Ternary systems equilibrium

In this system the situation is still further complicated by the fact that both cations have variable valency. This is not the place to give a detailed description of the data obtained by Markin et al. (1970) on the phase relationships, and by Markin and Crouch (1970) on the thermodynamic properties, but the results of this work further emphasize a major point of the earlier discussion on equilibria involving fluorite-type phases, namely that in ternary systems equilibrium is virtually unattainable at low temperature by conventional means. For this reason a brief discussioh is included. 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

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. 

For the first time through a liqmd-liquid extrac tion problem, the right-triangular graphical method may be preferred because it is completely rigorous for a ternary system and reasonably easy to understand. However, the shortcut methods with the Bancroft coordinates and the Kremser equations become valuable time-savers for repetitive calculations and for data reduction from experimental runs. The calculation of pseudo inlet compositions and the use of the McCabe-Thiele type of stage calculations lend themselves readily to programmable calculator or computer routines with a simple correlation of equilibrium data. 

Horvath, J. and Novak, M., Potential/pH Equilibrium Diagrams of Some Me-S-HjO Ternary Systems and Their Interpretation from the Point of View of Metallic Corrosion , Corros. Sci., 4, 159 (1964)... 

Horvith, J. and HackI, L., Check of the Potential/pH Equilibrium Diagrams of Different Metal-Sulphur-Water Ternary Systems by Intermittent Galvanostatic Polarisation Method , Corros. Sci., 5, 525 (1965)... 

In Part III heterogeneous equilibria involving clathrates are discussed from the experimental point of view. In particular a method is presented for the reversible investigation of the equilibrium between clathrate and gas, circumventing the hysteresis effects. The phase diagrams of a number of binary and ternary systems are considered in some detail, since controversial statements have appeared in the literature on this subject. 

Barrer s discussion4 of his analog of Eq. 28 merits some comment. Equation 28 expresses the equilibrium condition between ice and hydrate. As such it is valid for all equilibria in which the two phases coexist and not only for univariant equilibria corresponding with a P—7" line in the phase diagram. (It holds, for instance, in the entire ice-hydratell-gas region of the ternary system water-methane-propane considered in Section III.C.(2).) In addition to Eq. 28 one has Clapeyron s equation... 

The system H2S-CH4-H20 is an example of a ternary system forming a continuous range of mixed hydrates of Structure I. For this system Noaker and Katz22 studied the H2S/CH4 ratio of the gas in equilibrium with aqueous liquid and hydrate. From the variation of this ratio with total pressure at constant temperature it follows that complete miscibility must occur in the solid phase. 

Carbon tetrachloride-hydrogen sulfide-water ternary system, 49, 51, 52 Carboniuin ion polymerization, 158 Carboxylic groups initiator, 174 Catalyst clathrates equilibrium, 35 Cell partition function, in calculation of thermodynamic quantities of clathrates, 26... 

In practice, for a ternary system, the decomposition voltage of the solid electrolyte may be readily measured with the help of a galvanic cell which makes use of the solid electrolyte under investigation and the adjacent equilibrium phase in the phase diagram as an electrode. A convenient technique is the formation of these phases electrochemically by decomposition of the electrolyte. The sample is polarized between a reversible electrode and an inert electrode such as Pt or Mo in the case of a lithium ion conductor, in the same direction as in polarization experiments. The... 

Like other surfactants, alkanesulfonates generate lyotropic liquid-crystalline phases. But the phase equilibria can only be inadequately described because of the enormous experimental difficulties in, for instance, establishing an appropriate equilibrium. Nevertheless, for simple ternary systems the modeling of surfactant-containing liquid-liquid equilibria has been successfully demonstrated [60],... 

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... 

Equilibrium data are thus necessary to estimate compositions of both extract and raffinate when the time of extraction is sufficiently long. Phase equilibria have been studied for many ternary systems and the data can be found in the open literature. However, the position of the envelope can be strongly affected by other components of the feed. Furthermore, the envelope line and the tie lines are a function of temperature. Therefore, they should be determined experimentally. The other shapes of the equilibrium line can be found in literature. Equilibria in multi-component mixtures cannot be presented in planar graphs. To deal with such systems lumping of consolutes has been done to describe the system as pseudo-ternary. This can, however, lead to considerable errors in the estimation of the composition of the phases. A more rigorous thermodynamic approach is needed to regress the experimental data on equilibria in these systems. 

Schwartzentruber J., F. Galivel-Solastiuk and H. Renon, "Representation of the Vapor-Liquid Equilibrium of the Ternary System Carbon Dioxide-Propane-Methanol and its Binaries with a Cubic Equation of State. A new Mixing Rule", Fluid Phase Equilibria, 38,217-226 (1987). 

If pressure shift cannot be exploited, then the next option is to add an entrainer to the mixture that interacts differently with the components in the mixture to alter the vapor-liquid equilibrium behavior in a favorable way. When dealing with ternary systems, the mass balance and vapor-liquid equilibrium behavior can be represented on a... 

The vapor-liquid equilibrium for a ternary system of Components A, B and C can be represented by ... 

For three-component (C = 3) or ternary systems the Gibbs phase rule reads Ph + F = C + 2 = 5. In the simplest case the components of the system are three elements, but a ternary system may for example also have three oxides or fluorides as components. As a rule of thumb the number of independent components in a system can be determined by the number of elements in the system. If the oxidation state of all elements are equal in all phases, the number of components is reduced by 1. The Gibbs phase rule implies that five phases will coexist in invariant phase equilibria, four in univariant and three in divariant phase equilibria. With only a single phase present F = 4, and the equilibrium state of a ternary system can only be represented graphically by reducing the number of intensive variables. 

It is sometimes convenient to fix the pressure and decrease the degrees of freedom by one in dealing with condensed phases such as substances with low vapour pressure. The Gibbs phase rule for a ternary system at isobaric conditions is Ph + F = C + 1=4, and there are four phases present in an invariant equilibrium, three in univariant equilibria and two in divariant phase fields. Finally, three dimensions are needed to describe the stability field for the single phases e.g. temperature and two compositional terms. It is most convenient to measure composition in terms of mole fractions also for ternary systems. The sum of the mole fractions is unity thus, in a ternary system A-B-C ... 

In the present case there are no ternary invariant equilibria in the system, partly due to the complete solid solubility of the A-B system. In a ternary system composed from three binary eutectic sub-systems, three univariant lines would meet in a ternary eutectic equilibrium ... 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

For a binary mixture under constant pressure conditions the vapour-liquid equilibrium curve for either component is unique so that, if the concentration of either component is known in the liquid phase, the compositions of the liquid and of the vapour are fixed. It is on the basis of this single equilibrium curve that the McCabe-Thiele method was developed for the rapid determination of the number of theoretical plates required for a given separation. With a ternary system the conditions of equilibrium are more complex, for at constant pressure the mole fraction of two of the components in the liquid phase must be given before the composition of the vapour in equilibrium can be determined, even for an ideal system. Thus, the mole fraction yA in the vapour depends not only on X/ in the liquid, but also on the relative proportions of the other two components. 

Many different types of phase behaviour are encountered in ternary systems that consist of water and two solid solutes. For example, the system KNO3—NaNC>3— H20 which does not form hydrates or combine chemically at 323 K is shown in Figure 15.6, which is taken from Mullin 3 . Point A represents the solubility of KNO3 in water at 323 K (46.2 kg/100 kg solution), C the solubility of NaN(>3 (53.2 kg/100 kg solution), AB is the composition of saturated ternary solutions in equilibrium with solid KNO3 and BC... 

The formation of a proton addition complex can take place either in a binary system (equation (6)) or in a ternary system (equation (6)). Correspondingly, one obtains the basicity constants and K respectively, according to (7) and (8), and these are related to one another through the equilibrium (9) and the relationship (10). It is in the nature of these strongly acid systems that conventional methods for analysing the equilibrium composition can only be used with difficulty. 

Mackor and collaborators (1956, 1968a, b) carried out investigations of this type for the systems aromatic substance-[HP+NaF (or KF)]-n-heptane and aromatic substance-LJlF+BFg+NaBF4]-CCl4. As is clear from equations (9) and (10), the formation equilibrium of the tetrafluoroborate ion has to be taken into account for the ternary system. The relation (10) applies between the equilibria (5) (6) and (9) and the equilibrium constants (7), (8) and (9a). On the basis of the measurements of Mackor et al. (1958b) one finds, for equation (10) ... 

Aljimaz, A.S., Fandary, M.S.H., Alkandary, J.A., and Fahim, M.A. Liquid-liquid equilibrium of the ternary system water + acetic acid + 1-heptanol, /. Chem. Eng. Data, 45(2) 301-303, 2000. 

Bendova, M., Rehak, K.. Matous, J., and Novak, J.P. Liquid + liquid equilibrium in the ternary systems water + ethanol + dialkyl phthalate (dimethyl, diethyl, and dibutyl phthalate) at 298.15 K, /. Chem. Eng. Data, 46(6) 1605-1609, 2001. Benes M. andDohnal, V. Limiting activity coefficients ofsome aromatic and aliphatic nitrocompounds in water, / Chem. Eng. Data, 44(5) 1097-1102, 1999. 

General solvent extraction practice involves only systems that are unsaturated relative to the solute(s). In such a ternary system, there would be two almost immiscible liquid phases (one that is generally aqueous) and a solute at a relatively low concentration that is distributed between them. The single degree of freedom available in such instances (at a given temperature) can be construed as the free choice of the concentration of the solute in one of the phases, provided it is below the saturation value (i.e., its solubility in that phase). Its concentration in the other phase is fixed by the equilibrium condition. The question arises of whether or not its distribution between the two liquid phases can be predicted. 

Fig. 10.1 Different types of liquid-liquid systems, (a), (b) Solubility as function of temperature for binary systems (c), (d) ternary systems. (Dashed lines are examples of tie lines, which connect the two phases in equilibrium located at the binodal.)...

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