Behavior in the Liquid Phase

The thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

The influence of the model used to approximate the mass transfer behavior in the liquid phase (i.e., mixed, unmixed or finite mass transfer rate model). 

As-prepared catalysts showed most interesting behavior in the liquid phase hydrogenation of fra/i.x-2-hexcne-l-al. In contrast to the similarly prepared Ni/ZrO, catalyst, which produced selectively hexan-l-ol, with the Pd/ZrO, catalyst only the first step of reaction (4.1) is catalyzed and hexen-l-ol can be obtained selectively [4.65],... 

For the more nonvolatile species of mixtures, dependency of K-values on composition is due primarily to nonideal solution behavior in the liquid phase. Prausnitz, Edmister, and Chao showed that the relatively simple regular solu-... 

But unfortunately only the difference of the Porter parameters can be calculated. However, from the difference (A > B) it can be concluded that the activity coefficients in the liquid phase are larger than in the solid phase. Since ideal behavior in the liquid phase can be assumed for a mixture of enantiomers (i.e., Porter parameter A = 0), the results for a value of B = -1.313 are shown in Figure 8.10. For a given value of the temperature and the value for Xi can be calculated iteratively, so that Eqs. (8.20) and (8.21) are fulfilled. It can be seen that for the system D-carvoxime-L-carvoxime quite good agreement with the experimental findings [4] is obtained. 

As in Example 8.9, only the differences of the parameters are obtained. But for a system with a temperature minimum the activity coefficients in the solid phase are larger than in the liquid phase. The experimental and calculated data assuming ideal behavior in the liquid phase (A = 0) are shown in Figure 8.10 for a value B = 1.917. It can be seen that the results using the simple Porter equation are not satisfying. Therefore, Wilson parameters were directly fitted to the experimental data. It can be seen that much better results are obtained, if the nonideal behavior in the liquid and solid phase is taken into account. 

P8.14 The vapor pressures of liquid anthracene and phenanthrene can be described by the Antoine equation using the Antoine parameters given below. Calculate the vapor-liquid-solid equilibrium (VLSE) along the solid-liquid saturation curve assuming ideal mixture behavior in the liquid phase. Melting points and heats of fusion of both components are given in example P8.1 above. Compare the vapor-liquid separation factors to those of an isothermal VLE data set at 220 "C (calculate assuming ideal liquid mixture behavior). 

In the case of an ideal mixture, Ky is equal to 1 this means K = Kx. The deviation from ideal behavior in the liquid phase can be much stronger than that in the gas phase because of the small distance between the molecules. For a correct calculation of the equilibrium composition, the deviation from ideal behavior, this means Ky, has to be taken into account with the help of -models or group contribution methods (see Section 5.3 or 5.12). 

The axial dispersion model has been widely used to characterize the non-ideal mixing behavior in the liquid phase. In this model, axial dispersion coefficient is the single parameter representing the extent of backmixing. The following expression for the axial dispersion coefficient was derived by Kawase and Moo-Young [16] ... 

One step in the preparation of ultrapure water needed for various applications involves the removal of dissolved gaseous species 1 and volatile oiganic compound 2. This removal is to be implemented using N2 and/or vacuum to strip species 1 and 2. Develop an expression for the separation factor between species 1 and 2 in terms of the thermodynamic constants and temperature-dependent physical properties of the two compounds 1 and 2. Assume nonideal behavior in the liquid phase, an infinitely dilute solution of each species and ideal gas behavior. 

Plots like Figure 8.20 are only available for the aliphatic hydrocarbons, because of their practically ideal solution behavior in the liquid phase. No such plots seem to be available for seriously nonideal solutions, like ethanol-water. 

In practice, it is more convenient to predict the behavior of an ion, for any chosen set of conditions, by employing a much simpler distribution coefficient, which is defined as the concentration of a solute in the resin phase divided by its concentration in the liquid phase, or ... 

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... 

Deviations from Raonlt s law in solution behavior have been attributed to many charac teristics such as molecular size and shape, but the strongest deviations appear to be due to hydrogen bonding and electron donor-acceptor interac tions. Robbins [Chem. Eng. Prog., 76(10), 58 (1980)] presented a table of these interactions. Table 15-4, that provides a qualitative guide to solvent selection for hqnid-hqnid extraction, extractive distillation, azeotropic distillation, or even solvent crystallization. The ac tivity coefficient in the liquid phase is common to all these separation processes. 

GL 26] [R 3] [P 28] A simple reactor model was developed assuming isothermal behavior, confining mass transport to only from the gas to the liquid phase, and a sufficiently fast reaction (producing negligible reactant concentrations in the liquid phase) [10]. For this purpose, the Hatta number has to be within given limits. 

Fig. 3.2.12 Distribution and behavior of the liquid phases during in-bed filtration the basis of modeling.

Thus, by knowing aAB from vapor-liquid equilibrium and by specifying xA, A can be calculated. Figure 4.3a also shows a typical vapor-liquid equilibrium pair, where the mole fraction of benzene in the liquid phase is 0.4 and that in the vapor phase is 0.62. A diagonal line across the x-y diagram represents equal vapor and liquid compositions. The phase equilibrium behavior shows a curve above the diagonal line. This indicates that benzene has a higher concentration in the vapor phase than toluene, that is,... 

Pervaporation. Pervaporation differs from the other membrane processes described so far in that the phase-state on one side of the membrane is different from that on the other side. The term pervaporation is a combination of the words permselective and evaporation. The feed to the membrane module is a mixture (e.g. ethanol-water mixture) at a pressure high enough to maintain it in the liquid phase. The liquid mixture is contacted with a dense membrane. The other side of the membrane is maintained at a pressure at or below the dew point of the permeate, thus maintaining it in the vapor phase. The permeate side is often held under vacuum conditions. Pervaporation is potentially useful when separating mixtures that form azeotropes (e.g. ethanol-water mixture). One of the ways to change the vapor-liquid equilibrium to overcome azeotropic behavior is to place a membrane between the vapor and liquid phases. Temperatures are restricted to below 100°C, and as with other liquid membrane processes, feed pretreatment and membrane cleaning are necessary. 

Xi = mole fraction of Component i in the liquid phase Assuming ideal gas behavior (pi = y P),... 

The dynamic behavior of reactions in liquids may differ appreciably from that of gas phase reactions in several important respects. The short-range nature of intermolecular forces leads to several major differences in the macroscopic properties of the system, often with concomitant effects on the dynamics of chemical reactions occurring in the liquid phase. 

Stimulated by the Tokyo Tech results, several groups began studying similar bent-core mesogens. At the European Conference on Liquid Crystals, held in Zakopane, Poland, in March of 1997, Heppke et al. confirmed the Tokyo Tech results,46 and Weissflog et al. did as well, with the important exception that the Halle group found antiferroelectric behavior in the B2 phase.47... 

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