Cation distribution equilibria

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... 

Consider a system of two solvents in contact in which a single electrolyte BA is dissolved, consisting of univalent ions. A distribution equilibrium is established between the two solutions. Because, in general, the solvation energies of the anion and cation in the two phases are different so that the ion with a certain charge has a greater tendency to pass into the second phase than the ion of opposite charge, an electrical double layer appears at... 

The physical sense of the distribution potential can be demonstrated on the example of the distribution equilibrium of the salt of a hydrophilic cation and a hydrophobic anion between water (wt) and an organic solvent that is immiscible with water (org). After attaining distribution equilibrium the concentrations of the anion and the cation in each of the two phases are the same because of the electroneutraUty condition. However, at the phase boundary an electrical double layer is formed as a result of the greater tendency of the anions to pass from the aqueous phase into the organic phase, and of the cations to move in the opposite direction. This can be characterized quantita tively by quantities—and — AGJJ. ", for which... 

The data for the ion exchange isotherms were obtained from batch experiments conducted in a constant temperature agitated system utilizing tightly sealed polypropylene bottles. Conventional chemical analyses were used to obtain the cation distribution data in both zeolite and exchange solution phases. Most of the exchanges were carried out at ambient temperature for 24-72 hours. Preliminary tests had shown that equilibrium was essentially reached within a few hours. 

Consider the effect of the distribution equilibrium (9.8.32) for an ion-exchanging membrane system designed to detect cation M" ". The total activity of M" " in the test solution is... 

A simple review [6] of the definition of a distribution coefficient (equation 5) enables the calculation of the column capacity for a cation from equilibrium batch tests, provided that the concentration of the ion being scavenged by the zeolite is low in the solution being treated. This is particularly useful when removal of radioisotopes from aqueous nuclear waste is the intended use [30]. 

The cation distribution in zeolites is the result of an energy-minimization process. The site energy is determined by the interaction of the cations with the framework, with the adsorbed molecules and by the mutual repulsion between them. Provided that an equilibrium distribution is possible, we may expect that the cation distribution contains information about the enerav levels of the sites. 

The Donnan potential, Ai j, was calculated from the Donnan equilibrium and fulfilled the requirement for electroneutrality where the anion and cation distribution between the inside and the outside of the vesicle is determined by the potential... 

Figure 16.45. Schematic representation of the chemical corrosion of polypyrrole in three steps I, initial state 2, distribution equilibrium for nucleophiles 3, partial chemical conversion + radical cationic centre O nucleophiles in solution 9 nucleophile in the solid and reacted slates. Adapted from Werkstoffe und Korrosion 42, 341 (1991), with permission of VCH,...

The former two relationships (paragraphs (1) and (2) above) were focused on to access the distribution of quaternary cations. The equilibrium property cannot reveal when the total carbon number for various quaternary salts is the same. In paragraph 3, the Hildebrand parameter cannot be easily obtained for all quaternary salts. Hence, we took the results of paragraphs 1-3 and the concept of HLB for the surfactant to show that the dispersal efficiency of surfactant or emulsifier molecules is a function of the relative interactions of their polar, hydrophilic heads with the aqueous phase and of their nonpolar, lipophilic tails with the hydrocarbon phase [105,106]. We developed a new model as... 

With HILIC, various polar stationary phases with differing selectivity are used. Basically, it must be distinguished between three different selective types weak anion exchanger (silica modified with aminopropyl groups) and amide columns, weak cation exchanger (usually unmodified (bare) silica) and neutral supports (diol or zwitterionic stationary phases (ZIC-HILIC)). With ionizable compounds, in addition to the distribution equilibrium between the mobile phase ( pseudo-stationary phase ) near to the polar surface and the less polar mobile phase, ionic interactions can also occur, resulting in differing separation characteristics on the different stationary phases. 

A remarkable situation is observed in the case where a single salt is in a distribution equilibrium between the solvents w and o. With respect to Eqs. (2) and (5) we have for both the cation and the anion... 

The mechanism responsible for this structure and behavior is not known. Very probably, the complex of water — aluminosilicate framework and sodium formed at the precursor stage gives rise to a sublattice with more mobile cations. The temperature jump does not allow molecules of water and sodium to settle down into their equilibrium positions. (A process based on a nonequilibrium cation distribution is realized in Zeolite Mira, Italy), The two different approaches, APS decrease or formation of a metastable cation sublattice, are illustrated in Fig. 24. As well as... 

When an ionic liquid that consists of moderately hydrophobic cationic and anionic species is in contact with an aqueous solution, the phase-boundary potential, which is the inner potential of the W phase with respect to that of IL phase, is established across the interface at a distribution equilibrium, where the superscript W and subscript IL stand for the aqueous phase and the IL phase, respectively. 

In view of this, some reference state for the cation distribution needs to be defined to serve as a bench mark to which observed low-temperature states can be referred. Summerville (1973) has coined the phrase operational equilibrium to describe the state achieved after a low-temperature anneal when the anion sub-lattice adjusts to a random cation distribution this should be reproducible. Operational equilibrium will be achieved in principle with samples that have been melted initially, or in practice perhaps with those which have been heated above, say, 2000°C. Any tendency for changes in the random cation distribution thus achieved, which might stem from the stable existence below, say, 1600 C of some intermediate compound of defined composition, would only be revealed if the sample were annealed at close to this temperature for sufficient time for the diffusion-controlled reaction to take place. So it is that for the Zr02-Sc203 system, arc-nlelted samples of compositions between those of the y- and S-phases appear optically, to X-rays, but not to electrons as monophasic. However, after a week s annealing at 1600°C and subsequent quenching, phase separation does occur on a sub-microscopic scale, and is clearly shown in X-ray diffraction. 

Here is yet another and quite dramatic example of inconsistencies between various data sets, each of which must therefore be thought of as representing only observational equilibrium. Again the explanation of these differences is probably to be sought in the cation distribution achieved during reaction. What follows is a highly speculative attempt to rationalize in structural terms the reported observations. 

This equation can be obtained in another way which may be more instructive. Assume that the slow step in the oxidation is the transport of cation vacancies. The positive holes may then be considered to take up their equilibrium distribution, defined by Boltzmann s equation... 

---