Distribution coefficient, Nernst

Chromatographic techniques can be classified into three categories depending on the physical nature of the phases, on the process used, or on the physico-chemical phenomenon, which is at the basis of the Nernst distribution coefficient K, also defined as ... 

The capacity factor, k , is the product of the phase ratio between stationary and mobile phases in the separator column and the Nernst distribution coefficient, K ... 

K Nernst distribution coefficient Vs Volume of the stationary phase Vm Volume of the mobile phase Cs Solute concentration in the stationary phase Cm Solute concentration in the mobile phase... 

Chromatographic techniques can be classified according to various criteria as a function of the physical nature of the phases of the process used or by the physico-chemical phenomena giving rise to the Nernst distribution coefficient K. The following classification has been established by consideration of the physical nature of the two phases involved (Figure 1.14). 

If the value of the Nernst distribution coefficient is known (see (3.3.78)), then, for dilute solutions. 

Many attempts to model trace element abmdance variations in natural systems have employed the so-called Berthelot-Nernst distribution coefficient or distribution coefficients following the Henderson and Kracek treatment (see review of Mclntire, I963). Both Mclntire (1963) and Banno and Matsui (1973) have previously discussed the relative advantages and disadvantages of these distribution coefficients and reference is made to these works for additional discussion. 

For the distribution of a trace element i between a solid and a liquid phase, the Berthelot-Nernst distribution coefficient (D )... 

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 ... 

The high degree of success which has been obtained with the simple Berthelot-Nernst distribution coefficient must reflect the comparatively small effect of its deficiencies compared with the wide range of values of and the magnitude of trace element abundance variations in nature. Its great limitation is inevitably in the interpretation of more subtle variations, such as might arise through variations in temperature or pressirre of equilibration. 

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. 

Nevertheless, it is doubtful that geothermometers based upon the Berthelot-Nernst distribution coefficient will ever be useful in systems of variable composition. 

The interpretation and modelling of trace element abundance variations in rocks and minerals have employed Berthelot-Nernst distribution coefficients or less frequently compounded coefficients such as the Renderson-Kracek coefficients. Although from the standpoint of thermodynamics these are inadequate and may differ considerably from time equilibrium constants, their use has met with considerable success. 

The interface separating two immiscible electrolyte solutions, e.g., one aqueous and the other based on a polar organic solvent, may be reversible with respect to one or many ions simultaneously, and also to electrons. Works by Nernst constitute a fundamental contribution to the electrochemical analysis of the phase equilibrium between two immiscible electrolyte solutions [1-3]. According to these works, in the above system electrical potentials originate from the difference of distribution coefficients of ions of the electrolyte present in the both phases. 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

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 ... 

Analytes distribute themselves between aqueous and organic layers according to the Nernst distribution law, where the distribution coefficient, Kq. is equal to the analyte ratio in each phase at equilibrium. 

Check whether the Nernst Distribution Law applies. If not, what changes are needed to obtain a constant distribution coefficient What does this imply about the solution process of benzoic acid in the two phases ... 

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. 

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. 

The distribution coefficient, which for a substance is the ratio of its amount sorbed on the surface of a solid to its aqueous concentration, is also an expression of Nernst s law. (See Chap. 10.)... 

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. 

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... 

Table 1-6. Additional formulae of the Nernst distribution law. Correlations and conversion relationships for the distribution coefficient K.

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

In situations where trace element abimdance variations are large, the use of these distribution coefficients will certainly help to limit the possible ways in which the variations were generated. The fact that these distribution coefficients, particularly the Berthelot-Nernst coefficients, vary with P, T and composition, greatly limits their usefulness in situations where the variations in trace element chemistry are more subtle as could arise from P and T variations. For geothermometry and geobarometry, it is necessary to calculate true equilibrium constants and some possible approaches to this problem have been discussed here. 

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). 

Therefore, the distribution ratio of B remains constant only if the ratio of the activity coefficients is independent of the total concentration of B in the system, which holds approximately in dilute solutions. Thus, although solutions of metal chelates in water or nonpolar organic solvents may be quite nonideal, Nernst s law may still be practically obeyed for them if their concentrations are very low (JCchehte< 10" ). Deviations from Nernst s law (constant D ) will in general take place in moderately concentrated solutions, which are of particular importance for industrial solvent extraction (see Chapter 12). 

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