Solubility and Phase Diagrams

Studies on double salts have been carried out mostly on the basis of phase diagrams of the different components and crystallographic structures. A number of studies have been carried out on the double salts of the type MIX -MIIX2-nH20 with various combinations of M1, Mn, and X. Solubilities and phase diagrams of the salts have been studied under various conditions, and a wide variety of X-ray crystallographic investigations have been reported in the literature. 

These qualitative assumptions are not contradictory to the results of solid-state solubility and phase diagram studies. According to these findings, the rare earth oxides are completely or largely miscible with UO2, whereas the alkaline earth oxides and zirconium oxide show a limited solubility and M0O2 is only soluble to a neglibly small extent (Kleykamp, 1985). However, results from studies performed on binary systems are not directly applicable to multi-component fuel - fission product oxide systems. In general, the maximum solubility of the individual fission product species in the fuel matrix will be reduced in the presence of additional constituents. 

Formation of adducts between LiCl and c-caprolactam or pyrro-lidone having 1 4 composition was observed by solubility and phase diagram studies. Specific interactions between LiCl and the lactams were also evidenced in the amorphous state, and in the absence of water, by infrared spectroscopy. 

The objective of this section is much less ambitious and can be formulated as follows If the free-energy function for all phases in a given system were known as a function of temperature and composition, how could one construct the corresponding phase diagram In other words, what is the relationship between free energies and phase diagrams Two examples are considered below polymorphic transformation in unary systems and complete solid solubility. 

When two or more solutes are dissolved in the solvent, it is sometimes possible to separate these into pure components or separate one and leave the other in solution. Whether or not this can be done depends upon the solubility and phase relations of the system under consideration. How to plot and use this data is explained by Fitch (1970), and Campbell and Smith (1951). It is helpful if one of the components has a much more rapid change in solubility with temperature than does the other. A typical example, which is practiced on a large scale, is the separation of KCI and NaCl from water solution. A simplified phase diagram for this system is shown in Figure 5.1. In this case, the solubility of NaCl is plotted on the Y-axis as parts per 100 parts of solvent, and the solubility of the KCI is plotted on the X-axis in the same units. The isotherms show a marked decrease in solubility for each component as the other component is increased. This example is typical for many inorganic salts. 

The heat effects accompanying a crystallization operation may be determined by making heat balances over the system, although many calculations may be necessary, involving knowledge of specific heat capacities, heats of crystallization, heats of dilution, heats of vaporization, and so on. Much of the calculation burden can be eased, however, by the use of a graphical technique in which enthalpy data, solubilities and phase equilibria are represented on an enthalpy-composition H x) diagram, sometimes known as a Merkel chart. 

A mixture of d and l enantiomers in the presence of a solvent S constitutes a ternary system in whieh the equilibria are best represented on a triangular diagram (see section 4.6.3). The effects of temperature on solubility and phase change can also be ineluded. Figure 7.9a shows the transition of a racemic compound R, stable at the lower temperatures t and to a conglomerate at the higher temperature t. ... 

The second (and third) models for polyelectrolyte/surfactant interaction are based on the solubility and phase characteristics of the mixed systems. The general form of the solubility diagram of a polyelectrolyte/oppositely charged surfactant system, as illustrated by the Polymer JR/TEALS combination, has been referred to (57). It showed an intermediate zone of precipitation, but clarity for high (and low) concentrations of the surfactant. The line representing systems of maximum insolubility in the log polymer/log surfactant concentration plot had a 45° slope indicating constant composition of the insoluble complexes. 

While most of the work described in this monograph emphasizes the two-phased nature of IPNs and related materials, it is interesting to explore more deeply the characteristics of phase separation in polymer/polymer systems. Of key importance, McMaste/ " showed that most polymer/polymer phase diagrams are expected to exhibit a lower critical solution temperature (LOST). This means that as the temperature is raised the polymer pair becomes less mutually soluble, and phase separates. This effect is not immediately predicted by equations (2.1) and (2.2), which suggest the usual phenomenon of an upper critical solution temperature (UCST). 

The relationship between solubility and phase behavior may be illustrated using the diagram of the binary sodium chloride-water system (Fig. 2). To read this diagram, remember that at any particular point, the magnitude of the x coordinate equals gross composition (expressed as percent sodium chloride), whereas that of the y coordinate equals temperature. The phase boundaries within the diagram, which in this case have been firmly established [25], define and separate regions within which qualitatively similar phase behavior is found. To describe phase behavior, one states the number of phases present. 

The Kraft point (T ) is the temperature at which the erne of a surfactant equals the solubility. This is an important point in a temperature-solubility phase diagram. Below the surfactant cannot fonn micelles. Above the solubility increases with increasing temperature due to micelle fonnation. has been shown to follow linear empirical relationships for ionic and nonionic surfactants. One found [25] to apply for various ionic surfactants is ... 

Thus one must rely on macroscopic theories and empirical adjustments for the determination of potentials of mean force. Such empirical adjustments use free energy data as solubilities, partition coefficients, virial coefficients, phase diagrams, etc., while the frictional terms are derived from diffusion coefficients and macroscopic theories for hydrodynamic interactions. In this whole field of enquiry progress is slow and much work (and thought ) will be needed in the future. 

Experimental results describing limited mutual solubility are usually presented as phase diagrams in which the compositions of the phases in equilibrium with each other at a given temperature are mapped for various temperatures. As noted above, the chemical potentials are the same in the equilibrium phases, so Eqs. (8.53) and (8.54) offer a method for calculating such... 

Silicon is soluble in aluminum in the solid state to a maximum of 1.62 wt % at 577°C (2). It is soluble in silver, gold, and 2inc at temperatures above their melting points. Phase diagrams of systems containing silicides are available (2,3). 

Potassium Heptafluorotantalate. Potassium heptafluoiotantalate [16924-00-8], K TaF, ciystallizes in colodess, rhombic needles. It hydroly2es in Foiling water containing no excess of hydrofluoric acid. The solubility of potassium heptafluorotantalate in hydrofluoric acid decreases from 60 g/100 mL at 100°C to 0.5 g/100 mL at room temperature. The different solubility characteristics of K TaF and K NbOF are the fundamental basis of the Matignac process (16). A phase diagram exists for the system K TaF —NaCl—NaF—KCl (68). Potassium heptafluorotantalate has an LD q value of 2500 mg/kg. The recommended TWA maximum work lace exposure for K TaF in air is 2.5 mg /m (fluoride base) (69). 

Carbon disulfide is completely miscible with many hydrocarbons, alcohols, and chlorinated hydrocarbons (9,13). Phosphoms (14) and sulfur are very soluble in carbon disulfide. Sulfur reaches a maximum solubiUty of 63% S at the 60°C atmospheric boiling point of the solution (15). SolubiUty data for carbon disulfide in Hquid sulfur at a CS2 partial pressure of 101 kPa (1 atm) and a phase diagram for the sulfur—carbon disulfide system have been published (16). Vapor—Hquid equiHbrium and freezing point data ate available for several binary mixtures containing carbon disulfide (9). 

Solubility. Sohd—Hquid equihbrium, or the solubiHty of a chemical compound in a solvent, refers to the amount of solute that can be dissolved at constant temperature, pressure, and system composition in other words, the maximum concentration of the solute in the solvent at static conditions. In a system consisting of a solute and a solvent, specifying system temperature and pressure fixes ah. other intensive variables. In particular, the composition of each of the two phases is fixed, and solubiHty diagrams of the type shown for a hypothetical mixture of R and S in Figure 2 can be constmcted. Such a system is said to form an eutectic, ie, there is a condition at which both R and S crystallize into a soHd phase at a fixed ratio that is identical to their ratio in solution. Consequently, there is no change in the composition of residual Hquor as a result of crystallization. 

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