Gibbs Energy of Formation Values

In Chapters 12 and 13 we used the Gibbs energy and enthalpy of formation values in Table A.8, without explaining how those values were determined. This appendix discusses 

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From these latter stability constants, and the Gibbs energies of formation of the sulphate ion (Chapter IV) and Zr (Section V.2.1.1), the Gibbs energy of formation values of ZrSO, Zr(S04)2(aq) and Zr(S04)3 are ... 

While most tables like A.8 are at 25 °C = 298.15 K, the widely used JANAF tables for combustion calculations [6] give Gibbs energy of formation values from the elements at a wide range of temperatures, in effect defining a new datum state for each temperature. This works perfectly well if we understand what the datum state is (see Problem 12.6). 

Tide, D. R. Handbook of Chemistry and Physics, ed. 71, Boca Raton, EL CRC Press, pp. 10-29 (1990). The 91st edition (2010) does not contain Gibbs energy of formation values. 

Diakonov, Ragnarsdottir and Tagirov (1998) determined a Gibbs energy of formation value for Y(OH)3(s) from thermodynamic data available in the literature. They utilised heat capacity and entropy information from Chirico and Westrum (1981). They also utilised enthalpy data estimated from a function relating the enthalpy of the lanthanide hydroxides with the corresponding enthalpy of the... 

Diakonov, Ragnarsdottir and Tagirov (1998) determined a Gibbs energy of formation value for Pr(OH)g(s) from thermodynamic data available in the literature. 

Bard, Parsons and Jordan (1985) have listed a number of Gibbs energy of formation values for the polymeric vanadium(V) species. Typically, these values are in poor agreement with those derived in the present review and, consequently, have not been listed in Table 11.10. The values of Bard et al. are not accepted. 

The Gibbs energy of formation value determined for manganite, MnOOH(s), is in excellent agreement with the value listed by Bard, Parsons and Jordan (1985). 

The tables in this section contain values of the enthalpy and Gibbs energy of formation, entropy, and heat capacity at 298.15 K (25°C). No values are given in these tables for metal alloys or other solid solutions, for fused salts, or for substances of undefined chemical composition. 

In the case of hydrogen, for example, at a teiuperamre of 2500 K, the equilibrium constant for dissociation has the value, calculated from the tlrermo-dynamic relation between the Gibbs energy of formation and the equilibrium constant of 6.356 x 10 " and hence at a total pressure of 10 atmos, the degree of dissociation is 0.126 at 2500 K, which drops to 8.32 x 10 at 2000 K. 

TABLE 7.2 Standard Enthalpies and Gibbs Free Energies of Formation (Values are joules per mole of the substance formed)... 

The relationships of the type (3.1.54) and (3.1.57) imply that the standard electrode potentials can be derived directly from the thermodynamic data (and vice versa). The values of the standard chemical potentials are identified with the values of the standard Gibbs energies of formation, tabulated, for example, by the US National Bureau of Standards. On the other hand, the experimental approach to the determination of standard electrode potentials is based on the cells of the type (3.1.41) whose EMFs are extrapolated to zero ionic strength. 

References (20, 22, 23, 24, 29, and 74) comprise the series of Technical Notes 270 from the Chemical Thermodynamics Data Center at the National Bureau of Standards. These give selected values of enthalpies and Gibbs energies of formation and of entropies and heat capacities of pure compounds and of aqueous species in their standard states at 25 °C. They include all inorganic compounds of one and two carbon atoms per molecule. 

The difference in the Gibbs energies of formation corresponds to the integral of the cell voltage as a function of the composition between the limits of the starting and the final compositions. The value for ASf° is determined from the variation of the cell voltage as a function of the temperature... 

The conventional thermodynamic standard state values of the Gibbs energy of formation and standard enthalpy of formation of elements in their standard states are A(G — 0 and ArH = 0. Conventional values of the standard molar Gibbs energy of formation and standard molar enthalpy of formation of the hydrated proton are ArC (H +, aq) = 0 and Ar// (H +, aq) = 0. In addition, the standard molar entropy of the hydrated proton is taken as zero 5 (H+, aq) = 0. This convention produces negative standard entropies for some ions. 

This section contains data for the standard values of the Gibbs energies of formation and enthalpies of formation of some aqueous ions. The manner of their derivation is described briefly. 

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. 

The basis of the estimations of the absolute enthalpies of hydration of the main group ions is dealt with extensively in Chapter 2. In this section, the same principles are applied to the estimation of the enthalpies of hydration of the monatomic cations of the transition elements, i.e. those of the ions M" +. The standard enthalpies of formation of the aqueous ions are known from experimental measurements and their values, combined with the appropriate number of moles of dihydrogen oxidations to hydrated protons, gives the conventional values for the enthalpies of hydration of the ions concerned. Table 7.4 contains the Gibbs energies of formation and the enthalpies of formation of some ions formed by the first-row transition elements, and includes those formed by Ag, Cd, Hg and Ga. 

Since AG = AH - TAS, the net result is a negative value of AG, a "hydrophobic effect" that favors association of bases. Substantial efforts have been made to estimate quantitatively the Gibbs energies of formation of helical regions of RNA molecules in hairpin stem-loops such as that of Fig. 5-9. 4 45 49-54 Table 5-2 shows the observed increments in AGf° of such a helix upon addition of one base pair at the end of an existing helix. Addition of an AU pair supplies only -4 to -5 kj... 

Table 6-4 gives, in the first column, standard values of Gibbs energies of formation from the elements AGf° for a variety of pure solids, gases, and liquids as well as values for substances in solution at the hypothetical 1 M activity. As an example, consider the value of AGf 0 for pure liquid acetic acid, -389.1 kj mol-1. The equation for its formation from the elements is ... 

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