Phase equilibrium binary systems

The prerequisite of all types of extraction processes is the existence of a large miscibility gap between raffinate and extract. The thermodynamic principles of phase equilibrium are dealt with in Chap. 2. An extensive collection of liquid-liquid equilibria is given in the Dechema Data Collection (Sorensen and Arlt 1980ff). Volume 1 contains data of miscibility gaps of binary systems. Phase equilibrium data (miscibility gaps and distribution equilibrium) of ternary and quaternary mixtures are listed in volumes 2-7. 

The compositions of vapor and liquid phases of a binary system at equilibrium sometimes can be related by a constant relative volatility which is defined as... 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

Landolt-Bornstein Physikalische-chemische TabeUen, Eg. I, p. 303, 1927. Phase-equilibrium data for the binary system NH3-H2O are given by Clifford and Hunter,y. Fhys. Chem., 37, 101 (1933). 

Enthalpy and phase-equilibrium data for the binary system HCI-H2O are given by Van Nuys, Trans. Am. Inst. Chem. Engts., 39, 663 (1943). 

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. 

In distillation work for binary systems with constant relative volatility, the equilibrium between phases for a given component can be expressed by the following equation ... 

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 ... 

In most cases the critical temperature of the solute is above room temperature. As can be seen in the binary system H2S-H20 drawn in Fig. 6, the three-phase line HL2G is then intersected by the three-phase line HL G. The point of intersection represents the four-phase equilibrium HLXL2G and indicates the temperature... 

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

Because of the interest in its use in elevated-temperature molten salt electrolyte batteries, one of the first binary alloy systems studied in detail was the lithium-aluminium system. As shown in Fig. 1, the potential-composition behavior shows a long plateau between the lithium-saturated terminal solid solution and the intermediate P phase "LiAl", and a shorter one between the composition limits of the P and y phases, as well as composition-dependent values in the single-phase regions [35], This is as expected for a binary system with complete equilibrium. The potential of the first plateau varies linearly with temperature, as shown in Fig. 2. 

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... 

Ternary equilibrium curves calculated by Scott,who developed the theory given here, are shown in Fig. 124 for x = 1000 and several values of X23. Tie lines are parallel to the 2,3-axis. The solute in each phase consists of a preponderance of one polymer component and a small proportion of the other. Critical points, which are easily derived from the analogy to a binary system, occur at... 

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. 

Let us assume that for a binary system there are available N, VL E, N2 VL2E, N3 L]L2E and N4 VL)L2E data points. The light liquid phase is L, and L2 is the heavy one. Thus, the total number of available data is N=N +N2+N3+N4. Gas-gas equilibrium type of data are not included in the analysis because they... 

To calculate the compositions of the two coexisting liquid phases for a binary system, the two equations for phase equilibrium need to be solved ... 

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

Figure 4.2 Gibbs energy curves for the liquid and solid solution in the binary system Si-Ge at 1500 K. (a) A common tangent construction showing the compositions of the two phases in equilibrium, (b) Tangents at compositions that do not give two phases in equilibrium. Thermodynamic data are taken from reference [2],...

The relative amount of the different phases present at a given equilibrium is given by the lever rule. When the equilibrium involves only two phases, the calculation is the same as for a binary system, as considered earlier. Let us apply the lever rule to a situation where we have started out with a liquid with composition P and the crystallization has taken place until the liquid has reached the composition 2 in Figure 4.17(a). The liquid with composition 2 is here in equilibrium with a with composition 2. The relative amount of liquid is then given by... 

In the simplest binary system comprising two liquids (A and B), adding a small amount of either liquid to the other creates a single phase, as the one liquid dissolves completely in the other. As more of the second liquid is added, in this case B, the first liquid A becomes saturated with B and no more will dissolve. At this point, the system will consist of two phases in equilibrium with each other, one of liquid A saturated with B and the other of liquid B saturated with A. If B is continually added to A, there will come a point at which A becomes the minor component in the system and, ultimately, will dissolve completely in liquid B a single phase will be formed once more. The relative proportions of each liquid that are required to form single or biphasic systems depends both... 

A constant interaction parameter was capable of representing the mole fraction of water in the vapor phase within experimental uncertainty over the temperature range from 100°F to 460°F. As with the methane - water system, the temperature - dependent interaction parameter is also a monotonically increasing function of temperature. However, at each specified temperature, the interaction parameter for this system is numerically greater than that for the methane - water system. Although it is possible for this binary to form a three-phase equilibrium locus, no experimental data on this effect have been reported. 

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