Formation from the elements

The problem created by not having absolute energy values is handled very conveniently by determining and tabulating, for every pure compound, the difference between the (absolute) G or 7T of the compound itself and the sum of the (absolute) Got H values of its constituent elements. In other words, AG or Ai7 is determined for the reaction in which the compound is formed from its elements (in their stable states). These differences can be determined experimentally in spite of not knowing the absolute values involved. For example, the Gibbs free energy of formation (i.e. formation from the elements) of water is 

The subscript / signifies formation from the elements and the superscript ° signifies standard conditions of some kind, normally a pressure of one bar and pure substances, but any specified temperature. If both these quantities (that is, the free energies of formation of water and of ice) are known for our conditions of —2°C and one bar, then for the reaction 

In other words, the comparison we are making is really between the absolute quantities G°h20(s) and G°h20(d not between arbitrary functions of these quantities. Determining the differences between G or iT of compounds and their constituent elements thus allows convenient tabulations to be made which facilitate calculation of AG or AH for any reaction. 

Finally, we might emphasize that in spite of numerous statements to the contrary, the (absolute) enthalpies and free energies of the elements themselves are not assumed 

Tabulated values of A/G° and AfH° for the elements in their reference states at various temperatures therefore appear as a column of zeros—see Table 7.1 for example. This of course does not mean that the absolute values G and H are zero.  

---

Because the reaction takes place in the Hquid, the amount of Hquid held in the contacting vessel is important, as are the Hquid physical properties such as viscosity, density, and surface tension. These properties affect gas bubble size and therefore phase boundary area and diffusion properties for rate considerations. Chemically, the oxidation rate is also dependent on the concentration of the anthrahydroquinone, the actual oxygen concentration in the Hquid, and the system temperature (64). The oxidation reaction is also exothermic, releasing the remaining 45% of the heat of formation from the elements. Temperature can be controUed by the various options described under hydrogenation. Added heat release can result from decomposition of hydrogen peroxide or direct reaction of H2O2 and hydroquinone (HQ) at a catalytic site (eq. 19). 

To calculate the reaction s equilibrium constant, we note that the free energy change A Gsw of each of the swap reactions in Equation 11.1 is the negative free energy of formation from the elements of the corresponding species... 

The relationships between the two different states and between the enthalpy of formation from the elements at standard state (H°) and the lattice energy (U) are easily understood by referring to the Born-Haber-Fayans thermochemical cycle. In this cycle, the formation of a crystalline compound from isolated atoms in the gaseous state is visualized as a stepwise process connecting the various transformations. Let us follow the condensation process of a crystal MX formed from a metal M and a gaseous molecule X2 ... 

We then close the cycle by transforming crystal MX into its component elements in the standard state. To do this, we must furnish energy corresponding to the enthalpy of formation from the elements ... 

Table 5.12 reports a compilation of thermochemical data for the various olivine components (compound Zn2Si04 is fictitious, because it is never observed in nature in the condition of pure component in the olivine form). Besides standard state enthalpy of formation from the elements (2) = 298.15 K = 1 bar pure component), the table also lists the values of bulk lattice energy and its constituents (coulombic, repulsive, dispersive). Note that enthalpy of formation from elements at standard state may be derived directly from bulk lattice energy, through the Bom-Haber-Fayans thermochemical cycle (see section 1.13). 

Note that the Gibbs free energy of formation from the elements of the fictive constituent oxides does not correspond to the actual thermodynamic value. It differs from it by an empirical term (4G) siiioifioation) that accounts for the structural difference between the oxide in its stable standard form and as a formal entity present in the layered silicate (cf. table 5.58). 

Table 5.59 lists Gibbs free energies of formation from the elements of mica end-members obtained with the procedure of Tardy and Garrels (1974). For comparative purposes, the same table lists Gibbs free energies of formation from the elements derived from the tabulated and S% p values (same sources as in table 5.57) by application of... 

Table 8.13 Standard partial molal Gibbs free energy of formation from the elements cal/mole), standard partial molal... 

Table 8.16 Standard molal Gibbs free energies of formation from the elements for aqueous ions and complexes and condensed phases, partly adopted in constructing the Eh-pH diagrams in figure 8.21. Data in kcal/mole. Values in parentheses Shock and Helgeson s (1988) tabulation. Sources of data (1) Wagman et al. (1982) (2) Garrels and Christ (1965) (3) Pourbaix (1966) (4) Berner (1971)...

The standard partial molal volumes (V ), heat capacities (C >), and entropies (S ) of aqueous /i-polymers, together with their standard partial molal enthalpies AHj) and Gibbs free energies of formation from the elements AGf), are linear functions of the number of moles of carbon atoms in the alkyl chains (figure 8.28). 

---