Aqueous-phase nonidealities

This approach of considering the organic phase as ideal with all the nonidealities in the number of reactions, respectively of the complexes is quite often used in reactive solvent extraction modeling, even neglecting the aqueous phase nonideality. This approach results in system specific... 

Equation 11 implies that under these idealized conditions a log-log plot of S versus K will hage a slope ojj -1 and an intercept of -log V (19). The factors Yw/yw and 1/yq can be viewed as corrections for the activity change in the aqueous phase caused by the octanol dissolved in the water, and for nonideality in the octanol caused by the incompatibility of the solute with water-saturated octanol, respectively. 

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. 

In addition, a model is needed that can describe the nonideality of a system containing molecular and ionic species. Freguia and Rochelle adopted the model developed by Chen et al. [AIChE J., 25, 820 (1979)] and later modified by Mock et al. [AIChE J., 32, 1655 (1986)] for mixed-electrolyte systems. The combination of the speciation set of reactions [Eqs. (14-74a) to (14-74e) and the nonideality model is capable of representing the solubility data, such as presented in Figs. 14-1 and 14-2, to good accuracy. In addition, the model accurately and correctly represents the actual species present in the aqueous phase, which is important for faithful description of the chemical kinetics and species mass transfer across the interface. Finally, the thermodynamic model facilitates accurate modeling of the heat effects, such as those discussed in Example 6. 

Table I lists experimental results, comprising derived values of the fugacity of benzene at known total molarity in the aqueous phase, [B], and known molarity of 1-hexadecylpyridinium chloride [CPC] or sodium dodecylsulfate [SDS]. Fugacities have been calculated from total pressures by subtracting the vapor pressure of the aqueous solution in the absence of benzene from the measured total pressure and correcting for the small extent of nonideality of the vapor phase (15, 22). Results are given for temperatures varying from 25 to 45°C for the CPC systems and 15 to 45°C for the SDS systems.

If nonideality enhancement in the ion exchanger phase is respon sible the presence of the more highly ligand-coordinated species, the aqueous phase can be expected to be reduced to nondetectable concentration levels. 

Equation (1) is used to determine equilibrium between free products and dilute aqueous phases in terms of pure compound properties (solubility) adjusted for the composition of the product (mole fraction). The activity coefficient reflects the effect of phase composition on the equilibrium relation (nonideal behavior). If = 1, then Equation (1) reduces to Raoult s law, which states idealized... 

Similarly, chemical reactions may be used to convert a lipophilic chemical into a hydrophilic, water-seeking species. Solute mass transfer then occurs from the oily solvent phase into the aqueous phase. Pure fluids or mixtures of species that form hydrogen bonds or contain polar moieties are usually highly nonideal. In pure fluids, strong attractive interactions between like molecules may cause molecular aggregation through dipole-dipole and other interactions. In mixtures, specific interactions can occur between molecules of the same species (self-association) or between molecules of different species (solvation). 

An example of nonideal organic-phase behavior arises with di-2-ethylhexy phosphoric acid (DEHPA) in the extraction or metal cations. Equilibrium data of Troyer9 for extraction of copper in the presenes of nickel from sulfate solution into xylene solutions of DEHPA are shown in Fig. 8.3-10. Although the organic-phase copper concentration would be expected to rise in proportion to that in the aqueous phase,... 

The liquid streams from the separator and the bottom of the absorber are combined and fed into a distillation column. The bottoms from the column is split into two streams absorber lean oil and recycle acetic acid. The overhead vapor condenses into two liquid phases because of the nonideality of the phase equilibrium. The aqueous phase from the decanter is removed as product and sent to further processing, which we do not consider here. Some of the organic phase (mostly vinyl acetate) is refluxed back to the column, and some is removed for further processing. 

Nonideality of the aqueous phase is taken into account by refering to the components activity rather than to the components concentration, aj = Yi.Cj. Nonideality of the organic phases is related to their ability to form aggregates such as dimer molecules that decrease the extraction capacity. Determination of the nonideal behavior of organic phases is usually a more complex task than for aqueous phases, and several ways have been proposed for this purpose determination of the activity coefficients [1] calculation of the aggregation number [2] or description of the nonideal behavior as a function of the composition of the organic phase [3,4]. 

Figure 3.9 Conceptualization of the fugacity of a compound i (a) in an it/ea/ gas (h) in a pure liquid compound i (c) in an Wen/ liquid mixture and (d) in a nonideal liquid mixture (e.g., in aqueous solution). Note that in (b), (c), and (d), the gas and liquid phases are in equilibrium with one another.

The law of mass action is widely applicable. It correctly describes the equilibrium behavior of all chemical reaction systems whether they occur in solution or in the gas phase. Although, as we will see later, corrections for nonideal behavior must be applied in certain cases, such as for concentrated aqueous solutions and for gases at high pressures, the law of mass action provides a remarkably accurate description of all types of chemical equilibria. For example, consider again the ammonia synthesis reaction. At 500°C the value of K for this reaction is 6.0 X 10 2 F2/mol2. Whenever N2, H2, and NH3 are mixed together at this temperature, the system will always come to an equilibrium position such that... 

Eq. (28) thus obtained can be used to represent the solubility of poorly soluble drugs in aqueous mixed solvents if information about the properties of the binary solvent (composition, phase equilibria and molar volume), the nonideality parameters and the constant A is available. These parameters can be considered as adjustable, and determined by fitting the experimental solubilities in the binary solvent. We applied such a procedure to the solubilities of caffeine in water/AW-dimethylformamide (Herrador and Gonzalez, 1997) and water/1,4-dioxane (Adjei et al., 1980), of sulfamethizole in water/1,4-dioxane (Reillo et al., 1995) as well as of five solutes in water/ propylene glycol (Rubino and Obeng, 1991). It was shown that Eq. (28) provides accurate correlations of the experimental data. 

The main differences between adsorption from the gas phase and that from liquid phase are as follows [3]. First, adsorption from solution is essentially an exchange process, and hence, molecules adsorb not only because they are attracted by solids but also because the solution may reject them. A typical illustration is that the attachment of hydrophobic molecules on hydrophobic adsorbents from aqueous solutions is mainly driven by their aversion to the water and not by their attraction to the surface. Second, isotherms from solution may exhibit nonideality, not only because of lateral interactions among adsorbed molecules but also because of nonideality in the solution. Third, multilayer adsorption from solution is less common than from the gas phase, because of the stronger screening interaction forces in condensed fluids. 

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