Nernst distributions

To understand the fundamental principles of extraction, the various terms used for expressing the effectiveness of a separation must first be considered. For a solute A distributed between two immiscible phases a and b, the Nernst Distribution (or Partition) Law states that, provided its molecular state is the same in both liquids and that the temperature is constant ... 

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... 

Nernst Distribution Law Any neutral species will ilistribute between two iniscible solvents such that the ratio of the concentrations remains a constant. 

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 ... 

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. 

The behavioural pattern of two immiscible solvents, say a and ib is essentially nonideal with respect to one another. Now, if a third substance is made to dissolve in a two-phase mixture of the solvents (i.e., a and 3 ), it may behave ideally in either phases provided its concentration in each individual phase is approximately small. Therefore, under these prevailing experimental parameters the ratio of the mole fractions of the solute in the two respective immiscible phases ( a and A) is found to be a constant which is absolutely independent of the quantity of solute present. It is termed as the Nernst Distribution Law or the Partition Law and may be expressed as follows ... 

The primary parameter in solvent extraction is the measured distribution ratio, where it is up to the writer to define what is being measured, indicating this by an appropriate index. In the Nernst distribution experiment described earlier, the analytically measured concentration of benzoic acid is in the aqueous phase [Bz]aq,tot = [HBz]aq + [Bz ]aq, and in the organic phase [Bz] , tot= [HBzJorg + [HjBzjlo . Thus the measured distribution ratio, abbreviated Z)bz, becomes... 

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... 

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 ... 

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. 

When a liquid is extracted by a solid, phase A of the Nernst distribution law [equation (2.2)] refers to the liquid sample, and phase B, the extracting phase, represents the solid (or solid-supported liquid) phase ... 

The standard molar Gibbs energy of solvation can also be derived from pure component data using spectroscopic information for determining solvatochromic parameters in respect of activity, basicity, polarity, etc. There exists a number of linear solvatochromic scales, the most widely used of which is the linear solvation energy relationship (LSER) devised by Kamlet and Taft [37, 38]. The Nernst distribution of solute i according to Kamlet is ... 

Discuss whether the Nernst Distribution Law holds for this system. (b) For the distribution of benzoic acid in water and benzene, the following data have been reported at 20°C CH,o(g/100 cc) 0.289 0.1952 0.1500 0.0976 0.0788... 

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 relation Rpx = P"/x[ is simply a reformulation of Raoult Law when applied to the solvent. Any of the other relations are equivalent to Henry s Law when applied to the solute. Rxx = x [ x[ is also known as the Nernst Distribution Law. 

If we set the affinity equal to zero we obtain the general form of the Nernst distribution law (7.42) ... 

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. 

Prove that if a solute is distributed between two immiscible solvents (I and II), the ratio of the activities in the two solvents, i.e., ai/an, should be constant at constant temperature and pressure. Show that this result is the basis of the Nernst distribution law, i.e., ci/cii (or mi/mn) is constant for dilute solutions. 

A detailed description of this experiment and other comparable experiments for demonstrating the Nernst distribution law have recently been published by Elias et al. ... 

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... 

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. 

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). 

Thus if the solute follows Henry s Law in both phases the ratio of its concentrations in the phases will be constant. This result is sometimes referred to as the Nernst Distribution Law. 

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 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... 

This extraction of organic solutes, such as drug substances from biological samples, occurs based on the Nernst distribution law, sometimes known... 

For further information on Gibbs s phase rule, see Elements of Physical Chemistry in the Further Reading section at the end of this chapter. According to the Nernst distribution law. 

Molecule The smallest part of a substance that is composed of two or more atoms of the same or different type held together by chemical forces Nernst distribution law (partition law) The ratio (constant) at which an analyte will become distributed between two immiscible solvents at... 

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