Gibbs energy Born model

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

Models incorporating linear composition dependencies to O (the subregular solution model), as well as others allowing for complex composition dependencies, have been developed. The most commonly used model is by Austrian-born American immigrant Otto R. Redlich (1896-1978) and Albert Theodore Kister (d. 2002) of the Shell Development Company in 1948, which is now known as the Redlich-Kister polynomial (Redlich and Kister, 1948). The total Gibbs energy of a binary system, using the Redlich-Kister model is ... 

The Born model [11] provides a means of estimating the Gibbs energy of solvation for an ion in an infinitely dilute solution. It is based on a continuum description of the solvent as a uniform dielectric with a relative permittivity of The work of transferring the ion from vacuum to the dielectric medium is estimated on the basis of the following three-step process (a) the ion is reversibly discharged in vacuum (b) the discharged ion, which is assumed to be a sphere of radius, r, is... 

Table 3.4 Experimental Value and Estimates According to the Born Model and Mean Spherical Approximation for the Gibbs Energy and Entropy of Solvation of the Alkali Metal Cations and Halide Anions at 25°C...

Acetonitrile is a polar solvent with a relative permittivity of 35.9. It may be represented as a hard sphere with a diameter of 427 pm. Estimate the Gibbs energy of solvation of Na in acetonitrile according to the Born and MSA models. Compare the theoretical estimates with the experimental estimate given that the Gibbs energy of transfer for Na" " from water to acetonitrile is 15.1 kJmoP ... 

The Gibbs energy of solvation according to the Born model is given by equation (3.4.6). The constant AlCo /Stiso is equal to 6.945 x lO Jmmol" The radius of Na" " according to Shannon and Prewitt is 116 pm (table 3.1). The factor (1 — l/Sj) is equal to 0.972. The resulting value of AjGi is -581.9 kJmor ... 

At a microscopic level, solutes in polar solvents undergo strong solvation. For example, the Born model predicts that the Gibbs free energy of an ion with charge q (in Coulombs) and radius r will be changed in the solvent compared with the gas phase by an amount... 

Despite the simplifying assumptions in the derivation, such as assuming that the medium, water, is a continuum with no structure, and that the only work is electrostatic, and even more assumptions in calculating the properties of individual ions from the measured properties of electrolytes, as estimated by the Born function comes reasonably close to the measured Gibbs energy of ion solvation, as shown in Figure 6.7. Other thermodynamic properties such as the volume, entropy and enthalpy of solvation can also be obtained by appropriate differentiation of Equation (6.5). As a result, ever since its inception the Born equation has been used as a primitive model for the electrostatic contribution to the properties of an ion in a dielectric solvent. 

It is a serious drawback that it is not possible to determine the transfer activity coefficient of the proton (or of any other single-ion species) directly by thermodynamic methods, because only the values for both the proton and its counterion are obtained. Therefore, approximation methods are used to separate the medium effect on the proton. One is based on the simple sphere-in-continuum model of Born, calculating the electrostatic contribution of the Gibb s free energy of transfer. This approach is clearly too weak, because it does not consider solvation effects. Different ex-trathermodynamic approximation methods, unfortunately, lead not only to different values of the medium effect but also to different signs in some cases. Some examples are given in the following log yH+ for methanol -1-1.7 (standard deviation 0.4) ethanol -1-2.5 (1.8), n-butanol -t-2.3 (2.0), dimethyl sulfoxide -3.6 (2.0), acetonitrile -1-4.3 (1.5), formic acid -1-7.9 (1.7), NH3 -16. From these data, it can be seen that methanol has about the same basicity as water the other alcohols are less basic, as is acetonitrile. Di-... 

A comparison of anion solvation by methanol, a protic solvent, and dimethylformamide, a dipolar aprotic solvent, is instructive. The electrostatic contribution, d/i , to the Gibbs free energy of solvation per mole of an ion is sometimes estimated quite successfully (Stokes, 1964) from the Bom model, in which a charged sphere of radius r is transferred from vacuum to a medium of uniform dielectric constant, c. The Bom equation (17) suggests that an anion should be similarly solvated in methanol and in DMF, because these solvents have effectively the same dielectric constant (33-36). The Born equation makes no allowance for chemical interactions, such as hydrogen-bonding and mutual... 

---