Gibbs Energies of Transfer

This equation is derived by considering die transfer of material from a flat surface to a droplet. For the U ansfer of a small mass Sm from the flat surface of vapour pressure p° to the droplet of vapour pressure p, the Gibbs energy of transfer is... 

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... 

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] ... 

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

The voltammetric information given here suggests that the transfer of an objective cation from Wl to LM can be achieved under a smaller membrane potential when an anion for which the Gibbs transfer energy at the LM/W2 interface is smaller is added into W2. In the case of the above-mentioned membrane system, the transfer of K+ from Wl to LM in the presence of 0.01 M MgBr2 in W2 is expected to be attained even at the membrane potential 0.19 V (which corresponds to the Gibbs energy of transfer of 18.3... 

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... 

By varying the scan rate, this equation allows then the evaluation of the diffusion coefficient of the transferring ion. With the determination of the formal transfer potential of an ion and thus of its Gibbs energy of transfer by application of Eq. (10), this is the most important application of cyclic voltammetry. 

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 ... 

There are other ways of estimating inner potential differences. Gi rault and Schiffrin [4] assume that the difference in the inner potential is negligible at the pzc, because the interface consists of an extended layer where both solvents mix, so that any dipole potentials will be small. The resulting scale of Gibbs energies of transfer agrees reasonably well with the TPAs+/TPB scale, if the small difference in the radii of these ions is accounted for. 

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).

As ion-exchanger anion A is strongly hydrophobic and determinand J is hydrophilic, it must hold for the individual Gibbs energies of transfer for the t vo ions that... 

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. 

When solubility products in nonaqueous solvents are desired, tables [5-7] of the Gibbs energies of transfer of the ions from water to the desired solvent, org, must be consulted. For any ion... 

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. 

The electrode kinetics of the Zn(II)/ Zn(Hg) system was investigated in PC + DMSO mixtures [73] containing 0.1 M TEAP. It was found that the log A s,corr varies linearly with the Gibbs energy of transfer of the Zn(II) ion. 

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