Thermal functions

Bigeleisen, J. and Ishida, T. Application of finite orthogonal polynomials to the thermal functions of harmonic oscillators. I. Reduced partition function of isotopic molecules, J. Chem. Phys. 48, 1311 (1968). Ishida, T., Spindel, W. and Bigeleisen, J. Theoretical analysis of chemical isotope fractionation by orthogonal polynomial methods, in Spindel, W., ed. Isotope Effects on Chemical Processes. Adv. Chem. Ser. 89, 192 (1969). 

C6o fullerene surfaces were thermally functionalized with perfluoro-(3-oxo-penta-4-ene)sulfonyl fluoride and then converted into sulfonic acid derivatives by basic hydrolysis. The product mimiced the electroconductive properties of perfluorosulfonyl Nation 1100 resins. When the modified fullerence was blended with platinum nanoparticles imbedded in Nation 1100 the material was effective as electrodes in fuel cells. 

In spite of the wealth of information available on the preparative and structural aspects of the lanthanide chlorides (1-3), experimental thermodynamic, and, in particular, high-temperature vaporization data are singularly lacking. The comprehensive estimates of the enthalpies of fusion, vaporization, heat capacities and other thermal functions for the lanthanide chlorides by Brewer et ah (4, 5) appear internally consistent, but the relatively few experimental measurements (6-/2) do not permit confirmation of the estimates due to the narrow temperature ranges of study. Additionally, the absence of accurate molecular data for the gaseous species has hampered third-law treatment of the limited experimental vapor pressure data available. The one reported study (12) of the vaporization of EuC12 effected by a boiling-point method lacks accuracy for these reasons. 

The molecular constants derived by Hastie, Hauge and Margrave (30) were used for derivation of the thermal functions of EuCl2(g) (cf. Table 2). A statistical weight of 16 was assumed in the calculations for the Eu2+ ion (31, 32). On the assumption that the statistical weight may be in error by up to a factor of 2, the uncertainty in the free-energy functions is estimated to be 1.51 eu. 

Second-law data reduction with the thermal functions listed in Tables 1 and 2 give for Eq. (4) Aff298 = 84.9 2.5kcal/gfw and ASl9S = 48.3 + l.8eu. Average ACp° values for the solid-vapor and liquid-vapor... 

The standard entropy of EuC12(s), S298, computed from the experimental second-law values and S298 EuCl2(g) is 32.9 2.4eu by use of the third-law thermal functions. 

The enthalpy of formation of the gaseous compounds can be derived from the vapour pressure studies using the thermal functions for the condensed and gaseous states derived in the previous sections. Third-law and second-law thermodynamic analyses of the equilibrium... 

The third-law value for the enthalpy of sublimation is preferred in view of the accuracy of the thermal functions of the condensed and gaseous states presented in the previous sections, though it should be realised that all uncertainties/errors in the thermal functions (entropy, enthalpy) of solid as well as gaseous phase accumulate in this value. The results are presented in table E.l of Appendix E. 

For the third law evaluations of the reaction enthalpies from mass spectrometric equilibrium measurements the Gibbs free energy functions of the reactants are needed. Likewise the enthalpy functions are needed in order to correct the second law reaction enthalpies obtained at the average temperature of measurement to the desired reference temperature. These thermal functions can be calculated according to standard statistical... 

Wofford, B. A., Eliades, M. E., Lieb, S. G., and Bevan, J. W., Determination of dissociation energies and thermal functions of hydrogen-bond formation using high resolution FTIR spectroscopy, J. Chem. Phys. 87, 5674-5680 (1987). 

This procedure ensures that all thermal functions will be calculated using the same auxiliary data. Following a similar procedure for the formation properties has introduced slight inconsistencies in those tables for which the formation properties were derived from the previous thermal functions. 

The conversion equations used for the change in standard-state pressure are listed below together with some that apply to thermal functions. Superscript and denote values at 1 bar and 1 atm, respectively. These equations apply to the small change in pressure from 1 atm to 1 bar. 

The JANAF Thermochemical Tables consist of thermal functions and formation functions, both of which are temperature dependent. The thermal functions consist of heat capacity, enthalpy increments, entropy, and Gibbs en-... 

The construction of the liquid single-phase thermal functions is identical with that used for the solid phase however, the required data at 298.15 K are not usually readily available. The data are obtained by calculating a preliminary table using the chosen heat capacities with zero values for A fH (298.15 K) and 5 (298.15 K). The correct starting values are then determined by comparing the values from the tables of crystal and liquid, using the following equations ... 

The gas phase thermal functions are generated using statistical mechanical relationships. Minimal data required for the various types of molecules are summarized below. Some of the equations used are given in Sec. 6.1 on Calcula-tional Methods. The relative molecular mass is required for all molecules. Minimum information required is ... 

The calculation of the temperature-dependent values of the thermal function is performed using a variety of procedures. Some of these procedures were developed internally while others were developed at other locations. A general description of the traditional equations used in the JANAF project follows. Numerous higher order calculational schemes are used whenever the data are sufficient. These procedures are detailed on the appropriate tables. 

The method used in generating the thermal functions depends not only on the quality/quantity of information available but also on the specifics of the nature of the infor-... 

The thermal functions at 298.15 K agree with recent CODATA recommendations (6) except for two minor differences. First, the entropy differs by 0.1094 J K mol because this table uses a standard state pressure of 1 bar, whereas the CODATA... 

Bonnetot et al (4) measured C° in the region 15 to 308 K. Our adopted thermal functions at 300 K and below are based on the smoothed values and integration by those authors using S (15 K) 0.10 J K mol". Above 300 K we have used C values estimated by comparison with those for LiBH (cr), LlBOg(cr) and LiAlOg(cr) (5). 

The thermal functions were calculated using a direct summation technique analogous to the alkali dimers and diatomic halogens (12). As in the diatomic fluorine case, the values of G(v), and were directly input into the calculation. Values... 

Efimenko Q) has studied mass spectrometrlcally the reaction BeO(cr) + BeFg(g) 4- BegOFgCg) and also reported two sets of equilibrium constants. Unlng JANAF thermal functions, the enthalpy of reaction has been calculated from those reported equilibrium constants by the 2nd law and the 3rd law methods. 

The thermal functions are calculated using a direct summation technique. 

The thermal functions given here are those recommended by CODATA (j[). The low temperature heat capacity of o-CA(cr) has been measured many times Griffil et al. (1.8 - 4.2 K, 2), Agarwal and Betterton (1.1 - 4.2 K, 3), Roberts (1.5 - 20 K, 4), Clusius and Vaughen (10-200 K, 5), Gunther (22-62 K, 6), and Eastman and Rodebush (67 - 293 K, 7). The adopted heat capacity values are derived assuming that the heat capacity curve should lie below and be similar to the shape of the a-Sr(cr) curve, but remain... 

The thermal functions are calculated using a direct summation technique, analogous to the alkali dimers (13). 

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