Two liquid phase coexistence

This work was initiated for the purpose of evaluating the feasibility of synthesizing hexyl acetate (ROAc) fi-om n-hexyl bromide (RBr) and sodium acetate (NaOAc) by a novel PTC technique. In this new technique, the solid-liquid reaction was catalyzed by a catalyst-rich liquid phase in a batch reactor. Because there a solid phase and two liquid phases coexist, it is called as a SLL-PTC system [3]. Actually, this liquid phase is the third liquid phase in the tri-liquid PTC system. It might be formed when the phase-transfer catalyst is insoluble or slightly soluble in both aqueous and organic phases. Both aqueous and organic reactants can easily transfer to this phase where the intrinsic reaction occurs [4, 5]. 

This situation is typical for systems exhibiting a miscibility gap and is associated with a sufficiently large positive deviation from the ideal behavior. In the system, two liquid phases coexist in equilibrium. These two liquids of composition corresponding... 

C. As long as two liquid phases coexist at equilibrium, the boiling point and the... 

Since two liquid phases coexist at equilibrium only in systems that exhibit significant departure from ideality (Chapter 1), the / -values for three-phase equilibrium must be calculated using methods that are capable of predicting this non-ideality. The method based on liquid activity coefficients, described in Chapter 1, is recommended for this purpose ... 

Another example of potential three-phase distillation is provided by the methyl ethyl ketone (MEK)-water binary. This system forms two miscible regions and a two-liquid-phase region. Figure 10.8 is a Y-X plot of this binary at 100 kPa. Below 0.051 mole fraction MEK, a single, water-rich liquid phase exists, and above 0.652 mole fraction MEK, a single, MEK-rich liquid phase exists. Between these two concentrations, two liquid phases coexist. 

Figure 11.3-3 shows the vapor-liquid and liquid-liquid equilibrium behavior computed for the system of methanol and n-hexane at various temperatures. Note that two liquid phases coexist in equilibrium to temperatures of about 43°C. Since liquids are relatively incompressible, the species liquid-phase fugacities are almost independent of pressure (see Illustrations 7.4-8 and 7.4-9), so that the liquid-liquid behavior is essentially independent of pressure, unless the pressure is very high, or low enough for the mixture to vaporize (this possibility will be considered shortly). The vapor-liquid equilibrium curves for this system at various pressures are also shown in the figure. Note that since the fugacity of a species in a vapor-phase mixture is directly proportional to pressure, the VLE curves are a function of pressure, even though the LLE curves are not. Also, since the methanol-hexane mixture is quite nonideal, and the pure component vapor pressures are similar in value, this system exhibits azeotropic behavior. 

Figtire 1.37. State diagram (a pattern) of the mixture He + He near its tricritical point D is the curve of two liquid phase coexistence, A is the line of continuous phase transitions (Griffiths, 1970) [Rfiprinted with permission from R.B.Griffiths. Phys. Rev. Lett. 24 (1970)715 -717. Copyright 1970 by the American Physical Society)... 

As for real water, it is not clear if the orientation imposed by hydrogen bonding is so relevant as to actually lead to a critical line instead of a critical point at the end of the hypothetic two liquid phase coexistence. However, this picture can not be excluded. The peaks in the specific heat observed in the confined water system could be an indication of criticality, indication that would only be confirmed if experiments in bulk water would be possible [38]. 

The Uquids in the immiscible region boil at a constant temperature of about 200°F. As long as two liquid phases coexist at equilibrium, the boiUng point and the equiUbrium vapor composition are constant. This is a heterogeneous azeotrope The mixture has a minimum boiUng point and the vapor is at equilibrium with two liquid phases. The appearance of a second Uquid phase is a phenomenon that is used to effect separation in certain processes, as described in Chapter 10, by splitting the phases and processing each liquid phase separately. 

In a ternary system with two liquid phases a and ft, the coexistence curve is the locus of points satisfying the relationships... 

Case III. As the pressure increases still further, the solubility curve intersects larger liquid-liquid regions until the critical solution pressure of the system has been reached. Above this critical pressure, no vapor phase exists, and the phase diagram consists of only the coexistence curve, as shown in Fig. 28c. In Fig. 28, L, and L2 stand for the two liquid phases and F stands for a fluid phase. 

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

It has been proposed to define a reduced temperature Tr for a solution of a single electrolyte as the ratio of kgT to the work required to separate a contact +- ion pair, and the reduced density pr as the fraction of the space occupied by the ions. (M+ ) The principal feature on the Tr,pr corresponding states diagram is a coexistence curve for two phases, with an upper critical point as for the liquid-vapor equilibrium of a simple fluid, but with a markedly lower reduced temperature at the critical point than for a simple fluid (with the corresponding definition of the reduced temperature, i.e. the ratio of kjjT to the work required to separate a van der Waals pair.) In the case of a plasma, an ionic fluid without a solvent, the coexistence curve is for the liquid-vapor equilibrium, while for solutions it corresponds to two solution phases of different concentrations in equilibrium. Some non-aqueous solutions are known which do unmix to form two liquid phases of slightly different concentrations. While no examples in aqueous solution are known, the corresponding... 

Several liquid phases coexist in a system when the solvents are not completely miscible. Liquid-liquid equilibrium properties are very useful in solvent extraction and in biotransformation or enzymatic syntheses in two-solvent systems. One speaks about liquid-liquid equilibrium in two cases (1) if the two solvents are not completely miscible, it is said that there is partial miscibility of the two solvents (2) if there is distribution of a compound in the two non-miscible solvents. 

The mysteries of the helium phase diagram further deepen at the strange A-line that divides the two liquid phases. In certain respects, this coexistence curve (dashed line) exhibits characteristics of a line of critical points, with divergences of heat capacity and other properties that are normally associated with critical-point limits (so-called second-order transitions, in Ehrenfest s classification). Sidebar 7.5 explains some aspects of the Ehrenfest classification of phase transitions and the distinctive features of A-transitions (such as the characteristic lambda-shaped heat-capacity curve that gives the transition its name) that defy classification as either first-order or second-order. Such anomalies suggest that microscopic understanding of phase behavior remains woefully incomplete, even for the simplest imaginable atomic components. 

It has recently been pointed out by R0nne et al. [344] that the structure and dynamics of liquid water constitute a central theme in contemporary natural science [345-353]. Modem theoretical considerations are aimed at (a) a detailed description of an electronic structure model of hydrogen bonding, applied to water molecules (see, e.g., Ref. 354), (b) models that involve a certain critical temperature where the thermodynamic response functions of water diverge (see, e.g., Ref. 353), and (c) models that presuppose a coexistence between two liquid phases [344] a low-density liquid phase at the low-pressure side and a high-density liquid phase at the high-pressure side (see also Refs. 355-357). 

I. Loading capacity. This property refers to the maximum concentration of solute the extract phase can hold before two liquid phases can no longer coexist or solute precipitates as a separate phase. 

A non-ideal binary mixture may exist as a single liquid phase at certain compositions, temperatures, and pressures, or as two liquid phases at other conditions. Also, depending on the conditions, a vapor phase may or may not exist at equilibrium with the liquid. When two immiscible liquid phases coexist at equilibrium, their compositions are different, but the component fugacities are equal in both phases. 

Hydrocarbon processing often involves water in the streams, and this can resnlt in the coexistence of two liquid phases and a vapor phase. A valid approach in handling such VLLE conditions is to neglect the hydrocarbon solubility in water, and assume the water phase is pure water. This enables the use of a simplified mixed A -value formulation. 

Mixtures exhibiting nonideal solution behavior present both challenges and opportunities in connection with separation processes. Azeotropes cannot be separated by ordinary distillation, yet the formation of azeotropes itself may be used as a means for carrying out certain separations. The formation of two liquid phases in a column may complicate the separation process however, the coexistence of liquid phases with distinct compositions provides one more separation tool. Chemical reactions concurrent with distillation may be used either to enhance the separation or to perform both the reaction and the separation in one process. 

In this process the entrainer is added as redux to the azeotropic column. The ternary azeotrope is taken as column overhead and condensed, whereupon it separates in the receiver into two liquid phases, one rich in the entrainer and the other rich in component B. Compositions below the curve in the ternary diagram (Figure 10.5) form two coexisting liquid phases, and those above the curve form one liquid phase. The tie lines connect compositions in the two liquid phases at equilibrium with each other. 

Based on Illustration 8.4-2 this is a problem in vapor-liquid-liquid (3 phase) equilibrium. Also, from Problem 8.9-10, we have that the coexistence pressure is constant over the whole range of average (or total) mole fractions for which two liquid phases exist. From Illustration 8.4-2, one liquid phase is present for isobutane = xi -01128 and xx > 0.9284. For overall mole fractions in the range 0.1128 < Xj <0.9284, two liquid phases exist. To compute the V-L-L coexistence pressure in the one-liquid phase region, we use (neglecting fugacity coefficient corrections) x,7l/ vap + 72/>2vap = P where vap = 490.9 kPa, and... 

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