Chemical potential of electrolyte

These relationships can be looked at more generally by beginning with the equations for the chemical potential of electrolyte solutes, based on the three different concentration scales ... 

The chemical potential of electrolyte T, can be written in terms of the chemical potentials of its constituent ions in the form... 

Equation 10.3.3 relates the chemical potential of electrolyte B in a binary solution to the single-ion chemical potentials of its constituent ions ... 

In deriving Equation 1.8, it was assumed that both electrodes are made of identical metals and that they are in contact with electrolyte with identical composition and Galvani potential, O. Therefore, specific terms, depending on chemical potentials of electrolyte protons or metal electrons will cancel out of this equation. Indeed, the difference in electrochemical potentials jig- of metal electrons at cathode and anode is proportional to the EMF ... 

The electrochemical potential, )T, of a species is a function of the electrical state as well as temperature, pressure, and composition is the absolute activity, which can be broken down into three parts as shown. Eor an electrolyte. A, which dissociates into cations and v anions, the chemical potential of the electrolyte can be expressed by... 

For a strong electrolyte such as HC1 we assume that all of the electrolyte is dissociated to form the ionic species. In this case, it is appropriate to consider the chemical potential of the HC1 as the sum of the chemical potentials of the dissociated species. That isdd... 

In concentrated NaOH solutions, however, the deviations of the experimental data from the Parsons-Zobel plot are quite noticeable.72 These deviations can be used290 to find the derivative of the chemical potential of a single ion with respect to both the concentration of the given ion and the concentration of the ion of opposite sign. However, in concentrated electrolyte solutions, the deviations of the Parsons-Zobel plot can be caused by other effects,126 279"284 e.g., interferences between the solvent structure and the Debye length. Thus various effects may compensate each other for distances of molecular dimensions, and the Parsons-Zobel plot can appear more straight than it could be for an ideally flat interface. 

No. Because that would imply we know how to split, at least conceptually, the electrochemical potential, jl, of electrons (which is the same in the metal and in the electrolyte at their contact) into the chemical potential of electrons, p, and the electrical potential of electrons, (p, in the metal and in the electrolyte. 

In equilibrium dialysis of a solution of a polyanion (valence Zp negative) with molar concentration Cp against a solution of imi-imivalent electrolyte CA (C = cation, A = anion) with molar concentration Cqa it was shown that the requirement for equal chemical potentials of the salt in the polyanion (a) and diffusate ()) phases results in the following relation... 

The general way in which a Galvani potential is established is similar in all cases, but special features are observed at the metal-electrolyte interface. The transition of charged species (electrons or ions) across the interface is possible only in connection with an electrode reaction in which other species may also be involved. Therefore, equilibrium for the particles crossing the interface [Eq. (2.5)] can also be written as an equilibrium for the overall reaction involving all other reaction components. In this case the chemical potentials of aU reaction components appear in Eq. (2.6) (for further details, see Chapter 3). 

It is typical that in Eq. (3.23) for the EMF, all terms containing the chemical potential of electrons in the electrodes cancel in pairs, since they are contained in the expressions for the Galvani potentials, both at the interface with the electrolyte and at the interface with the other electrode. This is due to the fact that the overall current-producing reaction comprises the transfer of electrons across the interface between two metals in addition to the electrode reactions. 

Nucleation Consider an idealized spherical nucleus of a gas with the radius on the surface of an electrode immersed in an electrolyte solution. Because of the small size of the nucleus, the chemical potential, of the gas in it will be higher than that ( To) in a sufficiently large phase volume of the same gas. Let us calculate this quantity. 

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

A great many electrolytes have only limited solubility, which can be very low. If a solid electrolyte is added to a pure solvent in an amount greater than corresponds to its solubility, a heterogeneous system is formed in which equilibrium is established between the electrolyte ions in solution and in the solid phase. At constant temperature, this equilibrium can be described by the thermodynamic condition for equality of the chemical potentials of ions in the liquid and solid phases (under these conditions, cations and anions enter and leave the solid phase simultaneously, fulfilling the electroneutrality condition). In the liquid phase, the chemical potential of the ion is a function of its activity, while it is constant in the solid phase. If the formula unit of the electrolyte considered consists of v+ cations and v anions, then... 

In Equation 50 the chemical potential of non-electrolyte A depends on the usual choice of standard-state conventions described above, and the chemical potentials of both H2(g) and H+(sod are taken to be zero (this defines e.s.s., the electrolyte standard state). By setting the standard-state free energy of the solvated proton equal to zero, this standard-state convention... 

These facts would suggest that the electrolysis of molten alkali metal salts could lead to the introduction of mobile electrons which can diffuse rapidly through a melt, and any chemical reduction process resulting from a high chemical potential of the alkali metal could occur in the body of the melt, rather than being confined to the cathode volume. This probably explains the failure of attempts to produce the refractory elements, such as titanium, by electrolysis of a molten sodium chloride-titanium chloride melt, in which a metal dust is formed in the bulk of the electrolyte. 

It follows from Eqn. 4—13 that the electron level o u/av) in the electrode is a function of the chemical potential p.(M) of electrons in the electrode, the interfacial potential (the inner potential difference) between the electrode and the electrolyte solution, and the surface potential Xs/v of the electrolyte solution. It appears that the electron level cx (ii/a/v) in the electrode depends on the interfacial potential of the electrode and the chemical potential of electron in the electrode but does not depend upon the chemical potential of electron in the electrolyte solution. Equation 4-13 is valid when no electrostatic potential gradient exists in the electrolyte solution. In the presence of a potential gradient, an additional electrostatic energy has to be included in Eqn. 4-13. 

We have seen that the cell potential is generated at the interfaces between the electrodes and the electrolyte. Therefore, the composition of the electrode at this interface is important and this does not have to be identical with the bulk composition. In fact, large deviations have been observed due to segregation of some of the components of the electrode and especially due to impurities at the surface. If the surface of the electrode is equilibrated with the bulk, both have the same chemical potential of the electroactive component if that is sufficiently mobile in... 

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