Equilibrium electrolyte phase

Table 3. Equilibrium bromine concentrations in the aqueous electrolyte phase (taken from Ref. [491)...

Specific adsorption of ions (probably anions) of the electrolyte phase on the metal also should depend on the metal. Assuming a Langmuir-type equilibrium, one has22 for ions of charge qt and solution concentration c,... 

The interface structure for non-blocking interfaces is similar to that for related blocking interfaces. Thus the distribution of charge at the C/ Ag4Rbl5 interface will be similar to that at the Ag/Ag4Rbl5 interface. The major difference is that there is one particular interfacial potential difference at which the silver electrode is in equilibrium with Ag ions in the bulk electrolyte phase. At this value of A, there is a particular charge on the electrolyte balanced by an equal and opposite charge — on the metal. At any potential different from value of q different... 

In these systems there are a minimum of three phases a metal, an adherent layer of sparingly soluble salt of the metal, and an electrolyte phase containing the same anion as the latter. Equilibrium exists both between the metal and cations of the sparingly soluble salt and between anions in the salt and those in solution. For the half-reaction... 

In redox electrodes an inert metal conductor acts as a source or sink for electrons. The components of the half-reaction are the two oxidation states of a constituent of the electrolytic phase. Examples of this type of system include the ferric/ferrous electrode where the active components are cations, the ferricyanide/ferrocyanide electrode where they are anionic complexes, the hydrogen electrode, the chlorine electrode, etc. In the gaseous electrodes equilibrium exists between electrons in the metal, ions in solution and dissolved gas molecules. For the half-reaction... 

So far it has not been possible to measure the chemical potentials of the components in the mesophases. This measurement is possible, however, in solutions which are in equilibrium with the mesophases. If pure water is taken as the standard state, the activity of water in equilibrium with the D and E phases in the system NaC8-decanol-water is more than 0.8 (4). From these activities in micellar solutions, the activity of the fatty acid salt has sometimes been calculated. The salt is incorrectly treated as a completely dissociated electrolyte. The activity of the fatty acid in solutions of short chain carboxylates has also been determined by gas chromatography from these determinations the carboxylate anion activity can be determined (18). Low CMC values for the carboxylate are obtained (15). The same method has shown that the activity of solubilized pentanol in octanoate solutions is still very low when the solution is in equilibrium with phase D (Figure 10) (15). 

Far from third-phase formation, Kanellakopulos et al. (118) showed in an earlier study that the extraction behavior of given electrolytes with the same cation is primarily influenced by the solvation properties of the associated anions. They found that the electrolyte phase distribution can be explained by single ion solvation, by comparing the equilibrium constants for the extraction of acids by undiluted TBP with the free energies of transfer for the anions (Table 7.3). 

For Isolated spheres of water, the value to be taken for the equilibrium electrolyte concentration in a bulk phase, c( ), may be a problem. In the situation of fig. 3.16b, and c do not approach this value. When there is equilibrium with an external bulk phase, as with vesicles, this is no problem, because c (r = 0) and c.(r = 0) and c(oo) are simply related via the Boltzmann equation. When Boltzmann s law applies, the equilibrium concentration c(=o) in a (virtual) bulk phase can be written as c( o) = (c (r = 0) c (r = 0)). However, if there is no such equilibrium (say, for microdrops of water formed in a nonconducting oil. under highly dynamic conditions) c(o ) may differ between one drop and the other and nothing can be said in general. Alternatively, the negative adsorption of electrolyte can be computed if y is known (this is the Donnan effect). 

Figure 31 contains a schematic representation of the nanocrystalline semiconductor film-electrolyte interface at equilibrium (Figure 31a) and the corresponding situation under bandgap irradiation of the semiconductor (Figure 31b) [9]. Since the difiFusion length of the photogenerated carriers is usually larger than the physical dimensions of the structural units, holes and electrons can reach the impregnated electrolyte phase before they are lost via bulk recombination. This contrasts the situation with the single-crystal cases discussed earlier.

When the current does not flow through battery the measurable diflerence in electric potential between the terminals of the two electrodes is the result of all the equilibrium potential differences at the interphase between the conducting phases in contact. In the example of the Daniell cell, with both electrodes having copper terminals, there are three interfacial potential differences (apart from the small liquid junction potential difference at the contact between the two electrolyte phases) one potential difference at the contact between the zinc rod and the copper terminal (Zn/Cu) and two potential differences at the metal-solution interphases (Zn/Zn + and Cu/Cu +), which are mainly due to the charge transfer processes. 

When inorganic solids and water are present, an electrolyte phase equilibrium model must be selected for the aqueous phase, to properly account for the dissolution of the solid and formation of ions in solution. 

Relationships such as those expressed in equation (5.6) cannot be employed for species that are in chemical equilibrium but do not exist in the adjoining phases. Electrons, for example, are present in the metal of the electrode (phase LE) and in chemical equilibrium with ionic species in the electrolyte (phase E), but are not present in the electrolyte. An equilibrium relationship between the electrons and ionic species can be expressed, however, in terms of electrochemical reactions, and... 

In the preceding section, the remarkable salt concentration effect on the acid dissociation equilibria of weak polyelectrolytes has been interpreted in a unified manner. In this treatment, the p/( ,pp values determined experimentally are believed to reflect directly the electrostatic and/or hydrophobic nature of polyelectrolyte solutions at a particular condition. It has been proposed that the nonideality term (Ap/Q corresponds to the activity ratio of H+ between the poly electrolyte phase and the bulk solution phase, and that the ion distribution equilibria between the two phases follow Donnan s law. In this section, the Gibbs-Donnan approach is extended to the equilibrium analysis of metal complexation of both weak acidic and weak basic polyelectrolytes, i.e., the ratio of the free metal ion activity or concentration in the vicinity of polyion molecules to that of bulk solution phase is expressed by the ApAT term. In Section III.A, a generalized analytical treatment of the equilibria based on the phase separation model is presented, which gives information on the intrinsic complexation equilibria at a molecular level. In Secs. B and C, which follow, two representative examples of the equilibrium analyses with weak acidic (PAA) and weak basic (PVIm) functionalities have been presented separately, in order to validate the present approach. The effect of polymer conformation on the apparent complexation equilibria has been described in Sec. III.D by exemplifying PMA. 

Figure 2.3.1 Schematic view of the phases in cell (2.3.1). Equilibrium is established for certain charge carriers as shown, but at the liquid junction between the two electrolyte phases a and p, equilibrium is not reached.

All the laws of elementary qualitative analysis may be derived by making use of this equation combined with the conditions for heterogeneous equilibrium. As an example, the solubiUty product rule will be discussed. We consider a two-phase system. Phase a is a solution of a set of electrolytes including /, and phase P is pure solid /. At equilibrium between phase a and phase p... 

Equilibrium between a metal phase and an electrolyte phase... 

From a physicist s point of view, the condition for electronic equilibrium is equal values of the Fermi energy E. Electronic equilibrium concerns all charged particles and might also be formulated for the metal ions. The equilibrium contact between a metal phase and an electrolyte phase is shown in Figure 3.1. 

Figure 3.1 Electronic equilibrium between a metallic phase and an electrolyte phase. The electronic energy states in the metal are described by the energy band (Section 2.9). The occupied states are and The density of states of electrons in the electrolyte are the energy distribution functions of the reduced and oxidized components of a redox system, e.g., Fe and Fe ions (Section 2.9.10). The equilibrium condition is equal values of the electrochemical potentials /x of the electrons in both phases. An alternative condition is equal values of the Fermi energy Ep in both phases.

In electrochemistry the semiconductor (phase I) is connected to an electrolyte (phase II). In equilibrium the electrochemical potential for the electrons in both phases must be equal. The electrochemical potential of the electrons in the semiconductor is equal to the Fermi energy. 

Figure 12.15 Surface energies between particle-metal-electrolyte phases. In equilibrium, the forces must balance each other.

FIGURE 3.19. Equilibrium state of the NAFION/electrolyte interface compared with the NAFION surface withdrawn from the electrol5rte. When in contact with the electrolyte, the counter ions (+) can enter into the electrolyte phase (5), while the fixed ions cannot, thereby generating the Donnan potential In the withdrawn state, the asymmetrical arrangement of counterions around fixed ions in the surface region generates the surface dipole potential... 

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