Free energy of formation, apparent

Fig. 7.5. (a) Schematic representation of the absolute G of NaCl as a function of temperature, and the difference between this and the absolute G of (Na + Ch) which is fixed at its 298.15 K value. This difference we call the apparent free energy of formation, (b). Schematic representation of the difference function AaGSaci from Figure 7.5a, as a function of temperature. 

Calculation of the apparent free energy of formation of a compound at elevated temperatures from A/G and (G — values was discussed earlier in this... 

From the standard Flade potential for iron, calculate the apparent free energy of formation of the passive film per gram-atom of oxygen. Do the same for nickel and chromium. 

Using the Turnbull-Fischer expression for crystallisation rate [65], which is inversely related to induction time, plots can be made of ln(T ind) against IIT(AT ). Figure 9.18 demonstrates the dramatic difference in the apparent free energy of formation of (3 and 3 forms. Despite the difference in the sharpness of the peaks, it is found somewhat surprisingly that the half times for crystallisation of [3 and (3 forms as a function of driving force lie on one continuous curve. 

Powell and Searcy [1288], in a study of CaMg(C03)2 decomposition at 750—900 K by the torsion—effusion and torsion—Langmuir techniques, conclude that dolomite and C02 are in equilibrium with a glassy phase having a free energy of formation of (73 600 — 36.8T)J from 0.5 CaO + 0.5 MgO. The apparent Arrhenius parameters for the decomposition are calculated as E = 194 kJ mole-1 and activation entropy = 93 JK-1 (mole C02)-1. 

Here we have introduced a detailed formalism for building models of biochemical systems. This approach has the advantages that the influences of pH and metal ion concentrations on apparent thermodynamic properties are explicitly accounted for. This detailed accounting allows us to take advantage of the rich data available on dissociation constants and thermodynamic properties. Even so, the available data remain incomplete. While standard free energies of formation are... 

Misra, U.K. and Upchurch, W.J. Free energy of formation of beldellite from apparent solubility measurements. Clays Clay Min. 327-331 (1976). 

Many of the new tasks would be at the boundary with materials science. There are some that are obviously applications-oriented, like the electronic theory of high temperature superconduction in the layered copper-oxide perovskites, and other aspects of nanotechnology. There are also fundamental valence problems, such as accounting for the structures and properties of quasiciystals. Why is the association of transition metals and aluminium apparently of central importance How do we deal with the valence properties of systems where the free energy of formation or phase transition is dominated by the entropy term ... 

The procedure for calculating a phase boundary is, as just mentioned, to calculate the locus of P, T conditions such that A G = 0 for the reaction involving the phases on either side of the boundary. To do this we must be able to calculate the apparent or standard free energies of formation of the phases as a function of P and T, as outlined in Chapter 7. This is done for compound i with the equations... 

Let s suppose that a measurement of quartz solubility has been used to obtain the free energy of formation (standard or apparent) of H4Si04 in the ideal one molal standard state. This number can then be used (with A/G° terms for the minerals) to calculate the equilibrium constant of the albite-nepheline reaction (equation (13.11)), giving the equilibrium silica concentration in a solution that may never have been experimentally determined, or perhaps never existed, and in which quartz is not stable. Thus knowing the solubility of quartz, one could in a similar way calculate the silica concentration in fluids in contact with a variety of mineral assemblages. 

Because the free energy of formation of a surface is always positive, a particle that consists only of surfaces (that is, platelets or droplets of atomic dimensions) would be thermodynamically unstable. This is also apparent from the Kelvin equation [Eq. 3.70], which states that a particle that falls below a certain size will have an increased vapor pressure and will therefore evaporate. There must be a stabilizing influence, however, that allows small particles of atomic dimensions to form and grow a common occurrence in nature. This influence is given by the free energy of formation of the bulk condensed phase. In this process, n moles of vapor are transferred to the liquid phase under isothermal conditions. This work of isothermal compression is given by... 

It is apparent that any factors that reduce the volume of the nucleus reduce the critical Gibbs free energy of formation of that nucleus, making nucleation more probable (Ragone, 1994). 

The free energy of formation for ThC2 appears to be temperature independent at — 29.5 kcal/mole, if the vapor pressure measurements are compared to values obtained from other techniques at other temperatures. If this is the case, the slope produced by the Th,g, pressure (Fig. 57) is too great. Since the phase limit of ThCj apparently moves to a lower stoichiometry as the temperature is raised, the Th,g, pressure would increase faster, as the temperature was raised, than would be expected if the composition remained fixed (see Chapter XIII, Section G). Indeed, at 2800°, the measured pressure appears to be too great by about a factor of two. Although this is not the only explanation, it should be considered when future measurements are made. 

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