Chemical Potential of Electrolyte Solute

In Sect. 3.2.4 the internal energy was treated as a sum of the mechanical and heat energies. Here, in addition, we discuss the effect of an electrostatic field (p on the change of internal energy d Ug under the molar description. 

Let the electrical charge dQ move in the electrostatic field 4 , then the change of internal energy is given by 

Note E.l (Chemical potential in electrochemistry). In (E.88) the chemical potential is represented as the sum of the chemical potential pia and the change of electrostatic 

Since thermodynamic quantities such as the activity and activity coefficient for ionized species, give no physical background, they must be related to the original species by electrical neutrality. Let 1 mole of electrolyte A be ionized into v+ mole of cations with charge z+ and v mole of anions with charge z then, from the electroneutrality principle we have 

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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 ... 

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. 

For any imaginary ideal solution of an electrolyte, at any given T and P, in which all activity and osmotic coefficients are unity, we can write for the chemical potential of a solute s. 

In general, the chemical potential of the solution in the micellar phase must equal that in the surrounding aqueous medium when thermodynamic equilibrium is established. Nonpolar solutes, such as the permanent gases, which do not interact strongly with either phase may be distributed rather evenly over the whole microheterogeneous system (39). On the other hand, typical electrolytes are practically restricted to the aqueous medium, while molecules of hydrophobic substances, e.g. hydrocarbons, are almost totally sequestered in the micelles. 

Fig. 2. The chemical model of electrolyte solutions. O observer, i ion X, j ion Xj in an arbitrary position, fjj, with regard to the ion X, special positions (contact, separation by one or two orientated solvent molecules) are sketched with broken lines, r, a, R distance parameters W mean-force potentials and relative velocities of ions X, and Xj...

If the solute Y in a binary system is an electrolyte composed of a cation C + of valency z+ and an anion A of valency z (i.e., Y = C +A I), the appropriate form of the chemical potential of the solute is based on the single-ion chemical potentials of its cation and anion and is given by the relationship... 

The chemical model of electrolyte solutions introduces short-range interactions by means of potentials of mean force W , which can be considered as contributions to ion-pair formation. 

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 ... 

The linear term, Cm, was dealt with and interpreted in several ways. Empirically, C = 0.l z z was proposed by Davies [13] for fitting activity coefficients of aqueous electrolytes at 25°C up to 0.1 m. Stokes and Robinson [ 14] suggested that the amount of solvent bound by the solvated ions should be deducted from the total amount of solvent in order to represent the entropic part of the chemical potential of the solute appropriately. Therefore, the following expression results for the Unear term ... 

The main objective of this chapter is to introduce the reader to physical chemistry of electrolyte solutions. An electrolyte solution consists of charged species (ions), and it makes these solutions very useful for electrochanical science and engineering. Concentration, activity, activity coefQdent, and chemical potential of both solute and solvent are described in detail. The concentration of species in weak electrolytes and pH of aqueous solutions are discussed, and physical chemistry of buffer solutions is explained. 

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. 

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... 

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... 

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. 

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. 

For example, the empirical relation between the activity and the molality ratio can be understood on the assumption that the chemical potential of the electrolyte is the sum of the chemical potentials of the constituent ions. That is, for HCl as the solute. 

Earlier, Gavach et al. studied the superselectivity of Nafion 125 sulfonate membranes in contact with aqueous NaCl solutions using the methods of zero-current membrane potential, electrolyte desorption kinetics into pure water, co-ion and counterion selfdiffusion fluxes, co-ion fluxes under a constant current, and membrane electrical conductance. Superselectivity refers to a condition where anion transport is very small relative to cation transport. The exclusion of the anions in these systems is much greater than that as predicted by simple Donnan equilibrium theory that involves the equality of chemical potentials of cations and anions across the membrane—electrolyte interface as well as the principle of electroneutrality. The results showed the importance of membrane swelling there is a loss of superselectivity, in that there is a decrease in the counterion/co-ion mobility, with greater swelling. 

Thus, surface tension changes have been related to changes in the absolute potential differences across an electrode/electrolyte interface and to changes in the chemical potential of all the species, i.e., to changes in solution composition. Only one other quantity is missing, the surface excess. This can be easily introduced by recalling the definition of surface excess [Eq. (6.66)], i.e.,... 

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. 

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). 

The first term refers to the electrolyte. Accordingly, the sum runs over all ion types present in the electrolyte. The second term contains the contribution of the electrons in the metal. T and Te are the interfacial excess concentrations of the ions in solution and of the electrons in the metal, respectively, /x is the chemical potential of the particle type i, Fa is Faradays constant, and /x is the electrochemical potential of the electrons. Substitution leads to... 

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