Solute equilibrium solubility

From the standpoint of thermodynamics, the dissolving process is the estabHsh-ment of an equilibrium between the phase of the solute and its saturated aqueous solution. Aqueous solubility is almost exclusively dependent on the intermolecular forces that exist between the solute molecules and the water molecules. The solute-solute, solute-water, and water-water adhesive interactions determine the amount of compound dissolving in water. Additional solute-solute interactions are associated with the lattice energy in the crystalline state. 

Crystal Formation There are obviously two steps involved in the preparation of ciystal matter from a solution. The ciystals must first Form and then grow. The formation of a new sohd phase either on an inert particle in the solution or in the solution itself is called nucle-ation. The increase in size of this nucleus with a layer-by-layer addition of solute is called growth. Both nucleation and ciystal growth have supersaturation as a common driving force. Unless a solution is supersaturated, ciystals can neither form nor grow. Supersaturation refers to the quantity of solute present in solution compared with the quantity which would be present if the solution were kept for a veiy long period of time with solid phase in contac t with the solution. The latter value is the equilibrium solubility at the temperature and pressure under consideration. The supersaturation coefficient can be expressed... 

Fig. 10.5. TTT diagram for the precipitation of CuAh from the Al + 4 wt% Cu solid solution. Note that the equilibrium solubility of Cu in Al at room temperature is only 0.1 wt% (see Fig. 10.3). The quenched solution is therefore carrying 4/0.1 = 40 times as much Cu as it wants to.

The alloy aluminium-4 wt% copper forms the basis of the 2000 series (Duralumin, or Dural for short). It melts at about 650°C. At 500°C, solid A1 dissolves as much as 4 wt% of Cu completely. At 20°C its equilibrium solubility is only 0.1 wt% Cu. If the material is slowly cooled from 500°C to 20°C, 4 wt% - 0.1 wt% = 3.9 wt% copper separates out from the aluminium as large lumps of a new phase not pure copper, but of the compound CuAlj. If, instead, the material is quenched (cooled very rapidly, often by dropping it into cold water) from 500°C to 20°C, there is not time for the dissolved copper atoms to move together, by diffusion, to form CuAlj, and the alloy remains a solid solution. 

For a substance to dissolve in a liquid, it must be capable of disrupting the solvent structure and permit the bonding of solvent molecules to the solute or its component ions. The forces binding the ions, atoms or molecules in the lattice oppose the tendency of a crystalline solid to enter solution. The solubility of a solid is thus determined by the resultant of these opposing effects. The solubility of a solute in a given solvent is defined as the concentration of that solute in its saturated solution. A saturated solution is one that is in equilibrium with excess solute present. The solution is still referred to as saturated, even... 

Now interpret phase X as pure solute then Cs and co become the equilibrium solubilities of the solute in solvents S and 0, respectively, and we can apply Eq. (8-58). Again the concentrations should be in the dilute range, but nonideality is not a great problem for nonelectrolytes. For volatile solutes vapor pressure measurements are suitable for this type of determination, and for electrolytes electrode potentials can be used. 

Henry s Law. This is an empirical formulation that describes equilibrium solubilities of noncondensable gases in a liquid when Raoult s law fails. It states that the mole fraction of a gas (solute i) dissolved in a liquid (solvent) is proportional to the partial pressure of the gas above the liquid surface at given temperature. That is,... 

Expression (2) applies to a solubility equilibrium, provided we write the chemical reaction to show the important molecular species present. In Section 10-1 we considered the solubility of iodine in alcohol. Since iodine dissolves to give a solution containing molecules of iodine, the concentration of iodine itself fixed the solubility. The situation is quite different for substances that dissolve to form ions. When silver chloride dissolves in water, no molecules of silver chloride, AgCl, seem to be present. Instead, silver ions, Ag+, and chloride ions, Cl-, are found in the solution. The concentrations of these species, Ag+ and Cl-, are the ones which fix the equilibrium solubility. The counterpart of equation (7) will be... 

Experimentally, fCsp = 1.6 X 10 10 at 25°C, and the molar solubility of AgCl in water is 1.3 X 10 5 mol-IT. If we add sodium chloride to the solution, the concentration of Cl ions increases. For the equilibrium constant to remain constant, the concentration of Agf ions must decrease. Because there is now less Ag+ in solution, the solubility of AgCl is lower in a solution of NaCl than it is in pure water. A similar effect occurs whenever two salts having a common ion are mixed (Fig. 11.16). 

These opposing tendencies may defeat the purpose of the fractional precipitation process. The fractional precipitation of crystalline polymers such as nitrocellulose, cellulose acetate, high-melting polyamides, and polyvinylidene chloride consequently is notoriously inefficient, unless conditions are so chosen as to avoid the separation of the polymer in semicrystalline form. Intermediate fractions removed in the course of fractional precipitation may even exceed in molecular weight those removed earlier. Separation by fractional extraction should be more appropriate for crystalline polymers inasmuch as both equilibrium solubility and rate of solution favor dissolution of the components of lowest molecular weight remaining in the sample. 

The conformation of a polymer in solution is the consequence of a competition between solute intra- and intermolecular forces, solvent intramolecular forces, and solute-solvent intermolecular forces. Addition of a good solvent to a dry polymer causes polymer swelling and disaggregation as solvent molecules adsorb to sites which had previously been occupied by polymer intra- and intermolecular interaction. As swelling proceeds, individual chains are brought into bulk solution until an equilibrium solubility is attained. 

Fig. 22 Dissolution fates of various griseofulvin and gri-seofulvin-succinic acid samples as determined by the oscillating bottle method. , griseofulvin, crystalline A, griseofulvin, micronized , eutectic mixture 0> physical mixture at eutectic composition , solid solution A, physical mixture at solid solution composition. The dashed line indicates the equilibrium solubility of griseofulvin in water. (From Ref. 41.).

The concentration of a compound in water is controlled by its equilibrium solubility or solubility constant (the maximum amount of a compound that will dissolve in a solution at a specified temperature and pressure). Equilibrium solubility will change with environmental parameters such as temperature, pressure, and pH for example, the solubility of most organic compounds triples when temperature rises from 0°C to 30°C. Each type of waste has a specific equilibrium solubility at a given temperature and pressure. The solubility of toxic organic compounds is generally much lower than that of inorganic salts. This characteristic is particularly true of nonpolar compounds because of their hydrophobic character. 

Precipitation usually occurs when the concentration of a compound in solution exceeds the equilibrium solubility, although slow reaction kinetics may result in supersaturated solutions. For organic wastes in the deep-well environment, precipitation is not generally a significant partitioning process in certain circumstances, however, it may need to be considered. For example, pentach-lorophenol precipitates out of solution when the solution has a pH of <5,35,36 and polychlorophenols form insoluble precipitates in water high in Mg2+ and Ca2+ ions.37 Also, organic anions react with such elements as Ca2+, Fe2+, and Al3+ to form slowly soluble to nearly insoluble compounds. 

Coprecipitation is a partitioning process whereby toxic heavy metals precipitate from the aqueous phase even if the equilibrium solubility has not been exceeded. This process occurs when heavy metals are incorporated into the structure of silicon, aluminum, and iron oxides when these latter compounds precipitate out of solution. Iron hydroxide collects more toxic heavy metals (chromium, nickel, arsenic, selenium, cadmium, and thorium) during precipitation than aluminum hydroxide.38 Coprecipitation is considered to effectively remove trace amounts of lead and chromium from solution in injected wastes at New Johnsonville, Tennessee.39 Coprecipitation with carbonate minerals may be an important mechanism for dealing with cobalt, lead, zinc, and cadmium. 

Figure 10.19 Equilibrium solubility of solutes versus temperature.

When determining the solubility and dissolution rate of amorphous or partially crystalline solids, the metastability of these phases with respect to the highly crystalline solid must be considered. While the low diffusivity of the molecules in the solid state can kinetically stabilize these metastable forms, contact with the solution, for example during measurements of solubility and dissolution rate, or with the vapor, if the solid has an appreciable vapor pressure, may provide a mechanism for mass transfer and crystallization. Less crystalline material dissolves or sublimes whereas more crystalline material crystallizes out. The equilibrium solubility measured will therefore approach that of the highly crystalline solid. The initial dissolution rate of the metastable form tends to reflect its higher... 

It is important to ascertain whether the solid phase of the solute changes during equilibration to produce a different polymorph or solvate, by analyzing the solid phase (using either chemical or thermal analysis, or x-ray diffraction). If a solid-solid phase transition occurs during equilibration, the measured equilibrium solubility will be that of the new solid phase of the solute. Methods of circumventing this problem have been proposed and evaluated [26]. 

The solubility of hydrated copper sulfate (CuS04 5H20) provides a simple example of how the solubility of a compound can be manipulated. CuS04 5H20 itself is very soluble in water, exhibiting an equilibrium solubility of 207 mg/ml at 20°C [44]. This high solubility is due to the dissociation of copper sulfate into its component ions upon dissolution into an aqueous solution ... 

In some instances, distinct polymorphic forms can be isolated that do not interconvert when suspended in a solvent system, but that also do not exhibit differences in intrinsic dissolution rates. One such example is enalapril maleate, which exists in two bioequivalent polymorphic forms of equal dissolution rate [139], and therefore of equal free energy. When solution calorimetry was used to study the system, it was found that the enthalpy difference between the two forms was very small. The difference in heats of solution of the two polymorphic forms obtained in methanol was found to be 0.51 kcal/mol, while the analogous difference obtained in acetone was 0.69 kcal/mol. These results obtained in two different solvent systems are probably equal to within experimental error. It may be concluded that the small difference in lattice enthalpies (AH) between the two forms is compensated by an almost equal and opposite small difference in the entropy term (-T AS), so that the difference in free energy (AG) is not sufficient to lead to observable differences in either dissolution rate or equilibrium solubility. The bioequivalence of the two polymorphs of enalapril maleate is therefore easily explained thermodynamically. 

Figure 26 shows the ternary phase diagrams (solubility isotherms) for three types of solid solution. The solubilities of the pure enantiomers are equal to SA, and the solid-liquid equilibria are represented by the curves ArA. The point r represents the equilibrium for the pseudoracemate, R, whose solubility is equal to 2Sd. In Fig. 26a the pseudoracemate has the same solubility as the enantiomers, that is, 2Sd = SA, and the solubility curve AA is a straight line parallel to the base of the triangle. In Figs. 26b and c, the solid solutions including the pseudoracemate are, respectively, more and less soluble than the enantiomers. 

The composition of the equilibrium mixture shows that Br has been enriched significantly in the solid phase in comparison to the liquid phase (D > 1). If one considered the concentrations of aqueous [Br"] and [Ag+], one would infer, by neglecting to consider the presence of a solid solution phase, that the solution is undersaturated with respect to AgBr ([Ag+] [Br ]/KsoA Br = 0.1). Because the aqueous solution is in equilibrium with a solid solution, however, the aqueous solution is saturated with Br. Although the solubility of the salt that represents the major component of the solid phase is only slightly affected by the formation of solid solutions, the solubility of the minor component is appreciably reduced. The observed occurrence of certain metal ions in sediments formed from solutions that appear to be formally (in the absence of any consideration of solid solution formation) unsaturated with respect to the impurity can, in many cases, be explained by solid solution formation. 

Ion-Activity Products. As in the determination of the amount sorbed through Equation 2, the characterization of surface precipitates often utilizes measurements made solely on the aqueous solution phase. Solubility studies limited in this way run a risk of being ambiguous as to mechanism because of the lack of direct information about the solid phase (10). In respect to the aqueous solution phase, ambiguity can be minimized if equilibrium is approached both from supersaturation and from undersaturation if the equilibration time is varied... 

In this experiment, we used five different flowrates to assure ourselves that the column did approach equilibrium 20 cc/min was satisfactory, 25 cc/min was already questionable. The solute was soluble in both phases as evidenced by peak separation on the chromatogram. The stationary liquid was not soluble in the carrier gas as evidenced by no long time peak on the chromatogram. The carrier gas was slightly soluble in the stationary liquid. We checked this by injecting CO2 into the carrier and we did obtain a peak-however, analysis showed that... 

A review of the commonly used experimental methods for solubility determinations is presented in Table 1. Briefly, batch equilibration is the conventional method of preparing saturated solutions for solubility determinations, where an excess amount of solute chemical is added to water and equilibrium is achieved... 

A drug s solubility is usually determined by the equilibrium solubility method, by which an excess of fhe drug is placed in a solvent and shaken at a constant temperature over a prolonged period of time until equilibrium is obtained. Chemical analysis of the drug content in solution is performed to determine degree of solubility. 

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