Solubility liquid/solid equilibria

The behavior of the solubility curves in the same temperature region but at pressures above the critical was determined by Petit and Weil at Grenoble. Their results, obtained by the circulation method, show the t3rpical horizontal section above the 27 K temperature (see Fig. 4). This peculiar behavior was also noticed by us while making some isobaric measurements on the solid-gas equilibrium above the critical temperature of hydrogen when the flow method was used. From an inspection of Fig. 2, it follows that there is a possibility of the retrograde increase of the concentration of the fluid in the supercritical region. Such an effect, however, cannot easily be detected by adynamic method as applied to our measurements on liquid-solid equilibrium. Consequently, we used the static method in our determinations. 

Fig. 2.5 Phase diagram of the citric acid-water system. - liquid solid equilibrium (the solubility curve) - equilibrium melting curve - homogenous ice freezing temperature curve - the...

The principles of equilibrium have wide applicability and great utility. For example, they aid us in understanding and controlling the solubility of solids and gases in liquids. We shall consider, first, the solubility of a molecular solid in a liq-... 

In the same way we can investigate the equilibrium between a sparingly soluble liquid or solid substance and its solution (cf. 132). The change of molecular state which sometimes... 

The equilibrium pressure when (solid + vapor) equilibrium occurs is known as the sublimation pressure, (The sublimation temperature is the temperature at which the vapor pressure of the solid equals the pressure of the atmosphere.) A norma) sublimation temperature is the temperature at which the sublimation pressure equals one atmosphere (0.101325 MPa). Two solid phases can be in equilibrium at a transition temperature (solid + solid) equilibrium, and (liquid + liquid) equilibrium occurs when two liquids are mixed that are not miscible and separate into two phases. Again, "normal" refers to the condition of one atmosphere (0.101325 MPa) pressure. Thus, the normal transition temperature is the transition temperature when the pressure is one atmosphere (0.101325 MPa) and at the normal (liquid + liquid) solubility condition, the composition of the liquid phases are those that are in equilibrium at an external pressure of one atmosphere (0.101325 MPa). 

The equilibrium adsorption characteristics of gas or vapor on a solid resemble in many ways the equilibrium solubility of a gas in a liquid. Adsorption equilibrium data are usually portrayed by isotherms lines of constant temperature on a plot of adsorbate equilibrium partial pressure versus adsorbent loading in mass of adsorbate per mass of adsorbent. Isotherms take many shapes, including concave upward and downward, and S-curves. Equilibrium data for a given adsorbate-adsorbent system cannot generally be extrapolated to other systems with any degree of accuracy. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

As a technique for selective surface illumination at liquid/solid interfaces, TIRF was first introduced by Hirschfeld(1) in 1965. Other important early applications were pioneered by Harrick and Loeb(2) in 1973 for detecting fluorescence from a surface coated with dansyl-labeled bovine serum allbumin, by Kronick and Little(3) in 1975 for measuring the equilibrium constant between soluble fluorescent-labeled antibodies and surface-immobilized antigens, and by Watkins and Robertson(4) in 1977 for measuring kinetics of protein adsorption following a concentration jump. Previous rcvicws(5 7) contain additional references to some important early work. Section 7.5 presents a literature review of recent work. 

Gas-liquid relationships, in the geochemical sense, should be considered liquid-solid-gas interactions in the subsurface. The subsurface gas phase is composed of a mixture of gases with various properties, usually found in the free pore spaces of the solid phase. Processes involved in the gas-liquid and gas-solid interface interactions are controlled by factors such as vapor pressure-volatilization, adsorption, solubility, pressure, and temperature. The solubility of a pure gas in a closed system containing water reaches an equilibrium concentration at a constant pressure and temperature. A gas-liquid equilibrium may be described by a partition coefficient, relative volatilization and Henry s law. 

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... 

Solubilities of meso-tetraphenylporphyrin (normal melting temperature 444°C) in pentane and in toluene have been measured at elevated temperatures and pressures. Three-phase, solid-liquid-gas equilibrium temperatures and pressures were also measured for these two binary mixtures at conditions near the critical point of the supercritical-fluid solvent. The solubility of the porphyrin in supercritical toluene is three orders of magnitude greater than that in supercritical pentane or in conventional liquid solvents at ambient temperatures and pressures. An analysis of the phase diagram for toluene-porphyrin mixtures shows that supercritical toluene is the preferred solvent for this porphyrin because (1) high solubilities are obtained at moderate pressures, and (2) the porphyrin can be easily recovered from solution by small reductions in pressure. 

However, for mixtures of TPP and toluene, a third (liquid) phase forms in the presence of the gas and the solid, at pressures well below the critical pressure of toluene. At higher pressures, gas-liquid and solid-liquid equilibria were observed, rather than gas-solid equilibrium. Thus, phase compositions for gas-liquid equilibrium were measured for this binary mixture to give TPP solubilities in each of the fluid phases. Pressures and temperatures for three-phase, solid-liquid-gas equilibrium were also measured for both binary mixtures. 

The following experimental techniques were used to measure the pressures and temperatures for solid-liquid-gas equilibrium, phase compositions (bubble and dew points) for gas-liquid equilibrium, and solid solubilities in supercritical pentane. Experimental procedures and the apparatus are described in detail elsewhere (13). 

Pressure does not dramatically alter the solubility of solids or liquids, but kinetic molecular theory predicts that increasing the partial pressure of a gas will increase the solubility of the gas in a liquid. If a substance is distributed between gas and solution phases and pressure is exerted, more gas molecules will impact the gas/liquid interface per second, so more will dissolve until a new equilibrium is reached at a higher solubility. Henry s law describes this relationship as a direct proportionality ... 

Temperature-composition phase diagrams for mixtures of solids and the liquids in equilibrium with them are very important in metallurgy and electronics. Figure 4.8 shows a simplified phase diagram for two phases that have a limited solubility for each other. 

Several authors [3-9] studied the solubility of polymers in supercritical fluids due to research on fractionation of polymers. For solubility of SCF in polymers only limited number of experimental data are available till now [e.g. 4,5,10-12], Few data (for PEG S with molar mass up to 1000 g/mol) are available on the vapour-liquid phase equilibrium PEG -CO2 [13]. No data can be found on phase equilibrium solid-liquid for the binary PEG S -CO2. Experimental equipment and procedure for determination of phase equilibrium (vapour -liquid and solid -liquid) in the binary system PEG s -C02 are presented in [14]. It was found that the solubility of C02 in PEG is practically independent from the molecular mass of PEG and is influenced only by pressure and temperature of the system. 

In liquid/solid systems with a high mutual solubility (as for many metallic systems), calculations show that the size of the deformed area close to the triple line can attain dimensions of about a micron in a minute or so. However, in this case, the equilibrium configuration at the triple line can be masked by the dissolution of the solid in the liquid (Warren et al. 1998) as discussed in Section 2.2.1. 

The solubility of a solid (the solute) in a liquid (the solvent) is the maximum amount of that solute that can dissolve in a specified amount of the liquid at equilibrium. A solution that contains all the dissolved solute it can hold is saturated with that solute. If additional solute is added, it will not dissolve unless the temperature is changed in a way that increases the solubility. 

The application of UNIFAC to the solid-liquid equilibrium of sohds, such as naphthalene and anthracene, in nonaqueous mixed solvents provided quite accurate results [11]. Unfortunately, the accuracy of UNIFAC regarding the solubility of solids in aqueous solutions is low [7-9]. Large deviations from the experimental activity coefficients at infinite dilution and the experimental octanol/water partition coefficients have been reported [8,9] when the classical old version of UNIFAC interaction parameters [4] was used. To improve the prediction of the activity coefficients at infinite dilution and of the octanol/water partition coefficients of environmentally significant substances, special ad hoc sets of parameters were introduced [7-9]. The reason is that the UNIFAC parameters were determined mostly using the equihbrium properties of mixtures composed of low molecular weight molecules. Also, the UNIFAC method cannot be applied to the phase equilibrium in systems containing... 

The solubility of solid substances in pure and mixed solvents can be described by the usual solid-liquid equilibrium conditions (Acree, 1984 Prausnitz et al.,... 

When all hydrate cavities are filled, the three crystal types (I, n, and H) have remarkably high and similar concentrations of components 85 mol % water and 15 mol % guest(s). Hydrate formation is most probable at the interface of the bulk guest and aqueous phases because the hydrate component concentrations greatly exceed the mutual fluid solubilities. The solid hydrate film at the interface acts as a barrier to further contact of the bulk fluid phases, and fluid interface renewal is required for continued, rapid clathrate formation. Three phase interfacial hydrate formation occurs with equilibrium of gas, liquid, and hydrate phases in artificial situations such as laboratories or in man-made processes. 

The basis of LPE is the control of the liquid-solid phase equilibrium based on the solubility of silicon in a metallic solvent (In, Sn, Al, Ga,. ..)... 

The equilibrium solubility of a substance is defined as the concentration of solute in its saturated solution, where the saturated solution exists in a state of equilibrium with pure solid solute. As solutes and solvents can be gaseous, liquid, or solid, there are nine possibilities for solutions, although liquid-gas, liquid-liquid, and liquid-solid are of particular interest for pharmaceutical applications. Among these, the most frequently encountered solubility behavior involves solid solutes dissolved in liquid solvent, so systems of this type will constitute the examples of the following discussions. 

For binary systems. Fig. 1.6-1, shows these two extremes. In Fig. 1.6-la, there are two possible solid phases one of these is pure solid 1 and the other is pure solid 2. The curve on the left gives the solubility of solid 2 in liquid 1 the curve on the right gives the solubility of solid I in liquid 2. These solubility curves intersect at the eutectic point. The curve on the left is the coexistence line for solid 2 and the liquid mixture the curve on the right gives the coexistence line for solid I aed the liquid mixture. Al the eutectic point, all three phases are at equilibrium. For this type of system, there is no difference between freezing temperature and melting temperature. 

The study of vapor-liquid equilibria (Sec 10.1) of the solubility of gases in liquids (Sec. 11.1), and of the solubility of solids in liquids (Sec. 12.1), all involve nonsimple, mixtures. To see why this occurs, consider the criterion for vapor-liquid equilibrium ... 

In this chapter we consider several other types of phase equilibria, mostly involving a fluid and a solid. This includes the solubility of a solid in a liquid, gas, and a supercritical fluid the partitioning of a solid (or a liquid) between two partially soluble liquids the freezing point of a solid from a liquid mixture and the behavior of solid mixtures. Also considered is the environmental problem of how a chemical partitions between different parts of the environment. Although these areas of application appear to be quite different, they are connected by the same starting point as for all phase equilibrium calculations, which is the equality of fugacities of each species in each phase ... 

---