Equilibrium Nernst distribution

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... 

A review of several classic equilibrium equations is in order. The Nernst distribution law states that a neutral species will distribute between two immiscible solvents with a constant ratio of concentrations. 

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... 

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. 

The static - double-layer effect has been accounted for by assuming an equilibrium ionic distribution up to the positions located close to the interface in phases w and o, respectively, presumably at the corresponding outer Helmholtz plane (-> Frumkin correction) [iii], see also -> Verwey-Niessen model. Significance of the Frumkin correction was discussed critically to show that it applies only at equilibrium, that is, in the absence of faradaic current [vi]. Instead, the dynamic Levich correction should be used if the system is not at equilibrium [vi, vii]. Theoretical description of the ion transfer has remained a matter of continuing discussion. It has not been clear whether ion transfer across ITIES is better described as an activated (Butler-Volmer) process [viii], as a mass transport (Nernst-Planck) phenomenon [ix, x], or as a combination of both [xi]. Evidence has been also provided that the Frumkin correction overestimates the effect of electric double layer [xii]. Molecular dynamics (MD) computer simulations highlighted the dynamic role of the water protrusions (fingers) and friction effects [xiii, xiv], which has been further studied theoretically [xv,xvi]. 

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. 

This equilibrium constant (KD) is called 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. 

The equilibrium curve can often be described by the Nernst distribution law (Equation 2.3.4-3), but because of the concentration dependence it must often be determined experimentally ... 

For separation by liquid-liquid extraction, the Nernst distribution law describes the equilibrium between raffinate and extract phases if the carrier component T and solvent component L are not miscible (see Chapter 6). 

The loading capacity of the key component, or pollutant, to be transferred to the solvent gives the distribution of the component between the two liquid phases. This distribution equilibrium is described by the Nernst distribution law (Chapter 1.4.2.1). The amount of circulated solvent is a function of the loading capacity. The selectivity characterizes how much better the key component is extracted than the other components. The higher the selectivity of a solvent, the lower the number of separation stages required in the extractor. 

It is also possible to derive the Nernst distribution law from thermodynamic considerations using the concept of free energy (Lewis and Randall 1923). At equilibrium, the chemical potential of a solute X has to be the same in the aqueous and the organic phase, i.e.. 

The separation of components in gas chromatographic processes is the result of equilibrium distribution between a mobile gas phase and a liquid or solid stationary phase. The partition of a component between two phases is described by the Nernst distribution law. 

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 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. 

Nernst distribution law constant Boiling point elevation constant Freezing point depression constant Equilibrium constant Acid ionization constant Michaelis-Menten constant... 

The currently most useful approximations of trace element behavior for quantitative prediction are based on a simple Nernst distribution for equilibrium partitioning of a solute between two phases. This concept can be formalized to account for exchange between the trace element and the major ion it is deemed to replace, to account for effects of compensation of charge, etc. (e.g., Mclntire,... 

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. 

The Nernst partition isotherm applies to each individual species in an equilibrium mixture. The analyst is more directly concerned with the experimentally determinable distribution ratio, D, defined as... 

Maintenance of unequal concentrations of ions across membranes is a fundamental property of living cells. In most cells, the concentration of K+ inside the cells is about 30 times that in the extracellular fluids, while sodium ions are present in much higher concentration outside the cells than inside. These concentration gradients are maintained by the Na+-K+-ATPase by means of the expenditure of cellular energy. Since the plasma membrane is more permeable to K+ than to other ions, a K+ diffusion potential maintains membrane potentials which are usually in the range of -30 to -90 mV. H+ ions do not behave in a manner different from that of other ions. If passively distributed across the plasma membrane, then the equilibrium intracellular H+ concentration can be calculated from the Nernst equation via... 

Interface between two liquid solvents — Two liquid solvents can be miscible (e.g., water and ethanol) partially miscible (e.g., water and propylene carbonate), or immiscible (e.g., water and nitrobenzene). Mutual miscibility of the two solvents is connected with the energy of interaction between the solvent molecules, which also determines the width of the phase boundary where the composition varies (Figure) [i]. Molecular dynamic simulation [ii], neutron reflection [iii], vibrational sum frequency spectroscopy [iv], and synchrotron X-ray reflectivity [v] studies have demonstrated that the width of the boundary between two immiscible solvents comprises a contribution from thermally excited capillary waves and intrinsic interfacial structure. Computer calculations and experimental data support the view that the interface between two solvents of very low miscibility is molecularly sharp but with rough protrusions of one solvent into the other (capillary waves), while increasing solvent miscibility leads to the formation of a mixed solvent layer (Figure). In the presence of an electrolyte in both solvent phases, an electrical potential difference can be established at the interface. In the case of two electrolytes with different but constant composition and dissolved in the same solvent, a liquid junction potential is temporarily formed. Equilibrium partition of ions at the - interface between two immiscible electrolyte solutions gives rise to the ion transfer potential, or to the distribution potential, which can be described by the equivalent two-phase Nernst relationship. See also - ion transfer at liquid-liquid interfaces. 

Distribution (Nernst) potential — Multi-ion partition equilibria at the -> interface between two immiscible electrolyte solutions give rise to a -> Galvanipotential difference, Af(j> = (j>w- 0°, where 0wand cj>°are the -> inner potentials of phases w and o. This potential difference is called the distribution potential [i]. The theory was developed for the system of N ionic species i (i = 1,2..N) in each phase on the basis of the -> Nernst equation, the -> electroneutrality condition, and the mass-conservation law [ii]. At equilibrium, the equality of the - electrochemical potentials of the ions in the adjacent phases yields the Nernst equation for the ion-transfer potential,... 

Distribution potential established when ionic species are partitioned in equilibrium between the aqueous and organic phases, W and O, is a fundamental quantity in electrochemistry at liquid-liquid interfaces, through which the equilibrium properties of the system are determined. In any system composed of two immiscible electrolyte solutions in contact with each other, the equilibrium is characterized by the equality of the electrochemical or chemical potentials for each ionic or neutral species, respectively, commonly distributed in the two phases [4]. It follows from the former equality that the distribution potential Aq inner electrical potential of the aqueous phase, 0, with respect to the inner potential of the organic phase, 0°, is given by the Nernst equation [17,18],... 

In an ideal system therefore, the equilibrium ratio of mole fractions of a component in the two phases depends solely upon the temperature and pressure, and is independent of the composition of the system. This is Nernst s distribution law, examples of the application of which will be discussed later (chap. XX). 

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. 

In Vol I the question of heterogeneous equilibnum, i e equilibrium in a system consisting of more than one phase, was considered from the kinetic standpoint, the generalisation employed being the Distribution Law of Nernst We now take up the study of heterogeneous equilibnum from the standpomt of thermodynamics... 

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