Reduced Gibbs energy

Statistical thermodynamic mean-field theory of polymer solutions, first formulated independently by Flory, Huggins, and Staverman, in which the thermodynamic quantities of the solution are derived from a simple concept of combinatorial entropy of mixing and a reduced Gibbs-energy parameter, the X interaction parameter. 

The enthalpy of formation of ZrS3(cr) at 298.15 K was determined from this expression using the third law and was found to be - 619.7 kJ-moP (in the calculation, the reduced Gibbs energy value at 923 K estimated by [86VOL/KOV] for ZrS2(cr) was... 

Application of this method in the calculation of thermod)mamic functions leads to small differences in enthalpy and reduced Gibbs energy estimated from Cp cai(7 and Cp exp(T) values. Using this method, a significant amount of thermodynamic properties for halides was obtained for the first time for a number of lanthanides. 

The thermodynamic functions (and other properties needed for their calculations) of gaseous lanthanide trichlorides have been extensively studied for several decades. In our view, the primary data on molecular constants are adequate for the required revision and refinement of the reduced Gibbs energy for the compounds imder consideration. Moreover, this class of compounds perfectly demonstrates how the contribution from electronic excitation to reduced Gibbs energy can be considered. Therefore, we start by describing the properties of RQ3 (R = La-Lu) molecules. 

FIGURE 2 Temperature dependences of the electronic contributions to the reduced Gibbs energy for erbium trichloride. See text for explanations. Reproduced from Chervonnyi and Chervonnaya (2004g) with permission from Pleiades Publishing, Ltd. 

FIGURE 4 Reduced Gibbs energies of LaCl3(g) calculated in the harmonic and anharmonic approximations for the out-of-plane bending vibration frequency V2. See text for explanations. 

Because of the difference in the symmetry number and refined calculations of electronic excitation energies, the reduced Gibbs energy values obtained by Myers and Graves (1977a) are lower by 4-6 J/(moLK) for... 

In 2007, we carried out a systematic description of the molecular constants of this series of compounds and calculated the reduced Gibbs energy (Chervonnyi and Chervonnaya, 2007c). Previously, the thermod)mamic functions were known only for Lap2 (Hildenbrand and Lau, 1995 Krasnov and Danilova, 1969). The procedure used for selecting molecular constants and the method of calculating the excitation energies of individual electronic states of ions are described below. 

The ultimate goal of this work was the calculation of thermodynamic functions, primarily enthalpies and reduced Gibbs energies used in practical calculations, by the second and third laws of thermodynamics. In view of this, the applicability of the procedure used for heat capacity calculations can be estimated by comparing these thermophysical parameters. 

TABLE 16 Comparison of the enthalpy and reduced Gibbs energy values of lanthanide trifluorides at T —... 

The heat capacity values were calculated by Eq. (11). The enthalpy values and their absolute differences ((5abs) 3ie in kj/mol. The reduced Gibbs energy values and their absolute differences ((5abs) aie in J/(mol K). All relative differences are in %. 

A comparison (Chervonnyi and Chervonnaya, 2005a) of the reduced Gibbs energies and enthalpies obtained by us with those from Batin s handbook (Barin, 1995) shows that the relative difference can be as large as 2% for the first parameter and 8% for the second one. The data were compared for LaFs, CeFa, PrFa, NdFa, EuFa, GdFa, DyFa, and H0F3. The handbook (Barin, 1995) does not contain data on the other RF3 compoimds. 

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