Debye-Hiickel solvent parameters

The GB model is a modification of the Coulomb equation to include the Born radius of the particle or atom which estimates the degree of the particle s burial within the molecule. Equation 5 relates AGdec to the solvent/solute dielectric (e), the separation between the partial atomic charges r, the effective Born radii R(i and /), and the smoothing function fGR. A Debye-Hiickel screening parameter (k) similar to that used in the PB equation is used to account for the monovalent ions. 

Equation (7.44) is known as the third approximation of the Debye-Hiickel theory. Numerous attempts have been made to interpret it theoretically, hi these attempts, either individual simplifying assumptions that had been made in deriving the equations are dropped or additional factors are included. The inclusion of ionic solvation proved to be the most important point. In concentrated solutions, solvation leads to binding of a significant fraction of the solvent molecules. Hence, certain parameters may change when solvation is taken into account since solvation diminishes the number of free solvent molecules (not bonded to the ions). The influence of these and some other factors was analyzed in 1948 by Robert A. Robinson and Robert H. Stokes. 

Plotting ixbase VS. pH gives a sigmoidal curve, whose inflection point reflects the apparent base-pAi, which may be corrected for ionic strength, I, using Equation 6.11 in order to obtain the thermodynamic pATa value in the respective solvent composition. Parameters A and B are Debye-Hiickel parameters, which are functions of temperature (T) and dielectric constant (e) of the solvent medium. For the buffers used, z = 1 for all ions ao expresses the distance of closest approach of the ions, that is, the sum of their effective radii in solution (solvated radii). Examples of the plots are shown in Figure 6.12. 

The densities p° of the mixed solvents required to calculate the parameters A and B of the Debye-Hiickel equation were measured with a pycnometer of about 25-cm3 capacity. Duplicate determinations were always made, and the values agreed to within 0.005%. 

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). 

Debye-Hiickel parameter, estimated here as k = y/ c/3 A. 1 (assuming the dielectric constant of the solvent medium inside the double layer is 80). valence of charges (= 1) electronic charge... 

The electrostatic methods just discussed suitable for nonelectrolytic solvent. However, both the GB and Poisson approaches may be extended to salt solutions, the former by introducing a Debye-Huckel parameter and the latter by generalizing the Poisson equation to the Poisson-Boltzmann equation. The Debye-Huckel modification of the GB model is valid to much higher salt concentrations than the original Debye-Hiickel theory because the model includes the finite size of the solute molecules. 

Again, the coefficients are the same as defined earlier, with AH, Aj, and Av as the Debye-Hiickel parameters, and T as the temperature and Mw as the molecular weight of the solvent (water) in kg-mol. Values for the thermal coefficients for a number of electrolytes are given in Tables A7.8 to A7.10. 

The numbers 0.51 and 0.33 are constants for water at 25°C, and the former includes the —I power of both the dielectric constant of the solvent and the absolute temperature ct/ is the ion size parameter, which is the ejffective diameter of the hydrated ion in angstrom units, A. An angstrom is 100 picometers (pm, 10 ° meter). A limitation of the Debye-Hiickel equation is the accuracy to which a, can be evaluated. For many singly charged ions, a, is generally about 3 A, and for practical purposes Equation 6.19 simplifies to... 

The repulsive energy between two particles of size a in a medium is a function of the dielectric constant of the liquid medium. This means a smaller Vr for media of organic solvents with smaller e than that of water. The dielectric constants of some common liquids are listed in Table 1. The Debye-Hiickel parameter K in Eq. (1) also depends on e by... 

Figure 12. Salt effect on the relative R 0H/R 0 quantum yield in two different solvents Water (left panel) and a 50/50% (by volume) mixture of met Hanoi/water [11c]. Circles are experimental data obtained from the relative height ratio of the two peaks in the steady-state fluorescence spectrum e.g., Figure 10. Dashed and full curves correspond to the Debye-Hiickel expression (with finite ion-size correction) [21] and the Naive Approximation [17, 11c], respectively. Both models employ the zero-salt kinetic parameters.

Nonelectrolyte G mcxlels only account for the short-range interaction among non-charged molecules (—One widely used G model is the Non-Random-Two-Liquid (NRTL) theory developed in 1968. To extend this to electrolyte solutions, it was combined with either the DH or the MSA theory to explicitly account for the Coulomb forces among the ions. Examples for electrolyte models are the electrolyte NRTL (eNRTL) [4] or the Pitzer model [5] which both include the Debye-Hiickel theory. Nasirzadeh et al. [6] used a MSA-NRTL model [7] (combination of NRTL with MSA) as well as an extended Pitzer model of Archer [8] which are excellent models for the description of activity coefficients in electrolyte solutions. Examples for electrolyte G models which were applied to solutions with more than one solvent or more than one solute are a modified Pitzer approach by Ye et al. [9] or the MSA-NRTL by Papaiconomou et al. [7]. However, both groups applied ternary mixture parameters to correlate activity coefficients. Salimi et al. [10] defined concentration-dependent and salt-dependent ion parameters which allows for correlations only but not for predictions or extrapolations. 

The Pitzer model includes a modified Debye-Hiickel-like contribution and a virial term to take short range interactions into account. Only two parameters having physical meaning must be adjusted. Accurate results have been obtained for the properties of electrolyte solutions attaining molalities up to 6 moles/kg of solvent. Activity coefficients have been calculated from this model for solutions containing different salts. They have been correctly predicted for solutions of NaCl, KCl and CaCl2 (from [DEM 91]). 

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