Free energy temperature

Free Energy - Temperature Diagrams (Ellingham Diagrams)... 

Click Coached Problems for a self-study module on free energy temperature, AS, and AW. 

The relation between reaction free energy, temperature, cell voltage, and reversible heat in a galvanic cell is reflected by the Gibbs-Helmholtz equation [Eq. (31)]. 

Figure 3.6 Free energy-temperature diagram with scales showing oxygen pressures, C0/C02 and H2/H20 pressure gas ratios.

The empirically fitted free-energy-temperature relationship (in joules) is... 

Fig. 4.15 Characteristic free-energy temperature diagram (a) and DSC traces (b) for the enantiotropic relationship between polymorphs. The Gi and Gu curves cross at the transition temperature 7[ n below their melting points mpi, and mpn all indicated on the temperature axis. DSC trace A at the transition temperature modification I undergoes an endothermic transition to modification II, and the heat absorbed is A/fi n for that transition. Modification II then melts at mpn, with the accompanying AHfu. DSC trace B Modification I melts at mpi with A//n followed by crystaUization of II with A//ni at the intermediate temperature. Modification II then melts with details as above. DSC trace C modification II, metastable at room temperature, transforms exothermically to modification I with A/fn i at that transition temperature. Continued heating leads to the events in trace A. DSC trace D modification II exists at room temperature and no transition takes place prior to melting at mpn, with the appropriate A//ni- (After Giron 1995, with permission.)...

Although amorphous pharmaceutical materials can be readily isolated and may persist for many thousands of years,they are in fact a thermodynamically metastable state and will eventually revert to the more stable crystalline form. Fig. 4 shows a snapshot in time of the free energy-temperature relationship for a material that can be isolated as both an amorphous form and a crystalline form. This quasi-equilibrium thermodynamic view of the amorphous state shows that the amorphous form has a significantly higher free energy than the crystalline form, and illustrates why it is expected to have a much higher aqueous solubility and significantly different physical properties (e.g., density). 

The subject matter is introduced by a short exposition of the Gibbs phase rule in Sec. 8.2. Unary component systems are discussed in Sec. 8.3. Binary and ternary systems are addressed in Secs. 8.4 and 8.5, respectively. Sec. 8.6 makes the connection between free energy, temperature, and composition, on one hand, and phase diagrams, on the other. 

If macroscopic thermodynamics are applied to materials containing a population of defects, particularly nonstoichio-metric compounds, the defects themselves do not enter into the thermodynamic expressions in an explicit way. However, it is possible to construct a statistical thermodynamic formalism that will predict the shape of the free energy-temperature-composition curve for any phase containing defects. The simplest approach is to assume that the point defects are noninteracting species, distributed at random in the crystal, and that the defect energies are constant and not a function either of concentration or of temperature. In this case, reaction equations similar to those described above, equations (6) and (7), can be used within a normal thermodynamic framework to deduce the way in which defect populations respond to changes in external variables. 

The equilibrium constant at 25 °C is calculated directly from tabulations of the Gibbs free energy of formation. Once this value is known, the equilibrium constant can be calculated at any other temperature. To obtain the equation that governs the variation of the equilibrium constant with temperature, the starting point is ea. 00.5). which provides the relationship between the Gibbs free energy, temperature, pressure, and composition ... 

FREE ENERGY, TEMPERATURE, AND THE EQUILIBRIUM CONSTANT (SECTIONS 19.6 AND 19.7) The values of AH and AS... 

The relationship between the change in Gibbs free energy, temperature in kelvins, and an equilibrium constant is given by the equation AG = RT In K. ... 

Figure 19 Gibbs free energy-temperature relationship of monoacid triglyceride polymorphs. 

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