Electrostatic ion-solvent interaction

Within this frame, it is possible to show that the first term of Eq (39) represents the electrostatic ion-solvent interaction energy, in terms of the ZTS potential at nucleus V > Under the approximation ... 

We shall now show that the insertion energy may be cast into a form completely equivalent to Bom formula. This may be easily done by using the well known relationship between the electrostatic ion-solvent interaction energy and the electronic polarization energy [3,14], Namely... 

Extrapolation methods are based on the representation of the electrostatic ion-solvent interactions as a series expansion of type bj(ai), where a is one of the ionic radii. For example, in a series of electrolytes with a common cation and differing anions, the relationship... 

Further, in the case of virtually non-existent ion-solvent interactions (low degree of solvation), so that solute-solute interactions become more important, Kraus and co-workers47 confirmed that in dilute solutions ion pairs and some simple ions occurred, in more concentrated solutions triple ions of type M+ X M+ orX M+X andinhighly concentrated solutions even quadrupoles the expression triple ions was reserved by Fuoss and Kraus48 for non-hydrogen-bonded ion aggregates formed by electrostatic attraction. 

As has been previously mentioned, ion-solvent interactions involve several factors that include electrostatic and Lewis acid-base contributions. It would be helpful to be able to estimate the magnitude of the individual contributions from these separate factors, and much effort is being directed toward devising ways of estimating the polarity of solvents. Several methods have been proposed. One empirical approach to the problem involves use of the relation... 

Ion-dipole forces are important in solulions of ionic compounds in polar solvents where solvated species such as NatOH,) and F(H 20) (for solutions of NaF in H.O) exist. In the case of some metal ions these solvated species can be sufficiently stable to be considered as discrete species, such as [Co(NHj)6]j+. Complex ions such as the latter may thus be considered as electrostatic ion—dipole interactions, but this oversimplification (Crystal Field Theory sec Chapter 11) is less accurate than are alternative viewpoints. 

On treating ion solvation it is useful to differentiate between primary and secondary solvation shell or between chemical and physical solvation, respectively The electrostatic calculation of ion solvation is quite often less accurate because specific ion-solvent interactions have to be considered. In the primary solvation shell specific ion-solvent interactions are of much more importance than those with solvent molecules... 

The first term on the right hand side refers to the bare ion and disappears because we are engaged in differences of free energies. The second term refers to the coordination model of ion-solvent interaction in the primary solvation shell and the third term takes into account long range interactions. The last contribution may be approximated by the electrostatic interaction of a charged species with the solvent. The radius of the charged species is equal to that of the solvated ion e.g., ionic radius + diameter of the solvent molecules in the primary solvation shell). 

While at infinite dilutions only ion-solvent interactions occur and electrolyte solutions behave ideally, also at very low concentrations they deviate from ideality because of the electrostatic interaction energy of ions. Attractive forces between oppositely charged analytes lower the active concentration of each ionic species, because the attraction changes the way a given ion reacts chemically. Chemical laws are obeyed only if concentration is replaced by another physical quantity, the activity that is proportional to the concentration by a factor known as activity coefficient y. 

Conductometric and spectrophotometric behavior of several electrolytes in binary mixtures of sulfolane with water, methanol, ethanol, and tert-butanol was studied. In water-sulfolane, ionic Walden products are discussed in terms of solvent structural effects and ion-solvent interactions. In these mixtures alkali chlorides and hydrochloric acid show ionic association despite the high value of dielectric constants. Association of LiCl, very high in sulfolane, decreases when methanol is added although the dielectric constant decreases. Picric acid in ethanol-sulfolane and tert-butanol-sulfolane behaves similarly. These findings were interpreted by assuming that ionic association is mainly affected by solute-solvent interactions rather than by electrostatics. Hydrochloric and picric acids in sulfolane form complex species HCl and Pi(HPi). ... 

In the last few sections we have been using simple electrostatic models to compute the contribution to the free energy changes of the electrical interactions of charged particles. From the relations AaS = — [d(AF)/dT]i>, = AF + T AS, ACp = [d AH)/dT]p, and AV = [d AF)/dP)T it is possible from the same models to compute these other thermodynamic properties as well. The two types of interaction of interest are the ion-ion and ion-solvent interactions of these, the latter is much the larger. 

The theoretical discussion of the heats of ion-solvent interactions has been restricted so far to stressing the alkali metal and alkaline earth cations and halide anions. For these ions, a purely electrostatic theory (Section 2.15.10) provides fair coincidence with experiments. However, with the two- and three-valent transition-metal ions, where directed orbital interactions with water may have more influence. 

The final state is obvious it is ions in solution. The initial state is not so straightforward one cannot take ions in vacuum, because then there will be ion-solvent interactions when these ions enter the solvent. The following approach is therefore adopted. One conceives of a hypothetical situation in which the ions are there in solution but are nevertheless not interacting. Now, if ion-ion interactions are assumed to be electrostatic in origin, then the imaginary initial state of noninteracting ions implies an assembly of discharged ions. 

Born (1) and later Bjerrum (2) developed a theoretical approach to ion-solvent interactions based on a rather simple electrostatic model. Ions are considered as rigid spheres of radius r and charge z in a solvent continuum of dielectric constant e. Changes in enthalpy AH av) and in free energy AG av), respectively, associated with the transfer of the gaseous ions into the solvent are represented by the following equations ... 

Recently, detailed molecular pictures of the interfacial structure on the time and distance scales of the ion-crossing event, as well as of ion transfer dynamics, have been provided by Benjamin s molecular dynamics computer simulations [71, 75, 128, 136]. The system studied [71, 75, 136] included 343 water molecules and 108 1,2-dichloroethane molecules, which were separately equilibrated in two liquid slabs, and then brought into contact to form a box about 4 nm long and of cross-section 2.17 nmx2.17 nm. In a previous study [128], the dynamics of ion transfer were studied in a system including 256 polar and 256 nonpolar diatomic molecules. Solvent-solvent and ion-solvent interactions were described with standard potential functions, comprising coulombic and Lennard-Jones 6-12 pairwise potentials for electrostatic and nonbonded interactions, respectively. While in the first study [128] the intramolecular bond vibration of both polar and nonpolar solvent molecules was modeled as a harmonic oscillator, the next studies [71,75,136] used a more advanced model [137] for water and a four-atom model, with a united atom for each of two... 

A. 15.5 Three of the following. (1) A central reference ion of a specific charge can be represented as a point charge. (2) This central ion is surrounded by a cloud of smeared-out charge contributed by the participation of all of the other ions in solution. (3) The electrostatic potential field in the solution can be described by an equation that combines and linearizes the Poisson and Boltzmann equations. (4) No ion — ion interactions except the electrostatic interaction given by a l/z dependence are to be considered (i.e., dispersion forces and ion - dipole forces are to be excluded). (5) The solvent simply provides a dielectric medium, and the ion — solvent interactions are to be ignored, so that the bulk permittivity of the solvent can be used. 

Not only does neutron diffraction allow one to determine ionic size and hydration numbers in solution but it can also be used to assess changes in hydration with concentration. In the case of Li" ", the hydration number is 6 in dilute solutions but it drops to values below 4 in very concentrated solutions. Similar conclusions have been reached regarding divalent cations such as Ca for which the ion-solvent interactions are mainly electrostatic in nature. For this system the hydration number decreases from 10 in 1 M CaCl2 to 6 in a 4.5 M solution of the same salt. 

Numerous models predict the activity coefficient of individual ions in solution. The one by Debye and Hiickel [8] considers only electrostatic (columbic) interactions between cations and anions in a dilute solution of a single, completely dissociated salt. It is assumed that ion-ion interactions (as opposed to other phenomena such as ion-solvent interactions, ion solvation effects, and variations in the solvent dielectric constant with salt concentration) cause the ion activity coefficients to deviate from 1.0. From a practical point, only the Debye-Hiickel activity coefficient relationship is needed, along with some knowledge of the theory s shortcomings, which restrict its application. For a dilute electrolytic solution containing a binary salt (i.e., a salt with one type each of cation and anion species), the ion activity coefficient from Debye-Hiickel theory is given by... 

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