Extraction equilibria

For a linear equilibrium curve with constant film coefficients, Icl and Icq, the overall coefficient, Kl, will also be constant, but for the case of a non-linear equilibrium relationship, the value of m, which is the local slope of the equilibrium curve, will vary with solute concentration. The result is that the overall coefficient, Kl, will also vary with concentration, and therefore in modelling the case of a non-linear equilibrium extraction, further functional relationships relating the mass transfer coefficient to concentration will be required, such that... 

Figure 3.35. Information flow diagram for the continuous equilibrium extraction stage.

The modelling approach to multistage countercurrent equilibrium extraction cascades, based on a mass transfer rate term as shown in Sec. 1.4, can therefore usefully be applied to such types of extractor column. The magnitude of the... 

Figure 5.188. Countercurrent multistage equilibrium extraction unit.

The modelling approach to multistage countercurrent equilibrium extraction cascades, based on a mass transfer rate term as shown in Section 1.4, can therefore usefully be applied to such types of extractor column. The magnitude of the mass transfer capacity coefficient term, now used in the model equations, must however be a realistic value corresponding to the hydrodynamic conditions, actually existing within the column and, of course, will be substantially less than that leading to an equilibrium condition. 

If the solute A does not undergo any reaction in the two solvents, except for the solubility caused by the solvation due to the nonspecific cohesive forces in the liquids, the distribution of the solute follows the Nernst distribution law, and the equilibrium reaction can be described either by a distribution constant or an (equilibrium) extraction constant... 

A simplified equilibrium extraction model (Fig. 6) was presented by Dordick and colleagues [188] to explain the resolution behavior of glycoproteins in affinity based reverse micellar extraction and separation (ARMES). Their system for the study includes soybean peroxidase (SBP, MW 37 KDa, pi 4.1) and aj-acid glycoprotein (AGP, MW 43 KDa, pi 3.7) as glycoprotein solutes, concanavalin A (ConA) as the affinity ligand in AOT/isooctane RMs. The separation factor (a) for the separation of SBP from AGP can be given by... 

Fig. 6. Equilibrium extraction model involved in the ARMES process. (Reproduced from [188] with permission of AIChE)...

Fig. 11. Plot of initial cation transport rates for various carrier/alkali picrate pairs versus equilibrium extraction constants log Ke the points are experimental data, the curve is calculated [6.1, 6.4,6.17]. For analytical reasons the Ke values were determined in conditions different from those of the transport experiments the carriers are cryptands (for [2.2.C5] and [2.1.C5] see structures in [6.1]) dibenzo-18-crown-6, DB18-6 and valinomycin, VAL picrate, P.

The Freon TA Soxhlet extraction of the RTV silicone sample at different curing times with Freon reveals the degree of curing of the material. At time zero, when the RTV material was first coated for room temperature cure, almost 100% extractables were obtained (except residue of fillers). This 100% extractable indicates a 0% cure of the material. After 16 hrs. of room temperature cure at 50% relative humidity, most of the RTV material (>90%) was cured. After the second day, almost all of the RTVs studied were fully cured, and they seem to reach an extraction equilibrium. Further curing time shows no noticeable change in amount of extractables. For the fully cured RTV silicone, the level of extractables at their equilibrium extraction was a good indication of the unreactive cyclics present in this material. In Figure 5, the RTV silicone extractable is approximately 4%. 

FIGURE 12.2 Hollow-fiber devices for membrane extraction, (a) Hollow-fiber loops for equilibrium extraction redrawn after Liu et al. (From Liu, J.-F., Jbnsson, J.A., and Mayer, P., Anal. Chem., 77, 4800, 2005.) (b) Liquid-phase microextraction after Pedersen-Bjergaard and Rasmussen. (From Grpuhaug Halvorsen, T., Pedersen-Bjergaard, S., Reubsaet, J.L.E., and Rasmussen, K.E., J. Sep. ScL, 24, 615, 2001. With permission.) (c) Syringe-based hollow fiber LPME. (Erom Zhao, L. and Lee, H.K., Anal. Chem., 74, 2486, 2002. Copyright 2002 American Chemical Society. With permission.)... 

These initial parameters are easily accessible experimentally by equilibrium extraction experiments [75]. For example, extraction of titanium(lV) from 0.1 mol/kg Ti(IV) hydrochloric acid solutions at 0.45 mol/kg (pH = 0.65), 2 mol/kg and at 7 mol/kg HCl by 1 mol/kg DEHPA in benzene, at aqueous phase/organic phase = 5/1, have shown the initial distribution coefficients (for details, refer to [75]) ... 

In the above equilibrium, extractant dependency studies have indicated that n = 1 for Am" and Bk " and = 2 for Cf ". These stoichiometries have been observed for extractions into chloroform, and the self-adduct formation with trivalent actinides has been possibly cormected with tetrads where Cm is one of the minima. Extractions into xylene, however, leads to the formation of selfadducts with all four actinides due to better distribution coefficients in xylene over chloroform. The formation of self-adducts is due to ligand concentration, ionization constant of the ligand, basicity of the bound ligand, solvent identity, and oxidation state of the metal ion. 

Although SPME is mainly an equilibrium extraction technique, it has the ability to provide thorough extraction. If the coating/matrix partition coefficient, Ai,., is very large (i.e. K,J, F), the amount of analyte desorbed by the coating will be... 

Phenol, a common priority pollutant, was extracted from two environmental matrices, soil and water, using near critical and supercritical carbon dioxide. The primary objective of this study was to determine the distribution of the contaminant between the soil or water and the supercritical phase, and the effect of soil moisture and co-solvents on the distribution coefficients. Static equilibrium extractions were performed on dry and wetted soil contaminated with 1 wt.% phenol and on water containing 6.8 wt.% phenol. Supercritical carbon dioxide (with and without en-trainers) was chosen as the solvent for the study. An appropriate entrainer for dry soil extractions (methanol) ffiffered from that found for aqueous extractions (benzene). However, soil moisture was found to have a significant impact on the effectiveness of en-trainers for soil extractions of phenol. Entrainers appropriate for extracting wetted soil were found to be the same as those advantageous for aqueous extractions. Benzene was also extracted from dry and wetted soil to investigate the extractability of a hydrophobic compound. 

A detailed description of the experimental apparatus and procedure used for the aqueous study are given elsewhere (Roop and Akgerman, Ind. Eng. Chem. R., in review) Static equilibrium extractions were carried out in a high pressure equilibrium cell (300 mL Autoclave). After the vessel is initially charged with 150 mL of water containing 6.8 wt.% phenol and supercritical carbon dioxide (and a small amount of entrainer, if desired), the contents were mixed for one hour followed by a two hour period for phase separation. Samples from both the aqueous phase and the supercritical phase were taken for analysis and the distribution coefficient for phenol calculated. 

The 2-CP equihbrium concentration (Cg) in the aqueous phase measured in a test run and the equilibrium extraction capacity (Q<.) was readily calculated using the measured data and the known initial conditions. According to Eq. (58), a plot of 1/Qe versus l/Cg would yield a straight hne and the model parameters (a and b) are obtained from the slope and intercept. The model involved only single empirical parameter, which is easy to establish from the experimental data. 

Let us consider the equations that describe the equilibrium extraction of a material from one phase to another. In practice, equilibrium concentrations in two-phase systems are described in terms of a distribution coeffieient (sometimes called a partition coefficient), which relates the equilibrium concentrations of a species in each of the two phases. Physical chemistry texts usually... 

Although distribution coefficients in metal extraction systems are highly variable, they are thermodynamic quantities that can be mensured and correlated as functions of the state of the system. Because of the multicomponent ueiure of melal extraction systems, one must take care to identify a proper set of jedepeitdent variables in constructing a correlation of phase equilibrium data. Another consideration in treating equilibrium extraction data is tbat one desires a systematic method for treating the effects of... 

FIGURE 8.3-9 Comparison of chemical-equilibrium extraction models with stripping date for copper in Kelex 100. Curve A follows Eq. (8.3-1). Curve S is obtained by solving Eq. < 8,3- ) simultaneously with Eq. (8.3-2). From Ref, 5, with permission. 

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