Gibbs energy above

Figure 6-12. Schematic representation of the molar Gibbs energy (above) and the demixing temperature (below) as a function of the volume fraction of the solute for a partially miscible system, st. Stable region m, metastable region u, instable region b, binodals, sp, spinodals Ti, temperature for which the upper diagram is applicable.

Each reactant and product appears in the Nemst equation raised to its stoichiometric power. Thermodynamic data for cell potentials have been compiled and graphed (3) as a function of pH. Such graphs are known as Pourbaix diagrams, and are valuable for the study of corrosion, electro deposition, and other phenomena in aqueous solutions.Erom the above thermodynamic analysis, the cell potential can be related to the Gibbs energy change... 

These terms are obtained from die equation above by differentiation with respect to r, and setting the resultant equal to zero. This is equivalent to taking the point on the graph of the Gibbs energy of nucleus formation versus the size of the nucleus where the tangent has zero slope. 

Figure 1.9 The balance of endothermic surface energy and the exothermic formation of the stable condensed phase during nucleation from the vapour phase. The critical radius, above which the nuclei become stable, is where the resultant Gibbs energy change has zero slope...

If we combine the Gibbs energy of formation equations above to derive the equation... 

The voltammetric information given here suggests that the transfer of an objective cation from Wl to LM can be achieved under a smaller membrane potential when an anion for which the Gibbs transfer energy at the LM/W2 interface is smaller is added into W2. In the case of the above-mentioned membrane system, the transfer of K+ from Wl to LM in the presence of 0.01 M MgBr2 in W2 is expected to be attained even at the membrane potential 0.19 V (which corresponds to the Gibbs energy of transfer of 18.3... 

When the adsorbed components are electrically charged, then the partial molar Gibbs energy of the charged component depends on the charge of the given phase, and thus the chemical potentials in the above relationships must be replaced by the electrochemical potentials. The Gibbs adsorption isotherm then has the form... 

The Gibbs energy, AGcf, is often replaced by the enthalpy of Frenkel defect formation, AHcP, as described above, to give... 

The calculation of the number of Frenkel defects in a crystal proceeds along lines parallel to those above. The introduction of Frenkel defects causes the Gibbs energy of the crystal to change by an amount AGp ... 

These criteria can be used to get information on the coefficients of eq. (2.48). In the high-symmetry phase, stable above the transition temperature, the order parameter r= 0 and the equilibrium conditions imply that the two first constants in the polynomial expansion are restricted to a = 0 and b > 0. If we assume that b < 0, the low-symmetry phase is stable since r > 0 then implies that AtrsG < 0. The transitional Gibbs energy is thus reduced to... 

The formalism shown above is in general easily extended to multi-component systems. All thermodynamic mixing properties may be derived from the integral Gibbs energy of mixing, which in general is expressed as... 

In general, the first derivative of the Gibbs energy is sufficient to determine the conditions of equilibrium. To examine the stability of a chemical equilibrium, such as the one described above, higher order derivatives of G are needed. We will see in the following that the Gibbs energy versus the potential variable must be upwards convex for a stable equilibrium. Unstable equilibria, on the other hand, are... 

The specific processes discussed above are all special cases of the general process (9.2.1). In all of these cases we have seen the explicit modification of the equilibrium constant of the corresponding process. As indicated in Eq. (9.2.3), the general modification requires knowledge of the solvation Gibbs energies of all the components involved in the process. For macromolecules such as proteins or nucleic acid, none of these is known, however. Nevertheless, some specific solvation effects are examined in Sections 9.4 and 9.5. 

Continuing to assume that Gibbs energies and enthalpies are essentially equal, the above reaction is endothermic by 14 kJ moP for R = vinyl. However, it is exothermic for the other R groups cyclopropyl, —6 ethyl, —20 propyl, —22 isobutyl, —26 neopentyl, —31 cyclobutyl, —35 and cyclopentyl, —39 kJmoP. The values are in the order expected for carbanion stability. 

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