Free energies of transfer

A quantitative treatment of surfactant solubility has been successfully made empirically using linear free energy relationships. An important relation is that for the linear free energy of transfer of alkanes to water [23] ... 

If two neutral reactant molecules yield a polar product, then presumably the transition state will be intermediate in polarity, and we anticipate an increase in rate as the solvent polarity is increased. A quantitative formulation of this case is based on Kirkwood s expression for the free energy of transfer of a dipole of... 

The quantitative theory of ionic reactions, within the limitations of a continuum model of the solvent, is based on the Bom equation for the electrostatic free energy of transfer of an ion from a medium of e = 1 to the solvent of dielectric constant... 

The first case to be taken up is that for polar molecules. Kirkwood8 has developed an expression for the free energy of transfer of a polar molecule from a medium of unit dielectric constant to one with a value e. If the dipole moment of the molecule is denoted as jx and its radius as r, AGtr is... 

The same approach can be extended to reactions between two ions. The expression for the free energy of transfer of ions of charge Z and zb from infinite separation to the reaction distance is... 

For two relatively immiscible solvents log P can be considered [1] proportional to the molar Gibbs free energy of transfer between octanol and water ... 

Huber et al. [12] investigated the same model by Monte Carlo simulations however, they focused on a different aspect the dependence of the interfacial capacity on the nature of the ions, which in this model is characterized by the interaction constant u. Samec et al. [13] have observed the following experimental trend the wider the potential window in which no reactions take place, the lower the interfacial capacity. Since the width of the window is determined by the free energy of transfer of the ions, which is 2mu in this model, the capacity should be lower, the higher u. ... 

Huber et al. [12] (see Table 2). Another way of explaining this effect is the following when the interface is charged the ions experience a stronger field that pulls them toward the other side. Thus they penetrate further into the other solution, and pull a few of their surrounding molecules with them. As expected, this effect is more marked when the free energy of transfer of the ions is small, because then the energy barrier at the interface is lower. 

As noted above, the capacity of liquid-liquid interfaces depends on the nature of the ions dissolved in the two adjoining phases. In some cases the capacity is related o the free energy of transfer of the ions involved, but in other cases quite strong dependencies are observed which can be explained by a tendency to form ion pairs at the interface. Evidence for this effect, which was first discussed by Hajkova et al. [14], was obtained in a paper by Cheng et al. [15], who observed marked changes in the capacity when they varied the composition of the aqueous phase. Further examples were provided by Pereira et al. [16], who also performed explicit calculations for ion pairing based on the lattice-gas model. 

In the two bulk phases the potential of mean force is constant, but it may vary near the interface. The difference in the bulk values of the chemical part is the free energy of transfer of the ion, which in our model is —2mu (we assume u < 0). Let us consider the situation in which the ion-transfer reaction is in equilibrium, and the concentration of the transferring ion is the same in both phases the system is then at the standard equilibrium potential 0oo- In Ihis case the potential of mean force is the same in the bulk of both phases the chemical and the electrostatic parts must balance ... 

Parker, A. J., Solvation of ions—enthalpies, entropies and free energies of transfer, Electrochim. Acta, 21, 671 (1976). 

Vesala, A. (1974) Thermodynamics of transfer nonelectrolytes from light and heavy water. I. Linear free energy correlations of free energy of transfer with solubility and heat of melting of nonelectrolyte. Acta Chem. Scand. 28A(8), 839-845. 

While the PM3-SM4 model does appear to slightly underestimate the polarity of the enol component, there is some cancellation of errors upon considering the differential transfer free energies between cyclohexane and water. As noted above, experiment indicates that the differential free energy of transfer of the dione and the enol is 3.1 kcal/mol the PM3-SM4 model predicts this value to be 2.8 kcal/mol, in excellent quantitative agreement. AM1-SM4 is less satisfactory in this regard, predicting only 1.9 kcal/mol. 

The partition coefficient KmK is directly related to the free energy of transfer between the aqueous and the membrane phase. The enthalpy and entropy contri-... 

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. 

As indicated in the previous section, the derivation of Gibbs free energies of transfer, and thence of entropies of transfer, from trichloride... 

FIGURE 3.6. Plot of the interaction energies in the ion-radical pair against the standard free energies of transfer of Cl from water to the solvent. From left to right FA, EtOH, DMF, DCE. Energies in eV on the horizontal axis and in meV on the vertical axis. Adapted from Figure 5 of reference 13h, with permission from the American Chemical Society. 

The important parameters for substituting a solvent S for water (W) follow from the thermodynamic cycle (6). Ks and Ky, are related through the free energy of transfer terms (7). The enthalpy of transfer is given by (8). 

Free energies of transfer" of K+ complexes of dibenzo-18-crown-6 [11] and [2.2.2]-cryptand 137] from water to non-aqueous solvents at 25°C... 

Table 5.3 Solute and solvent solubility isotope effects for (benzene-water) solutions at 306.2 K obtained from IE s on Henry s Law coefficients, Ki and Kn- [Isotope effects on free energies of transfer, ideal gas to solution in the limit of infinite dilution] (Dutta-Choudhury, M., Miljevic, N.

At temperatures well below UCST, solubilities of hydrocarbons in water or water in hydrocarbons drop to very low values. The solutions are very nearly ideal in the Henry s law sense, and the isotope effects on solubility can be directly interpreted as the isotope effect on the standard state partial molar free energy of transfer from the Raoult s law standard state to the Henry s law standard state. Good examples include the aqueous solutions of benzene, cyclohexane, toluene,... 

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