Transfer energy standard

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The standard Gibbs energy of electrolyte transfer is then obtained as the difference AG° x ° = AG° ° - AG° x. To estabfish the absolute scale of the standard Gibbs energies of ion transfer or ion transfer potentials, an extrathermodynamic hypothesis must be introduced. For example, for the salt tetraphenylarsonium tetraphenyl-borate (TPAs TPB ) it is assumed that the standard Gibbs energies of transfer of its ions are equal. 

TABLE 32.2 Standard Gibbs Energy of Transfer and Standard Ion Transfer Potentials for Ion Transfer Between Water and Nitrobenzene Derived from Partition Measurements... 

This dependence is fundamental for electrochemistry, but its key role for liquid-liquid interfaces was first recognized by Koryta [1-5,35]. The standard transfer energy of an ion from the aqueous phase to the nonaqueous phase, AGf J, denoted in abbreviated form by the symbol A"G is the difference of standard chemical potential of standard chemical potentials of the ions, i.e., of the standard Gibbs energies of solvation in both phases. 

Le Hung presented a general theoretical approach for calculating the Galvani potential Ajyj at the interface of two immiscible electrolyte solutions, e.g., aqueous (w) and organic solvent (s) [25]. Le Hung s approach allows the calculation of when the initial concentration (Cj), activity coefficients (j/,) and standard energies of transfer of ions (AjG ) are known in both solutions. 

For symmetrical electrolytes, of, e.g., type 1 1, such a liquid-liquid interface, in equilibrium, is described by the standard Galvani potential, usually called the distribution potential. This very important quantity can be expressed in the three equivalent forms, i.e., using the ionic standard potentials, or standard Gibbs energies of transfer, and employing the limiting ionic partition coefficients [3] ... 

There are large cations in these cells, e.g., tetra-alkylammonium cations in the organic phase and the interfacial ion exchange involves only so-called critical ions, here X and LX ions are practically not transferred through the organic phase. Both liquid interfaces are reversible with respect to the appropriate anion, X or L. EMF is, in practice, also influenced by the diffusion potential in the organic phase, and in the case of cells of the type in Scheme 11 - by the difference of standard transfer energies of both ions (Section III.A)... 

TABLE 4 Standard Gibbs Energies of Transfer of Ions from NB to W and Their Charge-Independent and Charge-Dependent Components at 25°C... 

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 ... 

This equation is often called the Nernst equation for the ITIES, and the term A is in fact the standard Gibbs energy of transfer expressed on a potential scale, since,... 

P is a unique quantity related by Eq. (12) to its standard Gibbs energy of transfer, the... 

It is important to notice that the standard Gibbs energy of transfer refers to the transfer from pure w to pure organic o. It is therefore different from the Gibbs energy of partition, which refers to the transfer between mutually saturated solvents. Nevertheless, in the case of solvents of low miscibility such as water-DCE or water-nitrobenzene, the transferred ion is practically not hydrated by water present in the organic phase, so that... 

The determination of the standard Gibbs energies of transfer and their importance for potential differences at the boundary between two immiscible electrolyte solutions are described in Sections 3.2.7 and 3.2.8. 

All quantities in Eq. (12.6) are measurable The concentrations can be determined by titration, and the combination of chemical potentials in the exponent is the standard Gibbs energy of transfer of the salt, which is measurable, just like the mean ionic activity coefficients, because they refer to an uncharged species. In contrast, the difference in the inner potential is not measurable, and neither are the individual ionic chemical potentials and activity coefficients that appear on the right-hand side of Eq. (12.3). 

Although the inner potential difference is not measurable in principle, it would be useful to have at least good estimates. We can see from Eq. (12.3) that this problem is equivalent to determining the difference in the chemical potential of individual ions. If we knew the standard Gibbs energies of transfer of the 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. 

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. 

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,... 

Figure 7.3 Standard Gibbs energies of transfer for reactants and activated complex for the Diels-Alder reaction of cyclopentadiene ( , ) with ethyl vinyl ketone (2, A) from 1-PrOH to 1-PrOH-water as a function of the mole fraction of water initial state (1 + 2, ) activated complex (o).

It is apparent that the deviation from Nemstian behaviour depends on the activity of the determinand and anion B in the studied solution. It decreases with increasing magnitude of the sum of the standard Gibbs energies of transfer of ions J and B " from water into the membrane phase. The effect of the interfering anion is suppressed by increasing the concentration of the ion-exchanger ion in the membrane. 

In contrast to ISEs with neutral ion carriers in the membrane, not even qualitative rules have been formulated for the solvent effect on the behaviour of ISEs with ion-exchanger ions in a liquid membrane. A basic condition for the ion-exchanger ions is that they be strongly hydrophobic. It must hold for the standard Gibbs energy of transfer of the ion-exchanger ion X and the deter-minand Y that... 

The differences in the solvation abilities of ions by various solvents are seen, in principle, when the corresponding values of As ivG° of the ions are compared. However, such differences are brought out better by a consideration of the standard molar Gibbs energies of transfer, AtG° of the ions from a reference solvent into the solvents in question (see further section 2.6.1). In view of the extensive information shown in Table 2.4, it is natural that water is selected as the reference solvent. The TATB reference electrolyte is again employed to split experimental values of AtG° of electrolytes into the values for individual ions. Tables of such values have been published [5-7], but are outside the scope of this text. The notion of the standard molar Gibbs energy of transfer is not limited to electrolytes or ions and can be applied to other kinds of solutes as well. This is further discussed in connection with solubilities in section 2.7. 

The standard molar Gibbs energy of transfer of CA is the sum v AG°(C) -i-v AtG°(A), where the charges of the cation C and anion A " and the designation of the direction of transfer, (aq org), have been omitted. The values for the cation and anion may be obtained from tables [5-7], which generally deal with solvents org that are miscible with water and not with those used in solvent extraction. However, AtG°(C) depends primarily on the (3 solvatochromic parameter of the solvent and AtG°(A) on its a parameter, and these can be estimated from family relationships also for the latter kind of solvents. 

A concentration scale for solutes in aqueous solutions, equal to moles of solute/55.51 mol water. It is frequently used in studies of solvent isotope effects. As pointed out by Schowen and Schowen the choice of standard states can change the sign for the free energy of transfer of a species from one solvent to another, even from HOH and DOD. The commonly used concentration scales are molarity, mole fraction, aquamolality, and molality. Free energies tend to be nearly the same on all but the molality scale, on which they are about 63 cal mol more positive at 298 K than on the first three scales. The interested reader should consult Table I of Schowen and Schowen ... 

Use the cmc values of a homologous series of single-chained sodium sulphate surfactants, given below, to estimate the standard free energy of transfer of a methylene (-CH2-) group from an aqueous to a hydrocarbon environment. 

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