Tabulations of Thermodynamic Data

For practical applications it is necessary to have values of thermodynamic functions available, and in particular it is necessary to have values of enthalpy, entropy, heat capacity, and Gibbs energy for a wide range of temperatures and pressures. The critical evaluation of data is a difficult and important art, often made more difficult by the failure of authors of original papers to supply necessary information. Some comments on this subject can be found in a recent article.  

The results of recent measurements are described in other Chapters of this volume, but here collections of data will be reviewed. 

Reactions are often carried out at pressures in the neighbourhood of 101.325 kPa, and in this pressure region the thermodynamic properties of condensed phases (i.e. liquids and solids) do not change very rapidly with small changes in pressure. As a result, it is usual to adopt the following standard states when recording thermodynamic quantities  

Investigators must take care to read the foreword of the particular table they use so that they know which standard state has been employed, because most thermodynamic properties are calculated with respect to convenient scales. For example, the standard enthalpy of formation of a compound, AHf, is almost always quoted for a temperature of 298.15 K, and the enthalpy of formation of an element in its standard state must by definition be zero. It is therefore practically useful to look at a table and find, for an element, where a zero entry occurs. For example, the following values might appear C(graphite), A/ff = 0.000 kcalthmol C(diamond), AHf = 0.4532 kcalthmol . It is clear that C(graphite) is the standard state adopted for carbon in the table under consideration. Entropy, on the other hand, is usually defined by taking as zero the entropy, at T = 0, of the crystalline form in which all the molecules are orientated regularly. Because many of the extant tables have used thermochemical calories, care will also have to be taken in the future to see that values taken from different tables are corrected to the same units. 

The simplest thermodynamic tables list only values for 298.15 K, but more detailed tabulations present data for a wide temperature range. 

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This is an integral balance written for the whole system. The various terms deserve discussion. The enthalpies are relative to some reference temperature, Tref. Standard tabulations of thermodynamic data (see Chapter 7) make it convenient to choose rre/ = 298K, but choices of 7 re/ = 0K or Tref = Q°C are also common. The enthalpy terms will normally be replaced by temperature using... 

Note, in using Equations 50 and 53 above, that tabulations of thermodynamic data for electrolytes tend to employ a 1 molar ess concentration for all species in solution. For situations defined to have a standard-state pH value different from 0 (which corresponds to a 1 molar concentration of solvated protons), the standard-state chemical potentials for anions and cations are determined as... 

Benson, L. V. Teague L. S. "A Tabulation of Thermodynamic Data for Chemical Reactions Involving 58 Elements Common to Radioactive Waste Package Systems, Topical Report No. 4 for Rockwell Hanford Operations, LBL-11448, Lawrence Berkeley Laboratory, University-ofCalifornia, Berkeley, California, 1980. 

Numerous tabulations of thermodynamic property data are available in the literature. For example, a very recent tabulation of thermodynamic data by Jacobsen, et al (1997) covers all of the cryogenic fluids of interest. Sufficient detail on the models used for each fluid is available so... 

The reverse rate constants for the elementary reactions used in the present work were caJculated from the forward rate constants and the equilibrium constant by assuming microscopic reversibility. Standard states used in tabulations of thermodynamic data are invariably at 1 atm and the temperature of the system. Since concentration units were required for rate constant calculations, a conversion between Kp and Kc was necessary. Values of Kp were taken from the JANAF Thermochemical tables (1984). Kc was calculated from the expression ... 

Benson L.V., Teague L.S. (1980) A tabulation of thermodynamic data for chemical reactions involving 58 elements common to radioactive waste package systems. Report LBL-11448, Lawrence Berkeley Laboratory, Berkeley, USA, 97 p. 

We can calculate the standard free energy, AG°, of many reactions using tabulations of thermodynamic data. Consider the reaction between TiCU and CH, ... 

Useful tabulations of thermodynamic data have been published (165, 262), but the most comprehensive for the liquid and saturated vapor, as well as for the... 

The most complete tabulation of thermodynamic data available for neon is given in a paper by Yendall [1]. In this paper, Yendall used the 102 experimental PVT observations of the Leiden Laboratory [2] made between 1915 and 1919 to compute an equation of state. This equation of state was a modification of the Beattie-Bridgeman and Benedict-Webb-Rubin equations and used twelve coefficients. 

JANAF = Joint Army Navy Air Force, a useful tabulation of thermodynamic data published by the (US) National Institute of Standards and Technology (see http //webbooks.nist.gov/chemistry). 

If we have a value of Aj.G° for a reaction at a given temperature, we can use equation (13.17) to calculate an equilibrium constant K. This means that the tabulation of thermodynamic data in Appendix D can serve as a direct source of countless equilibrium constant values at 298.15 K. Knowing the value of K for a reaction turns out to be extremely useful because, as we will see in Chapter 15, the value of K and a set of initial reaction conditions are all that we need to be able to predict the equilibrium composition of a system. 

Systematic studies of the thermodynamic and kinetic acidity of metal hydrides in acetonitrile were carried out by Norton et al. [10, 11]. A review of the acidity of metal hydrides presents extensive tabulations of pKa data [12] only a few of the trends will be mentioned here. Metal hydrides span a wide range of pKa values considering only metal carbonyl hydrides shown in Table 7.1, the range exceeds 20 pfCa units. As expected, a substantial decrease in acidity is... 

For the convenience of tabulation and compulation of thermodynamic data, it is essential lo present them in a commonly accepted form relative to a single standard slate of reference. At all lemperatures, the standard stale for a pure liquid or solid is the condensed phase under a pressure of I atmosphere. The standard stale for a gas is the hypothetical ideal gas at anil fugarity (equivalent til a perfect gas" stale), in which state the enthalpy is that of the real gas at the same temperature when the pressure approaches aero. Values of thermodynamic quantities for standard-state conditions are identified by a superscriptQ. and Hn. for instance, is the enthalpy change of a reaction when reactants and products are in the standard state. 

The RT term amounts to 6.2n kJ mol-1 at 25 °C. This is small in relation to ionisation energies/enthalpies but is often far from trivial in thermodynamic arguments. However, it is rarely necessary to convert ionisation energies into enthalpies because, as we shall presently see, the RT terms ultimately cancel out. A number of tabulations of thermochemical data give enthalpies (or heats) of formation for ions in the gas phase these include the RT correction. 

In some cases, a literature source of thermodynamic data may exist, allowing one to perform the conversion. Fortunately, standard references (such as Refs. 168 and 180) frequently tabulate both the condensed and gas phase thermochemistry values. When that is not the case, the following relations may be used, where the enthalpies and entropies of vaporization and fusion must be at 25 °C ... 

In most tabulations of thermochemical data, such as that of Appendix B, values for the thermodynamic functions are given only at a single temperature, usually 298.15K.3 In order to convert standard heats of reaction to other temperatures, temperature variations at constant pressure must be considered. From Eq. (9),... 

When gas solubility data are lacking or are unavailable at the desired temperature, they can be estimated using available models. The method of Prausnitz and Shair (1961), which is based on regular solution theory and thus has the limitations of that theory. The applicability of regular solution theory is covered in detail by Hildebrand et al. (1970). A more recent model, now widely used, is UNIFAC, which is based on structural contributions of the solute and solvent molecular species. This model is described by Fredenslund et al. (1977) and extensive tabulations of equilibrium data, based on UNIFAC, have been published by Hwang et al. (1992) for aqueous systems where the solute concentrations are low and the solutions depart markedly from thermodynamic equilibrium. 

Preparation of consistent tabulations of thermod3maniic data is a difficult task because of the complex interrelations of the data. One new set of data can require changes in numerous related values. For inorganic thermodynamic compilations, the logical starting point is a reliable tabulation of data for the elements. If data for compounds are to be compared, they must be based on the same elemental data. Once the thermod3mamic data for the elements have been fixed, then equilibria involving the elements and compounds can be treated to fix the stabihty of the compounds. When the heats of subhmation and ionization of the elements are available, Bom-Haber cycle calculations can be carried out for ionic compounds to check the reliability of data for the compounds. 

Finally, although neither G nor H can be measured in absolute terms, so that we are forced always to use differences of these quantities, absolute values of S can be measured calorimetrically. Thus, tables of thermodynamic data for compound i contain values of A/G°, A fH°, and Sf, where S is the entropy of i. If we want a value of A fS°, we must calculate it from the tabulated values of S for the compound and its constituent elements. 

Note that these relations are also useful for predicting electrochemical properties from thermochemical data. Several problems following this chapter illustrate the usefulness of that approach. Large tabulations of thermodynamic quantities exist (5-8). 

The thermodynamic functions discussed in Section 3, which we shall call Lewis and Randall (LR) thermodynamic functions or functions in the LR system, are the quantities most frequently given in tabulations of experimental data. These functions differ slightly from those obtained most directly from calculations with MM-level models, in which the independent variables are the temperature T, solvent activity z , (or alternatively, Po t as defined in Fig. 1),... 

J. Chao, R. C. Wilhoit and B. J. Zwolinski, Ideal gas thermodynamic properties of ethane and propane , J. Phys. Chem. Ref. Data, 2, 427 (1973). Review and evaluation of structural parameters (including vibrational frequencies and internal rotation properties) tabulation of thermodynamic properties [C°, S°, H° — H°), (H° — H )/T, - G°-Hl)/T, AfG°,AfH°, logK ] for 0< T (K)< l500 calculated by statistical thermodynamic methods [rigid-rotor harmonic oscillator (RRHO) approximation]. 

The information contained in this book has been collected by hundreds of scientists and published in hundreds, perhaps a thousand, articles. We do hope that the reader will accept that we have found it too cumbersome to give a complete set of references to the primary research literature. Instead we refer to widely available tabulations of structure data, thermodynamic data and atomic energy levels. Only when the original work is considered to be of exceptional importance or originality, when it is relatively recent, or when it may be particularly difficult to locate, have we included a full reference. 

Gas-phase ionization energies or electron affinities for molecular species calculated by quantum mechanics do not include the thermodynamic properties of the free electron and can be compared directly to the tabulations of experimental data for these processes in the ion convention. To relate condensed- and gas-phase redox thermochemistry directly, however, a common convention must be adopted. Electrode potentials can be converted to the gas-phase convention for reaction in which there is a change in the number of electrons. The single electrode potential Es°) can be... 

This should point out how crucial it is to be consistent in the use of thermodynamic data and tabulated activity coefficient values. 

This book is a compilation of AfG", AH, S, and C values at 298.16 K for about 4000 substances in the condensed and gaseous"phases, and in aqueous solution. Covered are not only the inorganic elements and their compounds, but also data for the organic compounds through 34 carbon atoms. The authors point out that their tabulated values do not always form a self-consistent system of thermodynamic data. There are 2733 references. 

This reference book contains a compilation of thermodynamic data for about 2000 chemical compounds and aqueous ions (mostly inorganic). The thermodynamic properties tabulated are A-G , A,H , S , and C at 298.15 K, electrode potentials, enthalpies and entropies for phase transitions, A,G of inorganic aqueous ions from 25 to 350 C, partial molar heat capacities from 10 to 130 C, and the partial molar volumes of aqueous electrolytes at high temperatures and pressures. There are 1550 references given to the primary literature and to the literature evaluations of others. 

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