Potentials of Electrolyte Solutions

There exist solutions whose properties, such as their electrical conductivity, indicate that the solute molecules are at least partially dissociated into ions. These solutions are termed electrolyte solutions. In general, solute molecules in which the chemical bonds have a large degree of ionic, rather than covalent, character will dissolve in polar solvents to yield electrolyte solutions. A solute is called a strong electrolyte if it completely dissociates into ions in solutions. Weak electrolytes are those for which an equilibrium is set up between undissociated molecules and constituent ions in solutions. 

In this chapter we discuss some of the properties of electrolyte solutions. In Sec. 12-1, the chemical potential and activity coefficient of an electrolyte are expressed in terms of the chemical potentials and activity coefficients of its constituent ions. In addition, the zeroth-order approximation to the form of the chemical potential is discussed and the solubility product rule is derived. In Sec. 12-2, deviations from ideality in strong-electrolyte solutions are discussed and the results of the Debye-Hiickel theory are presented. In Sec. 12-3, the thermodynamic treatment of weak-electrolyte solutions is given and use of strong-electrolyte and nonelectrolyte conventions is discussed. 

In principle, the conventions used for nonelectrolyte solutions developed in Chap. 11 could be employed for electrolyte solutions which are subject to the condition of electroneutrality. Agreement with experimental data could be obtained by choosing the molecular weight to be some fraction of the formula weight. However, these conventions generally lead to activity coefficients which are rapidly varying functions of composition. In order to avoid this, we formally define chemical potentials and activity coefficients for ionic components. The definition of chemical potentials for ionic components does not have operational significance since their concentrations cannot be varied independently. 

Its formula weight is composed of v formula weights of ions (A = 1,2,. . . , r), where is the charge number of ion k and e is the protonic charge (4.8 x 10 °esu). We thus introduce a new set of components, the ions, subject to the condition of electroneutrality. 

The number of independent components in a solution composed of electrolyte Y, dissolved in a nonelectrolyte solvent is determined by the restrictions placed on making up the solution. If it is specified that the electrolyte be added to the solvent, the number of independent components is 2 if the ions may be added independently, subject to the restraint of electroneutrality, the number of independent components is r (r-1 ionic components and the solvent). 

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Fig. 4-10. Electron energy levels in (a) an isolated solid metal and in (b) a metal electrode immersed in an electrolyte solution M = metal S = electrolyte solution e(STD) = gaseous electrons in the standard state e

Fig. 4-16. Energy levels of metal ion and electron in an ionic electrode of metal ion transfer 4Cjn i = sublimation energy of solid metal /m" = ionization energy of gaseous metal atoms > >s = outer potential of electrolyte solution E s electrode potential (absolute electrode potential).

Fig. 4-24. Electron energy levels for electrode potential relative to a reference electrode E = electrode potential (absolute) E = relative electrode potential Ps = outer potential of electrolyte solution of test electrode = outer potential of electrolyte solution of reference...

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 ... 

Table 4.6 The surface potentials of electrolyte solutions relative to that of...

As mentioned, cations with L>0 are repelled from the surface (Cj<0), and if k >k, they are repelled more than the anions. This causes a charge imbalance in the surface layer leading to the establishment of an electric double layer. The surface potential of electrolyte solutions over that of pure water (with respect to vacuum/air/ dilute water vapor), A A f, was measured as a function of the electrolyte concentration. The available ISlS/ values at 1M MX, for M=, Na", and NH4 with a variety... 

Although in certain cells the liquid junction can be eliminated by appropriate choice of electrolyte solution, this is not always possible. However, the liquid junction potential can be minimised by the use of a salt bridge (a saturated solution of KCl of about 4-2m), and the liquid junction potential is then only 1-2 mV this elimination of the liquid junction potential is indicated... 

The measurement of change in the surface potentials of aqueous solutions of electrolytes caused hy adsorption of ionophore (e.g., crown ether) monolayers seems to he a convenient and promising method to ascertain selectivity and the effective dipole moments of the ionophore-ion complexes created at the water surface. 

LCEC is a special case of hydrodynamic chronoamperometry (measuring current as a function of time at a fixed electrode potential in a flowing or stirred solution). In order to fully understand the operation of electrochemical detectors, it is necessary to also appreciate hydrodynamic voltammetry. Hydrodynamic voltammetry, from which amperometry is derived, is a steady-state technique in which the electrode potential is scanned while the solution is stirred and the current is plotted as a function of the potential. Idealized hydrodynamic voltammograms (HDVs) for the case of electrolyte solution (mobile phase) alone and with an oxidizable species added are shown in Fig. 9. The HDV of a compound begins at a potential where the compound is not electroactive and therefore no faradaic current occurs, goes through a region... 

Recently, scanning Kelvin probes and microprobes, as high-resolution surface analysis devices, have been developed. They allow one to investigate the lateral distribution of the work functions of the surfaces of various phases, including the determination of the potential profiles of metals and semiconductors under very thin films of electrolytic solution, and also of the surface potential map of various polymer- and biomembranes [50-56], The lateral resolution and the sensitivity are in the 100 nm and ImV ranges, respectively [54],... 

Here, Ws is the work function of electrons in the semiconductor, q is the elementary charge (1.6 X 1CT19 C), Qt and Qss are charges located in the oxide and the surface and interface states, respectively, Ere is the potential of the reference electrode, and Xso is the surface-dipole potential of the solution. Because in expression (2) for the flat-band voltage of the EIS system all terms can be considered as constant except for tp (which is analyte concentration dependent), the response of the EIS structure with respect to the electrolyte composition depends on its flat-band voltage shift, which can be accurately determined from the C-V curves. 

At about the same time, Matsushita et al. reported a study of quasi-two-dimensional deposition in a thin layer of electrolyte solution [3], A binary zinc sulfate solution was confined within a planar disk, 17 cm in diameter, bounded on the bottom by a glass plate and on the top by a layer of immiscible organic liquid. Cell potentials of several volts were applied, and the deposits grew along the liquid-liquid interface. In this cell, the depth of solution was 10 cm, but the deposit formed only along the interface between the electrolyte solution and the organic layer. Since a... 

As in the nonelectrolyte case, the problem of representing the thermodynamic properties of electrolyte solutions is best regarded as that of finding a suitable expression for the non-ideal part of the chemical potential, or the excess Gibbs energy, as a function of composition, temperature, dielectric constant and any other relevant variables. 

In the cell used for measuring the electrode potential, in which the two electrodes are immersed in a single phase of electrolyte solution, the outer potential, tps, ofthe test electrode-solution is equal to the outer potential, ips, of the reference electrode-solution as shown in Fig. 4—24. The difference in the Fermi level of electrons, CFtu)- between the test electrode M and the reference electrode M , then, is represented by the difference in the real potential of electrons, M/aw) - .(M0/ V). tuid hence by the difference in the electrode potential (absolute electrode potential), AE = E-E°, between the two electrodes. This difference also equals the difference in the work function, 4>no/3/v - 4>ji/s/v> between the two electrodes. Thus, the potential E of the test electrode relative to the reference electrode is the difference in the electrode potential (absolute electrode potential) between the two electrodes as indicated in Eqn. 4-35 . 

Figure 2.14 Comparison between theoretical and experimental (i = 0.025 V/s) voltammetric peak potential for electrolyte solutions of different pH (prepared from 1 mM NaOH and HNO3 solutions containing 4 mM NaN03). Two different sets of experimental data are presented. Taken from Ref [119].

In 1848 du Bois-Reymond [21] suggested that the surfaces of biological formations have a property similar to the electrode of a galvanic cell and that this is the source of bioelectric phenomena observed in damaged tissues. The properties of biological membranes could not, however, be explained before at least the basic electrochemistry of simple models was formulated. The thermodynamic relationships for membrane equilibria were derived by Gibbs in 1875 [29], but because the theory of electrolyte solutions was formulated first by Arrhenius as late as 1887, Gibbs does not mention either ions or electric potentials. 

The electrochemical potential of the solution and semiconductor, see Fig. 3.6, are determined hy the standard redox potential of the electrolyte solution (or its equivalent the standard redox Fermi level, Ep,redo, and the semiconductor Fermi energy level. If these two levels do not lie at the same energy then movement of charge across the semiconductor - solution interface continues until the two phases equilibrate with a corresponding energy band bending, see Fig. 3.8. 

Schofield Phil. Mag. March, 1926) has recently verified this relation by direct experiment. In order to appreciate the significance of this result, it is necessary to consider in more detail the electrical potential difference V and the manner in which it arises. Instead of regarding the phenomenon from the point of view of the Gibbs equation, it has been, until recently, more usual to discuss the subject of electro-capillarity from the conceptions developed by Helmholtz and Lippmann. These views, together with the theory of electrolytic solution pressure advanced by Nemst, are not in reality incompatible with the principles of adsorption at interfaces as laid down by Gibbs. 

The two electrode potentials Fi and F3 are according to the Nemst conception of electrolytic solution pressure given by the expression... 

Figure 6.4 Estimates of the decay in electrostatic potential away from a charged flat plate in a range of electrolyte solutions.

Below we present a well-known calculation of membrane potential based on the classical Teorell-Meyer-Sievers (TMS) membrane model [2], [3]. The essence of this model is in treating the ion-selective membrane as a homogeneous layer of electrolyte solution with constant fixed charge density and with local ionic equilibrium at the membrane/solution interfaces. In spite of the obvious idealization involved in the first assumption the TMS model often yields useful results and represents in fact the main tool for practical membrane calculations. We shall return to TMS once again in 4.4 when discussing the electric current effects upon membrane selectivity. In the case of our present interest, the simplest TMS model of membrane potential for a 1,2 valent electrolyte reads... 

Solvation is a process in which solute particles (molecules or ions) in a solution interact with the solvent molecules surrounding them. Solvation in an aqueous solution is called hydration. The solvation energy is defined as the standard chemical potential of a solute in the solution referred to that in the gaseous state.11 The solvation of a solute has a significant influence on its dissolution and on the chemical reactions in which it participates. Conversely, the solvent effect on dissolution or on a chemical reaction can be predicted quantitatively from knowledge of the solvation energies of the relevant solutes. In this chapter, we mainly deal with the energetic aspects of ion solvation and its effects on the behavior of ions and electrolytes in solutions. 

The extreme nonidealities characteristic of electrolyte solutions warn of the dangers inherent in approximations commonly employed in general chemistry. Except in the crossover region of intermediate m where y + 1, blithe replacement of activity by molarity is seldom justified for strong electrolytes. Elementary treatments of acid dissociation, solubility products, and the like may therefore be subject to considerable error unless the realistic variations of chemical potential with concentration are properly considered. 

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