Activity coefficient from vapor-liquid data

Activity coefficients calculated by these methods agree fairly well for systems where the original equations, i.e., Eqs. (3.50) to (3.66), apply. Carlson and Colburn (5) and Colburn, Schoenborn, and Shilling (8) have shown that the van Laar constants cannot be calculated from solubility data for n-butanol-water and isobutanol-water, but the van Laar equations do not satisfactorily describe the activity coefficients obtained from vapor-liquid data in these systems either. 

Calculate activity coefficients for the system chloroform-acetone at 35.17 C. from vapor-liquid data reported in International Critical Tables (Vol. Ill, p. 286). Fit one of the integrated Gibbs-Duhem equations to the data. With the help of heat of solution data, ibid. Vol. V, pp. 151, 155, 158, estimate the values of the equation constants for 55.1 C., and calculate the activity coefficients for this temperature. Compare with those computed from vapor-liquid data at this temperature, ihid.j Vol. Ill, p. 286. 

The upper critical solution point for furfural-water lies at 122.7 C., 51 wt. per cent furfural. Calculate the van Laar and Margules constants from this datum, and compare with the values of activity coefficient at x = 0 and 1.0 obtained from vapor-liquid data, Chemical Engineers Handbook. Explain the results in terms of the applicability of the van Laar and Margules equations to this system. 

The analogy between equations derived from the fundamental residual- and excess-propeily relations is apparent. Whereas the fundamental lesidanl-pL-opeRy relation derives its usefulness from its direct relation to equations of state, the ci cc.s.s-property formulation is useful because V, and y are all experimentally accessible. Activity coefficients are found from vapor/liquid equilibrium data, and and values come from mixing experiments. 

The parameter An was calculated from vapor—liquid equilibrium data for binary solvents using Eq. (29). The activity coefficients of the components in the binary solvents were expressed via the Wilson equation (Wilson, 1964) and the Wilson parameters Ln and Ln were taken from GmehUng s vapor—liquid equilibrium data compilation (Gmehling et al., 1977—2003). 

Compilations of infinite-dilution activity coefficients, when available for the solute of interest, may be used to rank candidate solvents. Partition ratios at finite concentrations can be estimated from these data by extrapolation from infinite dilution using a suitable correlation equation such as NRTL [Eq. (15-25)]. Examples of these lands of calculations are given by Walas [Phase EquU ria in Chemical Engineering (Butterworth-Heinemann, 1985)]. Most activity coefficients available in the literature are for small organic molecules and are derived from vapor-liquid equilibrium measurements or azeotropic composition data. 

Experimental VLE data, namely equilibrium temperature, pressure, and vapor and liquid compositions, can be used to calculate the activity coefficients from Equation 1.29. The X-values are calculated from the composition data, /f = T/X . The fugacities and fugacity coefficients, /T, are calculated from the compositions, temperature, and pressure, using, for instance, an equation of state and liquid density data as described earlier. The activity coefficients are then calculated by rearranging Equation 1.29 ... 

Equation (1.5-6) follows from Eq. (1.2-58) it represents the effect of pressure on the activity coefficient sud requires liquid-phaw excess molar volume data. Equation (1.5-7) is a Foyniing correction Jsee Eq. (1.2-31) and the accompanying descussion. which requires volumetric data for pure liquid /. Equation (1.5-8) mpresenls the contributions of vapor-phase nonidealities, which are represented by a PVTx equation of stale. Nma here that the effects of vapor-phase nonidealities anter through beth and 4>T- Consistent description of subcrilical VLE via Eq. (1.5-4) requires that j>, end df bs evaluated in a consistent fashion. 

The illustrations of this section were meant to demonstrate how one can determine activity coefficients from measurements of temperature, pressure, and the mole fractions in both phases of a vapor-liquid equilibrium system. An alternative procedure is at constant temperature, to measure the total equilibrium pressure above liquid mixtures of known (or measured) composition. This replaces time-consuming measurements of vapor-phase compositions with a more detailed analysis of the experimental data and more complicated calculations. ... 

The values of the activity coefficients here are very large, especially compared with those we found previously from vapor-liquid equilibrium data. Such values for the activity coefficient of the dilute species in a mixture with species of very different chemical nature, such as carbon tetrachloride and water, is quite common. Note that because of the concentrations involved, the activity coefficients found are essentially the values at infinite dilution. ... 

Liquid Solution Behavior. The component activity coefficients in the liquid phase can be addressed separately from those in the solid solution by direct experimental determination or by analysis of the binary limits, since y p = 1. Because of the large amount of experimental effort required to study a ternary composition field and the high vapor pressures encountered in the arsenide and phosphide melts, a direct experimental determination of ternary activity coefficients has been reported only for the Ga-In-Sb system (26). Typically, the available binary liquidus data have been used to fix the adjustable parameters in a solution model with 0,p determined by Equation 7. The solution model expression for the activity coefficient has been used not only to represent the component activities along the liquidus curve, but also the stoichiometric liquid activities needed in Equation 7. The ternary melt solution behavior is then obtained by extending the binary models to describe a ternary mixture without additional adjustable parameters. In general, interactions between atoms in different groups exhibit negative deviations from ideal behavior... 

From the historical point of view and also from the number of applications in the literature, the common method is to use activity coefficients for the liquid phase, i.e., the polymer solution, and a separate equation-of-state for the solvent vapor phase, in many cases the truncated virial equation of state as for the data reduction of experimental measurements explained above. To this group of theories and models also free-volume models and lattice-fluid models will be added in this paper because they are usually applied within this approach. The approach where fugacity coefficients are calculated from one equation of state for both phases was applied to polymer solutions more recently, but it is the more promising method if one has to extrapolate over larger temperature and pressure ranges. 

Figure 3.10 is a comparison of activity coefficients calculated from these equations with those calculated from the vapor-liquid data of Furnas and Leighton [Ind, Eng, Chem. 29, 709 (1937)] at 760 mm. Hg. 

Calculate the activity coefficients from azeotropic data for the following systems using one of the integrated Gibbs-Duhem equations, obtaining the necessary data from the compilation of Horsley [Ind. Eng, Chem. Anal, Ed, 19, 508 (1947)]. Compare with those calculated from the complete vapor-liquid data, as reported in Chemical Engineers Handbook. ... 

We extract activity coefficients from the given azeotropic data and set a new boiling point, say 40°C, but keep liquid composition constant at Xa = 0.8943. This is followed by a calculation of total pressure at 40°C using the nonideal version of Equation 6.15d. The vapor composition i/a follows immediately from the ratio i/a = Pa/Pj 3T>d leads directly to tire new separation... 

The properties of dissolution as gas solubility and enthalpy of solution can be derived from vapor liquid equilibrium models representative of (C02-H20-amine) systems. The developments of such models are based on a system of equations related to phase equilibria and chemical reactions electro-neutrality and mass balance. The non ideality of the system can be taken into account in liquid phase by the expressions of activity coefficients and by fugacity coefficients in vapor phase. Non ideality is represented in activity and fugacity coefficient models through empirical interaction parameters that have to be fitted to experimental data. Development of efficient models will then depend on the quality and diversity of the experimental data. 

Carli, A. Activity coefficients from boiling data by computer. Brit. Chem. Eng. 17 (1972) 7 und 649. Chang, S. D., and Lu, B. C.-Y. A generalized virial equation of state and its application to vapor-liquid-equilibria at low temperatures. Adv. Cryogenic Eng. 17 (19 y2) 255. 

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Gmehhng and Onken (op. cit.) give the activity coefficient of acetone in water at infinite dilution as 6.74 at 25 C, depending on which set of vapor-liquid equilibrium data is correlated. From Eqs. (15-1) and (15-7) the partition ratio at infinite dilution of solute can he calculated as follows ... 

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. 

Experimental values for the activity coefficients for components 1 and 2 are obtained from the vapor-liquid equilibrium data. During an experiment, the following information is obtained Pressure (P), temperature (T), liquid phase mole fraction (x, and x2=l-X ) and vapor phase mole fraction (yi and y2=l—yi). 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

Although the methods developed here can be used to predict liquid-liquid equilibrium, the predictions will only be as good as the coefficients used in the activity coefficient model. Such predictions can be critical when designing liquid-liquid separation systems. When predicting liquid-liquid equilibrium, it is always better to use coefficients correlated from liquid-liquid equilibrium data, rather than coefficients based on the correlation of vapor-liquid equilibrium data. Equally well, when predicting vapor-liquid equilibrium, it is always better to use coefficients correlated to vapor-liquid equilibrium data, rather than coefficients based on the correlation of liquid-liquid equilibrium data. Also, when calculating liquid-liquid equilibrium with multicomponent systems, it is better to use multicomponent experimental data, rather than binary data. 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

Another way to obtain HENRY S constant H of undissociated acid is from high concentration vapor-liquid equilibria where dissociation is negligible. Using NRTL equation for the representation of the data of BROWN and EWALD (6) at high concentration in acetic acid (10 2 < x < 1), he finds the limiting activity coefficient of undissociated acid at 100°C... 

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