Solubility pure component phase diagrams

Eq. (1.41) gives us two important pieces of information. The first is that the ideal solubility of the solute does not depend on the solvent chosen the ideal solubility depends only on the solute properties. The second is that it shows the differences in the pure component phase diagrams that result from structural differences in materials will alter the triple point and hence the ideal solubility. 

Figure 2.1. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the solid and in the liquid states (L liquid field, S solid field). The melting behaviour of the Mo-V, Cs-Rb and Ca-Sr alloys is presented. Notice the different ranges of temperature involved. The melting points of the pure metal components are shown on the corresponding vertical axes. The Cs-Rb is an example of a system showing a minimum in the melting temperature. In the Sr-Ca system complete mutual solid solubility is shown in both the allotropic forms a and (3 of the two metals.

In Fig. 2.19, on the contrary, we observe that intermediate solid phases with a variable composition are formed (non-stoichiometric phases). In the diagrams shown here we see therefore examples both of terminal and intermediate phases. (For instance, the Hf-Ru diagram shows the terminal solid solutions of Ru in a and (3Hf and of Hf in Ru and the intermediate compound containing about 50 at.% Ru). These phases are characterized by homogeneity ranges (solid solubility ranges), which, in the case of the terminal phases, include the pure components and which, generally, have a variable temperature-dependent extension. 

This finding is illustrated on a free energy vs. composition diagram in Fig. C.6. The free-energy curve for the (3 phase is a vertical line at AT = 1, because the (3 phase has been assumed to be pure component B. Note especially that the change in fj>2 with P (or r) causes a change in the equilibrium solubility of component B in a. 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

It is essential to realize that any thermodynamic evaluation of this solubility "maximum" with standard reference conditions in the form of the three pure components in liquid form is a futile exercise. The complete phase diagram. Fig. 2, shows the "maximum" of the solubility area to mark only a change in the structure of the phase in equilibrium with the solubility region. The maximum of the solubility is a reflection of the fact that the water as equilibrium body is replaced by a lamellar liquid crystalline phase. Since this phase.transition obviously is more. related to packing constraints — than enthalpy of formation — a view of the different phases as one continuous region such as in the short chain compounds water/ethanol/ethyl acetate. Fig. 3, is realistic. The three phases in the complete diagram. Fig. 2, may be perceived as a continuous solubility area with different packing conditions in different parts (Fig. 4). 

In many cases, there is partial solid solubility between the pure components of a binary system, as in the Pb-Sn phase diagram of Figure 11.5, for example. The solubility limits of one component in the other are given by solvus lines. Note that the solid solubility limits are not reciprocal. Lead will dissolve up to 18.3 percent Sn, but Sn will dissolve only up to 2.2 percent Pb. In Figure 11.5, there are two two-phase fields. Each is bounded by a distinct solvus and liquidus line, and the common sofidus line. One two-phase field consists of a mixmre of eutectic crystals and crystals containing Sn solute dissolved in Pb solvent. The other two-phase field consists of a mixture of eutectic crystals and crystals containing Pb solute dissolved in Sn solvent. 

The temperature-composition phase diagram constructed from thermal arrests observed in the MoFe-UFa system is characteristic of a binary system forming solid solutions, a minimum-melting mixture (22 mole % UFe at 13.7°C.), and a solid-miscibility gap. The maximum solid solubility of MoFq in the UFe lattice is about 30 mole % MoFe, whereas the maximum solid solubility of UFe in the MoFe lattice is 12 to 18 mole % UFe- The temperature of the solid-state transformation of MoFe increases from ——lO C. in pure MoFe to 5°C. in mixtures with UFe, indicating that the solid solubility of UFe is greater in the low temperature form of MoFe than in the high temperature form of MoFe- This solid-solubility relationship is consistent with the crystal structures of the pure components The low temperature form of MoFe has an orthorhombic structure similar to that of UFe. 

This paper describes the results of an experimental study of condensed phase equilibria in the system MoFe-UFo carried out by thermal analysis and x-ray diffraction analysis. A temperature-composition phase diagram is constructed from the temperatures of observed thermal arrests in MoFe-UFe mixtures, and the basis for the formation of this particular type of diagram is traced to the physical properties of the pure components. The solid-solubility relations indicated by the diagram are traced to the crystal structures of the pure solids. 

In a miscible system of two liquids it is not expected that they will remain as a single phase over all ranges of composition and temperature. Instead there will be cloud points where two phases occur and the composition of the separated material will be close to that of the original pure components. Even in so-called two-phase systems there will be a partitioning of one component in the other corresponding to a small solubility at the particular temperature. An example of a phase diagram that may occur for two liquids, a polymer solution or a polymer blend is shown in Figure 1.28. 

If the third component is a water-insoluble alcohol (five carbons or more), amine, carboxylic acid, or amide, the phase topography is profoundly modified. The phase diagram shown in Figure 3.8b [7] shows in addition to LI and HI a very large lamellar phase, a narrow reverse hexagonal phase H2, and, even more important, a sector-like area of reverse micelles L2. This means that the solubility of n-decanol in a sodium octanoate-water mixture containing between 25 and 62% amphiphile is far more important (30 to 36%) than pure water (4%) and pure sodium octanoate (almost zero). This phase is essential to obtain water-in-oil (w/o) microemulsions. 

In figure 3.29b the pressure of the system has been increased to a point slightly below the critical pressure of the SCF. At this pressure the SCF still remains virtually insoluble in component A but its solubility in B has increased markedly, i.e., the tie line for the SCF-B mixture has gotten smaller to reflect the increased solubility of component B in the SCF-rich phase and of the SCF in the B-rich phase. The binodal curve in the ternary diagram now bends further toward the SCF apex. The vapor phase composition remains essentially pure SCF since, at this temperature, we are assuming that the vapor pressures of components A and B are extremely low. 

Eq. (1.41) gives the ideal solubility. Figure 1.13, an example phase diagram for a pure component, illustrates several points. First, we are interested in temperatures below the triple point since we are interested in conditions where the solute is a solid. Second, the subcooled liquid pressure is obtained by extrapolating the liquid-vapor line to the correct temperature. 

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. 

Phase diagrams. Crystallization from a solution is a selective process. It can be used to purify a desired product from imwanted impurities and also to separate the components of fairly comphcated mixtures. A very careful control over temperature and composition of the solution is needed to obtain pure products, and an exact knowledge of solubility relations is required. Such knowledge is summarized in phase diagrams, which are as useful and necessary in selective crystallizations as are road maps to the motorist. For a complete discussion of phase diagrams the reader is referred to textbooks of physical chemistry or... 

The carbon dioxide/water biphasic system is an example of binary mixtures consisting of components with widely separated critical temperatures. The critical properties of the pure compounds are given in Table 1. The typical phase diagram for such mixtures can be complex, including the possibility for areas of three-phase coexistence (LEV). For applications in biphasic catalysis, however, the key parameters to be discussed are solubility and cross-contamination, mass transfer, and chemical changes. 

When the mutual solubility of the liquids is so low that they maybe regarded as completely immiscible, certain simplifications are possible so that we may construct the phase diagrams without the need for activity coefficients. These simplifications arise from the fact that the two-liquid phases each practically consist of the pure components. 

To predict the solid solubihty, in addition to model-based property models, databases and numerical solvers are necessary. To better illustrate each step of the solid solubility calculation, the necessary workflow and dataflow are highhghted in Figure 10.1, starting with the necessary pure component properties and ending with the phase diagram generation. It is important to note that when the experimental values of the... 

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