Selectivity at Infinite Dilution

Figure 1.18 Selectivities at infinite dilution, S and capacities, fc , against the M-alkyl chain length, n in the cation of ionic liquid [C CjIm][Tf2N] S (n-hexane/ benzene) ( ), S (cyclohexane/benzene) ( ), and fc (benzene) (— —).

Selectivity at infinite dilution. Rank candidate solvents according to their selectivity at infinite dilution. The selectivity at infinite... 

In contrast to the previous attempts, our GC technique does not involve polynomial fits and integrations. It is especially developed to measure selectivity at infinite dilution of one of the components as a fimction of pressure. 

The selectivities, at infinite dilution are usually used for the selection of selective solvents. These values can be calculated from activity coefficients at infinite dilution (extractive distillation, extraction) or from Henry coefficients (absorption). 

Figure 5 Comparison cf the selectivity at infinite dilution of various selective solvents for...

A good indication of whether or not a certain component is a suitable entrainer from the thermodynamic point of view is the selectivity at infinite dilution. On the other hand, from the point of view of green separation processes, the amount of entrainer needed has to be minimized. Hence, the entrainer should combine a high selectivity with a high capacity. To classify selectivity and capacity of an entrainer the selectivity and capacity at infinite dilution, S-and k are used. The selectivity at infinite dilution S - is defined as the ratio of the activity coefficients at infinite dilution y It can be shown that the capacity k is also related to yf ... 

The entrainer should alter the separation factor in a way that the separation factor becomes different from unity. Since the entrainer has no influence on the pure component vapor pressures, the entrainer has to shift the ratio of the activity coefficients selectively. Although in practice a concentration of 50-80% entrainer is used in the columns, for the selection of a selective entrainer in the first step the selectivity at infinite dilution is used. 

The current pool of y 3 data for ionic liquid-organic solute interactions exceeds those obtained by alternative techniques such as headspace chromatography, dilutor and the static technique. As mentioned previously, experimental investigations on ionic liquids from an industrial perspective have largely been guided by separation problems of interest to the chemical and petrochemical industries such as alkane-aromatic, cyclo-alkane-aromatic and alkane-alkene mixtures. In this regard, selectivities at infinite dilution (5j ) are presented in Table 3 for (i) n-hexane-benzene, (ii) cyclohexane-benzene and (iii) n-hexane-l-hexene separations in various ionic liquid and commercially significant solvents. 

The selectivity at infinite dilution for the ionic liquid which indicated suitability of a solvent for separating mixtures of components i and j by extraction was given by... 

The selective binding of cations is not as sensitive to size as to valence. The value of Q for the condensation of counterions of the same valence is unaffected. In the case of monovalent cations, the dissociation of all counterions is complete at infinite dilution, when 2 1 When Q the... 

Conductometric titrations. Van Meurs and Dahmen25-30,31 showed that these titrations are theoretically of great value in understanding the ionics in non-aqueous solutions (see pp. 250-251) in practice they are of limited application compared with the more selective potentiometric titrations, as a consequence of the low mobilities and the mutually less different equivalent conductivities of the ions in the media concerned. The latter statement is illustrated by Table 4.7108, giving the equivalent conductivities at infinite dilution at 25° C of the H ion and of the other ions (see also Table 2.2 for aqueous solutions). However, in practice conductometric titrations can still be useful, e.g., (i) when a Lewis acid-base titration does not foresee a well defined potential jump at an indicator electrode, or (ii) when precipitations on the indicator electrode hamper its potentiometric functioning. 

It is fortunate that theory has been extended to take into account selective interactions in multicomponent systems, and it is seen from Eq. (91) (which is the expression used for the plots in Fig. 42 b) that the intercept at infinite dilution of protein or other solute does give the reciprocal of its correct molecular weight M2. This procedure is a straightforward one whereby one specifies within the constant K [Eq. (24)] a specific refractive index increment (9n7dc2)TiM. The subscript (i (a shorter way of writing subscripts jUj and ju3) signifies that the increments are to be taken at constant chemical potential of all diffusible solutes, that is, the components other than the polymer. This constitutes the osmotic pressure condition whereby only the macromolecule (component-2) is non-diffusible through a semi-permeable membrane. The quantity... 

Advanced Chemistry Development Inc. has built a sizeable proton chemical shift database derived from published spectra (most commonly in CDCI3 solution). Their H NMR predictor programme accesses this database and allows the prediction of chemical shifts. Whilst this software takes account of geometry in calculating scalar couplings, in predicting chemical shifts it essentially treats the structure as planar. It would therefore seem doomed to failure. However, if closely related compounds, run at infinite dilution and in the same solvent, are present in the database, the conformation is implied and the results can be quite accurate. Of course, the results will not be reliable if sub-structures are not well represented within the database and the wide dispersion of errors (dependent on whether a compound is represented or not) can cause serious problems in structure confirmation (later). ACD are currently revising their strict adherence to HOSE codes for sub-structure identification and this will hopefully remove infrequent odd sub-structure selections made currently. 

Activity coefficients at infinite dilution, of organic solutes in ILs have been reported in the literature during the last years very often [1,2,12,45,64, 65,106,123,144,174-189]. In most cases, a special technique based on the gas chromatographic determination of the solute retention time in a packed column filled with the IL as a stationary phase has been used [45,123,174-176,179,181-187]. An alternative method is the "dilutor technique" [64,65,106, 178,180]. A lot of y 3 (where 1 refers to the solute, i.e., the organic solvent, and 3 to the solvent, i.e., the IL) provide a useful tool for solvent selection in extractive distillation or solvent extraction processes. It is sufficient to know the separation factor of the components to be separated at infinite dilution to determine the applicability of a compound (a new IL) as a selective solvent. 

Table 1.9 Selectivities, S, at Infinite Dilution of Various Solvents for the n-Hexane/Benzene Separation S = rr3/>f3 at T = 298.15 K...

EQUIVALENT CONDUCTIVITY AT INFINITE DILUTION OF SELECTED CATIONS 1) AND ANIONS... 

Since the Margules expansions represent a convergent power series in the mole fractions,8 they can be summed selectively to yield closed-form model equations for the adsorbate species activity coefficients. A variety of two-parameter models can be constructed in this way by imposing a constraint on the empirical coefficients in addition to the Gibbs-Duhem equation. For example, a simple interpolation equation that connects the two limiting values of f (f°° at infinite dilution and f = 1.0 in the Reference State) can be derived after imposing the scaling constraint... 

This means that the partial specific enthalpy of NaOH at infinite dilution ( at xN.OH 0) is aibirarily set equal to zero at 68(T). The graphical interpretation that the diagram is constructed in such a way that a tangent drawn to the isotherm at xNaOH = 0 intersects the xn oh = 1 ordinate (not shown) at an entl of zero. The selection of ff ttOH as zero at 68(°F) automatically fixes the values the enthalpy of NaOH in all other states. 

Selectivity. The selectivity, S00, is defined as the ratio of the activity coefficients of the key components when each alone is present in the solvent at infinite dilution. Thus, for the propane-propylene system... 

Using physical interaction alone, Prausnitz and Anderson (9) and Weimer and Prausnitz (10) have developed this simplified expression for hydrocarbon selectivity, S°23, at infinite dilution in a solvent ... 

Figure 3 shows the variation of selectivity with pressure at infinite dilution conditions for bodi the gases. The broken horizontal line is the result from the Langmuir mode] which is same at infinite dilution of either gas. The selectivities predicted by lAST are different for the two gases as shown by the solid lines. The points are experimental data. 

Activity Coefficient at Infinite Dilution. A procedure similar to that employed by Wilson will be used here to obtain an expression for the excess Gibbs energy. Wilson started from the Flory and Huggins expression" 2 for the excess free energy of athermal solutions, but expressed the volume fractions in terms of local molar fractions. We selected Wilson s approach from a number of approaches, because it provided a better description of phase equilibria and because the interactions that count the most are the local one, but started from the more... 

Consequently, the method suggested in the current paper allows one to estimate not only the thickness of the layer of water that is affected by a solute molecule, but also the mutual affinity of solute molecules at infinite dilution. The compounds selected, hydrocarbons and alcohols, allowed one to investigate the hydrophobic effect for pure hydrophobic molecules (hydrocarbons) and for less hydrophobic substances such as the alcohols. 

The present paper is devoted to the local composition of liquid mixtures calculated in the framework of the Kirkwood—Buff theory of solutions. A new method is suggested to calculate the excess (or deficit) number of various molecules around a selected (central) molecule in binary and multicomponent liquid mixtures in terms of measurable macroscopic thermodynamic quantities, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volumes. This method accounts for an inaccessible volume due to the presence of a central molecule and is applied to binary and ternary mixtures. For the ideal binary mixture it is shown that because of the difference in the volumes of the pure components there is an excess (or deficit) number of different molecules around a central molecule. The excess (or deficit) becomes zero when the components of the ideal binary mixture have the same volume. The new method is also applied to methanol + water and 2-propanol -I- water mixtures. In the case of the 2-propanol + water mixture, the new method, in contrast to the other ones, indicates that clusters dominated by 2-propanol disappear at high alcohol mole fractions, in agreement with experimental observations. Finally, it is shown that the application of the new procedure to the ternary mixture water/protein/cosolvent at infinite dilution of the protein led to almost the same results as the methods involving a reference state. 

The required activity coefficients can either be calculated (predicted) with the help of thermodynamic models (group contribution methods) or obtained from factual data banks. The procedure for the selection of selective solvents for extractive distillation processes is given in refs. 4 and 5. The capacity C, of extractants can be estimated using activity coefficients at infinite dilution. 

---