Gibbs energy of solvation

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. 

The transfer of one mole of ions from a vacuum into the solution is connected with work Na(wi + vv2). This work is identical with the molar Gibbs energy of solvation A Gs i ... 

The Born equation for the Gibbs energy of solvation is thus... 

Since the absolute and the conventional electrode potentials differ only by an additive constant, the absolute potential depends on the concentration of the reactants through the familiar Nernst s equation. This dependence is implicitly contained in Eq. (2.6) the real Gibbs energies of solvation contain an entropic term, which depends on the concentration of the species in the solution. 

Note, however, that the terms in Eq. (9.4.2) do not correspond to the terms in the potential (9.4.1). Even when (9.4.1) is exact, the Gibbs energy of solvation of the functional groups is not additive. For more details, see Chapter 8 in Ben-Naim (1992). 

In Section 9.2 we have defined the Gibbs energy of solvation AGo in the T, P, N ensemble. In the T, V, N (canonical) ensemble the appropriate quantity is A4a, the Helmholtz energy of solvation. It can be shown that the two are equal for macroscopic systems, provided the volume V in the T, V, N ensemble is equal to the average volume of a system in the T, P, N ensemble. 

As an example, consider phenol as the solute and water and toluene as two solvents. The parameters for phenol are A = 5.7, A = -12.9, A = -18.3, and A5 = 0.0091, whereas Aq is unspecified, but a negative quantity. With the solvent parameters from Tables 2.1 and 2.3, the standard Gibbs energy of solvation of phenol in water becomes Aq + 3.39, and in toluene Ao -1- 4.11 kJ mol". It is seen that As i,Gb is lower in water than in toluene, so that the transfer of phenol from water to toluene entails an increase in AjoItGb. The consequence of this is that phenol prefers water over toluene, since work would be required to make this transfer. It should be remembered that the standard Gibbs energies of solvation refer to the state of infinite dilution of the solute (solute-solute... 

Note that the tGA are the standard molar Gibbs energies of solvation of the (combined ions of the) electrolyte [5]. Alternatively, a transfer activity coefficient can be defined as... 

AH , AS at, AG°at Lattice enthalpy, entropy, and Gibbs energy of the crystalline electrolyte AH v, AS V, AG°V Enthalpy, entropy, and Gibbs energy of solvation of the electrolyte AG° Gibbs energy of solution of the crystalline electrolyte. Taken from Table 1 in Ref. [3], Chapter 1. 

Dipole moments of solutes are also involved in the so-called reaction-field theory1112 which predicts generally the Gibbs energy of solvation, and from it the stability of con-formers as dependent on solvents. Besides the dipole the quadrupole moment is also taken into the calculations. For instance, conformational equilibria of cyclic halo ketones were predicted from the dipole moments of the two conformers with fair success13. However, the whole theory was criticised1415 that there is too much arbitrariness in the... 

It should be noted that either the insertion or annihilation of the particle can be used to calculate the Gibbs energy of solvation, and both are related by a change of sign. With an appropriate method for solving the solubility calculations in aqueous solution, such as the one presented here, one can parameterize a model of C02 for a particular water model to reproduce these values over an extended thermodynamic window, such as over a desired temperature range that would encompass any type of brine aquifer. 

The standard molar Gibbs energy of solvation can also be derived from pure component data using spectroscopic information for determining solvatochromic parameters in respect of activity, basicity, polarity, etc. There exists a number of linear solvatochromic scales, the most widely used of which is the linear solvation energy relationship (LSER) devised by Kamlet and Taft [37, 38]. The Nernst distribution of solute i according to Kamlet is ... 

Fig. 2-8. The relationship between standard molar Gibbs energies of solvation and solution and the crystal lattice energy of an ionophore A B AG =AG, -AG .

For a comprehensive compilation of Gibbs energies of solvation, see C. M. Criss and M. Salomon Thermodynamic Measurements - Interpretation of Thermodynamic Data. In A. K. Covington and T. Dickinson (eds.) Physical Chemistry of Organic Solvent Systems, Plenum Press, London New York 1973, p. 253 ff. - Cf also D. W. Smith Ionic Hydration Enthalpies, J. Chem. Educ. 54, 540 (1977). - A critical selection of standard molar heat capacities of hydration, AhydC°/ (J K") moF ), of single ions has been given by M. H. Abraham and Y. Marcus, J. Chem. Soc., Faraday Trans. 1 82, 3255 (1986). 

The most direct measure of the energetics of ion solvation is, without doubt, their standard molar Gibbs energy of solvation, i.e. transfer from the gas phase to the solvent (c/ Fig. 2-8). However, this quantity is generally unknown, particularly for ions in nonaqueous solvents. Therefore, is advantageously replaced by the standard... 

From investigations of the solvation of ions and dipolar molecules in binary solvent mixtures it has been found that the ratio of the solvent components in the solvent shell can be different from that in the bulk solution. As expected, the solute is surrounded preferably by the component of the mixture which leads to the more negative Gibbs energy of solvation, The observation that the solvent shell has a compo-... 

In most cases, the gas-phase acidity orders differ dramatically from those observed in solution since the Gibbs energies of solvation ca. 200-600 kJ/mol cf. Table 2-8 in Section 2.3) are much larger than the intrinsic acidity differences for most pairs of compounds. Thus, the relative acidities in solution are often dictated by the differential Gibbs energies of solvation rather than by the intrinsic properties of the solute molecules. 

The difference in the Gibbs energy of solvation, for two species in equi-... 

Thus, the problem of making quantitative allowances for solvent-induced changes in the rate constant of a reaction A -I- B (AB) C + T> cf. Eq. (5-1) in Section 5.1) is reduced to the calculation of the difference between the partial Gibbs energies of solvation of the activated complex (AB) and the initial reactants A and B as given in Eq. (5-75) [28]. 

By considering the ehanges in standard molar Gibbs energy of solvation, of reac-... 

A positive value of Ig indicates that the ion is better solvated by water than by solvent S a negative value means that the ion is more strongly solvated by transferring it to the solvent S. A difference in Ig of unity corresponds to a difference in Gibbs energy of solvation of Ig 10 RT Ig i.e. 5.7 kJ/mol at 25 °C. 

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... 

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