Solutions, associated thermodynamic properties

SOL.6. 1. Prigogine, V. Mathot et A. Desmyter, Proprietes thermodynamiques des solutions associees (Thermodynamic properties of associated solutions). Bull Soc. Chim. Beiges 58, 547-565... 

Other thermodynamic properties of aqueous solutions are being evaluated. A recent publication reports values calculated for the association constants of aqueous ionic species at 298 K for alkaline earth salts (Staples, 1978). 

Medium-chain alcohols such as 2-butoxyethanol (BE) exist as microaggregates in water which in many respects resemble micellar systems. Mixed micelles can be formed between such alcohols and surfactants. The thermodynamics of the system BE-sodlum decanoate (Na-Dec)-water was studied through direct measurements of volumes (flow denslmetry), enthalpies and heat capacities (flow microcalorimetry). Data are reported as transfer functions. The observed trends are analyzed with a recently published chemical equilibrium model (J. Solution Chem. 13,1,1984). By adjusting the distribution constant and the thermodynamic property of the solute In the mixed micelle. It Is possible to fit nearly quantitatively the transfer of BE from water to aqueous NaDec. The model Is not as successful for the transfert of NaDec from water to aqueous BE at low BE concentrations Indicating self-association of NaDec Induced by BE. The model can be used to evaluate the thermodynamic properties of both components of the mixed micelle. 

The partial structure factors for binary (Bhatia and Thorton, 1970) and multicomponent (Bhatia and Ratti, 1977) liquids have been expressed in terms of fluctuation correlation factors, which at zero wave number are related to the thermodynamic properties. An associated solution model in the limits of nearly complete association or nearly complete dissociation has been used to illustrate the composition dependence of the composition-fluctuation factor at zero wave number, Scc(0). For a binary liquid this is inversely proportional to the second derivative of the Gibbs energy of mixing with respect to atom fraction. 

This treatment assumes that the forces between molecules in relative motion are related directly to the thermodynamic properties of the solution. The excluded volume does indeed exert an indirect effect on transport properties in dilute solutions through its influence on chain dimensions. Also, there is probably a close relationship between such thermodynamic properties as isothermal compressibility and the free volume parameters which control segmental friction. However, there is no evidence to support a direct connection between solution thermodynamics and the frictional forces associated with large scale molecular structure at any level of polymer concentration. 

Interestingly, there have been repeated attempts to view such gradual structural changes due to chemical equilibria as phase transitions as well [262]. Instructive examples for such an analysis are living polymers — for example, in demixing solutions of polymers [263] and in sulfur [264], where the reversible polymerization process has been treated as a second-order phase transition. The experimental evidence for such an interpretation is, however, at best weak [265], and classical association models [266] describe the thermodynamic properties equally well. 

In considering the thermodynamics properties associated with a surface, it is convenient to choose a position for the dividing plane that makes the surface concentration zero. For a single component (pure substance), it is possible to do this. From equation (12.55), we can show that this occurs when the two areas in Figure 12.5b are equal. This will be our choice for the phase boundary for a pure substance. With two or more components, in general it is not possible to make more than one T, equal to zero. In this case, we usually choose the boundary to make Tj the surface concentration of the solvent zero. With this choice, T,- for a solute will not be zero unless cu = c j. 

Solvent effects in electrochemistry are relevant to those solvents that permit at least some ionic dissociation of electrolytes, hence conductivities and electrode reactions. Certain electrolytes, such as tetraalkylammonium salts with large hydrophobic anions, can be dissolved in non-polar solvents, but they are hardly dissociated to ions in the solution. In solvents with relative permittivities (see Table 3.5) s < 10 little ionic dissociation takes place and ions tend to pair to neutral species, whereas in solvents with 8 > 30 little ion pairing occurs, and electrolytes, at least those with univalent cations and anions, are dissociated to a large or full extent. The Bjerrum theory of ion association, that considers the solvent surrounding an ion as a continuum characterized by its relative permittivity, can be invoked for this purpose. It considers ions to be paired and not contributing to conductivity and to effects of charges on thermodynamic properties even when separated by one or several solvent molecules, provided that the mutual electrostatic interaction energy is < 2 kBT. For ions with a diameter of a nm, the parameter b is of prime importance ... 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

Two additional observations should be made. First, the methods used here treat each of the ionic types as a separate species that influences the thermodynamic properties of solutions very strongly by virtue of its associated charge. Second, it is instructive to examine the dependence of the mean molal activity coefficient for several different electrolytes as a function of the molality. Representative examples are shown in Fig. 4.3.1. One sees at first a very steep drop in as m is increased, and then either a gradual or a very sharp... 

Various thermodynamic properties of 178 have been studied. Lucken early recognized that the radical associates to a dimeric form in solid salts and certain solutions. This association has been the object of recent scrutiny. Optical spectra of 178 free, in ion-paired form with perchlorate, and in a dimeric form associated with two perchlorate ions have been recognized. The exact nature of the forms present in a solution depends upon the solvent equilibrium constants and activation parameters for the association were determined. 

The results established in the preceding paragraph may be verified by comparing the thermodynamic properties and the spectroscopic properties of associated solutions. Let us consider, for example, a solution of ethanol in carbon tetrachloride. The valency vibration of the OH group gives rise to two distinct infra-red absorption bands depending upon whether the OH group is in a monomer or in an associated complex. The fraction of molecules of alcohol which remain in the monomeric state can therefore be determined from measurements... 

Carpenter MA, McCoimell JDC, Navrotsky A (1985) Enthalpies of ordering in the plagioclase feldspar solid solution. Geochim Cosmochim Acta 49 947-966 Carpenter MA, Salje EKH, Graeme-Barber A, Wmck B, Dove MT, Kiught KS (1998) Calibration of excess thermodynamic properties and elastic constant variations associated with the a< p phase transition in quartz. Am Mineral 83 2-22... 

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. 

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