Four-component mixtures phase equilibrium

More than one phase border loop exists at one temperature for some mixtures of components of greater disparity. Figure 4.11 shows the isothermal gle of n-heptane + ethanol at 313° and 333°K. Two connected loops occur at each temperature. Both branches of the lower curves are dew-point states the upper curve, bubble-point states. The dew state and bubble state on the same branch of the saturation loop and at the same T and p are at phase equilibrium. To illustrate, two phases are at equilibrium at 313°K and 20 kPa and also at 333° and 50 kPa. All four pairs are shown with dashed line segments. 

As an example of the application of the phase rule with reaction, consider a mixture of four components in which only two participate in a reaction. If all components are present in the gas phase, then F = 4 + 2- l- l=4. Hence, only four intensive variables are independently variable (e.g., T, P, yi, and y2, or P, y, y, and y ) if the vapor is ideal. For example, the independent reaction yields the following form of the equilibrium constant ... 

A principal advantage of this algorithm is that it applies to any number of components C > 3, though in every case we solve only fhe two equations (11.1.31) and (11.1.32). However, this method fails for binary mixtures. To see why, note that for binaries in three-phase equilibrium, (11.1.23) requires us to specify values for T = 3 variables. We then have five equations that can be solved for five unknowns. The five equations are four phase-equilibrium relations (11.1.15) and (11.1.24) plus the one Rachford-Rice function (11.1.31). In the Rachford-Rice approach, the five unknowns would be i/p plus the fractions L and V. However, L and V appear in only one... 

This is an important method of preparing mono- and di-acylglycerols. The composition of the equilibrium mixture of all four components depends on the relative amount of triacylglycerol and of glycerol dissolved in the lipid phase. 

As a result, we have four best sequences of five-component mixture in four columns (Fig. 8.24). Each sequence contains one autoextractive column with two feed flows, one autoextractive column with one feed flow (with preliminary recycle), one simple column with one distributed component, and one complex column with two feeds and one side product. Such a set of columns is a consequence of the structure of phase equilibrium coefficients field in concentration pentahedron, (only... 

Consider a system containing solid carbon (graphite) and a gaseous mixture of O2, CO, and CO2. There are four species and two phases. If reaction equilibrium is absent, as might be the case at low temperature in the absence of a catalyst, we have r = 0 and C = s — r = 4. The four components are the four substances. The phase rule tells us the system has four degrees of freedom. We could, for instance, arbitrarily vary T, p, yo2 and yco-... 

Winsor [15] classified the phase equilibria of microemulsions into four types, now called Winsor I-IV microemulsions, illustrated in Fig. 15.5. Types I and II are two-phase systems where a surfactant rich phase, the microemulsion, is in equilibrium with an excess organic or aqueous phase, respectively. Type III is a three-phase system in which a W/O or an O/W microemulsion is in equilibrium with an excess of both the aqueous and the organic phase. Finally, type IV is a single isotropic phase. In many cases, the properties of the system components require the presence of a surfactant and a cosurfactant in the organic phase in order to achieve the formation of reverse micelles one example is the mixture of sodium dodecylsulfate and pentanol. 

In the system C12+H20, there are two components, just indicated two solid phases—ice and chlorine hydrate, C12.8H20 two soln.—one a soln. of water in an excess of chlorine, Sol. I, and a soln. of chlorine in an excess of water, Sol. II and a gas phase—a mixture of chlorine and water vapour in varying proportions. The system has not been completely studied, but sufficient is known to show that the equilibrium curves take the form shown diagrammatically in Fig. 20. The two invariant systems L and B have four coexisting phases—... 

In the last common condition, for four phases in equilibrium (such as I-Lw-H-V) at the lower quadruple point, the number of intensive variables must equal the number of components minus two. For a mixture of methane and water (or for a gas mixture in large excess so that the composition does not change) no intensive variables are required—that is, the lower quadruple point is fixed at a unique pressure, temperature, as well as the composition of all the phases. 

Since all points on a tie line have the same temperature, pressure, component concentration in one phase, and component concentration in the other phase, one more variable must be specified to define the relative amounts of the phases at equilibrium. The specihed variable could itself be either the fraction of one phase out of the total or the mixture composition. Note that only two component concentrations are independent in a ternary. In the single-phase region there are four degrees of freedom according to the phase rule. Therefore, if the fraction of one phase or whether one or two phases exist is unknown, four independent variables must be specihed to completely dehne the system. 

Consider a mixture of components 1 and 2 in vapor-liquid equilibrium in a closed vessel at temperature T and pressure P. Let the composition of the liquid phase be represented by the mole fraction Xi and that of the vapor by mole fraction i/j. The properties of first importance are the four measurables T, P, X, and yx- absence... 

Microemulsions are ternary systems containing oil, water, and surfactant. The terms oil and water in a microemulsion system normally refer to oil phase (oil and oil soluble components such as cyclosporine) and aqueous phase (water and water soluble components such as sodium chloride), respectively. The phase behavior of water-oil-surfactant mixtures was extensively studied by Winsor (1948). Based on his experimental observations, Winsor classified equilibrium mixtures of water-oil-surfactant into four systems (1) type I (Winsor I) system where water continuous or oil-in-water (0/W) type microemulsion coexists with the oil phase. In these systems, the aqueous phase is surfactant-rich (2) type II (Winsor II) system where oil continuous or water-in-oil (W/0) type microemulsion coexists with the aqueous phase. In these systems, the oil phase is surfactant-rich (3) type III (Winsor III) system where bicontinuous type microemulsion (also referred to as surfactant-rich middle-phase) coexists with excess oil at the top and excess water at the bottom and (4) type IV (Winsor IV) system where only a single-phase (microemulsion) exists. The surfactant concentration in type IV microemulsion is generally greater than 30 wt%. Type IV microemulsion could be water continuous, bicontinuous, or oil continuous depending on the chemical composition. The phase behavior of microemulsions is often described as a fish diagram shown in Figure lO.I (Komesvarakul et al. 2006). 

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