Permittivity of the solvent

It is necessary to use the bulk permittivity of the solvent in the equation, instead of the unknown but more correct effective permittivity of the medium between the charges in the transition state. 

Table 8-2 lists several physical properties pertinent to our concern with the effects of solvents on rates for 40 common solvents. The dielectric constant e is a measure of the ability of the solvent to separate charges it is defined as the ratio of the electric permittivity of the solvent to the permittivity of the vacuum. (Because physicists use the symbol e for permittivity, some authors use D for dielectric constant.) Evidently e is dimensionless. The dielectric constant is the property most often associated with the polarity of a solvent in Table 8-2 the solvents are listed in order of increasing dielectric constant, and it is evident that, with a few exceptions, this ranking accords fairly well with chemical intuition. The dielectric constant is a bulk property. 

The conductometric titration shown in Fig. 6 (adapted from Ref. [135]) exhibits the expected conductivity increase for LiBF4 and LiS03CF3 solutions in PC / 5-crown-5 mixtures at 25 °C, i.e., for salts which are known to be strongly associated despite the relatively high permittivity of the solvent. 

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 ... 

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... 

In contrast to points (l)-(3) of discussion, the effect of ion association on the conductivity of concentrated solutions is proven only with difficulty. Previously published reviews refer mainly to the permittivity of the solvent or quote some theoretical expressions for association constants which only take permittivity and distance parameters into account. Ue and Mori [212] in a recent publication tried a multiple linear regression based Eq. (62)... 

Although the Born equation is a rough approximation, it is often used for comparison of the solvation effects of various solvents. The simplification involved in the Born theory is based primarily on the assumption that the permittivity of the solvent is the same in the immediate vicinity of the ion as in the pure solvent, and the work required to compress the solvent around the ion is neglected. 

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 structure of the compact layer depends on whether specific adsorption occurs (ions are present in the compact layer) or not (ions are absent from the compact layer). In the absence of specific adsorption, the surface of the electrode is covered by a monomolecular solvent layer. The solvent molecules are oriented and their dipoles are distorted at higher field strengths. The permittivity of the solvent in this region is only an operational quantity, with a value of about 12 at the Epzc in water,... 

There are three properties that are important here the permittivity of the solvent, the viscosity of the solvent and the polarizability of the molecules of the solvent. 

E is an activation energy, and Z the collision number for molecules in the gas phase, and neither has been modified to account for either electrostatic interactions, or the effect of the relative permittivity of the solvent. 

For reactions in solution, the exponential term appropriate to the gas phase has to be modified to include the contribution accounting for the charges and the solvent. Calculations show that AG has to be modified by a term involving er, the relative permittivity of the solvent, and the charges on the ions. This term turns out to be the same as that appearing in the collision formula, Equation (7.3), i.e. z.KZ.ne1 / 47T o r ry, so that... 

Association phenomena increase and become much more important as the relative permittivity of the solvent decreases. Electrolytes which are completely, or nearly completely, dissociated in water are extensively associated in low relative permittivity solvents. 

In this equation Eox(D) and G,.cd(A) are the oxidation and reduction potentials of the donor and acceptor molecules or moieties measured in a solvent with relative permittivity srcj, whilst Eqq is the energy of the excited state from which the electron transfer occurs and Rcc is the centre-to-centre distance of the positive and negative charges in the charge-separated state. The radii of the positive and negative ions are given by r+ and r, es is the relative permittivity of the solvent, — e is the electron charge and So is the vacuum permittivity. 

Since the electrostatic component of AGsoi depends on the permittivity of the solvent, e, and on the cavity size (represented by means of the vector normal to the cavity surface, n), the electrostatic contribution to the enthalpy of solvation, A//ele, can be determined as indicated in Eq. 4-10 ... 

The expression given in Eq. (10) for the work assumes that p = 0, where p is the ionic strength of the medium. AG is the free-energy of the equilibrated excited-state (AG AE00), rD and rA are the molecular radii of the donor and acceptor molecules, e5 is the static dielectric constant or permittivity of the solvent, and z is the charge on each ion. ss is related to the response of the permanent dipoles of the surrounding solvent molecules to an external electrical field. Equation (9), the Bom equation, measures the difference in solvation energy between radical ions in vacuo and solution. 

The term A is related to the solvent density and molecular weight and to the free volumes of the ions and the ion-pair [59]. Fjoi is the difference between the molar ion-pair solvation energy and the free ion solvation energy. The theory does not predict a simple linearity of In with lie. Actually solvent effects other than that due to the relative permittivity of the solvent are easily predicted, since the macroscopic e is only a rudimentary description of the real attenuation of the ionic interactions due... 

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