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Activity coefficient systems

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... [Pg.18]

Figure 4-7. Vapor-liquid equilibria and activity coefficients in a binary system showing a weak minimum in the activity coefficient of methanol. Figure 4-7. Vapor-liquid equilibria and activity coefficients in a binary system showing a weak minimum in the activity coefficient of methanol.
Figure 4-9. Vapor-liquid equilibria for a binary system where one component dimerizes in the vapor phase. Activity coefficients show only small deviations from liquid-phase ideality. Figure 4-9. Vapor-liquid equilibria for a binary system where one component dimerizes in the vapor phase. Activity coefficients show only small deviations from liquid-phase ideality.
Moderate errors in the total pressure calculations occur for the systems chloroform-ethanol-n-heptane and chloroform-acetone-methanol. Here strong hydrogen bonding between chloroform and alcohol creates unusual deviations from ideality for both alcohol-chloroform systems, the activity coefficients show... [Pg.53]

Null (1970) discusses some alternate models for the excess Gibbs energy which appear to be well suited for systems whose activity coefficients show extrema. [Pg.55]

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1... [Pg.58]

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. [Pg.59]

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... [Pg.61]

Evaluation of the activity coefficients, (or y for noncondensable components),is implemented by the FORTRAN subroutine GAMMA, which finds simultaneously the coefficients for all components. This subroutine references subroutine TAUS to obtain the binary parameters, at system temperature. [Pg.76]

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. [Pg.99]

The computer subroutines for calculation of vapor-phase and liquid-phase fugacity (activity) coefficients, reference fugac-ities, and molar enthalpies, as well as vapor-liquid and liquid-liquid equilibrium ratios, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements and CDC 6400 execution times for these subroutines are given in Appendix J. [Pg.289]

GIVEN TEMPERATURE T K) AND ESTIMATES OF PHASE COMPOSITIONS XR AND XE (USED WITHOUT CORRECTION TO EVALUATE ACTIVITY COEFFICIENTS GAR AND GAE), LILIK NORMALLY RETURNS ERR=0, BUT IF COMPONENT COMBINATIONS LACKING DATA ARE INVOLVED IT RETURNS ERR=l, AND IF A K IS OUT OF RANGE THEN ERR=2 key SHOULD BE 1 ON INITIAL CALL FOR A SYSTEM, 2 (OR 6)... [Pg.294]

GAMMA calculates activity coefficients for N components (N 20) at system temperature. For noncondensable components effective infinite-dilution activity coefficients are calculated. [Pg.310]

The stabiHty criteria for ternary and more complex systems may be obtained from a detailed analysis involving chemical potentials (23). The activity of each component is the same in the two Hquid phases at equiHbrium, but in general the equiHbrium mole fractions are greatiy different because of the different activity coefficients. The distribution coefficient m based on mole fractions, of a consolute component C between solvents B and A can thus be expressed... [Pg.60]

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). [Pg.61]

Fig. 3. Binary activity coefficients for two component systems having (a) positive and (b) negative deviations from Raoult s law. Conditions are either... Fig. 3. Binary activity coefficients for two component systems having (a) positive and (b) negative deviations from Raoult s law. Conditions are either...
Terminal activity coefficients, 7°, are noted in Figure 3. These are often called infinite dilution coefficients and for some systems are given in Table 1. The hexane—heptane mixture is included as an example of an ideal system. As the molecular species become more dissimilar they are prone to repel each other, tend toward liquid immiscihility, and have large positive activity coefficients, as in the case of hexane—water. [Pg.157]

If the molecular species in the liquid tend to form complexes, the system will have negative deviations and activity coefficients less than unity, eg, the system chloroform—ethyl acetate. In a2eotropic and extractive distillation (see Distillation, azeotropic and extractive) and in Hquid-Hquid extraction, nonideal Hquid behavior is used to enhance component separation (see Extraction, liquid—liquid). An extensive discussion on the selection of nonideal addition agents is available (17). [Pg.157]

Based on Hquid—Hquid equiHbrium principles, a general model of octanol—water partitioning is possible if accurate activity coefficients can be determined. First, phase equiHbrium relationships based on activity coefficients permit Hquid—Hquid equiHbrium calculations for the biaary octanol—water system. Because the two components are almost immiscible ia each other, two phases form an octanol-rich phase containing dissolved water, and a water-rich phase containing dissolved octanol. [Pg.238]

The use of UNIFAC for estimating activity coefficients in binary and multicomponent organic and organic—water systems is recommended for those systems composed of nonelectrolyte, nonpolymer substances for which only stmctural information is known. UNIFAC is not recommended for systems for which some reUable experimental data are available. The method, including revisions through 1987 (39), is available in commercial software packages such as AspenPlus (174). [Pg.253]

Hctivity Coefficients. Most activity coefficient property estimation methods are generally appHcable only to pure substances. Methods for properties of multicomponent systems are more complex and parameter fits usually rely on less experimental data. The primary group contribution methods of activity coefficient estimation are ASOG and UNIEAC. Of the two, UNIEAC has been fit to more combinations of groups and therefore can be appHed to a wider variety of compounds. Both methods are restricted to organic compounds and water. [Pg.253]

An alternate method for binary concentrated liquid systems where activity coefficients are not available or estimable is the method of Leffler and Cullinan previously given in Eq. (2-156). Absolute errors average 25 percent. [Pg.415]

Gamma/Phi Approach For many XT E systems of interest the pressure is low enough that a relatively simple equation of state, such as the two-term virial equation, is satisfactoiy for the vapor phase. Liquid-phase behavior, on the other hand, may be conveniently described by an equation for the excess Gibbs energy, from which activity coefficients are derived. The fugacity of species i in the liquid phase is then given by Eq. (4-102), written... [Pg.535]

When Eq. (4-282) is applied to XT E for which the vapor phase is an ideal gas and the liquid phase is an ideal solution, it reduces to a veiy simple expression. For ideal gases, fugacity coefficients and are unity, and the right-hand side of Eq. (4-283) reduces to the Poynting factor. For the systems of interest here this factor is always veiy close to unity, and for practical purposes <1 = 1. For ideal solutions, the activity coefficients are also unity. Equation (4-282) therefore reduces to... [Pg.536]

The binary interaction parameters are evaluated from liqiiid-phase correlations for binaiy systems. The most satisfactoiy procedure is to apply at infinite dilution the relation between a liquid-phase activity coefficient and its underlying fugacity coefficients, Rearrangement of the logarithmic form yields... [Pg.539]

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. [Pg.539]

Concentrated, Binary Mixtures of Nonelectrolytes Several correlations that predict the composition dependence of Dab. re summarized in Table 5-19. Most are based on known values of D°g and Dba- In fact, a rule of thumb states that, for many binary systems, D°g and Dba bound the Dab vs. Xa cuiwe. CuUinan s equation predicts dif-fusivities even in hen of values at infinite dilution, but requires accurate density, viscosity, and activity coefficient data. [Pg.598]

Table 13-1, based on the binary-system activity-coefficient-eqnation forms given in Table 13-3. Consistent Antoine vapor-pressure constants and liquid molar volumes are listed in Table 13-4. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanol-hexane system, whose activity coefficients are snown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may... Table 13-1, based on the binary-system activity-coefficient-eqnation forms given in Table 13-3. Consistent Antoine vapor-pressure constants and liquid molar volumes are listed in Table 13-4. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanol-hexane system, whose activity coefficients are snown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may...
As shown by Marek and Standart [Collect. Czech. Chem. Commun., 19, 1074 (1954)], it is preferable to correlate and utilize hquid-phase activity coefficients for the dimerizing component by considering separately the partial pressures of the monomer and dimer. For example, for a binary system of components 1 and 2, when only compound 1 dimerizes in the vapor phase, the following equations apply if an ideal gas is assumed ... [Pg.1258]

FIG. 13-20 Liqi lid-phase activity coefficients for an ethanol-n-hexane system, [Henleij and Seader, Eqiiilihriiim-Stage Separation Operations in Chemical Engineering, Wileif, New York, 1931 data of Si nor and Weher, J, Chem, Eng, Data, 5, 243-247 (I960).]... [Pg.1260]

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... [Pg.1293]


See other pages where Activity coefficient systems is mentioned: [Pg.51]    [Pg.289]    [Pg.14]    [Pg.175]    [Pg.285]    [Pg.156]    [Pg.159]    [Pg.179]    [Pg.189]    [Pg.225]    [Pg.236]    [Pg.237]    [Pg.238]    [Pg.249]    [Pg.252]    [Pg.252]    [Pg.524]    [Pg.1293]    [Pg.1293]    [Pg.1294]   
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