Nernst partition coefficients

SClLLs are limited to biphasic systems, that is, the IL (e.g., [BMIM][0cS04 ) has to be insoluble in the organic phase, for example, in the case of COD hydrogenation in a mixture of the solvent -dodecane with the organic reactant COD and the products COE and cyclooctane (COA). With regard to the effective concentrations of the reactants at the surface of the IL-coated catalyst, concentrations in the IL layer have to be considered, which are governed by the Nernst s law of partition. The Nernst partition coefficient of a substance i (e.g., of COD, COE, or COA), 

In general, the solubility of an intermediate in the IL should be as low as possible (compared to the feed) to remove the intermediate from the IL phase that is in direct contact with the catalyst s surface to suppress further hydrogenation. The values, which were measured by the initial and final concentrations of COD, COE, or COA in the organic phase in contact with different ILs (Table 14.2), indicate that the feed COD (Kn.so C = bas a higher solubility in the IL [BMIM][0cS04] than the intermediate COE (fCN,50°c = 0.31). This was one of the reasons to choose this system for the initial investigations of the SCILL concept as this would increase the COE-selectivity if the catalyst is coated with an IL ( physical solvent effect ). 

For the other ILs, the partition coefficients of COD and COE were slightly lower, but the partition coefficient of COE was still always lower compared to that of COD (Table 14.2). 

For the hydrogenation of octine, cinnamaldehyde, and naphthalene, the Kjj values are given in Chapter 12 (Tables 14.3 and 14.4), indicating that the intermediates octene, hydrocinnamaldehyde, and tetrahn should be favored for SCILL catalysts ( N,intermediate/ N,feed 1) whetcas for the intermediate cinnamyl alcohol this should be the reverse = % 

Hydrogenation of Nernst Reaction rate at 50% coefficient feed conversion 

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The approach just used for fractional crystallization can be transposed immediately to fractional melting, a process by which each packet of melt is withdrawn from the source thereby prevented from equilibration with the solid. Again, these equations will be developed in Chapter 9, but the present section emphasizes a representation which does not require constant Berthelot-Nernst partition coefficients, and therefore is more useful for major elements. 

Nernst partition coefficient of the system IL/n-dodecane (for qfdooctodiene and octane) and of IL/n-heptane (for... 

The theoretical value given in brackets is estimated by Eq. (14.13) based on the Nernst partition coefficient of the feed and the measured decrease of the internal surface area. It is thereby assumed that the rate is zero order with regard to hydrogen, which was only verified for the hydrogenation of cyclooctadiene. 

Many ILs show extractive properties of hydrocarbon contaminants (sulfurated and nitrogenated compounds), however much of these compoimds required several extraction cycles for "quantitative" remotion of contaminants, even when in some cases a 1 1 ratio (IL/hydrocarbons) is required, it is, their extractive properties are very pwor. The Nernst partition coefficient (Kn) favors extraction of most aromatic components of the fuel oil and this can be a limitation of the extractive method. 

If the substance shared between two solvents can exist in different molecular states in them, the simple distribution law is no longer valid. The experiments of Berthelot and Jungfleiscli, and the thermodynamic deduction show, however, that the distribution law holds for each molecular state separately. Thus, if benzoic acid is shared between water and benzene, the partition coefficient is not constant for all concentrations, but diminishes with increasing concentration in the aqueous layer. This is a consequence of the existence of the acid in benzene chiefly as double molecules (C6H5COOH)2, and if the amount of unpolymerised acid is calculated by the law of mass action (see Chapter XIII.) it is found to be in a constant ratio to that in the aqueous layer, independently of the concentration (cf. Nernst, Theoretical Chemistry, 2nd Eng. trans., 486 Die Verteilnngssatz, W. Hertz, Ahrens h annulling, Stuttgart, 1909). 

Moreover, as the ratio uf/uf is by definition the partition coefficient of I, P , this parameter can be defined by putting into evidence the ratio of the ion activities in the Nernst equation ... 

The second boundary condition arises from the continuity of chemical potential [44], which implies - under ideally dilute conditions - a fixed ratio, the so-called (Nernst) distribution or partition coefficient, A n, between the concentrations at the adjacent positions of both media ... 

We have already seen that, within the range of Nernst s law, the solid/liquid partition coefficient differs from the thermodynamic constant by the ratio of the Henry s law activity coefficients in the two phases—i.e.,... 

The equilibrium constant Ki(T,p), which is independent of mole fraction is called the distribution or partition coefficient of the substance i between the solutions 1 and 2. This equation is the generalized form of the Nernst distribution law. 

DYNAMICS OF DISTRIBUTION The natural aqueous system is a complex multiphase system which contains dissolved chemicals as well as suspended solids. The metals present in such a system are likely to distribute themselves between the various components of the solid phase and the liquid phase. Such a distribution may attain (a) a true equilibrium or (b) follow a steady state condition. If an element in a system has attained a true equilibrium, the ratio of element concentrations in two phases (solid/liquid), in principle, must remain unchanged at any given temperature. The mathematical relation of metal concentrations in these two phases is governed by the Nernst distribution law (41) commonly called the partition coefficient (1 ) and is defined as = s) /a(l) where a(s) is the activity of metal ions associated with the solid phase and a( ) is the activity of metal ions associated with the liquid phase (dissolved). This behavior of element is a direct consequence of the dynamics of ionic distribution in a multiphase system. For dilute solution, which generally obeys Raoult s law (41) activity (a) of a metal ion can be substituted by its concentration, (c) moles L l or moles Kg i. This ratio (Kd) serves as a comparison for relative affinity of metal ions for various components-exchangeable, carbonate, oxide, organic-of the solid phase. Chemical potential which is a function of several variables controls the numerical values of Kd (41). 

I he simplest is the partition of a solute between two immiscible solvents. In this case [0] /[Z)], = K, where K is the partition coefficient. This equilibrium is often referred to as the Nernst distribution. When [Z)], is plotted against [Z)], at constant temperature the curve is a straight line which terminates at the point when both the fibre and the dyebath are saturated. There are slight deviations from the linearity of the curve, particularly as the solutions become more concentrated. This system is probably exhibited in its ideal form when dyeing cellulose acetate rayon from an alcoholic dye solution, but it is also essentially true in the case of the application of disperse dyes in aqueous suspension to cellulose acetate, because the dyes are all soluble in water to a very limited extent and the undissolved particles act as a reservoir to maintain the concentration of the solution. The curve for this isotherm is shown in Fig. 12.14. 

Thermodynamic partition coefficient. In chromatographic applications the Nernst distribution constant it of a component i, referred to as the... 

Despite the apparently over-sin lified form of the Berthelot-Nernst distribution coefficient, it has been extensively employed in trace element geochemistry often with considerable success. In this respect it is instructive to compare D. with the true equilibrium constant for a given reaction. As an example the partition of Ni between olivine and clinopyroxene (Hakli and Wright, 1967 Broecker and Oversby, 1971 Banno and Matsui, 1973 Carmichael Consider the following exchange reaction ... 

Ideally a trace element geothermometer should be based upon a reaction with a large AH and small AV and vice versa for a geobarometer. A number of experimental studies have now demons trated the temperature dependence of Berthelot-Nernst distribution coefficients. Noteworthy amongst these are the experiments of Shimizu (l97 ) on the distribution of Sr, Ba, K, Rb, and Cs between clinopyroxenes and liquid and those of Drake and Weill (1973) on the partitioning of Sr, Ba and Eu between plagioclase and liquid. 

In other words, the mole fraction ratio of / in the coexisting phases at equilibrium for a given T and P should be constant. This is Nernst s law (cf. Lewis and Randall 1961). K is also called the distribution coefficient, often symbolized by >, and is used in the study of trace element partitioning between coexisting mineral solid solutions. 

For either NaCl or for HOAc or for any other solute distributed between immiscible liquids at a fixed temperature and pressure, provided that the concentration of solute is low (i.e., for the dilute solution case), can be set equal to the partition constant Kj) because activity coefficients can be set equal to 1. The partition constant or Nernst distribution constant in our illustration for acetic acid partitioned between ether and water can be defined as... 

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