Evaluation of Thermodynamic Data

The basic aim of these thermodynamic property tables is to provide a related and consistent set of enthalpies of formation and Gibbs energies of formation. This allows the prediction of the enthalpy and Gibbs energy changes and the equilibrium constants for any reaction among the constituents of the tables. 

The enthalpy of formation and Gibbs energy of formation are related to each other through the entropy of formation of the substance. Self-consistency can be assured by use of this constraint to derive any one property from selected 

Enthalpy changes are relative quantities, so it is important to relate each substance to an interconsistent base. This is done by referring each enthalpy of formation to the chemical elements in their standard reference states. By convention, the enthalpy of formation of an element in its standard reference state is zero at all temperatures. 

The reference state table may involve a single phase or several phases and examples of both kinds are found in this compilation. For elements which are solid at room temperature, the reference state is normally the stable solid state(s) up to the melting point, the liquid up to the boiling point at 1 bar, and thereafter the gas phase which may be monatomic or diatomic. For other elements, the choices for the reference states are  

These choices are arbitrary and vary in different compilations. Enthalpies or Gibbs energies of formation taken from different sources should be converted to common reference states before use. 

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In addition to the analytical applications discussed above, controlled-potential methods are used for the evaluation of thermodynamic data and diffusion coefficients in both aqueous and nonaqueous solvents. Polarographic and voltammetric methods provide a convenient and straightforward means for evaluation of the diffusion coefficients in a variety of media. The requirements are that the current be diffusion-controlled, the number of electrons in the electrode reaction be known, and the concentration of the electroactive species and the area of electrodes be known. With these conditions satisfied, diffusion coefficients can be evaluated rapidly over a range of temperatures and solution conditions. 

Perhaps a more fundamental application of crystal field spectral measurements, and the one that heralded the re-discovery of crystal field theory by Orgel in 1952, is the evaluation of thermodynamic data for transition metal ions in minerals. Energy separations between the 3d orbital energy levels may be deduced from the positions of crystal field bands in an optical spectrum, malting it potentially possible to estimate relative crystal field stabilization energies (CFSE s) of the cations in each coordination site of a mineral structure. These data, once obtained, form the basis for discussions of thermodynamic properties of minerals and interpretations of transition metal geochemistry described in later chapters. 

An evaluation of thermodynamic data for modeling the aqueous environmental geochemistry of arsenic... 

Table IV-2 Selected thermodynamic data for reactions involving auxiliary compounds and complexes used in the evaluation of thermodynamic data for the NEA-TDB Project data. All ionic species listed in this table are aqueous species. Unless noted otherwise, all data refer to 298.15 K and a pressure of 0.1 MPa and, for aqueous species, a standard state of infinite dilution (/ = 0). The uncertainties listed below each value represent total uncertainties and correspond in principle to the statistically defined 95% confidence interval. Systematically, all the values are presented with three digits after the decimal point, regardless of the significance of these digits. The reference listed for each entry in this table indicates the NEA-TDB Review where the corresponding data have been...

Se4(g) is a minor species in selenium vapour and the situation is even worse than for Se3(g) with respect to fragmentation problems. The evaluation of thermodynamic data for Se4(g) has therefore been avoided except in three studies, summarised in Table V-9, where the investigators thought the fragmentation was under control. The study of Keller [70KEL] is the only one in which the fragmentation has been monitored properly and the review selects from this study ... 

Garvin, D., Parker, V. B., Wagman, D. D., Evans, W. H., "A combined Least Sums and Least Squares Approach to the Evaluation of Thermodynamic Data Networks, NBSIR 76-1147, U. S. Department of Commerce, National Bureau of Standards, Washington, DC 20234, July 1976. 

The emf-study of Ni2Si04 done by Jacob et al. was not used for the evaluation of thermodynamic data by this review, because the results were presented only in graphical form, making accurate recovery of experimental values difficult. 

The evaluation of thermodynamic data follows the same principles as described in the previous chapters but the existence of intermetallic phases or compounds must be taken into account. The extrapolation to well-defined limiting values is restricted. While for solid solutions thermodynamic functions are mostly defined for a composition A Bj ... 

This extensive series represents many years of effort by numerous Russian thermodynamicists engaged in the critical evaluation of thermodynamic data. Included in the tables are carefully selected values of A,G , S ,... 

These considerations based on thermodynamic functions can be made by utilizing thermodynamic database including advanced software. Thermodynamic database MALT [7] or FACTSage [8] are used widely. Evaluations of thermodynamic data have been also progressed on SOFC-related materials [9]. 

Evaluation of laboratoiy data. Location and confirmation of saddle ternaiy azeotropes and a check of thermodynamic consistency of data. 

Reliable data on the thermodynamic and phase relationships of actinide oxide systems are essential for reactor safety analysis. This paper reviews certain aspects of thermodynamic data currently available on the nonstoichiometric Pu-0 system, which may serve as a basis for use in reactor safety analysis. Emphasis is placed on phase relationships, vaporization behavior, oxygen-potential measurements, and evaluation of pertinent thermodynamic quantities. 

Are the equilibrium constants for the important reactions in the thermodynamic dataset sufficiently accurate The collection of thermodynamic data is subject to error in the experiment, chemical analysis, and interpretation of the experimental results. Error margins, however, are seldom reported and never seem to appear in data compilations. Compiled data, furthermore, have generally been extrapolated from the temperature of measurement to that of interest (e.g., Helgeson, 1969). The stabilities of many aqueous species have been determined only at room temperature, for example, and mineral solubilities many times are measured at high temperatures where reactions approach equilibrium most rapidly. Evaluating the stabilities and sometimes even the stoichiometries of complex species is especially difficult and prone to inaccuracy. 

Haas, J.L., Jr. and J.R. Fisher, 1976, Simultaneous evaluation and correlation of thermodynamic data. American Journal of Science 276,525-545. 

The first step is the evaluation of thermodynamic and kinetic data by quantitative energy calculations and qualitative considerations as discussed in Chapter 2. The results may provide a satisfactory answer as to whether the reaction can be performed in the open laboratory or requires a high-pressure cell arrangement on the small scale. Further evaluations are required for scale-up. Toxicity, corrosivity, type of apparatus, size, and other criteria must also be considered. 

The esterification of TPA with EG is a reaction between two bifunctional molecules which leads to a number of reactions occurring simultaneously. To simplify the evaluation of experimental data, model compounds have been used for kinetic and thermodynamic investigations [18-21], Reimschuessel and coworkers studied esterification by using EG with benzoic acid and TPA with 2-(2-methoxyethoxy) ethanol as model systems [19-21], The data for the temperature dependency of the equilibrium constants, AT, = K,(T), given in the original publications are affected by printing errors. The corrected equations are summarized in Table 2.3. 

Thermo-Calc (Sundman et al. 1985, Andersson et al. 2002). ft features a wide spectrum of thermodynamic models, databases and modules making it possible to perform calculations on most problems involving phase equilibria (phase transformation, stable and metastable equilibria, etc.). The calculations are performed using databases produced by an expert evaluation of experimental data. There are thermodynamic databases available for many different systems and applications. 

Fig. 8.10 Principles of GITT for the evaluation of thermodynamic and kinetic data of electrodes. A constant current Iq is applied and interrupted after certain time intervals t until an equilibrium cell voltage is reached. The combined analysis of the relaxation process and the variation of the steady state voltage results in a comprehensive picture of fundamental electrode properties.

In addition, there is one other equilibrium constant, an intersystem constant, necessary to relate the system of zf molecules with that of the z molecules. Although this constant, Kit may be written in a number of ways, the following format has been chosen for this constant since this is the form which is most readily evaluated from existing compilations of thermodynamic data ... 

Evaluation of A Energy separations between resolved 3d orbital energy levels correspond to visible and near-infrared radiation. Measurements of absorption spectra of transition metal compounds and minerals are used to obtain A and to evaluate the CFSE of the ions. Crystal field splittings may also be estimated from plots of thermodynamic data for the first-series transition metal compounds. The magnitude of A depends on ... 

Chapter 7 discusses some of the thermodynamic properties of transition metal compounds and minerals that are influenced by crystal field effects. The characteristic double-humped curves in plots of thermodynamic data for suites of transition metal-bearing phases originate from contributions from the crystal field stabilization energy. However, these CFSE s, important as they are for explaining differences between individual cations, make up only a small fraction of the total energy of a transition metal compound. In the absence of spectroscopic data, CFSE s could be evaluated from the double-humped curves of thermodynamic data for isochemical compounds of the first transition series. 

As shown in Chap. 6, ideal-gas heat capacities, rather than the actual heat capacities of gases, are used in the evaluation of thermodynamic properties such as internal energy and enthalpy. The reason is that thermodynamic-property evaluation is conveniently accomplished in two steps first, calculation of ideal-gas values from ideal-gas heat capacities second, calculation from PVT data of the differences between real-gas and ideal-gas values. A real gas becomes ideal in the limit as P - 0 if it were to remain ideal when compressed to a finite pressure, its state would remain that of an ideal-gas. Gases in these hypothetical ideal-gas states have properties that reflect their individuality just as do real gases. Ideal-gas heat capacities (designated by Cf and Cy) are therefore different for different gases although functions of temperature, they are independent of pressure. 

Equations (6.7) through (6.10) are the basis not only for derivation of the Maxwell equations but also of a large number of other equations relating thermodynamic properties. We develop here only a few expressions useful for evaluations of thermodynamic properties from experimental data. Their derivation requires application of Eqs. (6.8) and (6.16). 

Of the two kinds of data needed for evaluation of thermodynamic properties, heat capacities and PVT data, the latter are most frequently missing. Fortunately, the generalized methods developed in Sec. 3.6 for the compressibility factor are also applicable to residual properties. 

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