Equilibrium Between Two Liquid Phases

From the measured boiling point elevation, ATb = 0.421 K, we may deduce that the mole fraction of the solute in the solution is x = 0.421/28.5 = 0.0148. But since the solution is known to contain (5.000/Afj) mol of solute, where Ms is the solute molecular weight, and 100.0 g/18.016 g/mol = 5.551 mol of water, we may write 

From Equation 6.5-2 the effective solvent vapor pressure at 25 C is determined from the vapor pressure of pure water at this temperature (found in Table B.3) as 

Finally, substituting values of the melting point and heat of fusion of water (from Table B.l) and the gas constant into Equation 6.5-5, we obtain 

A solution contains an unknown amount of table salt dissolved in water. List as many ways as you can think of to measure or estimate the concentration of salt in the solution without leaving the kitchen of your home. The only instruments you are allowed to bring home from work are a thermometer that covers the range - 10°C to 120°C and a small laboratory balance. (Example Make up several solutions with known salt concentrations, and compare their tastes with that of the unknown solution.) 

If water and methyl isobutyl ketone (MIBK) are mixed at 25°C, a single phase results if the mixture contains more than either 98% water or 97.7% MIBK by mass otherwise, the mixture separates into two liquid phases, one of which contains 98% H2O and 2% MIBK and the other 97.7% MIBK and 2.3% H2O. Water and MIBK are examples of partially miscible liquids they would be termed immiscible if one phase contained a negligible amount of water and the other a negligible amount of MIBK. 

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Ic. Ternary Systems Consisting of a Single Polymer Component in a Binary SolventMixture.—Three conditions must be satisfied for equilibrium between two liquid phases in a system of three components. In place of the conditions (1) we have... 

The partitioning coefficient K (equation 1) describes the distribution of a solute, in equilibrium, between two liquid phases. This coefficient is a function of several factors, such as the molecular size, pH, temperature, concentration, and type of components in both phases. In Equation (1), y and x are the solute concentrations in the extract and in the original solution, respectively. 

The condition for equilibrium between vapor and liquid phases, expressed by Equation 1.19 as the equality of each component fugacity in the two phases, applies to equilibrium between two liquid phases or any number of phases such as two liquids and a vapor. When the deviations from ideality are large enough, mixtures can form two immiscible liquids at equilibrium with each other. It is easy to see that an ideal solution cannot form two liquid phases at equilibrium. In order for this to occur, the condition = (p,%)P, where a and P designate each liquid phase, must be satis-... 

Lekhal et al. [6] proposed a pseudo-homogeneous gas-liquid-liquid model based on the Higbie penetration theory to account for simultaneous absorption of two gases into the liquid phases. Because of the assumption of rapid liquid-liquid mass transfer of reactants leading to the equilibrium between two liquid phases, the model was simplified greatly and the detail of phase dispersion and distribution and multiphase flow was avoided. Reasonable success was achieved and the results of analysis suggested that the only limitation to the conversion of hydroformylation of 1-octene was the gas-liquid mass transfer of CO and H2. 

We refer the reader in particular to Part II/2a of the 6th edition, section 22263, for those cases where data on the equilibrium between two liquid phases are needed for extraction or where the liquid-solid equilibrium is demanded for crystallisation. 

All points on the two tangents HRi, HR2, to the curve of solutions represent heterogeneous systems composed of solid hydrate in contact with solutions. If the curve between Ri and R2 is convex the heterogeneous systems are stable, and inversely. At a given temperature and pressure the hydrate can be in equilibrium with two liquid phases of different composition, one containing relatively more, the other relatively less, salt than the hydrate. With rise of temperature the form of the curve and the altitude of H change ... 

The equilibrium condition for the distribution of one solute between two liquid phases is conveniently considered in terms of the distribution law. Thus, at equilibrium, the ratio of the concentrations of the solute in the two phases is given by CE/CR = K, where K1 is the distribution constant. This relation will apply accurately only if both solvents are immiscible, and if there is no association or dissociation of the solute. If the solute forms molecules of different molecular weights, then the distribution law holds for each molecular species. Where the concentrations are small, the distribution law usually holds provided no chemical reaction occurs. 

In Fig. 1.2, phase transformations are pnt into their context of physical processes used for separation of mixtures of chemical compounds. However, the figure has been drawn asymmetrically in that two Uqnids (I and II) are indicated. Most people are familiar with several organic Uqnids, Uke kerosene, ether, benzene, etc., that are only partially miscible with water. This lack of miscibility allows an equilibrium between two liquids that are separated from each other by a common phase boundary. Thus the conventional physical system of three phases (gas, liquid, and solid, counting all solid phases as one), which ordinarily are available to all chemists, is expanded to four phases when two immiscible liquids are involved. This can be of great advantage, as will be seen when reading this book. 

The distribution ratio of a solute between two liquid phases at equilibrium is a constant, provided that the solute forms a dilute ideal solution in each phase. 

A very significant observation connecting the interfacial tension between two liquid phases in equilibrium with the surface tension of each separately against the vapour phase was discovered by Antonow. The interfacial tension is equal to the difference between the two surface tensions. It is important to notice that we must deal with phases in equilibrium, since it often happens that the tension of the one pure liquid is greatly reduced by the addition of the second even though the solubility may be exceedingly small In the extreme case, the solubility of one phase in the other is too small to be measured, as in the case of palmitic acid in water, but the surface tension of the solvent may, as we have already seen, nevertheless be reduced very much. The following examples may be quoted in support of Antonow s rule. 

The concept of equilibrium distribution is another area where names can cause much confusion. The equilibrium distribution of a compound between the gas and liquid phase has been expressed in various forms, i. e. Bunsen coefficientfi, solubility ratio s, Henry s Law constant expressed dimensionless Hc, or with dimensions H. These are summarized in along with equations showing the relationships between them. Another more general term to describe the equilibrium concentrations between two phases is the partition coefficient, denoted by K. It is often used to describe the partitioning of a compound between two liquid phases. 

As the area is diminished below some thousands of sq. A., where the molecules cover only a small fraction of the surface, the surface pressure rapidly becomes much smaller than that of a perfect gas, and in the four acids with the longest chains becomes constant over a considerable region. The curves are indeed a very faithful reproduction of Andrews s curves for the relation between pressure and volume, for carbon dioxide, at temperatures near the critical. The horizontal regions in the curves correspond to the vapour pressure of liquids, and indicate the presence of an equilibrium between two surface phases, the vapour film, and islands of liquid, coherent film. 

Because of the assumption made above, the solution is limited to the linear region of analyte partitioning and adsorption isotherms. The analyte distribution between two liquid phases (eluent and adsorbed phase) at equilibrium could be described as follows ... 

Figure 3.26. Equilibrium relationship between two liquid phases.

Extraction involves the transfer of components between two liquid phases, much as absorption or stripping involves the transfer of components from liquid to vapor phase or vice versa. As in vapor-liquid multistage separation processes, the device employed to carry out liquid-liquid extraction is usually a counterflow column that performs the function of a number of equilibrium stages interconnected in counterflow configuration. In each stage, two inlet liquid streams mix, reach equilibrium, and separate into two outlet liquid streams. As in vapor-liquid columns, the lack of complete equilibrium in liquid-liquid extractors is accounted for by some form of tray efficiency. Liquid-liquid extraction may also be carried out in a cascade of mixing vessels connected in series in counterflow. 

The discussion in this section has been concerned with the distribution of a solute between two liquid, phases whose equilibrium is unaffected by the added solute. This will occur if the amount of added solute is very small, or if the solvents are essentially immiscible at all conditions. However, if the amount of dissolved solute is so large as to affect the miscibility of the solvents, the solute addition can have a significant effect on the solvents, including the increase (salting in) or decrease (saltin out) of the mutual solubility of the two solvents, as was discussed in Sec. 11.2. It is important to emphasize that such situations are described by the methods in Sec. 11.2 as a multicomponent liquid-liquid equilibrium problem, in contrast to the procedures in this section, which are based on the assumption that the partial or complete immiscibility of the solvents is imaffected by the addition of the partitioning solute. 

Liquid-liquid extraction is a separation process which relies on uneliquid phases. Mass transfer will therefore occur as a spontaneous process if the phases are not at equilibrium. The transferred components are referred to as solutes and the carrier liquids as solvents. The solvents may be practically immiscible or partially miscible. 

The equilibrium condition for a species i, partitioning between two liquid phases, e.g. water (W) and chemical (c), is ... 

The drop shape method is possibly the most useful one for the investigation of the adsorptive transfer, i.e. the adsorption kinetics at the interface between two liquid phases containing the surfactant from the partition equilibrium. This phenomenon is particularly significant when situations far from the partition equilibrium are considered, in systems characterised by a high solubility of the surfactant in the recipient phase or by a large solubility of the surfactant in both phases. The latter case represents a typical situation for many types of ionic surfactants in water-oil and water-alkane systems, as demonstrated by the partition coefficients measured for various solvents [52, 53, 54, 55, 56]. 

The previous three types of liquid-solid equilibria considered equilibrium between two bulk phases we will now briefly look at two types of interfacial adsorption systems where the two bulk phases are either fluid-fluid or fluid-solid. Consider first the interfacial equilibrium relation for a nonelectrolytic surface active solute in an air-water system (a fluid-fluid system). If the surface active solute i is such that the interfacial tension decreases linearly with the surfactant concentration C,i as... 

For this reason, with a fast change in the parameters of a polymer system, equilibrium phases with a minimum level of free energy are not formed at once in many cases. For example, a crystalline polymer is not separated immediately, but successively passes through the stages of equilibrium between two amorphous phases (liquid equilibrium), then equilibrium with the formation of a liquid-crystalline phase, and finally, equilibrium with separation of the cryskdline phase of the polymer. 

In a simple liquid-liquid extraction the solute is partitioned between two immiscible phases. In most cases one of the phases is aqueous, and the other phase is an organic solvent such as diethyl ether or chloroform. Because the phases are immiscible, they form two layers, with the denser phase on the bottom. The solute is initially present in one phase, but after extraction it is present in both phases. The efficiency of a liquid-liquid extraction is determined by the equilibrium constant for the solute s partitioning between the two phases. Extraction efficiency is also influenced by any secondary reactions involving the solute. Examples of secondary reactions include acid-base and complexation equilibria. 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

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