Ideal mixture vapor-liquid equilibrium

Assuming a mixture of n-pentane and n-heptane is ideal, prepare vapor-liquid equilibrium diagrams for this mixture at... 

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.. ... 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

Consider first, a binary mixture of two Components A and B the vapor-liquid equilibrium exhibits only a moderate deviation from ideality, as represented in Figure 4.4a. In this case, as pure A boils at a lower temperature than pure B in the temperature-composition... 

A distillation calculation is to be performed on a multicomponent mixture. The vapor-liquid equilibrium for this mixture is likely to exhibit significant departures from ideality, but a complete set of binary interaction parameters is not available. What factors would you consider in assessing whether the missing interaction parameters are likely to have an important effect on the calculations ... 

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

Deviations from ideality often occur, and the Kt value depends not only on temperature and pressure but also on the composition of the other components of the mixture. A more detailed discussion of vapor-liquid equilibrium relationships for nonideal mixtures is outside the scope of this article. 

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. 

When liquid and gas phases are both present in an equilibrium mixture of reacting species, Eq. (11.30), a criterion of vapor/liquid equilibrium, must be satisfied along with the equation of chemical-reaction equilibrium. There is considerable choice in the method of treatment of such cases. For example, consider a reaction of gas A and water B to form an aqueous solution C. The reaction may be assumed to occur entirely in the gas phase with simultaneous transfer of material between phases to maintain phase equilibrium. In this case, the equilibrium constant is evaluated from AG° data based on standard states for the species as gases, i.e., the ideal-gas states at 1 bar and the reaction temperature. On the other hand, the reaction may be assumed to occur in the liquid phase, in which case AG° is based on standard states for the species as liquids. Alternatively, the reaction may be written... 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

The application of Eq. (10.3) to specific phase-equilibrium problems requires use of models of solution behavior, which provide expressions for G or for the Hi as functions of temperature, pressure, and composition. The simplest of such expressions are for mixtures of ideal gases and for mixtures that form ideal solutions. These expressions, developed in this chapter, lead directly to Raoult s law, the simplest realistic relation between the compositions of phases coexisting in vapor/liquid equilibrium. Models of more general validity are treated in Chaps. 11 and 12. 

For example, suppose there is a stream in the process that is a binary mixture of chemical components A and B. If these components obey ideal vapor-liquid equilibrium behavior, we can use a single distillation column to separate them. If they form an azeotrope, we may have to use a two-column separation scheme. If the azeotropic composition... 

Although the widely used equilibrium-stage models for distillation, described above, have proved to be quite adequate for binary and closeboiling, ideal and near-ideal multicomponent vapor-liquid mixtures. 

For azeotropic distillation especially the systems are non-ideal which makes calculating vapor-liquid equilibrium properties more difficult than, for example, in distillation of mixtures of simple hydrocarbons. Work predicting the vapor-liquid equilibrium properties of ternary mixtures of... 

A gas-liquid system in which the vapor-liquid equilibrium relationship for every volatile species is either Raoult s law or Henry s law is said to exhibit ideal solution behavior. An ideal liquid solution is a mixture of liquids that exhibits ideal solution behavior at equilibrium. 

All calculations were carried out at T = 313.15 K. The vapor-liquid equilibrium (VLB) data for the ternary mixture and the corresponding binaries were taken from [32]. The excess volume data for the ternary mixture A,A-dimethylformamide-methanol-water and binary mixtures A, A-dimethylformamide-methanol and methanol-water were taken from [33], and the excess volume data for the binary mixture A,A-dimethylformamide-water from [34]. There are no isothermal compressibility data for the ternary mixture, but the contribution of compressibility to the binary KBls is almost negligible far from the critical point [6]. For this reason, the compressibilities in binary and ternary mixtures were taken to be equal to the ideal compressibilities, and were calculated from the isothermal compressibilities of the pure components as follows ... 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

Once the interaction energies were obtained, they were used to calculate the parameters in the UNIQUAC and Wilson models given by Eq. (24). To test the validity of the method, low-pressure vapor-liquid equilibrium (VLE) predictions were made for several binary aqueous systems. The calculations were done using the usual method assuming an ideal vapor phase (Sandler, 1999). Figures 7 and 8 show the low-pressure VLE diagrams for the binary aqueous mixtures of ethanol and acetone [see Sum and Sandler (1999a,b) for results for additional systems and values of the... 

Be able to compute the vapor-liquid equilibrium compositions when the liquid is an ideal mixture and the vapor is an ideal gas mixture (that is, to be be able to... 

As the first illustration of the use of these equations, consider vapor-liquid equilibrium in the hexane-triethylamine system at 60°C. These species form an essentially ideal mixture. The vapor pressure of hexane af this temperature is 0.7583 bar and that of triethylamine is 0.3843 bar these are so low that the fugacity coefficients at saturation and for the vapor phase can be neglected. Consequently, Eqs. 10.1-3 and 10.1-4 should be applicable to this system. The three solid lines in Fig. 10.1-1 represent the two species partial pressures and the total pressure, which were calculated using these equations and all are linear functions of the of liquid-phase mole fraction the points are the experimental results. The close agreement between the computations and the laboratory data indicates that the hexane-triethylamine mixture is ideal at these conditions. Note that this linear dependence of the partiaLand total pressures on mole fractions predicted by Eqs. 10.1-2 and 10.1-3 is trae only for ideal mixtures it is not true for nonideal mixtures, as we shall see in Sec. 10.2. 

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