Born solvation energy

The Born solvation equation is based on the difference in the energy needed to charge a sphere of radius r,- in a solvent of dielectric constant e, and in vacuum having a dielectric constant of unity. Thae are basic flaws in the concept of the Born solvation equation (5) on which the continuum theory of ET reactions is based. First, Bom Eq. (5) does not take into account the interaction of ions with a water solvent that has a dielectric constant of approximately 80 at room temperature. Hence, the Born solvation energy will have negligible contribution from solvents with high dielectric constants. Consequently, for solvents of high dielectric constant, Eq. (5) can be written as... 

What is the Born solvation energy of Fe3+ in water having a dielectric constant of 78, and what is its value when it is in ethanol, which has dielectric constant of 36 (b) What is the self-energy of Fe3+ in a vacuum (c) Is there any meaningful difference between the Born solvation energy and the self-energy of an Fe3+ ion The radius of this ion is 0.64 A and the diameter of water is 2.76 A. (c) Where do you think there is a possible flaw in Born s solvation equation (Khan)... 

Tetraphenylborate — A large, weakly solvated anion of tetrahedral shape used in electrochemical measurements as the anion of the -> supporting electrolyte in nonaqueous solutions. Due to its weak -> solvation (see -> hydration and -> Born solvation energy) it is especially... 

The Gibbs electrostatic energy at the boundary depends symmetrically on the two dielectric permittivities, but is not equal to the average of the two Born solvation energies. 

In the above calculations for the charging energy of an ion, we have actually integrated the energy of the electric field over the entire volume of the dielectric with the exception of the ion itself, which is the source of this field. Such an approach, which is quite natural for calculating the Born solvation energy for an isolated ion, has to be refined when we are dealing with a reaction between two ions, especially if the second ion is close to the first one (this actually is the most typical situation). Indeed, the field... 

Much attention has been directed since olden times towards ion solvation, which is a key concept for understanding various chemical processes with electrolyte solutions. In 1920, a theoretical equation of ion solvation energy (AG ) was first proposed by Born [1], who considered the ion as a hard sphere of a given radius (r) immersed in a continuous medium of constant permittivity (e), and then defined AG as the electrostatic energy for charging the ion up to ze (z, the charge number of the ion e, the elementary charge) ... 

The structure of the ions, where the bulky phenyl groups surround the central ion in a tetrahedron, lends validity to the assumption that the interaction of the shell of the ions with the environment is van der Waals in nature and identical for both ions, while the interaction of the ionic charge with the environment can be described by the Born approximation (see Section 1.2), leading to identical solvation energies for the anion and cation. 

These points indicate that the continuum theory expression of the free energy of activation, which is based on the Born solvation equation, has no relevance to the process of activation of ions in solution. The activation of ions in solution should involve the interaction energy with the solvent molecules, which depends on the structure of the ions, the solvent, and their orientation, and not on the Born charging energy in solvents of high dielectric constant (e.g., water). Consequently, the continuum theory of activation, which depends on the Born equation,fails to correlate (see Fig. 1) with experimental results. Inverse correlations were also found between the experimental values of the rate constant for an ET reaction in solvents having different dielectric constants with those computed from the continuum theory expression. Continuum theory also fails to explain the well-known Tafel linearity of current density at a metal electrode. ... 

The simplest approach to describing the interactions of metal cations dissolved in water with solvent molecules is the Born electrostatic model, which expresses solvation energy as a function of the dielectric constant of the solvent and, through transformation constants, of the ratio between the squared charge of the metal cation and its effective radius. This ratio, which is called the polarizing power of the cation (cf Millero, 1977), defines the strength of the electrostatic interaction in a solvation-hydrolysis process of the type... 

Effective Electrostatic Radius, Born Coefficient, and Solvation Energy... 

The solvation energy described by the Born equation is essentially electrostatic in nature. Born equations 8.116 and 8.120 are in fact similar to the Born-Lande equation (1.67) used to define the electrostatic potential in a crystal (see section 1.12.1). In hght of this analogy, the effective electrostatic radius of an ion in solution r j assumes the same significance as the equilibrium distance in the Born-Lande equation. We may thus expect a close analogy between the crystal radius of an ion and the effective electrostatic radius of the same ion in solution. 

In the Coulomb term, the electrostatic and solvation effects depending on the polarity of the media are summarized. For solvent-separated ion pairs (solvation energy calculated by the Born equation), it is given by... 

Systems of ionic radii have also been used to discuss the solvation-energies of ionic crystals. Fifty years ago Born 42) deduced for the free energy AG of transfer of an ion of valency Z from vacuum to a medium of dielectric constant C ... 

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