Metastable precipitate, solubility

The solubility of a substance B is the relative proportion of B (or a substance related chemically to B) in a mixture which is saturated with respect to solid B at a specified temperature and pressure. Saturated implies the existence of equilibrium with respect to the processes of dissolution amd precipitation the equilibrium may be stable or metastable. The solubility of a substance in metastable equilibrium is usually greater than that of the corresponding substance in stable equilibrium. (Strictly speaking, it is the activity of the substance in metastable equilibrium that is greater.) Care must be taken to distinguish true metastability from supersaturation, where equilibrium does not exist. 

There are other soUd states which sometimes confuse the measurement and definition of solubiUty. The dmg may crystaUize as a hydrate, i.e. under inclusion of water molecules. If the hydrate form is more stable than the pure form it may be difficult to measure the intrinsic solubility of the drug at all. Often drugs tend to precipitate in an amorphous form, often under the inclusion of impurities. As with metastable polymorphs, such amorphous precipitates may lead to erroneously high solubility measurements. CommerciaUy, drugs are often crystallized in salt form, e.g. as the hydrochloride salt, a cation with a chloride anion. In these co-crystallized salts, a much lower solubility than the intrinsic solubility will typi-... 

Fig. 5 Dissolution profiles obtained from the solubility determination of two polymorphic forms of the same drug substance. A is the stable form with solubility 31 mg/mL. B is the profile of the metastable form with solubility 46 mg/mL. This solubility (circles) is not achieved in many instances, and precipitation of the stable form occurs at a point beyond the solubility of A, and the trace becomes B. C is the hypothetical profile of the metastable form. 

At point 1, the only form that is supersaturated is Form I, and because supersaturation is a pre-requisite to crystallization it is the only form that could precipitate as a solid phase. If the metastable zone is crossed for Form I before the solubility curve is reached for Form II then Form I will crystallize first and continue to grow unhindered. Unfortunately the width of the metastable zone cannot be predicted theoretically at the present time and is sensitive to physical and chemical impurities and the surface quality of the crystallization vessel. This leads to uncertainty in process scale up. 

Metastable crystalline phases frequently crystallise to a more stable phase in accordance with Ostwald s rule of stages, and the more common types of phase transformation that occur in crystallising and precipitating systems include those between polymorphs and solvates. Transformations can occur in the solid state, particularly at temperatures near the melting point of the crystalline solid, and because of the intervention of a solvent. A stable phase has a lower solubility than a metastable phase, as indicated by the solubility curves in Figures 15.7a and 15.7/ for enantiotropic and monotropic systems respectively and,... 

The ratio of the instantaneous solute concentration c to the solute s solubility s, where the latter is the solute concentration in equihbrium with its crystalline or precipitated phase. Hence, RS = c/s, and a supersaturated solution experiences a thermodynamic driving force (AG = RT ln[RS]). A supersaturated solution will remain as a metastable state, because crystallization or precipitation requires a mechanism for relieving the supersaturated condition (eg., nucleation or addition of crystallite/precipitate). See Biomineralization... 

If the product of the concentrations of the ionic species exceeds the Ksp value then either precipitation occurs or a metastable condition of supersaturation develops. When reporting solubility products, the temperature should always be provided. Examples of a few relevant Ksp values (at 25°C) are given below. 

The area of conditions called the metastable zone is situated between the solubility and supersolubility curves on the crystallization phase diagram (Fig. 3.1). The supersolubility curve is defined as the line that separates the conditions where spontaneous nucleation (or phase separation or precipitation) occurs, from those where the crystallization solution remains clear if left undisturbed (Ducruix and Giege, 1992 Ducruix and Giege, 1999). 

Figure 14.2 Solubility diagram. During equilibration, the concentration of both precipitant and macromolecule increase until precipitation occurs. The formation of crystal nuclei reduces the amount of solvated macromolecule and allows the system to remain in the metastable zone where crystals can grow.

Metastability of Hydrolyzed Iron (III) Solutions The low solubility of ferric hydroxide has been alluded to in the Introduction. Feitknecht and Michaelis (29) have observed that aU ferric perchlorate solutions to which base has been added are unstable with respect to eventual precipitation of various forms of hydrated ferric oxides. In 3 M NaC104 at 25° C the two phase system reaches an apparent equilibrium after 200 hours, according to Biedermann and Schindler (6), who obtained a reproducible solubility product constant for ferric hydroxide at varying degrees of hydrolysis. It appears that many of the solutions used in the equilibrium studies of Hedstrom (9) and Biedermann (22) were metastable, and should eventually have produced precipitates. Nevertheless, since the measured potentials were reversible, the conclusions reached about the species present in solution remain valid. 

According to simple solubility considerations, a precipitate will be formed when the product of the concentrations of anions and cations exceeds the solubility product. From another viewpoint, phase transformation occurs when the free energy of the new phase is lower than that of the initial (metastable) phase. However, there are many examples where the ion product exceeds K p, yet no precipitation occurs—the phenomenon of supersaturation. The solubility product also does not provide information on how the particles of the precipitate form—nucleation. Nucleation involves various physical processes, and both thermodynamic and kinetic aspects must be considered. 

Careful studies by Doyle et al. (163) have also shown that soluble ruthenium species are inactive for hydrocarbon formation. A soluble system could be maintained in heptane solvent at 250°C under 100 atm of 1 1 H2/CO for many hours by taking precautions to avoid the possible introduction of impurities into the system and by slowly raising the temperature. No hydrocarbon formation was observed in this reaction. Only upon heating to about 260°C was the disappearance of soluble ruthenium complexes noted, along with the formation of linear alkanes. These results may suggest that metastable homogeneous ruthenium solutions can be formed, as has been reported for cobalt complexes (56) precipitation of the metal may be an autocatalytic process. 

It is most likely then that the effective (although metastable) SiO equilibria in most geological environments of low temperature and pressure, weathering, sedimentation and the early stages of compaction as well as surface hydrothermal alterations, are governed by the solubility and precipitation of amorphous silica in aqueous solution. As a result, the existence of quartz in an assemblage of clay minerals in these environments does not necessarily represent a compositional limit or saturation with respect to SiC and, therefore, such an assemblage cannot be considered, a priori, as a system with silica as an effective component in excess. 

Often a transition precipitate forms before the equilibrium precipitate. Figure 11.14 is a schematic plot of the free energy versus composition curves for such a case. Note that when a is in metastable equilibrium with ft its solubility for B is greater than when a is in equilibrium with ft. 

A systematic study of salting-out precipitation is carried out to obtain the operational limits within which this precipitation method can be applied for the production of fines (mean particle size <10 xm) with acceptable quality and productivity. The model substances glycine and sodium chloride are salted-out from their aqueous solutions by using ethanol as antisolvent. The main operational parameter is the initial supersaturation of the solutions. It is shown that the smallest particles can be produced at the limits of the metastability domain determined by three optional process parameters the initial solution concentration, the equilibrium solubility and the operational time. The product quality (crystallinity, polymorphic states, aggregation) and productivity considerably change with the operational conditions. 

Eventually this process forms the neutral species Fe(H2O)3(OH)30, which precipitates as amorphous iron hydroxide, which may settles out of the water column. Figure 3 shows the predicted effect of pH on the relative concentrations of the various iron hydrolysis species with and without considering the iron hydroxide solid, which dominates the speciation above pH 3.0 at 1 dM total iron. The log of the solubility product of this solid is -38.8, indicating that iron is very insoluble at natural pH values. Over time, this metastable amorphous material converts to more thermodynamically... 

A classic example of metastability is surface-seawater supersaturation with respect to calcite and other carbonate minerals (Morse and Mackenzie 1990 Millero and Sohl 1992). The degree of calcite supersaturation in surface seawater varies from 2.8- to 6.5-fold between 0 and 25 °C (Morse and Mackenzie 1990). In Fig. 3.18, experimental calcite solubility (metastable state) is approaching model calcite solubility (stable state) at subzero temperatures. In Table 5.1, the difference in seawater pH, assuring saturation or allowing supersaturation with respect to calcite, is 0.38 units. Moreover, in running these calculations, it was necessary to remove magnesite and dolomite from the minerals database (Table 3.1) because the latter minerals are more stable than calcite in seawater. But calcite is clearly the form that precipitates... 

---