Ternary systems pressure dependence

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... 

Iron(III)-catalyzed autoxidation of ascorbic acid has received considerably less attention than the comparable reactions with copper species. Anaerobic studies confirmed that Fe(III) can easily oxidize ascorbic acid to dehydroascorbic acid. Xu and Jordan reported two-stage kinetics for this system in the presence of an excess of the metal ion, and suggested the fast formation of iron(III) ascorbate complexes which undergo reversible electron transfer steps (21). However, Bansch and coworkers did not find spectral evidence for the formation of ascorbate complexes in excess ascorbic acid (22). On the basis of a combined pH, temperature and pressure dependence study these authors confirmed that the oxidation by Fe(H20)g+ proceeds via an outer-sphere mechanism, while the reaction with Fe(H20)50H2+ is substitution-controlled and follows an inner-sphere electron transfer path. To some extent, these results may contradict with the model proposed by Taqui Khan and Martell (6), because the oxidation by the metal ion may take place before the ternary oxygen complex is actually formed in Eq. (17). 

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. 

In the studies described here, we examine in more detail the properties of these surfactant aggregates solubilized in supercritical ethane and propane. We present the results of solubility measurements of AOT in pure ethane and propane and of conductance and density measurements of supercritical fluid reverse micelle solutions. The effect of temperature and pressure on phase behavior of ternary mixtures consisting of AOT/water/supercritical ethane or propane are also examined. We report that the phase behavior of these systems is dependent on fluid pressure in contrast to liquid systems where similar changes in pressure have little or no effect. We have focused our attention on the reverse micelle region where mixtures containing 80 to 100% by weight alkane were examined. The new evidence supports and extends our initial findings related to reverse micelle structures in supercritical fluids. We report properties of these systems which may be important in the field of enhanced oil recovery. 

The solid products in the reactions with S02 depended on the partial pressures of the reacting gases. A low-temperature study of the ternary system N2H4-NH3-H20 has revealed seven solid phases below -80°C anhydrous N2H4 is precipitated from solution.27 Since it is of importance in... 

The separation process depends on the nature of the vapor-liquid equilibrium relationships of the system, which can be represented on a ternary diagram. Figure 10.3a shows a ternary diagram at some fixed system pressure. Components A and B are close boilers, and A forms an azeotrope with the entrainer E. The curves in the triangle represent liquid isotherms. A corresponding vapor isotherm (not shown) could be drawn to represent the vapor at equilibrium with each liquid curve with tie lines joining vapor and liquid compositions at equilibrium. The temperature of the isotherms reaches a minimum at point Z that corresponds to the composition of the azeotrope formed between A and E. 

Figure 3.3 A schematic of the core of a high-pressure mixing (two-pump) system. The pumps are called binary, ternary or quaternary depending upon the number of solvents that can be mixed together (here binary). The mixing chamber, which controls the mobile phase composition, is at the output of the two high-pressure pumps on the downstream side of the pumps.

Regarding the ternary system SCF-OS-HC, the most important information to look for is the pressure dependence of the HC solubility in the liquid phase. Again, this can be obtained either experimentally or by a suitable thermodynamic model, which is difficult to develop. However, Chang and Randolph [10] proposed a simple and approximate expression which is independent of the HC ... 

While it is believed that solute-solute interactions are not as large as solute-solvent interactions, there is clear evidence that some type of solute-solute interaction is present in SCF/high molecular mass systems. Lockemann [49] studied the phase behaviour of the ternary system C02/methyl myristate/methyl palmitate and found that these two components can be separated using SC CO2. However, the separation factor, which dictates the degree or difficulty of separation, is dependent on the composition of the feed to be separated and the operating pressure and temperature. They found that while the composition does not significantly affect the separation factor, better separation can be achieved at lower composition of the component to be extracted. 

One way to overcome such problems is to consider solvent(l)/polymer(2)/ polymer(3) ternary systems any method that determines either AG or its derivatives should make it possible to calculate Xi3- Thus, for example, osmotic pressure measurements were used to characterize PS/PVME blends dissolved in either toluene or ethylbenzene (Shiomi et al. 1985). The Xi3 was found to depend on the blends composition. Elimination of the solvent effects gave X23/E1 = —10 (7.41 — 11.0103). Thus, the system was expected to remain miscible up to a PVME volume fraction of 03 = 0.67. Osmotic pressure has also been used to determine X23 = 0.070 for PS with poly(p-chloro styrene) in toluene, 2-butanone, and cumene (Ogawa et al. 1986). For the same system, X23 = 0.087 was calculated from intrinsic viscosity measurements. Thus, the system is thermodynamically immiscible. More recently, osmotic pressure measurements in cyclohexanone of a ternary system resulted in X23ipoly(vinylchloride-co-vinylacetate) blends with a series of acrylic copolymers (Sato et al. 1997). 

According to the Gibbs phase rule, temperature and pressure of a CEP are unique for binaiy systems and, thus, are independent of the overaJl composition of the sample, see section 2. For the ternary systems examined, a dependency of the CEP data from the mole fraction of CO2 (xco2) could not be determined, as has been suggested by Patton et al. [4]. The differences were all found to be within the experimental error, see below. Note also that fluid three-phase behavior only occurs in a small range of xco2 ( 3 mole%). However, in order to avoid any influence whatsoever, for each ternary system examined, samples were prepared at constant CO2 mole fractions of 0.95 to 0.%. 

In ord to optimize the applications of SSI technique different problems should be solved with the help of experimental determinations coupled widi some theoretical analysis. It is obvious that the polymer in contact with the supercritical fluid swells (the CO2 dissolves in the polymer) and the extent of swelling depends from the pressure. When the polymer is in contact with the supercritical fluid saturated with the pharmaceutical the solvent again diffuses in the polymer, it swells the polymer and in this way the solubilization of the drug in the polymer is fricilitated. As a consequence in addition to the kinetic problems (diffusion in the polymer matrix) the thermodynamic description of the ternary systems, supa critical fluid, pharmaceutical and polymer, is essential. 

Suppose, for example, that two binary oxides react to form one or more ternary oxides as in Fig. 6-2. In order to properly understand the reaction, we must first be completely clear as to the number of independent thermodynamic variables. For a given total pressure and a given reaction temperature, there will still be one more independent variable in a binary system, and two more independent variables in a ternary system. Therefore, the experimental conditions are only completely defined if the activity of the component common to all compounds (i. e. the oxygen activity in this case) is fixed in the reaction zone. Only then are the local chemical potentials of the components and the transport coefficients (which depend, in general, upon these potentials) uniquely determined. 

Amphiphiles, the representatives of which are soap, surfactant and lipid, have a hydrophilic polar head and lipophilic nonpolar tails. They always remain on the interface between water and oil and form monolayers of surfactants in a water/oil/amphiphile ternary system. This monolayers or interfacial film reduce the surface tension between water and oil domains. In a three-component system the surfactant film exists in various topologically different structures such as micelles, vesicles, bicontinuous microemulsions, hexagonal arrays of cylinders or lamellar structures depending upon the pressure, temperature and the concentration of the components [1,2]. Microemulsions are thermodynamically stable, isotropic and transparent mixtures of ternary amphiphilic systems. When almost equal volume fractions of water and oil are mixed with a dilute concentration of surfactants, they take... 

Jenner and Kellou recently studied the pressure effect on azeotropy in free-radical terpolymerization of MA with acrylonitrile, dielthyl fumarate, methyl acrylate, methyl methacrylate, methyl vinyl ketone, vinylidene chloride, norbornene, a-methylstyrene, indene, and vinyl acetate, with styrene as the second comonomer common in all cases. It was found that ternary azeotropes were only possible for those systems where the first comonomers had positive e values, i.e., diethyl fumarate, acrylonitrile, methyl acrylate, methyl methacrylate, methyl vinyl ketone, and vinylidene chloride. Surprisingly, the coordinates of the ternary azeotropes were very little affected by variations of the pressure from 1-3,000 bars. Since reactivity ratios in multi-component polymerizations are sensitive to pressure, causing terpolymer composition to also be pressure dependent, a shift of the ternary azeotropic point would be expected. Why this occurs awaits further clarification. 

This standard chemical potential depends on the nature of both the solute and the solvent, as well as on the external variables (e.g., temperature and pressure). The physicochemical formulation variables are thus at least five in a true ternary system in an actual SOW system, there are many more formulation variables, as all components are often very... 

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