Thermodynamic data accuracy

A combination of uncertainty in thermodynamic data accuracy at elevated temperatures and overall lack of completeness with respect to organic compound class and interaction types (complex formation, adsorption, solid precipitate) poses some real limitations in the use of chemical and reaction path models. Thus, a cautionary note is that to compare results of different numerical studies it is necessary to know whether similar thermodynamic data bases were used. As we will show below, apparently discrepant conclusions drawn from modeling studies probably result from the use of more or less complete thermodynamic data. Of concern in the investigation of organic acid interactions in silicate rocks is the complete lack of any equilibrium measurements of silica-organic acid anion interactions, although dissolution rate measurements have been made (Bennett et al. 1988 Bennett 1991). 

By use of Othmer plots of reference substances, large tables of thermodynamic data can be expressed as simple correlations which are extremely accurate and easy to use. The real power of these correlations is the abiUty to interpolate and extrapolate the correlations beyond the experimental values with considerable accuracy. Mathematically stated... 

Does the thermodynamic dataset contain the species and minerals likely to be important in the study A set of thermodynamic data, especially one intended to span a range of temperatures, is by necessity a balance between completeness and accuracy. The modeler is responsible for assuring that the database includes the predominant species and important minerals in the problem of interest. 

Note These data have been obtained from the complete thermodynamic data tabulated in Kubaschewski et al. (loc. cit.), with the approximation of the simple two-term equation. This should serve for calculations not requiring an accuracy of better than 2kJmol 1 02, which is normally the case for industrial applications. Solid state crystal transformations which usually only have relatively small heats of transformation, have been ignored. 

By these methods, one can obtain fairly reliable estimates of enthalpies of formation of many compounds. As the bond enthalpies used are average values, they cannot be expected to result in highly accurate results for enthalpies of formation. More complex procedures also have been developed that will provide greater accuracy [14]. Related methods for estimation of thermodynamic data are discussed in Appendix A. 

Accuracy. Quantitative estimates of radionuclide solubility and speciation need reliable thermodynamic data, that is,... 

Chemical kinetic models require as a minimum thermodynamic and reaction-specific information. If problems involve transport, also proper transport coefficients are necessary. Since the accuracy of a kinetic model is often associated specifically with the chemical reaction mechanism, it is important to note that also the thermodynamic data are essential for the reliability of predictions. Fortunately the quality and quantity of data on thermochemistry of species and on the kinetics and mechanisms of individual elementary reactions have improved significantly over the past two decades, because of advances made in experimental methods. This has facilitated considerably our ability to develop detailed chemical kinetic models [356],... 

Chapter 6, which immediately follows, presents experimental methods and data for comparison with predictions in the present chapter. Such data will form the foundation for future modifications of theory in hydrate phase equilibria. However, the above thermodynamic prediction accuracies are usually satisfactory for engineering calculations, so that the state-of-the-art in hydrates is turning from thermodynamic (time-independence) to kinetics (time-dependence) phenomena,... 

Under natural conditions, these organisms derive little energy from nitrate reduction so the total biomass increase is small and slow in comparison to the turnover of reactants. Equilibrium models from thermodynamic calculations can often provide a useful first approximation for a real system. These models are limited by the accuracy and availability of thermodynamic data including temperature, pressure and activity dependencies, knowledge of all pertinent chemical species and related equilibria. 

Cells with Liquid Junctions and Elimination of Junction Potentials. When electrochemical cells are employed to obtain thermodynamic data, high accuracy ( 0.05 mV) requires the use of cells that are free from liquid junction (in the sense that the construction of the cell does not involve bringing into contact two or more distinctly different electrolyte solutions). Otherwise, the previously discussed uncertainties in the calculation of liquid-junction potentials will limit the accuracy of the data. 

By combining the thermodynamic data with those on the structure of the equilibrium binary phase diagram, R. Pretorius et al 261,262 were able to improve the accuracy of predicting the sequence of compound-layer formation in the transition metal-aluminium systems. For this, they used the values of the standard enthalpies (heats) of formation of the compounds. 

An attempt to make this application prompted the appearance of The Thermodynamics of Soil Solutions (Oxford University Press, 1981). Besides its evident purpose, to demonstrate the use of chemical thermodynamics, this book carried a leitmotif on the fundamental limitations of chemical thermodynamics for describing natural soils. These limitations referred especially to the influence of kinetics on stability, to the accuracy of thermodynamic data, and to the impossibility of deducing molecular mechanisms. The problem of mechanisms vis-a-vis thermodynamics cannot be expressed better than in the words of M. L. McGlashan 2 what can we learn from thermodynamic equations about the microscopic or molecular explanation of macroscopic changes Nothing whatever. What is a thermodynamic theory (The phrase is used in the titles of many papers published in reputable chemical journals.) There is no such thing. What then is the use of thermodynamic equations to the chemist They are indeed useful, but only by virtue of their use for the calculation of some desired quantity which has not been measured, or which is difficult to measure, from others which have been measured, or which are easier to measure. This point cannot be stated often enough. 

In all calculations only as much detail was developed as was needed to generate insight. The process was broken down into subsections to identify the sources of loss. Subsequent breakdowns continued only until a clear picture of the sources on inefficiency was developed. A check on accuracy was maintained by insuring that the work balance, i.e., W ost = Wactuaj - W deal was reasonably close. As indicated above, the various segments of the process were listed in priority order based on the potential for improvement. Idea generation was then carried out based on the thermodynamic data. 

The accuracy of the thermodynamic data has a significant effect on RCM computation. In the case of slow reactions both kinetics and phase equilibrium should be modelled accurately. If the reaction is fast enough the chemical reaction prevails. In many cases chemical equilibrium may be taken as the reference. Consequently, accurate knowledge of the chemical equilibrium constant is needed. When reactive azeotropes and/or phase splitting might occur accurate modelling of phase equilibrium is also needed. 

Thermodynamic data, and especially AS values, are generally unreliable or lacking for important phosphate complexes. Until such AS data is measured, it can be estimated with fair accuracy using the Fuoss equation for monovalent and divalent-bonded complexes and the electrostatic model when trivalent and quadrivalent addends are associated. Unfortunately, published AG and AS data on HS , s2 , and Se and Te aquo-complexes are suspect or largely lacking (Barnes, H. L., Pennsylvania State University, personal communication, 1978). Both the stoichiometry and stability of such complexes remains in doubt. Once a few such data have been accurately measured, plots with EN (10) or Q (44) as a variable, or using hard and soft acid and base concepts (3, 40) should permit the useful estimation of many as yet un-... 

In conclusion, it should be pointed out again that all these methods require the accuracy of a vast amount of subsidiary thermochemical and thermodynamic data, and the results should therefore be interpreted with caution. 

Rate coefficients for recombination reactions are related to those for dissociation via the equilibrium constant, which can generally be calculated from thermodynamical information with a high degree of precision, although the accuracy depends on the quality of the thermodynamic data. The rate coefficients are pressure dependent and the theoretical framework of unimolecular reactions can therefore be used to describe them. Because there is little or no activation energy for the recombination process, rates of radical association reactions can be measured over a wide range of temperatures and can be used, in combination with thermodynamic information, to calculate rate coefficients for unimolecular dissociations. The availability of data for a number of radical recombination reactions over a wide range of pressures and temperatures makes these reactions excellent test beds for theoretical models of pressure dependent reactions. 

The limited accuracy of much thermodynamic data can sometimes present problems. The best kinetics data have an accuracy approaching 10%... 

The relationship between the rate constants for forward and reverse steps and the equilibrium constant has already been discussed in describing its use in the evaluation process. Where the thermodynamic data are accurately known the relationship can be used with confidence to estimate the rate constant of a reaction from a knowledge of data on its reverse. The limitations are the accuracy of the thermodynamic data and the possibility that the reaction may proceed by a different channel to that defined by the equilibrium constant. 

A number of proton-transfer equilibrium constants for reactions similar to those shown in Eq. (3) have been measured by ion cyclotron resonance, high-pressure mass spectroscopy, flowing afterglow, MIKES, and MIKES/CID techniques. These studies allowed the relative proton affinities of a variety of bases to be determined with an accuracy of better than +0.2 kcal mol" and compared with related thermodynamic data measured in solution. 

Apparently alacrinite is also a low-temperature polymorph that simply stacks differently as well (Burns and Percival, 2001). We are not aware of any thermodynamic data on either pararealgar or alacrinite but since the crystal structures are identical except for molecular stacking, the free energies should be very similar to within the accuracy of calorimetric or solubility measurements. Duranusite and dimorphite (and possibly uzonite) are secondary alteration products of realgar (Clark, 1972 Marquez-Zavalia et al., 1999). 

The difficulty of reaching general conclusions is most serious, however. Comparisons are possible only between carefully optimized procedures, which may take a significant amount of time, as it requires the acquisition of a large amoimt of accurate thermodynamic data. Band profiles depend so much on the exact features of the isotherms that a high degree of accuracy, first in the measmement and then in the modeling of the equilibrium data, is required. 

Due to the fact that CVD is a non-equilibrium process, the investigations indicate that thermodynamic calculations and predictions are sensitive to the accuracy and quality of the original thermodynamic data calculated, which may contain errors and inaccuracies due to system complexity and theoretical assumptions. Therefore, thermodynamic calculations can only provide some indicative information and the final phase diagram should be modified by the experimental results. 

---