Thermodynamics of solvation

The central quantity in this chapter is the free energy of solvation, AGj. This quantity, with our choices (one molar ideal solution and one molar ideal gas) for standard states, is the free energy of transfer of a molecule X from an ideal gas at 1 mol/L concentration to an ideal solution at the same solute concentration [X] and temperature T. In practice, this is determined by  

We may derive the corresponding equation involving the logarithm of Henry s constant as 

Some workers, while retaining the one-molar ideal solution standard state for the solution phase, use a one-atmosphere standard state in the gas 

It is particularly unfortunate that many calculated free energies of solvation are published without explicit reference to the chosen standard state. By noting the particular value cited for an experimental free energy of solvation, it is sometimes possible to infer the choice of standard state (if one assumes the workers took care to be consistent), but this is dangerous. We have made every effort to convert all results presented in this chapter to the standard state used in Equation [2] that is, one molar in both gaseous and solution phases. But some caution should be applied in accepting results where such conversion is necessary. 

To relate these thermodynamic quantities to molecular properties and interactions, we need to consider the statistical thermodynamics of ideal gases and ideal solutions. A detailed discussion is beyond the scope of this review. We note for completeness, however, that a full treatment of the free energy of solvation should include the changes in the rotational and vibrational partition functions for the solute as it passes from the gas phase into solution, AGjnt.  

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DR. P. P. SCHMIDT, (Oakland University) I m working on lithium. That s a pretty simple system, especially without its single 2s electron. And yet it s still complicated. There are several problems. One is how to model the effect of the solvent and whether, in fact, you want to throw away the modeling that has been used, namely the continuum approximation. I think the answer to that is no, you don t want to throw it away completely. But one of the notions which has been developing, and is now being tested in the thermodynamics of solvation and other problems, is what is called the semi-continuum model. In... 

Jacquemin, J. et al.. Low-pressure solubilities and thermodynamics of solvation of eight gases in l-butyl-3-methylimidazolium hexafluorophosphate. Fluid Phase Equilib., 240, 87, 2006. 

Krestov, G.A. Thermodynamics of Solvation. Solutions and Dissolution Ions and Solvents Structure and Energetics, Ellis Horwood, Chichester, 1991. 

The metal/ligand ratios in the complexes listed in Table 2 are obviously related to the proportions of vertices, edges and faces of the various metal polyhedra. The charges of the metals and ligands need not balance in these compounds. There is, however, another set of complexes (MX)f or (RMXR )p with no net charge, where the thermodynamics of solvation rather than symmetry might appear to be the primary determinant of composition and structure. In these cages the structure must adapt to the fixed M/X ratio. 

I. A. Topol, G. J. Tawa, S. K. Burt and A. A. Rashin, On the structure and thermodynamics of solvated monoatomic ions using a hybrid solvation model, J. Chem. Phys. Ill (1999) 10998-11014. 

Fig. 2.67. Dependence of for KCI in aqueous solutions of (a) methanol, (b) ethanol, (c) 1-propanol, and (d) 2-propanol on composition at different temperatures. (Reprinted from G. A. Krestov, Thermodynamics of Solvation, Ellis Harwood, London, 1991.)...

G. A. Krestov, Thermodynamics of Solvation, EUis Harwood, New York (1991). 

In summary, the empirical approach to ionic solvation based on the MSA is quite successful for monoatomic ions of the main group elements. It helps one to understand the important differences between the way cations and anions are solvated in water. It can also be applied to other ions, including polyatomic ions, provided the solvation is essentially electrostatic in character. Thus, one may estimate effective radii for anions such as nitrate and perchlorate from the Gibbs solvation energy using the value of 8s calculated for the halide ions. Considering the simplicity of the model, it provides an useful means of understanding the thermodynamics of solvation. 

In the previous section, we derived a general and formal relationship between thermodynamics of solvation and structural changes induced in the water. Now, we present an approximate relationship between the structure of water,... 

The type of construction given in Fig. 10a, which utilizes the Hess s law of constant heat summation, can serve as a means of quantitatively analyzing the thermodynamics of solvation. Further, this view of the solvation process provides a method for considering different standard states. For nonionic species a commonly used standard state is infinite dilution. Although activities become infinite for ions in this limit, it is still a useful reference state because the analytic Debye-Hiickel limiting law is valid in this regime.168... 

Krestow G A (1991) Thermodynamics of solvation, Ellis Horwood Ser Phys Chem, Univ Warwick. 

The site-site RISM/HNC theory has been coupled with the ab initio molecular orbital (MO) theory in a self-consistent field (SCF) calculation of the electronic and solvation structure of a solute molecule immersed in molecular solvent, referred to as the RISM-SCF method [59, 60, 61]. Since the site-site treatment of the solute-solvent correlations involves the approximation of radial averaging, it constitutes a bottleneck of the RISM-SCF method. Although this approach yields reasonable results for the thermodynamics of solvation for many solute species and solvents [62], it lacks a 3D picture of the solvation structure for complex solutes and oversimplifies the contribution to the solvation properties from highly directed electron orbitals of the solute molecule. 

Table J. 2. Thermodynamics of solvation of the Cl and Na+ ions in ambient water.

Marcus Y (1987) The thermodynamics of solvation of ions, part 2. The enthalpy of hydration at 298.15 K. J Chem Soc Faraday Trans 83 339-349 Marcus Y (1988) Ionic radii in aqueous solutions. Chem Rev 88 1475-1498 Marcus Y (1988a) Preferential solvation of ions, part 2. The solvent composition near the ion. J Chem Soc Faraday Trans 1(84) 1465-1475... 

We shall discuss at length solvation quantities in Chapter 3. Here, we present some values of the thermodynamics of solvation of water in pure water. It should be noted that in the traditional approach to solvation, only solvation of one component in very dilute solution in a solvent can be defined and measured. In the definition used here, the concept of solvation can be applied to any molecule in any liquid at any concentration. We define the solvation process as the transfer of a molecule from a fixed position in an ideal gas phase to a fixed position... 

In this book, I shall use the concepts of solvation and the corresponding thermodynamics of solvation as defined below. 

It should be noted that the SPT is not a pure molecular theory in the following sense. A molecular theory is supposed to provide, say, the Gibbs free energy as a function of T, P, N as well as of the molecular parameters of the system. Once this function is available, the density of the system can be computed from the relation p = (9/x/9 )t (with pi = G/N). The SPT utilizes the effective diameter of the solvent molecules as the only molecular parameter (which is the case for a hard-sphere fluid) and, in addition to the specification of T and P, the solvent density Pw is also used as input in the theory. The latter being a measurable quantity carries with it implicitly any other molecular properties of the system. The first application of the SPT to calculate the thermodynamics of solvation in liquids was carried out by Pierotti (1963, 1965). 

To summarize this section and the whole chapter, we can pause to reflect on the merits of the various models suggested for water in 1-D, 2-D, and 3-D. In my opinion, the molecular reasons underlying the anomalous thermodynamics of solvation of inert solutes in water are now well understood. This situation has been arrived at mainly by studying simple molecular models of water. Further refinements of the models will certainly add more detail but no new insights into the molecular origins of the outstanding properties of aqueous solutions of inert solutes. 

G. A. Krestov, Thermodynamics of Solvation Solution and Dissolution, Ions and Solvents, Structure and Energetics, Ellis Norwood Ser. Phys. Chem., Ellis Horwood, New York, 1991, p. 106. 

Although the kinetics and thermodynamics of solvation at the macroscopic level are reasonably well characterized, a more microscopic understanding at the quantum state level of detail has remained elusive. At the most basic level, potential energy surfaces capable of reproducing solute-solvent and solvent-solvent interactions to spectroscopic accuracy are extremely difficult to obtain. Second, even with such pair potentials, there is an incomplete knowledge about the importance and magnitude of nonpairwise additive... 

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