Thermodynamic data error

Some points should be noted from this example. Firstly, ideal gas behavior has been assumed. This is an approximation, but it is reasonable for the low pressure assumed in the calculation. Later the calculation will be repeated at higher pressure when the ideal gas approximation will be poor. Also, it should be clear that the calculation is very sensitive to the thermodynamic data. Errors in the thermodynamic data can lead to a significantly different result. Thermodynamic data, even from reputable sources, should be used with caution. 

Mathematical Consistency Requirements. Theoretical equations provide a method by which a data set s internal consistency can be tested or missing data can be derived from known values of related properties. The abiUty of data to fit a proven model may also provide insight into whether that data behaves correctiy and follows expected trends. For example, poor fit of vapor pressure versus temperature data to a generally accepted correlating equation could indicate systematic data error or bias. A simple sermlogarithmic form, (eg, the Antoine equation, eq. 8), has been shown to apply to most organic Hquids, so substantial deviation from this model might indicate a problem. Many other simple thermodynamics relations can provide useful data tests (1—5,18,21). 

All of the information obtained in this research area depends upon indirect evidence through the use of nonisotopic carriers or normalized data in the form of ratios. These are subject to error but the trends and insights that have been obtained are very useful to the description of the behavior of plutonium in the environment. Better thermodynamic data in the range of environmental concentrations would be helpful in further quantification of chemical species, as would phenomenalogical descriptions of the behavior of plutonium in reasonably good models of the environment. 

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. 

For these reasons, the thermodynamic data on which a model is based vary considerably in quality. At the minimum, data error limits the resolution of a geochemical model. The energetic differences among groups of silicates, such as the clay minerals, is commonly smaller than the error implicit in estimating mineral stability. A clay mineralogist, therefore, might find less useful information in the results of a model than expected. 

Most importantly, has the modeler conceptualized the reaction process correctly The modeler defines a reaction process on the basis of a concept of how the process occurs in nature. Many times the apparent failure of a calculation indicates a flawed concept of how the reaction occurs rather than error in a chemical analysis or the thermodynamic data. The failed calculation, in this case, is more useful than a successful one because it points out a basic error in the modeler s understanding. 

The choice of a given database as source of auxiliary values may not be straightforward, even for a thermochemist. Consistency is a very important criterion, but factors such as the publication year, the assignment of an uncertainty to each value, and even the scientific reputation of the authors or the origin of the database matter. For instance, it would not be sensible to use the old NBS Circular 500 [22] when the NBS Tables of Chemical Thermodynamic Properties [17], published in 1982, is available. If we need a value for the standard enthalpy of formation of an organic compound, such as ethanol, we will probably prefer Pedley s Thermodynamic Data and Structures of Organic Compounds [15], published in 1994, which reports the error bars. Finally, if we are looking for the standard enthalpy of formation of any particular substance, we should first check whether it is included in CODATA Key Values for Thermodynamics [16] or in the very recent Active Thermochemical Tables [23,24],... 

Despite the importance of mixtures containing steam as a component there is a shortage of thermodynamic data for such systems. At low densities the solubility of water in compressed gases has been used (J, 2 to obtain cross term second virial coefficients Bj2- At high densities the phase boundaries of several water + hydrocarbon systems have been determined (3,4). Data which would be of greatest value, pVT measurements, do not exist. Adsorption on the walls of a pVT apparatus causes such large errors that it has been a difficult task to determine the equation of state of pure steam, particularly at low densities. Flow calorimetric measurements, which are free from adsorption errors, offer an alternative route to thermodynamic information. Flow calorimetric measurements of the isothermal enthalpy-pressure coefficient pressure yield the quantity 4>c = B - TdB/dT where B is the second virial coefficient. From values of obtain values of B without recourse to pVT measurements. 

Consideration of the effects of anharmonicity involved two empirical constants Z and vanh. Because only three quantities could be evaluated from the calorimetric data with any reliability, A was taken as 5.5 kcal mol"1 (cf. cyclohexane3). Fitting of the thermodynamic data then gave Z = 1.85 kcal mol", vanh = 750 cm 1 and AE = 0.57 kcal mol", favoring the Af-Heq conformer. Whereas A was found to be insensitive to the value of A , A was shown to be sensitive to the experimental error in the calorimetrically determined value of the entropy. 

Not all published and widely accepted thermodynamic values are reliable. Nordstrom and Archer (2003) provide a detailed review of the controversies, uncertainties, and problems related to thermodynamic data for arsenic and its compounds and aqueous species. Many of the data are contradictory and the methods that produce the data are sometimes questionable or have not been thoroughly documented. Too often, data in the literature have been passed from reference to reference without critical evaluations. Some of the data have high measurement errors, were produced under undefined or poorly defined laboratory conditions, and involved unrepresentative sampling (Matschullat 2000, 298 Nordstrom and Archer, 2003). Furthermore, other questionable data originate from obscure documents or are written in languages that many individuals cannot read and properly interpret. Therefore, thermodynamic results must be accepted with a certain amount of caution. The table in this appendix includes thermodynamic data from various sources, which provide users with some idea of their variability. Although sometimes unavoidable, users... 

As a very simple case, consider the reactions, and the pertinent thermodynamic data for them, given in Table 1-1. In this case the enthalpy difference is well within experimental error the chelate effect can thus be traced entirely to the entropy difference. 

This value rests on the experimental and thermodynamic data for the absolute rate of recombination of CH3 radicals, thermodynamic data for C2H6, CH4, etc., the bond energy in methane (CH3—H), and an assumed value for the entropy of CJIT3. It is very doubtful if all of these collectively could be sufficiently in error at 900°K to cause an error in k of as much as a factor of 10 to 20. (Note that this would require errors in A// of 4 to 6 Kcal and errors in AaS of 4 to 5 cal/mole-°K.) And observe that the chain varies only as... 

Using our experimental activity data for Na20 in glass, we have modeled the effect of a typical combustion gas mixture on alkali vaporization ( ). For this purpose we have acquired, and adapted to our computers, a code known as SOLGASMIX (7 ) which is unique in its ability to deal with non-ideal solution multicomponent heterogeneous equilibria. Previous attempts to model this type of problem have been limited to ideal solution assumptions ( ). As is demonstrated in Table III, if solution non-ideality is neglected, drastic errors result in the prediction of alkali vapor transport processes. Table III and Figure 21 summarize the predicted alkali species partial pressures. The thermodynamic data base was constructed mainly from the JANAF (36) compilation. Additional details of this study will be presented elsewhere. 

Figure 8. PE-pH stability diagram of the system H2S-S8—H20-NaCl (0.7M) for " [S] = 10 g-atom/kg. The grey curve on the diagram for [S] = 10 corresponds to the experimental error on PE computed from the uncertainties on the thermodynamic data (5, 17).

It appears that the largest source of error in these comparisons is the analytical data. The next largest source of error seems to be the adequacy of activity coefficients and stability constants used in the model and last is the reliability of the field Eh measurement. Close inspection of Figure 3 shows a slight bias of calculated Eh values towards more oxidizing potentials. Fe(III) complexes are quite strong and it is likely that some important complexes, possibly FeHSO " (5 4,5 5), should be included in the chemical model, but the thermodynamic data are not reliable enough to justify its use. 

Standard Deviations. In order to evaluate the effect on the modeling calculations of errors in the analytical input data, propagated standard deviations are now computed for a subset of the solid phase activity products considered in the model. Arrangements have also been made to enter and output standard deviations for thermodynamic data. 

Because the author was unable to review the proofs to the second edition, numerous printing errors appeared in that edition. Apologies are due for the inconveniences caused. Much care has been exercised in the printing of this edition. SI units are used where appropriate throughout, particularly for thermodynamic data so that these data are now consistent with the JANAF tables in the appendix. In some instances where certain cgs databases have not been updated and where cgs units are so ingrained that SI may have proved an inconvenience, cgs units have prevailed. The table of conversion factors in the appendix should reduce any inconveniences. 

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