant recrystallisation of the initial solid or precipitation of a secondary solid-phase occurs. For such situations, the stoichiometric saturation concept may apply. 

Figures 2A and 2B show the case of a solid-solution series, (Ca,Cd)COs, with a much less soluble trace end-member. If the mole-fraction of trace component is sufficiently high ( cdCO > lO- -S), the aqueous phase at stoichiometric saturation will be supersaturated with respect to the trace end-member (except at unrealistic negative ao values not shown on the plot). The lower solubility of the trace component will generally cause negative SI values for the major component, except at high ao values (higher than 7.5 in the (Ca,Cd)CO case) for which the solid-solutions will generally be metastable or unstable. Calcite SI values drawn in figure 2A show that the mole-fraction of trace component must be sufficiently high ( cdcos > 10-2-5) for this effect to be measurable in the field (typical uncertainty 0.01) or in the laboratory.

Stoichiometric saturation measurements in carefully controlled laboratory experiments offer perhaps the most promising technique for the estimation of thermodynamic mixing parameters (3 Glynn and Reardon, Am. J. ScL, in press). Unfortunately, the results obtained can usually not be verified by a second independent and accurate method, such as reaction calorimetry or measurement of thermodynamic equilibrium solubilities (4). The conditions necessary in obtaining good stoichiometric saturation data (as opposed to thermodynamic equilibrium data) were discussed earlier. 

C18-0138. Quinine, an alkaloid derived from a free that grows in tropical rain forests, is used in the treatment of malaria. Like all alkaloids, quinine is a sparingly soluble weak base 1.00 g of quinine will dissolve in 1.90 X 10 L of water, (a) What is the pH of a saturated solution of quinine (b) A 100.0-mL sample of saturated quinine is titrated with 0.0100 M HCl solution. What is the pH at the stoichiometric point of the titration ... 

An alternative way of expressing the partition constant of a sparingly soluble salt is to define its solubility product Rsp (also called the solubility constant Rs). Ks is defined as the product of the ion activities of an ionic solute in its saturated solution, each raised to its stoichiometric number v . Ks is expressed with due reference to the dissociation equilibria involved and the ions present. 

Metal cations may be soluble, readily exchangeable, complexed with organic matter, or hydrous oxides, substituted in stoichiometric compounds, or occluded in mineral structures (see reviews by Brummer et al., 1986 Beckett, 1989 Forstner, 1991). The chemical factors that affect the retention of a specific chemical form of a trace metal (e.g. effects of pH and I on specific adsorption ) are well documented (Jones and Jarvis, 1981 Tiller, 1983 McBride, 1989 1991 Alloway, 1990 Forstner, 1991). When several components co-exist in a soil, the distribution of a trace metal among them will also depend on the type and relative quantities of the soil components how they change with pH, I, etc. and the extent of saturation of adsorption sites on soil adsorbents. 

One of the primary concerns in a study of the geochemistry of carbonates in marine waters is the calculation of the saturation state of the seawater with respect to carbonate minerals. The saturation state of a solution with respect to a given mineral is simply the ratio of the ion activity or concentration product to the thermodynamic or stoichiometric solubility product. In seawater the latter is generally used and Qmjneral is the symbol used to represent the ratio. For example ... 

Because of difficulties in precisely calculating the total ion activity coefficient (y) of calcium and carbonate ions in seawater, and the effects of temperature and pressure on the activity coefficients, a semi-empirical approach has been generally adopted by chemical oceanographers for calculating saturation states. This approach utilizes the apparent (stoichiometric) solubility constant (K ), which is the equilibrium ion molal (m) product. Values of K are directly determined in seawater (as ionic medium) at various temperatures, pressures and salinities. In this approach ... 

The interest in the carbonate system is related to attempts to understand the uptake of fossil fuel produced CO2 by the oceans. The carbonate system can be studied by measuring pH, total alkalinity (TA), total inorganic carbon (TCO2), and the fugacity of CO2 (fco )- At least two of these variables are needed (Park, 1969) to characterize the CO2 system in the oceans. Reliable stoichiometric constants (K ) for the carbonate system are needed to determine the concentration, mol (kg solution) of the components of the CO2 system ([HCOa"], [CO2], [COa ]) and the saturation state of CaCOa as a function of salinity, temperature, and pressure (Culberson and Pytkowicz, 1968 Ingle, 1975 Millero, 1995, 2001). This includes constants for the solubility of CO2 in seawater (Weiss, 1974)... 

Based on these concepts a reaction crystallization process may be designed such that the solution is supersaturated with respect to cocrystal only, while it is below, or, at saturation with respect to the individual components. Supersaturation can be generated by various approaches according to the solubility product behavior. These processes include (i) mixing solutions of reactants or cocrystal components in non-stoichiometric concentrations or (ii) dissolving one or more solid reactants so that non-stoichiometric conditions are generated. 

M For slightly soluble salts with stoichiometries other than 1 1, the mass-balance expression is obtained by multiplying the concentration of one of the ions by the stoichiometric ratio. For example, in a solution saturated with PbU, the iodide ion concentration is twice that of the Pb. That is,... 

Compute the total or stoichiometric and effective ionic strengths, and corresponding total- and free-ion activity coefficients of Ca and SO in pure water saturated with gypsum at 25"C. It is given that the solubility product of gypsum, and that at gypsum saturation... 

The solubility of SrSe04(cr) in water has been determined over the temperature interval 273 to 373 K. Crystalline strontium selenate was prepared by mixing stoichiometric amounts of strontium nitrate and selenic acid. Under the light microscope the crystals appear as very thin needles. The strontium concentration in saturated solution was obtained by polarographic (half-wave potential at -2.1 V) and gravimetric measurements. Both methods gave concordant results, Table A-18. 

The inventor proposes an alternate process in claim 1 in which the oxides are dissolved into an unspecified supercritical fluid at unspecified conditions but at 1 to 25 wt% below the solubility of the least soluble cranponent, rapidly expanding the fluid to precipitate a uniform and stoichiometrically accurate mixture, and thermally treating the powder. We wonder how this patent was allowed since the patent by Sievers and Hansen (U.S. 4,970,093) reviewed in this edition of the book, states explicitly the process and conditions neededlo dissolve metal complexes for superconductor fabrication. Sievers and Hansen are not quoted by the inventor nor is their quantitative data quoted. We also wonder if the inventor has ever tried to dissolve some of the materials that are listed in the claims section since the instant patent teaches to operate at 1 to 25 wt% less than the saturation amount of the least soluble component. Can we expect compounds such as yttrium to have solubilities at weight percent levels We do not believe so. 

Finally, the saturation indexes of each precipitated species are calculated. When a precipitated species is present, the corresponding value of saturation index is appended to the matrix of the residues for the Newton-Raphson method. The saturation index values are calculated by the sum of the product of the stoichiometric coefficients corresponding to the precipitates (Ep) and the logarithm of the corresponding values of the concentrations of the master species minus the logarithm of the corresponding solubility product constant ... 

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