Liquid-Phase Nonideality

For liquids the situation is different. If we rewrite Eq. 12.30 using the normal definition of activity for the liquid phase, and considering the reaction -butane isobutane, we will have 

For this reaction the two rightmost ratios (normally called Ky and the pressure term, which has no common name or symbol) are both practically 1.00, so this is almost the same result as in Example 12.1. However, if the reaction of interest were one in which the liquid-phase nonideality were substantial, Eq. 12.36 shows how that would be accounted for (see Problems 12.30 and 12.31). 

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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. 

The convergence rate depends somewhat on the problem and on the initial estimates used. For mixtures that are not extremely wide-boiling, convergence is usually accomplished in three or four iterations,t even in the presence of relatively strong liquid-phase nonidealities. For example, cases 1 through 4 in Table 1 are typical of relatively close-boiling mixtures the latter three exhibit significant liquid-phase nonidealities. 

Equations for Liquid-Phase Nonidealities A. Modified UNIQUAC Equation... 

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 ... 

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 ... 

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

The equilibrium conversion can be calculated from knowledge of the free energy, together with physical properties to account for vapor and liquid-phase nonidealities. The equilibrium conversion can be changed by appropriate changes to the reactor temperature, pressure and concentration. The general trends for reaction equilibrium are summarized in Figure 6.8. 

The solvophobic model of liquid-phase nonideality takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. First, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbability, Henry s constant, and aqueous solubility (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

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. 

Pure-component vapor pressure can be used for predicting solubilities for systems in which Raoult s law is valid. For such systems pA = p°Axa, 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. 

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. 

K VALUE FOR IDEAL LIQUID PHASE, NONIDEAL VAPOR PHASE 3.7... 

Compute the Gfj parameters for the Wilson equation. General engineering practice is to establish liquid-phase nonideality through experimental measurement of vapor-liquid equilibrium. Models with adjustable parameters exist for adequately representing most nonideal-solution behavior. Because of these models, the amount of experimental information needed is not excessive (see Example 3.9, which shows procedures for calculating such parameters from experimental data). 

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. 

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. 

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 ... 

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

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 ... 

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

Equation (1.5-11) is an expression for the difference between (he acinal bubble pressure P given by Eq. (1.5-10) aed the Ranult s Law bubble pressure PBL given by Eq. (1.5-9). To the extent that the approximate Eq. (1.5-10) is valid, Eq. (1.5-11) asserts diet deviations from Raoult s Law result from liquid-phase nonidealities liquid-phase activity coefficients greater than unity promore positive deviations from Raoult s Law. and liquid-phase activity coefficients less than unity promote negative deviations from Raonlt s Law. 

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. 

Perhaps the most important term in Eq. (5.2-3) is the liquid-phase activity coefficient, and mathods for its prediction have been developed in many forms and by many workers. For binery systems die Van Laar [Eq. (1.4-18)]. Wilson [Eq. (1.4-23)]. NRTL (Eq. (1.4-27)], and UNIQUAC [Eq. (1.4-3 )] relationships are useful for predicting liquid-phase nonidealities, but they require some experimental data. When no data are available, and an approximate nonideality correction will suffice, the UNiFAC approach Eq-(1.4-31)], which utilizes functional group contributions, may be used. For special cases Involving regular solutions (no excess entropy of mixing), the Scatchard-Hiidebmod mathod provides liquid-phase activity coefficients based on easily obtained pane-component properties. 

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. 

Nonideal solution effects can be incorporated into /f-value formulations in two different ways. Chapter 4 described the use of the fugacity coefficient, in conjunction with an equation of state and adequate mixing rules. This is the method most frequently used for handling nonidealities in the vapor phase. However, tv reflects the combined effects of a nonideal gas and a nonideal gas solution. At low pressures, both effects are negligible. At moderate pressures, a vapor solution may still be ideal even though the gas mixture does not follow the ideal gas law. Nonidealities in the liquid phase, however, can be severe even at low pressures. In Section 4.5, il was used to express liquid-phase nonidealities for nonpolar species. When polar species are present, mixing rules can be modified to include binary interaction parameters as in (4-113). 

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... 

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. 

The liquid-phase nonideality is so large that a heterogeneous azeotrope is formed. The molecules are so dissimilar that two liquid phases are formed. The composition of the vapor is 75.17mol% water at 1 atm. The compositions of the two liquid phases that are in equilibrium with this vapor are 43.86 and 98.05 mol% water, respectively. 

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