In order to model liquid-phase nonideality at moderate pressures, the liquid activity coefficient y, must be known [Pg.62]

K VALUE FOR IDEAL LIQUID PHASE, NONIDEAL VAPOR PHASE 3.7 [Pg.104]

The excess enthalpy due to liquid-phase nonideality can be determined by applying (4-57) to (5-26), assuming the temperature dependence of (5-31). The result is the approximate relation [Pg.113]

Equations for Liquid-Phase Nonidealities A. Modified UNIQUAC Equation [Pg.212]

Since Raoulrs Jaw is p, = x-pf, the liquid-phase activity coefficient in Eq. (3.2-9) is a "Raouh s law correction factor that lakes info account liquid-phase nonideality. Since most distillations are carried out at relatively low pressure and moderate-lo-high temperature, Eq- (5.2-9) is the most generally used relationship in distillation system analysis and design. [Pg.233]

Comparing Equations 4.28 and 4.29, the liquid-phase nonideality is characterized by the activity coefficient yt. When Yi = 1, the behavior is ideal. If y, V I, then the value of Yi can be used to characterize the nonideality [Pg.61]

A procedure for approaching the problem of liquid phase nonideality through the use of activity coefficients is given in Table 12.2. [Pg.982]

Numerous analytical models have also been developed for binary liquid phase surface excess isotherms. A model equation that accounts for adsorbate size differences, bulk liquid phase nonideality, as well as a simplified description of adsorbent heterogeneity is given below [Pg.30]

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. [Pg.51]

Departures from Raoult s law are primarily from liquid-phase nonidealities (y 1). [Pg.585]

The case of binary solid-liquid equilibrium permits one to focus on liquid-phase nonidealities because the activity coefficient of solid component ij, Yjj, equals unity. Aselage et al. (148) investigated the liquid-solution behavior in the well-characterized Ga-Sb and In-Sb systems. The availability of a thermodynamically consistent data base (measurements of liquidus, component activity, and enthalpy of mixing) provided the opportunity to examine a variety of solution models. Little difference was found among seven models in their ability to fit the combined data base, although asymmetric models are expected to perform better in some systems. [Pg.162]

Modified Raonlt s law includes the activity coefficientto accountfor liquid-phase nonidealities, but is limited by the assumption of vapor-phase ideality. This is overcome by introdnction of tire vapor-pliase fugacity coefficient. For species i in a vapor mixtnre, Eq. (11.48) is written [Pg.507]

Example 15.5. The separation of benzene B from n-heptane H by ordinary distillation is difficult. At atmospheric pressure, the boiling points differ by 18.3°C. However, because of liquid-phase nonideality, the relative volatility decreases to a value less than 1.15 at high benzene concentrations. An alternative method of separation is liquid-liquid extraction with a mixture of dimethylformamide (DMF) and water. The solvent is much more selective for benzene than for n-heptane at 20°C. For two different solvent compositions, calculate interstage flow rates and compositions by the rigorous ISR method for the countercurrent liquid-liquid extraction cascade, which contains five equilibrium stages and is shown schematically in Fig. 15.22. [Pg.686]

Extractive distillation works by the exploitation of the selective solvent-induced enhancements or moderations of the liquid-phase nonidealities of the components to be separated. The solvent selectively alters the activity coefficients of the components being separated. To do this, a high concentration of solvent is necessaiy. Several features are essential [Pg.1313]

Related Calculations. Graphic representation of liquid-liquid equilibrium is convenient only for binary systems and isothermal ternary systems. Detailed discussion of such diagrams appears in A. W. Francis, Liquid-Liquid Equilibrium, Interscience, New York, 1963. Thermodynamic correlations of liquid-liquid systems using available models for liquid-phase nonideality are not always satisfactory, especially when one is trying to extrapolate outside the range of the data. [Pg.122]

In most cases, the solvent is much less volatile than the feed components it is therefore present mainly in the liquid phase in the primary column. This is desirable, as it is the liquid-phase nonidealities which give rise to the greater separation factor between the feed components. However, there is a relatively small amount of solvent in the vapor phase, and to avoid excessive loss of this solvent with the top product in the primary column, sufficient trays are provided above the solvent addition plate to reduce the solvent concentration in the top product to an acceptable level. [Pg.26]

Table 10.8 presents a comparison of SR-Polar EOS and Wilson-HOC with Henry components. The predictions by the two methods are in good agreement, although surprisingly for the ability of SR-Polar to account for liquid-phase nonideality. [Pg.299]

Flgare 1.5-2 shows exparimental and correlated binary VLE data for three dioxane-n-alkane systems at 80°C.m The pressure levels are modest (0.2-1.4 amt) liquid-phase nonidealities are sufficiently large to promote a2eotropy in all threa cases. Equations (1.5-12)—(1.5-15) were used for the data reduction, with experimental values for the Pf1 and virial coefficients were estimated from the correlation of Tsono-poulos.7 Activity coefficients were assumed to be represented by the three-parameter Margules equation, aed (he products of the data rednction were seis of valnes for parameters Al2, Ait. and D in Eqs. (1.4-10) and (1.4-11). The parameters so determined produce the correlations of the data shown by the solid curves in Fig. 1.5-2. For all threa systems, the data are represented to within their exparimental uncertainty. [Pg.37]

Equation (1.5-11) is an expression for the difference between the actual bubble pressure P given by Eq. (1.5-10) and the Raoult s Law bubble pressure Frl given by Eq. (1.5-9). To the extent that the approximate Eq. (1.5-10) is valid, Eq. (1.5-11) asserts that deviations from Raoult s Law result from liquid-phase nonidealities liquid-phase activity coefficients greater than unity promote positive deviations from Raoult s Law, and liquid-phase activity coefficients less than unity promote negative deviations fiom Raoult s Law. [Pg.36]

Pure-component vapor pressure can be used for predicting solubilities for systems in which Raoult s law is valid. For such systems = where p A is the pure-component vapor pressure of the solute and Pa is its partial pressure. Extreme care should be exercised when using pure-component vapor pressures to predict gas absorption behavior. Both vapor-phase and liquid-phase nonidealities can cause significant deviations from Raoult s law, and this is often the reason particular solvents are used, i.e., because they have special affinity for particular solutes. The book by Poling, Prausnitz, and O Connell (op. cit.) provides an excellent discussion of the conditions where Raoult s law is valid. Vapor-pressure data are available in Sec. 3 for a variety of materials. [Pg.1562]

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