Presentation of Vapor-Liquid Equilibrium Data

It is usually desirable to present the experimental vapor-liquid equilibrium data graphically. A number of methods of presentation have been developed, but the most important are the temperature-composition and the vapor-liquid composition diagrams. 

Phase Rule. The method of presentation must be consistent with the number of variables involved. For equilibrium conditions the number of independent variables can be obtained from the phase rule which states that the number of phases plus the degrees of variance F is equal to the number of components C plus 2. 

In the usual vapor-liquid equilibria two phases are involved liquid and vapor, hlowever, in some systems more than one liquid phase may be encountered. For the two-phase system the phase rule states that the degrees of freedom or variance are equal to the number of components. Thus a binary system has two degrees of freedom and can be represented by two variables on rectangular coordinates. Three-component systems involve three degrees of freedom and are usually presented on triangular coordinates. Multicomponent systems with more than three components are difficult to present, and special methods are employed for such systems. 

Starting with a mixture of the composition x at a constant total pressure equal to 760 mm., and at a temperature below 2, there will be but one phase present, the liquid mixture of CCI4 and CS2. As the temperature is raised, only a liquid phase will be present until the vertical line at X intersects the curve ABCy when a vapor phase of 

If the foregoing process is reversed, the steps can be followed in the same way. Starting with superheated vapor of a composition yn = Xi and at a temperature 5, condensation will first occur when the vertical line 6 cuts the vapor line ADC, when liquid of a composition xs will separate out. Further cooling will change both the composition of the liquid and the vapor along the lines ABC and ADC, respectively, until the liquid has reached the composition x when all the vapor will have disappeared. 

---

PRESENTATION OF VAPOR-LIQUID EQUILIBRIUM DATA 23 Table 2-1. Vapor-Liquid Equilibrium Data Continued)... 

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

A review is presented of techniques for the correlation and prediction of vapor-liquid equilibrium data in systems consisting of two volatile components and a salt dissolved in the liquid phase, and for the testing of such data for thermodynamic consistency. The complex interactions comprising salt effect in systems which in effect consist of a concentrated electrolyte in a mixed solvent composed of two liquid components, one or both of which may be polar, are discussed. The difficulties inherent in their characterization and quantitative treatment are described. Attempts to correlate, predict, and test data for thermodynamic consistency in such systems are reviewed under the following headings correlation at fixed liquid composition, extension to entire liquid composition range, prediction from pure-component properties, use of correlations based on the Gibbs-Duhem equation, and the recent special binary approach. 

We will present two applications of the restricted form of the Gibbs-Duhem equation in Examples 11.3 and 11.4, while Eq. 11.6.3 will be used in Chapter 13 to evaluate the thermodynamic consistency of vapor-liquid equilibrium data. 

Several activity coefficient models are available for industrial use. They are presented extensively in the thermodynamics literature (Prausnitz et al., 1986). Here we will give the equations for the activity coefficients of each component in a binary mixture. These equations can be used to regress binary parameters from binary experimental vapor-liquid equilibrium data. 

Vapor-liquid equilibrium data at atmospheric pressure (690-700 mmHg) for the systems consisting of ethyl alcohol-water saturated with copper(II) chloride, strontium chloride, and nickel(II) chloride are presented. Also provided are the solubilities of each of these salts in the liquid binary mixture at the boiling point. Copper(II) chloride and nickel(II) chloride completely break the azeotrope, while strontium chloride moves the azeotrope up to richer compositions in ethyl alcohol. The equilibrium data are correlated by two separate methods, one based on modified mole fractions, and the other on deviations from Raoult s Law. 

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... 

So that an azeotrope with acetone does not form, the alcohol used must have a high enough boiling point. This requirement is reliably established only if vapor-liquid equilibrium data for at least two, preferably three, of the members of the series with acetone are known. The Pierotti-Deal-Derr method (4) (discussed later) or the Tassios-Van Winkle method (5) can be used in this case. In the latter method a log-log plot of y°i vs. P°i should yield a straight line. Figure 1 presents results for n-alco-hols and benzene from the isobaric (760 mm Hg) data of Wehe and Coates (6). Reliable infinite dilution activity coefficients are established for the other n-alcohols from data for at least two, and preferably three, of them. These y° values are used with equations like those of Van Laar or Wilson (7) to generate activity coefficients at intermediate compositions and to check for an existing azeotrope or a difficult separation (x-y curve close to the 45° line). 

Ternary System. The values of all binary parameters used in predicting the ternary data are shown in Table IV. The predicted values of the vapor-liquid equilibrium data—i.e.9 the boiling point, and the composition of the vapor phase, y, for given values of the liquid composition, x, are presented in Tables V, VI, and VII. Also shown are the measured boiling points for the given values of the liquid composition. The RMSD value between the predicted and measured boiling points for the systems water-ethanol-l-propanol, water-ethanol-2-methyl-l-propanol, and water-ethanol-2-methyl-l-butanol are 0.23°C, 0.69°C, and 2.14°C. It seems therefore that since the NRTL equation successfully predicts temperature, the predicted values of y can be accepted confidently. 

Isobaric vapor-liquid equilibrium data at atmospheric pressure are reported for the four systems of the present investigation in Tables I-VI. Salt concentrations are reported as mole fraction salt in the solution, while mixed-solvent compositions are given on a salt-free basis. A single fixed-liquid composition was used for potassium iodide and sodium acetate potassium acetate used three—all chosen from the region of ethanol-water composition where relative volatility is highest. In the... 

A method to predict salt effect on vapor-liquid equilibrium in which salt is dissolved in a saturated state is introduced. In this method, salt effect is predicted by using preferential solvation numbers, the concentration of the salt, and the vapor-liquid equilibrium data for which salt is not involved. It is possible to predict salt effect completely without using actually measured data if the preferential solvation number can be predicted. Presently, however, it is impossible to completely predict preferential solvation number. Hence, the preferential solvation numbers are obtained through actual measurements, and these numbers are used for the prediction. If preferential solvation number can be predicted independently in the future, this method will be an extremely hopeful one. The salt effect prediction method is entirely in reverse sequence of that used to obtain preferential solvation number. Specifically, it is carried out in the following sequence. 

Our work gives insight into the many problems that would be met in trying to account for the influence of the concentration of water and acid both on reactions and physicochemical processes that take place in a solvent such as sulfolane. Our results also indicate some possible methods for solving such problems. For example, our present vapor-liquid equilibrium data on solutions of water and acid in sulfolane were correlated with solution composition along lines previously used for the system NH3-Cu(II) salts in aqueous solution (35) in this latter system... 

All of the necessary experimental data [Vf, H2,i, 7 2,3, and E (Margules parameter)] were taken from the original publications (indicated as footnotes to Table 1) or calculated using the data from Gmehling s vapor-liquid equilibrium data compilation. Figure 1 and Table 1 show that the present eq 25 is in much better agreement with experiment than Krichevsky s eq 1 and equations A2-3—5 from Appendix 2, which involve the Margules expression for the activity coefficient. The new eq 25 provides predictions that are comparable to those of an empirical correlation for aqueous mixtures of solvents, which involves three adjustable parameters. 

The more difficult problem is deciding upon the appropriate choice of activity coefficient model and values of the model parameters. Numerous models are available, some of which are presented in Section 2.4. A valuable reference for choosing an appropriate model is Volume 1 - Vapor-Liquid Equilibrium Data Collection of the DECHEMA Chemistry Data Series (Gmehling and Onken 1977), This volume ... 

With all these choices, and limited knowledge of your system, you will likely want to use the recommended options and make predictions of vapor-liquid equilibrium using Aspen Plus in order to compare those predictions with experimental data. Chapter 3 presented an example of such a comparison for the ethanol-water system. 

Group volume R and surface area Q are presented for 50 groups by Hansen et al. [17]. While the group volume R and surface area Q are obtained from analysis of pure substance data, the group-interaction parameters are obtained from correlation of mixture vapor-liquid equilibrium data. 

Other approaches to the computation of solid-liquid equilibria are shown in Table 11.2-3. The Soave-Redlich-Kwong equation of state evaluates fugacities to calculate solid-liquid equilibria,7 while Wenzel and Schmidt developed a modified van der Waals equation of state forthe representation ofphase equilibria. The Wenzel-Scbmidt approach generates fugacities, from which the authors developed a trial-and-error approach to compute solid-liquid equilibrium. Unno et a .9 recently presented a simplification of the solution of groups model (ASOG) that allows prediction of solution equilibrium from limited vapor-liquid equilibrium data. 

---