Nonideal solutions liquid-vapor

In 1958, Pitzer (141), in a remarkable contribution that appears to have been the first theoretical consideration of this phenomenon, likened the liquid-liquid phase separation in metal-ammonia solutions to the vapor-liquid condensation that accompanies the cooling of a nonideal alkali metal vapor in the gas phase. Thus, in sodium-ammonia solutions below 231 K we would have a phase separation into an insulating vapor (corresponding to matrix-bound, localized excess electrons) and a metallic (matrix-bound) liquid metal. This suggestion of a "matrix-bound analog of the critical liquid-vapor separation in pure metals preceeded almost all of the experimental investigations (41, 77, 91,92) into dense, metallic vapors formed by an expansion of the metallic liquid up to supercritical conditions. It was also in advance of the possible fundamental connection between this type of critical phenomenon and the NM-M transition, as pointed out by Mott (125) and Krumhansl (112) in the early 1960s. 

The properties of mixtures of ideal gases and of ideal solutions depend solely on the properties of the pure constituent species, and are calculated from them by simple equations, as illustrated in Chap. 10. Although these models approximate the behavior of certain fluid mixtures, they do not adequately represent the -behavior of most solutions of interest to chemical engineers, and Raoult s law is not in general a realistic relation for vapor/liquid equilibrium. However, these models of ideal behavior—the ideal gas, the ideal solution, and Raoult s law— provide convenient references to which the behavior of nonideal solutions may be compared. 

Experimental vapor-liquid-equilibrium data for benzene(l)/n-heptane(2) system at 80°C (176°F) are given in Table 1.8. Calculate the vapor compositions in equilibrium with the corresponding liquid compositions, using the Scatchard-Hildebrand regular-solution model for the liquid-phase activity coefficient, and compare the calculated results with the experimentally determined composition. Ignore the nonideality in the vapor phase. Also calculate the solubility parameters for benzene and n-heptane using heat-of-vaporization data. 

Compute the Gfj parameters for the Wilson equation. General engineering practice is to establish liquid-phase nonideality through experimental measurement of vapor-liquid equilibrium. Models with adjustable parameters exist for adequately representing most nonideal-solution behavior. Because of these models, the amount of experimental information needed is not excessive (see Example 3.9, which shows procedures for calculating such parameters from experimental data). 

Sidebar 7.10 describes the mathematical relationship between xBq and Xbp for an ideal solution, showing how (7.54a, b) are achieved in this simple case. However, the physically reasonable relationships (7.54a, b) between coexisting liquid and vapor compositions are also satisfied in more general nonideal solutions described below. 

We conclude this discussion with one final reminder. The vapor-liquid equilibrium calculations we have shown in Section 6.4c are based on the ideal-solution assumption and the corresponding use of Raoult s law. Many commercially important systems involve nonideal solutions, or systems of immiscible or partially miscible liquids, for which Raoult s law is inapplicable and the Txy diagram looks nothing like the one shown for benzene and toluene. 

FIGURE 11.15 Vapor pressures above a mixture of two volatile liquids. Both ideai (biue lines) and non-ideai behaviors (red curves) are shown. Positive deviations from ideal solution behavior are illustrated, although negative deviations are observed for other nonideal solutions. Raoult s and Henry s laws are shown as dilute solution limits for the nonideal mixture the markers explicitly identify regions where Raoult s law and Henry s law represent actual behavior. 

Repeat Prob. 2-7 for the case where both the vapor and liquid phases form nonideal solutions. That is, given ... 

The behavior of solvents in the vapor and liquid phases which form nonideal solutions are described by the same set of expressions as those given by Eq. (5-1). Further insight into the behavior of solvents in azeotropic and extractive distillation may be gained by the reconsideration of the first expression of Eq. (5-1), which may be restated in the following form... 

Begin with first principles and obtain the expressions given by Eqs. (13-68) and (13-69) for mr 13-8 Carry out the developments given by Eqs. (13-82) through (13-91) for the case where both the vapor and liquid phases form nonideal solutions. 

Few liquid mixtures are ideal, so vapor-liquid equilibrium calculations can be more complicated than is the case for the hexane-triethylamine system, and the system phase diagrams can be more structured than Fig. 10.1-6. These complications arise from the (nonlinear) composition dependence of the species activity coefficients. For example, as a result of the composition dependence of y, the equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction. Thus nonideal solutions exhibit deviations from Raoult s law. We will discuss this in detail in the following sections of this chapter. However, first, to illustrate the concepts and some of the types of calculations that arise in vapor-liquid equilibrium in the simplest way, we will assume ideal vapor and liquid solutions (Raoult s law) here, and then in Sec. 10.2 consider the calculations for the more difficult case of nonideal solutions.. ... 

Nonideal solution effects can be incorporated into /f-value formulations in two different ways. Chapter 4 described the use of the fugacity coefficient, in conjunction with an equation of state and adequate mixing rules. This is the method most frequently used for handling nonidealities in the vapor phase. However, tv reflects the combined effects of a nonideal gas and a nonideal gas solution. At low pressures, both effects are negligible. At moderate pressures, a vapor solution may still be ideal even though the gas mixture does not follow the ideal gas law. Nonidealities in the liquid phase, however, can be severe even at low pressures. In Section 4.5, il was used to express liquid-phase nonidealities for nonpolar species. When polar species are present, mixing rules can be modified to include binary interaction parameters as in (4-113). 

Nonideal Solutions, The final level of complexity for modeling the relationship between vapor and liquid compositions accounts for nonideal interactions in the liquid phase. The equilibrium ratio is still ased for such systems, but in this instance it is defined as... 

In 10.1 we present the basic thermodynamic relations that are used to start phase-equilibrium calculations we discuss vapor-liquid, liquid-liquid, and liquid-solid calculations. We have seen that the most interesting phase behavior occurs in nonideal solutions, but when we describe nonidealities using an ideal solution as a basis, we must select an appropriate standard state. Common options for standard states are discussed in 10.2 they include pure-component standard states and dilute-solution standard states. 

A solution in which the components have vapor pressures as given by Baoult s law is called an IDEAL SOLUTION. (An ideal solution has nothing to do with an ideal gas, except that each is described by an especially simple law.) Probably there are no exacdy ideal solutions, but many solutions are nearly ideal. C Hc and CCI4 illustrate a case in which two liquids form a slightly but measurably nonideal solution. 

Figure 7.12 shows a liquid-vapor phase diagram for positive deviations from Raoult s law. Each component has a higher-than-expected vapor pressure, so the total pressure in equilibrium with the liquid solution is also higher than expected. Ethanol/benzene, ethanol/chloroform, and ethanol/water are systems that show a positive deviation from Raoult s law. Figure 7.13 shows a similar diagram, but for a solution that shows a negative deviation from Raoult s law. The acetone/chloroform system is one example that exhibits such nonideal behavior. 

FIGURE 7.14 Temperature-composition phase diagram for a nonideal solution showing a positive deviation from Raoult s law. Notice the appearance of a point at which liquid and vapor have the same composition. 

Example 8.3 How much difference does nonideal solution behavior make in the acetone-water VLE To answer this, compute the boiling temperature and vapor composition that would correspond to a liquid with Xacetone = 0.05, if this were an ideal solution (7, = 1.00),—Raoult s law—and compare them to the experimental values. 

The thermodynamic model nsed is the nonrandom two liquid (NRTL), which can be used to describe vapor-liquid and liqnid-liquid equilibrium of strongly nonideal solutions. The NRTL model can handle any combination of polar and nonpolar compounds, up to very strong nonideality. In addition, many parameters for xylitol pure component were not available in the databanks of Aspen Plus and had to be acquired from the literature and from regression of experimental data (Table 12.1). 

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