Gibbs hydration energy

Table 5.1 Crystal radii, Stokes radii and Gibbs hydration energies of various ions...

In principle, Gibbs free energies of transfer for trihalides can be obtained from solubilities in water and in nonaqueous or mixed aqueous solutions. However, there are two major obstacles here. The first is the prevalence of hydrates and solvates. This may complicate the calculation of AGtr(LnX3) values, for application of the standard formula connecting AGt, with solubilities requires that the composition of the solid phase be the same in equilibrium with the two solvent media in question. The other major hurdle is that solubilities of the trichlorides, tribromides, and triiodides in water are so high that knowledge of activity coefficients, which indeed are known to be far from unity 4b), is essential (201). These can, indeed, be measured, but such measurements require much time, care, and patience. 

The enthalpies of solution and solubilities reviewed here provide much of the experimental information required in the derivation of single-ion hydration and solvation enthalpies, Gibbs free energies, and entropies for scandium, yttrium, and lanthanide 3+ cations. 

It must be noted here that, because there are 16 melt components in the model, there should be 120 binary interaction parameters. Only 55 of these are hsted in table 6.15, because the remaining ones are considered virtually equal to zero. Lastly, it must be noted that the Gibbs free energy of hydrated magmas cannot be obtained simply by apphcation of equations 6.78 to 6.85, but requires additional considerations that cannot be outlined in this context (see Ghiorso and Carmichael, 1980, and Ghiorso et al., 1983, for detailed treatment of the method). 

Tremaine, P.R. and Goldman, S., "Calculations of Gibbs Free Energies of Aqueous Electrolytes to 350°C from an Electrostatic Model for Ion Hydration", Jr. Phys. Chem., in press. Helgeson, H.C., "Evaluation of Irreversible Reactions in Geochemical Processes Involving Minerals and Aqueous Solutions - I Thermodynamic Relations", Geochimica et Cosmochimica Acta, (1968), 3, 853. 

Englezos et al. (1987a) andEnglezos and Bishnoi (1988) determined an expression for the radius of the hydrate critical nucleus using the Gibbs free energy per unit volume of hydrate formed (Agv) in a modification of Equations 3.2a and b as... 

The above path only considers gas and water that react to hydrate. If the molar Gibbs free energy of (1) separation, (3) reaction at equilibrium, and (5)... 

Section 5.1 presents the fundamental method as the heart of the chapter— the statistical thermodynamics approach to hydrate phase equilibria. The basic statistical thermodynamic equations are developed, and relationships to measurable, macroscopic hydrate properties are given. The parameters for the method are determined from both macroscopic (e.g., temperature and pressure) and microscopic (spectroscopic, diffraction) measurements. A Gibbs free energy calculation algorithm is given for multicomponent, multiphase systems for comparison with the methods described in Chapter 4. Finally, Section 5.1 concludes with ab initio modifications to the method, along with an assessment of method accuracy. 

These differences stimulated our interest and prompted us to study the effects of solvation on (R,R )-tartaric acid amides. Encouraged by the widespread usage ofAMSOL [42] (vide infra) we decided to use it to calculate Gibbs free energies of hydratation. We performed the calculations with the use of the solvation model SM5.4 [43-46] and hamiltonian PM3 [47] for all structures, optimized at the RHF/6-31G level [20],... 

In water solution, as shown by AMSOL calculations, the conformational preferences of the studied amides show up. Gibbs free energies ofhydratation calculated with the SM5.4 model and PM3 hamiltonian for structures optimized at the RHF/6-3 1G level indicated that those most favored by hydratation are the T- and G-conformers for the diamide and A, A,A ,A -tetramethyldiamide of (R, R (-tartaric acid, respectively. 

TABLE 21.6 Enthalpies, entropies, and Gibbs free energy of hydration for sulfuric acid dimer calculated at T = 298.15 K and P = 101.3 kPa. Abbrevi- ... 

Gibbs free energies of formation of the CaCO and Ca(OH)2, respectively, in Eqs. 9 and 10. From Eqs. 11 and 12, it appears that one should be able to deduce the conditions for caborization or hydration however, a further reaction must be considered, namely... 

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