Standard Gibbs energy of hydration

This equation is often called the Nernst equation for the ITIES, and the term A is in fact the standard Gibbs energy of transfer AG°t ° expressed on a potential scale, since, by definition, AG is equal to the difference between the standard Gibbs energy of solvation fif0 and the standard Gibbs energy of hydration q. 1 ... 

In this section, we are mainly concerned with redox processes in aqueous solution see Section 16.1 for a list of relevant topics already covered in the book. Values of E° for halfreactions 16.78 can be measured directly for X = Cl, Br and I (Table 16.1) and their magnitudes are determined by the X—X bond energies (Figure 16.3), the electron affinities of the halogen atoms (Table 16.1) and the standard Gibbs energies of hydration of the halide ions (Table 16.1). This can be seen from scheme 16.79 for X = Br and I, an additional vaporization stage is needed for the element. 

Standard Gibbs energy of hydration of M +, Ahyd<7°(298K)/kJmoP -2410 -1836 -1517 -1390 -1256 -... 

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 thermodynamically stable form of bulk platinum in oxygen saturated water at ambient conditions is the completely hydrated platinum(IV)oxide, Pt02 4H20, also referred to as platinic acid H2Pt(OH) 14yl5) with a standard Gibbs energy of formation of -84 kJ mol" The formation of this compound will be even more favoured in the case of incompletely coordinated platinum. 

Table 2.3 contains the standard Gibbs energies of formation and the standard enthalpies of formation of a selection of main group cations at 25 °C. They refer to the formation of 1 mol dm- solutions of the cations from their elements and are relative to the values for the hydrated proton taken as zero. 

Table 2-8. Standard molar Gibbs energies of hydration, AG+, , of some representative single ions at 25 °C [241, 242] ).

Considering the first equality, Is measurable. It Is the Isothermal reversible work required to extract ions from phase a for electrons In a metal It represents the electronic work function. For metals, a, can also be obtained from thermo-emission or the photo-electric effect. Sometimes a is called the real (Gibbs) energy of hydration of ion i. The logic behind this last definition stems from the second equality In [3.9.61. The standard molar Gibbs energy of solvation of an Ion [1.5.3.11 equals when Is referred to the gas... 

Subsequently, there has been no lack of Improved methods to narrow down the uncertainty margin. These approaches invoke information on standard potentials, on improved models to establish individual ionic activities (to determine x " only for one ion is such a datum required) or individual (Gibbs) energies of hydration. For instance, Alfenaar and de Ligny" experimented with... 

Average number of water molecules in the electrostricted hydration shell, estimated from standard molar Gibbs energies of hydration [121]. 

The thermodynamic parameters of hydration for many ions have been determined [121,125,126]. Table 3 gives the values of the standard molar Gibbs energy of hydration AGh and standard molar enthalpy of hydration AH , at 25°C for the alkali metal cations. The tabulated values are based on the respective choices A= - 1056 kj/mol and AHh(H ) = -1103 kj/mol, which result from the extrathermodynamic assumption that the thermodynamic parameters of the tetraphenylarsonium cation and tetraphen-ylborate anion are equal [127]. This reasonable and useful assumption, often... 

Cs (g) q Na (S)[Eq. (10)]. Values of4G s(Na) and 4 (7s(Cs) were obtained from the relation AG° = AGl AGh [Eq. (13)], where the standard molar Gibbs energies of hydration AGh were taken from Table 3 and the standard molar Gibbs energies of transfer AG°r were taken from columns 4 and 7. 

As in the special case of hydration, solvation of metal ions has been related successfully to electrostatic interactions. From the SL model of Eqs. (5)-(8), but on the mole fraction scale and neglecting AGh.unsym, good agreement between calculated and experimental solvation standard Gibbs energies of solvation has been obtained [131]. Thus, the solvation effects can be related in a straightforward manner to cation size and to solvent dielectric constant. This result raises the possibility that the selectivity of ion-transfer processes between water and various solvents can be predicted, and the remainder of Sec. 111.A will be devoted to this objective. 

Plyasunov AV, Shock EL. (2000). Standard state Gibbs energies of hydration of hydrocarbons at elevated temperatures as evaluated from experimental phase equilibria studies. Geochimica et Cosmochimica Acta 64(16) 2811-2833. 

The standard molar Gibbs energy of hydration of an ion, AhydrGi° , can now be obtained from a combination of the standard molar enthalpy and entropy of hydration ... 

The standard molar Gibbs energy of hydration of the hydrogen ion noted above, AhydrG° (H+, aq)= -l,064 7kJmol is compatible with the estimates -1,056 6 kJ mor (Marcus 1991) and -1,066 17 kJ mol (Conway 1978) but not with -1,113 8 kJ mol obtained from the cluster pair approximation used by Kelly et al. (2006). The assumptions involved in obtaining the latter value lead to a surface potential of water of Ax = 0.34 0.08 V (Marcus 2008), which, in turn, is not consistent with the recent estimate of Ax = 0.1 V (Parfenyuk 2002) deemed to be the most nearly correct one. 

So called real standard molar Gibbs energies of hydration are obtained from the electromotive force of specially constructed cells. These consist of a jet of aqueous solution flowing downward in the middle of a tube, along the inner surface of which another solution, concentric with the jet, flows with a narrow vapor gap between them. The measurable real standard molar Gibbs energy of hydration is ... 

The standard reduction potentials for the M /M couples (Table 13.1) show that Al (aq) is much less readily reduced in aqueous solution than are the later ions. This can be attributed, in part, to the more negative Gibbs energy of hydration of the smaller Al ion. However, an important contributing factor (scheme 13.71) in differentiating between the values of for the Al /Al and Ga /Ga couples is the significant increase in the sum of the first three ionization energies (Table 13.1). 

Estimation of reasonably correct A,G" values [8] results from the sum of the electrostatic terms, Equations 4.13 and 4.14, and the cavity formation term, Equation 4.10. Such values are shown in Table 4.1. It should be noted that the ionic standard molar Gibbs energies of hydration need to be compatible with the corresponding enthalpies and entropies of hydration (see the following text) according to A G, = A /f,°°-TA Sj . The latter quantities are more directly available from experimental data, so that values adopted from Ref 8 are presented in Table 4.1... 

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