Thermodynamic functions, calculated from phase integral

The boiling point is calculated from the adopted thermodynamic functions and the chosen enthalpy of sublimation at 298.15 K so that the Gibbs energy functions calculated by integration of the crystal liquid data and by statistical methods from the gas phase are equal at the boiling point. 

According to our treatment it follows that AcGm = M TiOa / 02 BaO — Concentration-dependent terms do not occur here (more precisely they can be neglected), and AcG (T) can be calculated at any temperature from the values of the phases (see Table 4.1, see page 78). BaTiOs is thermodynamically stable with respect to decomposition into the oxides at all temperatures at which - cG < 0. There is no mass action effect. If AcG is known at a temperature To, it is possible to calculate the reaction parameters for all other temperatures via the specific heats using Eq. (4.42). If Cp is approximated by means of a series with coefficients ajk it is technically much more economical to carry out the calculation via integration of AcCp, i.e. via Acaj (see page 86), than to determine the thermodynamic functions of the reaction participants individually at temperatme T and then to calculate the difference (operation Ac). 

FIGURE 6.11 TCFIs for (a) water/water, (b) water/t-butanol, and (c) t-butanol/t-butanol obtained from simulation of water/t-butanol mixtures using the Verlet method (crosses) versus the water mole fraction Xj, compared with TCFIs obtained from experimental data nsing the Wooley/O Connell procedure, where either the Wilson (black line), NRTL (red Une), or mM (green line) models were employed for obtaining the activity coefficient derivatives. Note that the NRTL and mM model approaches infinity since they predict a phase split. (Calculated values from R. J. Wooley and J. P. O Connell, 1991, A Database of Flnctuation Thermodynamic Properties and Molecular Correlation-Function Integrals for a Variety of Binary Liquids, Fluid Phase Equilibria, 66, 233.) (See color insert.)... 

Methods to apply quantum corrections for this inadequacy of classical mechanics when applied to crystals, as well as other phases, have been explored (124-127), but there is not yet general agreement on how best to calculate thermodynamic properties for these types of systems. The practical solution of Berens and co-workers (124) entails. . calculating the velocity spectrum S(v) from molecular dynamics and then integrating S(v) over all frequencies with a weighting fimction which is the difference between the quantum and classical harmonic weighting functions for the thermodynamic variable of interest. However, as the statement avers, anharmonic contributions to the vibrational modes will not be captured correctly this relatively minor shortcoming was addressed by Hardy and co-workers (128). 

---