Permittivity of electrolyte solutions

Debye and Falkenhagen [92] also predicted that the permittivity of electrolyte solutions should increase as c,/2 where c is the ionic concentration. According to Hasted [105], such an effect has not been demonstrated experimentally, probably because the high conductivity of such solutions can mask permittivity changes. On the contrary, the permittivity of electrolyte solutions decreases with concentration [106] by 25—50% at lmoldm-3. This is probably associated with the binding of dipolar solvent molecules to ions, thus reducing the solvent orientational contri-butional to the permittivity (dielectric saturation). 

Ionic Equilibria and Their Effect on the Permittivity of Electrolyte Solutions. Most of the commonly used solvents exhibit several relaxation processes that show up in the change of dielectric constant with frequency (see Section 2.12). These relaxation processes include rotation and libration of the molecules of the solvents, aggregates of ionic species, and H-bonding dynamics. 

The Onsager theory was first successfully applied to the static permittivities of electrolyte solutions by Ritson and Hasted, who showed that almost the entire depression of the pemuttiidty arises from the region lying between two spheres, of radius 2 and 4 A, centred on the ion. Dielectric deorements were calculated, and in a subsequent paper plausible hydration numbers were obtained. In their calculation a discontinuous model was used, with the assumption that the first sheath of water molecules was fiilly saturated, i.e. oriented to a (positive) ion. 

Figure 9 Comparison of measured variation with concentration of permittivity of electrolytic solutions " with calculations from Clueckauf s continuous model, which gives the full line...

Perie and Perie in Paris (71). More will be said about concentration dependence in the last section of this article. Transference numbers also play a role in theories of the concentration variation of certain other properties such as the permittivity of electrolyte solutions (TJ.), to take a recent example. 

The results cited show that kinetic effects play an important role in determining measured permittivities of electrolyte solutions and must be considered as well as static solvation effects. Properly a self consistent unified theory of both is needed (83) but as yet does not exist. In the case of aqueous salt solutions Patey and Carnie (84) have recently applied LHNC theory to calculations of the equilibrium permittivity and found reasonably good agreement with experimental values at low concentrations (79) after taking account of an assumed additive kinetic contribution calculated by HO theory. For further discussion of the equilibrium problem reference should be made to the original paper and to work of Friedman (85). 

Ionic Dielectric Decrements Ions in dilute aqueous solutions diminish the permittivity of the solution, in a manner proportional to the concentration, an effect called the dielectric decrement. The permittivity of electrolyte solutions is measured as a function of both the concentration c and the frequency of the applied electric field co and extrapolated to zero values of both, hence obtaining the static decrement = lim c->0,(o- 0)d ldc. The infinite dilution electrolyte values at 25°C are additive in the ionic contributions and Marcus [130] proposed to split them into the latter, 5, on the assumption adopted for the viscosity B-coefficients (Section 2.3.2.3), namely (Rb ) = 5 (Br ), with results shown in Table 2.12. The uncertainties of the values are 2M . The values of 5., are approximately linearly... 

Figure 1. Frequency regions and respective processes contributing to the permittivity of electrolyte solutions and solvents. ...

FTIR spectroscopy of electrolyte solutions has been employed to distinguish among free solvent molecules, solvent molecules bound to ions, and ion aggregates themselves. Furthermore, solvation numbers and association constants have been calculated from quantitative absorption measurements. Microwave spectra confirm the information from FTIR investigations. High frequency permittivity data deduced from MW and IR measurements yield information on the dynamic processes in electrolyte solutions. 

Inclusion of the change in solvent permittivity in the MSA description is an effective way of dealing with the change of solvent properties which accompany the addition of an electrolyte to a polar solvent. Since permittivity data are now available for a large number of electrolyte solutions in water [23], the MSA model can be applied to a wide variety of systems. However, there is one feature of electrolyte solutions which has been neglected in the treatments presented up to this point, namely, the existence of ion aggregates. This feature of electrolyte solutions is discussed in the following sections of this chapter. 

Results of such an analysis for the MgS04 system are shown in fig. 3.11. The best values of a and for this system are 610 pm and 185LmoP, respectively. On the basis of dielectric relaxation experiments, the permittivity of MgS04 solutions as a function of electrolyte concentration is given by... 

In conclusion, the MSA provides an excellent description of the properties of electrolyte solutions up to quite high concentrations. In dilute solutions, the most important feature of these systems is the influence of ion-ion interactions, which account for almost all of the departure from ideality. In this concentration region, the MSA theory does not differ significantly from the Debye-Hiickel model. As the ionic strength increases beyond 0.1 M, the finite size of all of the ions must be considered. This is done in the MSA on the basis of the hard-sphere contribution. Further improvement in the model comes from considering the presence of ion pairing and by using the actual dielectric permittivity of the solution rather than that of the pure solvent. 

In this chapter, the properties of polar solvents are discussed, especially as they relate to the formation of electrolyte solutions. Polar solvents are arbitrarily defined here as those liquids with a relative permittivity greater than 15. Solvents with zero dipole moment and a relative permittivity close to unity are non-polar. These include benzene, carbon tetrachloride, and cyclohexane. Solvents with relative permittivities between 3 and 5 are weakly polar, and those with values between 5 and 15 are moderately polar. The latter systems are not considered in the discussion in this chapter. 

The theoretical basis of his calculation is less secure than Bjerrum s, but his work had the merit of inspiring high precision work on the behaviour of electrolyte solutions over a range of relative permittivities. Bjenum s and Fuoss theories predicted different dependencies of association (sce Section 12.16). 

The Debye-Htickel model considered the solvent to be a structureless medium whose only property is to reduce the interactions between ions in a vacuum by a factor given by the macroscopic relative permittivity, e. No cognisance was taken of the possibility of ion-solvent interactions, and the size of the ion was assumed to be that of the bare ion. Gurney in the 1930s introduced the concept of the co-sphere and this has proved to be a useful concept in the theory of electrolyte solutions. Many recent theories of conductance are based on the Gurney co-sphere concept (see Section 12.17). 

The properties of the ions and the solvent which are ignored are similar to those ignored in the Debye-Hiickel treatment. These are very important properties at the microscopic level, but it would be a thankless task to try to incorporate them into the treatment used in the 1957 equation. Furthermore, Stokes Law is used in the equations describing the movement of the ions. This law applies to the motion of a macroscopic sphere through a structureless continuous medium. But the ions are microscopic species and the solvent is not structureless and use of Stokes Law is approximate in the extreme. Likewise, the equations describing the motion also involve the viscosity which is a macroscopic property of the solvent and does not include any of the important microscopic details of the solvent structure. The macroscopic relative permittivity also appears in the equation. This is certainly not valid in the vicinity of an ion because the intense electrical field due to an ion will cause dielectric saturation of the solvent immediately around the ion. In addition, alteration of the solvent stmcture by the ion is an important feature of electrolyte solutions (see Section 13.16). However, solvation is ignored. As in the Debye-Hiickel treatment the physical meaning of the distance of closest approach, i.e. a is also open to debate. 

The range of permittivities can be extended by using mixed solvents. Many studies of the behaviour of electrolyte solutions have been carried out in mixed solvents. But it is important to realise that there may be preferential solvation by one of the solvents under these conditions, and this could affect the correctness or otherwise of the interpretations which can be made. 

The relative permittivity measures the alignment of the solvent dipoles and production of induced dipoles by an electric field. An ion produces an intense field on bound solvent molecules, and will cause partial, if not complete, alignment of the dipoles of the solvent molecules affected by the ion. This results in a drop in the observed relative permittivity of the solution relative to the pure solvent. This drop is related to the number of bound solvent molecules. Controversy exists as to whether the effect is restricted to bound molecules only, or whether other solvent molecules are involved. Both theoretical and experimental studies have been carried out. The dependence of the relative permittivity on the distance from a given ion is of fundamental importance in theories of electrolyte solutions where generally the bulk relative permittivity is used in the theoretical expressions. But it is more likely that a varying relative permittivity should be used. 

If the dependence of the relative permittivity of the solvent on the electric field strength of the ions is also taken into account, then other thermodynamic parameters of electrolyte solutions (activity coefficient, heat of dilution, partial molar enthalpy content of the solute etc.) can likewise be calculated in better agreement with the experimental data. Although the introduction of the field-dependent relative permittivity into the ion-ion and ion-solvent interactions is accompanied by very great mathematical difficulties, the problem can be solved successfully by employing various approximations. 

Barthel J, Gerber R, Gores HI (1984) The temperature dependence of the properties of electrolyte solutions. VI. Triple ion formation in solvents of low permittivity exemplied by lithium tetra uoroborate solutions in dimethoxyethane. Ber Bunsenges 88 616-622... 

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]. 

However, in contrast to dielectric permittivity of solvents which can be estimated with an acceptable degree of precision [30], there is up to now no valid approach to estimate the viscosity of solvents [31] and its temperature dependence and the conductivity of concentrated solutions and its temperature dependence, especially not when the solvent blend shows a low dielectric permittivity. A remarkable approach for the calculation of conductivity of electrolyte solutions (lithium salts in organic carbonates) was published in 2005 [31]. With this approach it is possible to obtain conductivities without any... 

The intrinsic properties of an electrolyte evaluated at low concentrations of the salt and from the viscosity and permittivity of the solvent also determine the conductivity of concentrated solutions. Various systems were studied to check this approach. The investigated parameters and effects were ... 

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