Molar Gibbs energy of water

Figure 5.5 The Molar Gibbs Energy of Water as a Function of Temperature Near the Liquid-Vapor Phase Transition (Schematic).

Sketch rough graphs representing the molar Gibbs energy of water as a function of the temperature and as a function of the pressure in the vicinity of the solid-liquid phase transition. Liquid water has a smaller molar volume than solid water but a larger molar entropy. 

Construct an accurate graph of the molar Gibbs energy of water as a function of pressure from 0.100 atm to... 

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. 

The extent of the reaction of carbon dioxide with water to form carbonic acid is fairly well known—less than 1%. However, for thermodynamic purposes we make no distinction between the two nonionized species, C02 and H2C03. We are thus concerned with the sum of the concentration of these species, a quantity that can be determined experimentally. We must therefore develop the methods used to define the standard state of the combined nonionized species and the standard molar Gibbs energies of formation. 

When the standard Gibbs energy of formation of the hydrogen ion is defined as zero, the standard molar Gibbs energy of hydronium ion must equal that of water. The change of state related to AGP(H30 + ) is... 

Experimentally, the molar Gibbs energy of transfer of an anion X is obtained from the combined results of four solubility measurements, namely of the salts Ph4As Ph4B and Ph4As X in water, W, and of the same salts in the solvent S. The Gibbs energy of transfer is then ... 

Table 2-9. Selected standard molar Gibbs energies of transfer of single ions X from water (W) to seven nonaqueous solvents (S), AG,°(X, W — S)/ (kJ mor ) , at 25 °C (molar scale), taken from the compilation of Marcus [244]. Values for F were taken from G. T. Hefter, Pure Appl. Chem. 63, 1749 (1991). 

A further quantitative measure of the solvent solvophobic effecfi has been introdueed by Abraham et al. [282]. It has been shown that the standard molar Gibbs energies of transfer of nonpolar, hydrophobic solutes X (X = argon, alkanes, and alkane-like compounds) from water (W) to other solvents (S) can be linearly correlated through a set of equations such as Eq. (7-12b),... 

The is the molar Gibbs energy of pure water the are the chemical potentials of the solutes in the hypothetical ideal solution of unit molarity. 

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

Table 7 Standard Molar Gibbs Energies of Transfer and Partitioning of Alkali Metal Cations from Water to Nitrobenzene at 25°C ...

At the expense of added complexity, the SL model more satisfactorily explains the major energy contributions to the ion-transfer process. The analysis requires evaluation of the terms A (S S.ei, A (S s.neut, and A Gl.unsym, yielding the value of AGs as the sum of these terms via Eq. (8) for both water and solvent. Since AG°r = AG% AGh [Eq. (13)], one can in principle calculate standard molar Gibbs energies of transfer. In fact, the applicability of this approach was demonstrated earlier by Abraham and Liszi [53], although on the mole fraction scale and without the unsymmetric term. It is convenient to examine the electrostatic, neutral, and unsymmetric contributions to AG°r separately according to ... 

Figure 1 Electrostatic and neutral contributions to the standard molar Gibbs energy of transfer of univalent cations from water to solvents having five different dielectric constants, calculated from the single-layer electrostatic model. Calculations are valid for 25°C and assume a hypothetical constant solvent molar volume of 100 cm /mol. Solid lines correspond to the electrostatic term AGtr.ii [from Eqs. (5) and (18)] and the dashed line corresponds to the neutral term A C r.m.-ui [Eq. (26)]. Radii of the alkali metal ions are indicated along the X-axis (Table 2).

Table 18 Standard Molar Gibbs Energy of Partitioning of Alkali Metal Cations from Solvent-Saturated Water to Water-Saturated Solvents ... 

Standard molar Gibbs energy of partitioning (kJ/mol) refers here to the transfer of an ion from solvent-saturated water to water-saturated solvent... 

Standard molar Gibbs energy of solvation (kJ/mol) added subscripts el, neut, and unsym refer respectively to the electrostatic [Eq. (5)], neutral, and unsymmetric terms Standard molar Gibbs energy of transfer (kJ/mol) refers here to the transfer of an ion from pure water to pure solvent and employs the TATB extrathermodynamic assumption added subscripts el, neut, and unsym refer respectively to the electrostatic, neutral, and unsymmetric terms clarifying subscripts W—> S and W(S)—> S(W) distinguish between respectively transfer from pure water to pure solvent and partitioning from solvent-saturated water to water-saturated solvent... 

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. 

The standard molar Gibbs energy of transfer of the ion from water to the mixture,... 

TABLE 2.6 The Standard Molar Gibbs Energies of Stepwise Clustering of Water Molecules Around Anions in the Ideal Gas Phase, -A, G7kJ-mol" at =293.15 K ... 

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