The Thermodynamics of Electrolyte Solutions

It is important to note that ionophores are not always completely dissociated. For example, when NaCl is dissolved in a solvent of lower relative permittivity, such as methanol, it is ion paired to some extent. The thermodynamics of systems with ion pairing is considered separately in section 3.10. Under these circumstances the ionophore behaves in the same way as a weak electrolyte. On the other hand, all ionogenes are not weak electrolytes. For example, HCl, which is a molecule in the gas phase, is completely dissociated in water and therefore is a strong electrolyte. Acetic acid is completely dissociated in liquid ammonia, which is a much stronger base than water. Thus, the solvent plays an important role in determining the extent of electrolyte dissociation in solution. In the following discussion the traditional terms, strong and weak electrolytes, are used. 

Consider a simple 1-1 electrolyte MX which is completely dissociated in dilute solutions. The chemical potential of MX can be written as 

Since individual ionic activity coefficients cannot be measured experimentally, only the mean quantity is tabulated. It follows that the activity of a 1-1 electrolyte is given by 

The concentration dependence of y is an important feature involved in the experimental and theoretical evaluation of electrolyte behavior. The chemical potential of the standard state, p x, is that for a hypothetical one-molal solution in which all real interactions are imagined to be absent (y =1.00). Thus, the 

One may also write expressions for the chemical potential of the electrolyte on the molarity and mole fraction scales. In the former case, the expression is 

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Card D N and Valleau J 1970 Monte Carlo study of the thermodynamics of electrolyte solutions J. Chem. Phys. 52 6232... 

Andrew Dickson (Chair) is an Associate Professor-in-Residence at the Scripps Institution of Oceanography. His research focuses on the analytical chemistry of carbon dioxide in sea water, biogeochemical cycles in the upper ocean, marine inorganic chemistry, and the thermodynamics of electrolyte solutions at high temperatures and pressures. His expertise lies in the quality control of oceanic carbon dioxide measurements and in the development of underway instrumentation for the study of upper ocean biogeochemistry. Dr. Dickson served on the NRC Committee on Oceanic Carbon. He is presently a member of the IOC C02 Advisory Panel and of the PICES Working Group 13 on C02 in the North Pacific. 

These considerations can make the thermodynamics of electrolyte solutions tricky. Despite such possibilities, the right side of Eq. (3.18), p. 40, is typically inoffensive for the problems of ionic contributions to single-ion activities. In... 

Properties of ntmaqueous electrolyte solutions have been widely studied in fundamental research due to the possibility to vary parameters such as the viscosity and dielectric permittivity of the solvent. The result of these studies mainly conducted in the last century was a better knowledge of spectroscopic and transport properties as well as the thermodynamics of electrolyte solutions [3-17]. The observed behavior was interpreted in terms of stracture formation in solutions including solvation of ions, ion pair formation, formation of triple ions and clusters caused by the underlying interactions, the ion/ solvent molecule interaction and the ion/ion interaction [2, 5, 6, 9,14,18-21]. 

D. N. Card and J. P. Valleau, J. Chem. Phys., 52, 6232 (1970). Monte Carlo Study of the Thermodynamics of Electrolyte Solutions. 

Ingold quickly found a valuable colleague in H. M. Dawson, who had studied at Manchester with Arthur Smithells and in Germany with van t Hoff, K. Elbs, and Abegg. Thermodynamics and kinetics were Dawson s principal interests "Dawson taught me a lot of physical chemistry in a quiet way, and I became very interested in his attempts to sort out the kinetic effects of the constitutents of electrolytic solutions," Ingold later reminisced. 15... 

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. 

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

Pitzer s solution to the problem was the development of a set of analytical equations that are thermodynamically consistent after transformations through the Gibbs-Duhem equation. These equations are known as the Pitzer equations, in recognition of the major role that he played in developing them and the major contributions he made in the understanding of electrolyte solutions through a lifetime of work. We will now summarize these equations and describe their usefulness. For details of the derivation we refer the reader to Pitzer s original paper.6... 

The three appendices in this volume give selected sets of thermodynamic data (Appendix 5), review the statistical calculations covered in Principles and Applications (Appendix 6), and summarize the equations and parameters required to calculate the properties of electrolyte solutions, principally from Pitzer s equations (Appendix 7). 

A difficulty encountered in the measurement of the surface tension of solutions is that it is often different when measured by so-called dynamic methods (vibrating jets, etc.), in which the value for a freshly-formed surface is measured rapidly, and when measured by so-called static methods (capillary rise, etc.), which determine the value for a surface which has been in existence for some time. The difference is due to the fact that the composition of the surface is different from that in the bulk of the solution, and in a fresh surface a change of concentration occurs, which, as it involyes diffusion, usually occurs slowly, so that rapid measurements give results different from those which deal with a surface which has come into equilibrium. In capillary active solutions, the surface is enriched in solute, whilst in capillary inactive it is usually richer in solvent. In the case of electrolyte solutions, the surface layer is considered to consist of a unimolecular layer of solvent molecules. The thermodynamic theory was established by Gibbs, and indicates that when the solute... 

Abstract Analytical solution of the associative mean spherical approximation (AMSA) and the modified version of the mean spherical approximation - the mass action law (MSA-MAL) approach for ion and ion-dipole models are used to revise the concept of ion association in the theory of electrolyte solutions. In the considered approach in contrast to the traditional one both free and associated ion electrostatic contributions are taken into account and therefore the revised version of ion association concept is correct for weak and strong regimes of ion association. It is shown that AMSA theory is more preferable for the description of thermodynamic properties while the modified version of the MSA-MAL theory is more useful for the description of electrical properties. The capabilities of the developed approaches are illustrated by the description of thermodynamic and transport properties of electrolyte solutions in weakly polar solvents. The proposed theory is applied to explain the anomalous properties of electrical double layer in a low temperature region and for the treatment of the effect of electrolyte on the rate of intramolecular electron transfer. The revised concept of ion association is also used to describe the concentration dependence of dielectric constant in electrolyte solutions. 

In this chapter some aspects of the present state of the concept of ion association in the theory of electrolyte solutions will be reviewed. For simplification our consideration will be restricted to a symmetrical electrolyte. It will be demonstrated that the concept of ion association is useful not only to describe such properties as osmotic and activity coefficients, electroconductivity and dielectric constant of nonaqueous electrolyte solutions, which traditionally are explained using the ion association ideas, but also for the treatment of electrolyte contributions to the intramolecular electron transfer in weakly polar solvents [21, 22] and for the interpretation of specific anomalous properties of electrical double layer in low temperature region [23, 24], The majority of these properties can be described within the McMillan-Mayer or ion approach when the solvent is considered as a dielectric continuum and only ions are treated explicitly. However, the description of dielectric properties also requires the solvent molecules being explicitly taken into account which can be done at the Born-Oppenheimer or ion-molecular approach. This approach also leads to the correct description of different solvation effects. We should also note that effects of ion association require a different treatment of the thermodynamic and electrical properties. For the thermodynamic properties such as the osmotic and activity coefficients or the adsorption coefficient of electrical double layer, the ion pairs give a direct contribution and these properties are described correctly in the framework of AMSA theory. Since the ion pairs have no free electric charges, they give polarization effects only for such electrical properties as electroconductivity, dielectric constant or capacitance of electrical double layer. Hence, to describe the electrical properties, it is more convenient to modify MSA-MAL approach by including the ion pairs as new polar entities. 

In the beginning of this section the AMSA approach will be applied to the description of this model of electrolyte solution. The obtained results will be applied to describe the thermodynamic properties of electrolyte solution and to study the effect of electrolyte solution on intramolecular transfer reactions. Finally, the specific features of the effect of ion association on the properties of electrical double layer will be discussed. 

In summary, diffraction techniques provide a powerful means of investigating the structure of electrolyte solutions. They give information about the pair correlation functions which can be directly related to modern theoretical techniques such as molecular dynamics calculations. This information can also be used to improve the statistical thermodynamic models of electrolyte solutions discussed in chapter 3. 

In this chapter the focus will be on K, the equilibrium constant, and the following thermodynamic quantities, U, the energy, H, the enthalpy, G, the free energy, S, the entropy, V, the volume, C the heat capacity, and /x, the chemical potential. The significance of standard changes in the values of these quantities. At/, A//, AG, AS, ACp, and AV for the study of electrolyte solutions will be discussed. 

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. 

The information on the structure of electrolyte solutions provided by thermwlynamic and transport properties on the one hand and by spectroscopic, relaxation and kinetic investigations on the other, complement one another with regard to the chemical model. Thermodynamic and transport properties provide the distance parameter R, the overall association constant Ka, and the activity coeffident y linked to it. No direct information can be achieved on the structure of the region a g r R and possible regions a Rj Rj. .. R. This problem, however, can be solved by modem spectroscopic and relaxation methods. 

While the viscosity of electrolytic solutions is not a thermodynamic property, such data frequently are reported with partial molal volumes, and viscosities are often valuable in elucidating the structure of solutions. Therefore, a few viscosity data which have a direct bearing on the discussion of the nature of these solutions are included. 

Although the viscosity of an electrolytic solution is not a thermodynamic function, such data are frequently found in conjunction with the thermodynamic quantity. Kg, and the information which can be derived from accurate viscosity measurements is often useful in gaining an insight into the structure of electrolytic solutions. Consequently, it seems appropriate to digress momentarily and include a brief discussion of the subject in this section. 

The models of electrolyte solutions and the fundamentals of thermodynamics and statistical thermodynamics are given in Electrolyte Solutions, Thermodynamics. 

Also, from the measurements of diffusion coefficients of the ternary systems already studied (e.g., y -cyclodextrin plus caffeine [15], 2-hydroxypropyl-p-cyclodextrin plus caffeine [16], CuCl (1) plus caffeine [10], and KCl plus theophylline (THP) [18]), it is possible to give a contribution to the understanding of the stmcture of electrolyte solutions and their thermodynamic behavior. For example, by using Equations (22) and (23), and through the experimental tracer ternary diffusion coefficients of KCl dissolved in supporting THP solutions, D (c/c = 0) and tracer ternary diffusion coefficients of THP dissolved in supporting KCl solutions, D°2 (c /Cj = 0) [18], it will be possible to estimate some parameters, such as the diffusion coefficient of the aggregate between KCl and THP [18] and the respective association constant. 

A major objective in improving battery performance is the optimization of the power of a ceU. The power of the cell is governed by thermodynamic, kinetic, transport, and geometric parameters [14-25]. The conductivity of electrolyte solutions is mainly determined by following parameters [26] ... 

The discussion of electrolyte solutions requires the estimation of the Reynolds number for the particular case where L is of the order of the mean diameter of the particles, i.e. 0.1 nm. All liquids commonly used as solvents show dynamic viscosities of the order of 1 cPoise and densities of the order of 1 g cm . Then the order of magnitude of Re can be evaluated if for U an estimate of the hydrodynamic velocity of the sphere in the liquid can be made. The order of magnitude of U can be derived from the linear transport theory, where the motion of a particle in a liquid is described at a local level by the action of a friction force F (eq 1.1). In the steady state of motion this force is supposed to equilibrate the thermodynamic force ... 

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