The 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. 

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. 

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. ...

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...

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 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. 

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]. 

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). 

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 ... 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

The nonideality of electrolyte solntions, cansed nltimately by the electrical fields of the ions present, extends also to any nonelectrolyte that may be present in the aqueous solution. The nonelecttolyte may be a co-solvent that may be added to affect the properties of the solntion (e.g., lower the relative permittivity, e, or increase the solubility of other nonelecttolytes). For example, ethanol may be added to the aqueous solution to increase the solnbility of 8-hydroxyqni-noline in it. The nonelectrolyte considered may also be a reagent that does not dissociate into ions, or one where the dissociation is snppressed by the presence of hydrogen ions at a sufficient concentration (low pH cf Chapter 3), snch as the chelating agent 8-hydroxyquinoline. 

Here v is the velocity of the particle, E is the electric field strength, eo is the - permittivity of vacuum, eT is the dielectric constant of the electrolyte solution, ( is the equilibrium potential at the plane of shear (- zeta potential), and tj is the -> viscosity. See also -> Smolu-chowski equation (for the case of xr 1). 

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