Permittivity solvents

For simple salts the influence of parameters (1)—(3) can be studied separately by the investigation of series of salts with a common anion or cation in a solvent of high dielectric permittivity. Flowever, high solvent permittivity is only a necessary, but not a sufficient, condition for complete dissociation. High permittivity of the solvents does not prevent ions from associating, if these ions interact specifically... 

Chemical reactions in solutions are often affected drastically by the solvents used. The main objective of this book is to correlate the properties of solvents and the solvent effects on various chemical processes relevant to electrochemistry. The most important solvent properties in considering solvent effects are the solvent permittivity and the solvent acidity and basicity. If the permittivity of one solvent is high (er>30) and that of the other is low (er<10), the difference in a chemical process... 

Fig. 2.2 The effect of solvent permittivity on the electrostatic solvation energy of an ion (curve 1) and that of a neutral dipolar molecule (curve 2). Curve 1 was obtained from Eq. (2.3) assuming r=0.2 nm. For curve 2, see4).

The values of ds in seven dipolar aprotic solvents have been reported to be 80 + 5 pm for cations and 44 4 pm for anions [10]. The MSA is also used in treating ionic activity coefficients in a recent study [11], the change in solvent permittivity with electrolyte concentration was taken into account in addition to the change in ionic radius, and excellent agreements were obtained between the experimental and theoretical results for 1 1 electrolytes of up to 2.5 M. 

Fig. 2.12 Relationship between the ion association constants (log KA) and the reciprocal of solvent permittivity (1 /er) (solid line) and between the degree of ion association (a) and log (c/(A) (dotted curve), (open circles Bu4NPic in AN, NB, MeOH, Ac, Py, DCE, o-dichlorobenzene, acetic acid, chlorobenzene and benzene closed squares KCI in ethanolamine, MeOH, EtOH, acetic acid and H20-dioxane mix-tures). The solid line was obtained using a Eq. (2.19) for 0 = 0.6 nm.

Static solution permittivity, e(c), and static solvent permittivity, es(c), for solutions of various electrolytes at various concentrations (c) have been obtained by dielectric relaxation spectroscopy [44]. Ion-pairs contribute to permittivity if their lifetime is longer than their relaxation time. However free ions do not contribute to permittivity. Thus,... 

Here, A denotes an add of type HA-, HA or BH+, and z and q denote the charge and the radius, respectively, of species i. The influence of permittivity on p/C, depends on the charges, radii and the charge locations of the add and its conjugate base. Table 3.3 shows the pKa values of some acids and add-base indicators in water, methanol and ethanol [3], The solvent effects on pK l are smaller for BH+-type adds than for HA- or HA-type acids. For the BH+-type acids, zA=l and zB=0 in Eq. (3.16), and the influence of solvent permittivity is expeded to be small. 

However, because of the low solvent permittivities, the dissociation of the ion-pair to free ions is difficult. Thus, even a strong acid in water behaves as a weak acid, e.g. the pKa of HC104 is 3.9 in t-butanol, 4.9 in acetic acid, and 3.1 in ethylenediamine. 

Some redox couples of organometallic complexes are used as potential references. In particular, the ferrocenium ion/ferrocene (Fc+/Fc) and bis(biphenyl)chromium(I)/ (0) (BCr+/BCr) couples have been recommended by IUPAC as the potential reference in each individual solvent (Section 6.1.3) [11]. Furthermore, these couples are often used as solvent-independent potential references for comparing the potentials in different solvents [21]. The oxidized and reduced forms of each couple have similar structures and large sizes. Moreover, the positive charge in the oxidized form is surrounded by bulky ligands. Thus, the potentials of these redox couples are expected to be fairly free of the effects of solvents and reactive impurities. However, these couples do have some problems. One problem is that in aqueous solutions Fc+ in water behaves somewhat differently to in other solvents [29] the solubility of BCr+BPhF is insufficient in aqueous solutions, although it increases somewhat at higher temperatures (>45°C) [22]. The other problem is that the potentials of these couples are influenced to some extent by solvent permittivity this was discussed in 8 of Chapter 2. The influence of solvent permittivity can be removed by... 

However, the latter formula is not more applicable, if xlaa is rather long and/ or Cm is rather high, so that the zero-frequency ionic contribution Aefon(0) to permittivity is noticeable in comparison with the static permittivity es of the solution. We note that the Kirkwood correlation factor g is used for calculation of the component p in Eq. (387). Thus, even in our additivity approximation the solvent permittivity )jip is determined in this case by concentrations of both solution components. This complication leads to a new self-consistent calculation scheme. 

Change of solvent, permittivity, viscosity and ionic strength can all affect the rates of reactions in solution. 

Fig. 9.13 Dependence of the calculated heats of formation, AHf, for the discussed states of 9d on solvent permittivity ground state black), local excited state blue), BCT green), CT red)...

Water has provided a convenient solvent in which to study the kinetics of reactions involving ions, but the low solubility of neutral organic solutes often leads to difficulties. In such cases, aqueous mixtures have been extensively used because, by judicious choice of the non-aqueous component and the composition, the solubilities of both ionic and neutral solutes are sufficiently large to overcome these problems. Further, in testing correlations between kinetic parameters and solvent permittivity, the latter can be varied, by changing the composition of an aqueous mixture, over a considerable range, e.g. 2 < er < 80 for dioxan + water at 298 K. 

Some emf studies have been reported for salt solutions in sulpho-lane + water mixtures (Tommila and Belinskij, 1969). It is noteworthy that p/ a for m-nitroanilinium ions in these mixtures does not change regularly with change in solvent permittivity (Ang, 1972). Covington et al. (1974) have suggested that, in these mixtures, Cs+ ions are preferentially solvated by sulpholane. The Walden product, A°r , for KC104 has a minimum near x2 = O 2 in sulpholane + water mixtures at 298 K (D Aprano et al., 1972). 

The temperature dependence of the solvent permittivity, (de/dT)P, and of the cavity size, (dn/dT)P, for water were approximated by empirical values equal to -0.3554 and 2.56 10-4 K 1 respectively [25], The values of (dGeie/de) and (3Geie/3n) were estimated numerically from the AGeie values calculated by varying both e and k (i.e., the scaling factor used to modulate the size of the cavity ... 

Static solvent effect — is widely understood as the dependence of -> reaction rate on solvent -> permittivity. The most systematic studies of this effect were stimulated by the early version of -> Marcus theory and mostly consisted in experimental verification of Mar-... 

Solvent permittivity — is an index of the ability of a solvent to attenuate the transmission of an electrostatic force. This quantity is also called the -> dielectric constant. -> permittivity decreases with field frequency. Static (related to infinite frequency) and optical op (related to optical frequencies) permittivities are used in numerous models evaluating the solvation of ions in polar solvents under both static and dynamic conditions. Usually the refractive index n is used instead of op (n2 = eop), as these quantities are available for the majority of solvents. The theory of permittivity was first proposed by Debye [i]. Systematic description of further development can be found in the monograph of Frohlich [ii]. Various aspects of application to reactions in polar media and solution properties, as well as tabulated values can be found in Fawcetts textbook [iii]. 

The fit of the MSA to activity coefficient data for aqueous electrolyte solutions can be considerably improved if one takes into consideration the decrease in solvent permittivity which accompanies the increase in electrolyte concentration. This phenomenon is clearly related to the effect that ions have on solvent structure and was studied originally in aqueous solutions by Hasted et al. [21, 22]. More recently, data have been collected for a large number of electrolytes by Barthel and coworkers [23]. In the case of NaCl solutions, the change in dielectric permittivity with electrolyte concentrations up to 2 M is given by... 

The fit of the MSA model with varying solvent permittivity is shown in fig. 3.9. These results demonstrate the importanee of eonsidering the true solvent permit-... 

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. 

Some molecular properties of polar solvents are summarized in table 4.3. The dipole moment and molecular polarizability are the molecular parameters which lead to the solvent permittivity. The other parameters listed are the molecular diameter and the Lennard-Jones interaction energy, Elj. These are of interest in assessing the role of van der Waals forces in determining the properties of a polar liquid. 

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