Phase equilibria diagrams

Figure 11.1 Phase diagram, phase equilibriums, and concentration profile in a binary multiphase system a and fS are solid solutions 1, 2, 3 are stable and 4 is a metastable intermediate phase.

Ternary-phase equilibrium data can be tabulated as in Table 15-1 and then worked into an electronic spreadsheet as in Table 15-2 to be presented as a right-triangular diagram as shown in Fig. 15-7. The weight-fraction solute is on the horizontal axis and the weight-fraciion extraciion-solvent is on the veriical axis. The tie-lines connect the points that are in equilibrium. For low-solute concentrations the horizontal scale can be expanded. The water-acetic acid-methylisobutylketone ternary is a Type I system where only one of the binary pairs, water-MIBK, is immiscible. In a Type II system two of the binary pairs are immiscible, i.e. the solute is not totally miscible in one of the liquids. 

DEF. An equilibrium-constitution diagram or equilibrium diagram for short (or, shorter still, phase diagram), is a diagram with T and Xg (or Wg) as axes. It shows the results of experiments which measure the equilibrium constitution at each T and Xg (or Wg). 

Figure 45. Futjural-ethylene glycol-water phase equilibrium diagram.

As an acidic oxide, SiOj is resistant to attack by other acidic oxides, but has a tendency towards fluxing by basic oxides. An indication of the likelihood of reaction can be obtained by reference to the appropriate binary phase equilibrium diagram. The lowest temperature for liquid formation in silica-oxide binary systems is shown below ... 

An example for a partially known ternary phase diagram is the sodium octane 1 -sulfonate/ 1-decanol/water system [61]. Figure 34 shows the isotropic areas L, and L2 for the water-rich surfactant phase with solubilized alcohol and for the solvent-rich surfactant phase with solubilized water, respectively. Furthermore, the lamellar neat phase D and the anisotropic hexagonal middle phase E are indicated (for systematics, cf. Ref. 62). For the quaternary sodium octane 1-sulfonate (A)/l-butanol (B)/n-tetradecane (0)/water (W) system, the tricritical point which characterizes the transition of three coexisting phases into one liquid phase is at 40.1°C A, 0.042 (mass parts) B, 0.958 (A + B = 56 wt %) O, 0.54 W, 0.46 [63]. For both the binary phase equilibrium dodecane... 

Figure 2, Polymer/solvent phase equilibrium diagram...

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

It is known that in five of the six principal types of binary fluid phase equilibrium diagrams, data other than VLE may also be available for a particular binary (van Konynenburg and Scott, 1980). Thus, the entire database may also contain VL2E, VL E, VL]L2E, and L,L2E data. In this section, a systematic approach to utilize the entire phase equilibrium database is presented. The material is based on the work of Englezos et al. (1990b 1998)... 

Thus, by knowing aAB from vapor-liquid equilibrium and by specifying xA, A can be calculated. Figure 4.3a also shows a typical vapor-liquid equilibrium pair, where the mole fraction of benzene in the liquid phase is 0.4 and that in the vapor phase is 0.62. A diagonal line across the x-y diagram represents equal vapor and liquid compositions. The phase equilibrium behavior shows a curve above the diagonal line. This indicates that benzene has a higher concentration in the vapor phase than toluene, that is,... 

Perkins, E. H., 1992, Integration of intensive variable diagrams and fluid phase equilibrium with SOLMINEQ.88 pc/shell. In Y. K. Kharaka and A. S. Maest (eds.), Water-Rock Interaction, Balkema, Rotterdam, p. 1079-1081. 

Figure 2.12a. Building blocks of binary phase diagrams examples of single-phase (two-variant) and two-phase (mono-variant) fields. In the figure the indication is given of the phases existing in the various fields and respectively of their number. The phase equilibrium composition in the two-phase fields is defined by the boundary (saturation) lines of the single-phase regions. (Pt), (Ag),...

Chvoj, Z., Sestak, J. andTriska, A. (ed.) (1991) Kinetic Phase Diagrams. Non Equilibrium Phase Transitions (Elsevier Science, Amsterdam). 

The pressure-temperature-composition diagram presented by Morey is shown in Fig. 8. The vapor pressure of pure water (on the P-T projection) terminates at the critical point (647 K, 220 bar). The continuous curve represents saturated solutions of NaCl in water, i.e., there is a three-phase equilibrium of gas-solution-solid NaCl. The gas-phase pressure maximizes over 400 bar at around 950 K. Olander and Liander s data for a 25 wt. % NaCl solution are shown, and T-X and P X projections given. At the pressure maximum, the solution phase contains almost 80% NaCl. 

Figure 2.14 Electrochemical phase diagram for chalcopyrite with elemental sulphur as metastable phase. Equilibrium lines (solid lines) correspond to dissolved species at 10 mol/L. Plotted points show the upper and lower limit potential of collectorless flotation of chalcopyrite reported from Sun (1990), Feng (1989) and Trahar (1984)...

Figure 2.18 rpH diagram for jamesonite in aqueous solutions with elemental sulphur as metastable phase. Equilibrium lines correspond to dissolved species at 10 moFL... 

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