Solid-liquid equilibrium . phase equilibria

The data for the phase equilibrium solid-liquid for the binary system cocoa butter-CC>2 and for the equilibrium solubility data of CO2 in the liquid phase of cocoa butter have been presented [70],... 

Weidner E, Wiesmet V, Knez Z et al (1997) Phase equilibrium (solid-liquid-gas) in polyethylene glycol-carbon dioxide systems. J Supercrit Fluids 10(3) 139-147... 

WEI Weidner, E., Wiesmet, V., Knez, Z., and Skerget, M., Phase equilibrium (solid-liquid-gas) in polyethyleneglycol-caibon dioxide systems, J. Supercrit. Fluids, 10, 139, 1997. 

Equifibrium involving a sofid phase, including solid-liquid equilibrium (SLE), solid-solid equilibrium (SSE), and solid-solid-liquid equilibrium (SSLE), can take two forms (1) pure solids, which are immiscible with other species, and (2) solid solutions, which, Hke Hquid solutions, contain more than one species. If the solid phase exists as a pure species, the condition for ph ase equilibrium with a Hquid becomes ... 

The solid is the more dense phase (Figure 9.7a). The solid-liquid equilibrium line is inclined to the right, shifting away from the y-axis as it rises. At higher pressures, the solid becomes stable at temperatures above the normal melting point In other words, the melting point is raised by an increase in pressure. This behavior is shown by most substances. 

Under certain pressure and temperature conditions, a system can contain two or more phases in equilibrium. An example is the temperature and pressure where solid and liquid are in equilibrium. We refer to this condition as (solid + liquid) equilibrium, and the temperature as the melting temperature. This temperature changes with pressure and with composition. The melting temperature when the... 

Effect of Pressure on Solid + Liquid Equilibrium Equation (6.84) is the starting point for deriving an equation that gives the effect of pressure on (solid + liquid) phase equilibria for an ideal mixture in equilibrium with a pure... 

The melting point of carbon dioxide increases with increasing pressure, since the solid-liquid equilibrium line on its phase diagram slopes up and to the right. If the pressure on a sample of liquid carbon dioxide is increased at constant temperature, causing the molecules to get closer together, the liquid will solidify. This indicates that solid carbon dioxide has a higher density than the liquid phase. This is true for most substances. The notable exception is water. 

Fig. 3.2. A stylized phase diagram for a simple pure substance. The dashed line represents 1 atm pressure and the intersection with the solid-liquid equilibrium line represents the normal boiling point and the intersection with the liquid-vapor equilibrium line represents the normal boiling point.

The structural constraints used in the first case study namely, Eqn s 27,28 and 29 are used again. The melting point, boiling point and flash point, are used as constraints for both solvent and anti-solvent. Since the solvent needs to have high solubility for solute and the anti-solvent needs to have low solubility for the solute limits of 17 <8 < 19 and 5 > 30 (Eqn s. 33 and 37) are placed on the solubility parameters of solvent and anti-solvents respectively. Eqn.38 gives the necessary condition for phase stability (Bernard et al., 1967), which needs to be satisfied for the solvent-anti solvent pairs to be miscible with each other. Eqn. 39 gives the solid-liquid equilibrium constraint. 

Equation 27 is similar to the solid-liquid equilibrium relation used for non-electrolytes. As in the case of the vapor-liquid equilibrium relation for HC1, the solid-liquid equilibrium expression for NaCl is simple since the electrolyte is treated thermodynamically the same in both phases. 

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

A confirmation of this conclusion also is provided by an examination of the solid-liquid equilibrium in the neighborhood of 0 K. As shown in Equation (8.9), a two-phase equilibrium obeys the Clapeyron equation ... 

In Chapter 13 we discussed briefly the solid-liquid equilibrium diagram of a feldspar. Feldspar is an ideal, solid solution of albite (NaAlSiaOg) and anorthite (CaAlSi20g) in the solid state as well as an ideal, liquid solution of the same components in the molten state. The relationships that we have developed in this chapter permit us to interpret the feldspar phase diagram (Figure 13.4) in a quantitative way. 

The procedure used to define an equilibrium model is to (1) define all the variables and (2) define independent equilibria as a function of phase equilibria. The variables are defined as the chemical parameters typically measured in water chemistry. For the major constituents and some of the more important minor constituents, these are calcium, magnesium, sodium, potassium, silica, sulfate, chloride, and phosphate concentrations as well as alkalinity (usually carbonate alkalinity) and pH. To this list we would also add temperature and pressure. The phase equilibria are defined by compiling well-known equilibria between gas-liquid phases and solid-liquid equilibria for the solids commonly found forming in nature in sedimentary rocks. Within this framework, one can construct different equilibrium models depending upon the mineral chosen actual data concerning the formation of specific minerals therefore must be ascertained to specify a particular model as valid. 

For solid-liquid equilibrium in a quaternary system, the Gibbs phase rule allows four degrees of freedom. If T, P, xc, and xD (in which x is the mole fraction of component i in liquid solution) are specified, then xA, x, t/, and xAC (in which x is the mole fraction of component ij in solid solution) are determined, and the system is invariant. These variables are defined by the following equations ... 

The case of binary solid-liquid equilibrium permits one to focus on liquid-phase nonidealities because the activity coefficient of solid component ij, Yjj, equals unity. Aselage et al. (148) investigated the liquid-solution behavior in the well-characterized Ga-Sb and In-Sb systems. The availability of a thermodynamically consistent data base (measurements of liquidus, component activity, and enthalpy of mixing) provided the opportunity to examine a variety of solution models. Little difference was found among seven models in their ability to fit the combined data base, although asymmetric models are expected to perform better in some systems. 

PI4.2 Given the following (solid + liquid) equilibrium temperatures for phase changes in the JC1CFCI3 + X2HCON(CH3)2 system 7... 

An interesting case of solid-liquid equilibrium is one in which a solvent dissociates at least to some extent in the liquid phase and a solute is one of the species formed by the dissociation. We show in Section 10.20 that the experimental temperature-composition curve has a maximum at the composition of the pure solvent. We consider here that the solid phase is the pure, undissociated component, designated by the subscript 1 that this component dissociates in the liquid phase according to the reaction... 

The Earth s core is thought to be mainly iron, and seismic data indicate that the inner core is solid and the outer core is liquid. The pressure at the center of the Earth is 3.6 x 1011 Pa, and at this pressure, iron melts at 6350 K. From this information, what can you infer about the solid-liquid equilibrium boundary in the iron high-pressure phase diagram (Pressure and temperature both increase toward the Earth s center.)... 

Equation (25.7) now gives an expression for the rate of change of pressure with temperature (= dP/dT ) which corresponds to the gradient of the line representing the solid-liquid equilibrium in the phase diagram (gradient of AD Figure 25.1). This quantitative equation (25.7) now enables us to rationalise that since ... 

This is one form of the Clapeymn Equation which gives the slope of the P, T line (AD) for the solid-liquid equilibrium in the phase diagram (Figure 25.1, Frame 25). 

Of interest in crystallization calculations is solid-liquid equilibrium. When the solid phase is a pure component, the following thermodynamic relationship holds ... 

F liquid + vapor G liquid + vapor (critical point) H vapor the first dashed line (at the lower temperature) is the normal melting point, and the second dashed line is the normal boiling point. The solid phase is denser because of the positive slope of the solid/liquid equilibrium line. 

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