Thermochemical calculation 3.37

Bond energy values can be obtained from thermochemical calculations (p. 72) and a number are included in Table 2.70 together with the compound used in the calculation. 

The Complete Basis Set (CBS) methods were developed by George Petersson and several collaborators. The family name reflects the fundamental observation underlying these methods the largest errors in ab initio thermochemical calculations result from basis set truncation. 

Because of uncertainties of equilibrium constants, ES, pH, temperature, /02 and other parameters (activity coefficient, ionic strength, activity of water, pressure), the estimated values of concentrations may have uncertainties of 1 in logarithmic unit. However, it can be concluded from the thermochemical calculations and fluid inclusion data that the Kuroko ore fluids have the following chemical features. 

Origin of ore fluids is constrained by (1) chemical compositions of ore fluids estimated by thermochemical calculations (section 1.3.2) and by fluid inclusion analyses, (2) isotopic compositions of ore fluids estimated by the analyses of minerals and fluid inclusions (section 1.3.3), (3) seawater-rock interaction experiments, (4) computer calculations on the seawater-rock interaction, and (5) comparison of chemical features of Kuroko ore fluids with those of present-day hydrothermal solutions venting from seafloor (section 2.3). 

Figure 1.95. Activity of component ZnCOs versus /oj. Carbonate containing ZnCOs is in equilibrium with sphalerite. Thermochemical calculation was made under the following conditions temperature = 200°C, ionic strength = 1, ES = 10 m, and pH = 5. (1) CH4 and H2S region. (2) H2CO3 and H2S region. (3) H2CO3 and (Na, K) SOj region (Shikazono, 1977b).

Figure 1.100. Typical /coj-temperature ranges for Au-Ag-rich, Pb-Zn-Mn-rich, and Cu-Pb-Zn-rich vein-type deposits estimated from gangue mineral assemblages, homogenization temperatures of fluid inclusions, and thermochemical calculations (Shikazono, 1985b).

The above interpretation of formation of epithermal Au-Ag vein-type deposits is supported by (1) thermochemical calculations on this type of mixing (Reed and Spycher, 1985), and (2) the geological occurrence of epithermal Au-Ag vein-type deposits and associated advanced argillic alteration. 

Reed and Spycher (1985) pointed out based on thermochemical calculations that gold does not precipitate due to boiling because pH increases by boiling, leading to an increase in gold solubility due to gold-thio complexes. They indicated that acidification... 

It has been pointed out by Giggenbach (1981) on the basis of thermochemical calculations that epidote occurs at higher temperatures of at least more than 240°C, and K-feldspar occurs at restricted temperatures, i.e. below ca. 250°C, in active geothermal systems. These theoretical results seem to be consistent with those observed in epithermal vein-type deposits in Japan. 

The /CO2-temperature relationships for the above-mentioned mineral-fluid equilibria are shown in Fig. 3.6. Based on the thermochemical calculations, minerals summarized above and temperatures estimated, we could estimate typical /CO2-temperature ranges for hydrothermal solutions from midoceanic ridges and back-arc basins. 

The analytical data on CO2 in hydrothermal solutions and fluid inclusions and measured temperatures (Table 3.2) are consistent with the thermochemical calculations mentioned above. 

Liu and Schmitt (1984, 1993a,b, 1996) and Liu et al. (1988) derived the relationship between the negative Ce anomaly of seawater and PcOj from thermochemical calculations. Liu and his coworkers estimated Pco2 variation during the last 120 Ma based on this method. Pco2 middle Miocene age estimated by Liu and his coworkers is high and seems to be consistent with that by Ishikawa (1996). However, Liu s method was criticized by Elderfield and Schultz (1987). Ce anomaly depends not only on Pco2> but on many other factors such as P02, pH and SCe. 

WEBER, H. F. (1980) Ann Phy. Chem. 10, 103. Untersuchungen liber die warmeleitung in fliissigkeiten. Werner, R. R. (1941) Thermochemical Calculations (McGraw-Hill). 

Radialene 52 has been envisaged as a precursor to hexaethynyl[3]radialene, a potential building block for carbon networks. However, desilylation under very mild conditions led to an unstable product of so far unknown identity. In this context, it should be mentioned that according to thermochemical calculations, the still unknown hexaethynyl[3]radialene has an increased conjugation energy with respect to vinylacetylene, probably because of partial relief of strain in the radialene corc26b. A remarkable aspect of 52 is its color the crystals are deep-red and a hexane solution has a purple color. In this respect, 52 differs from the yellow radialenes 50 and 51 and resembles [3]radialenes such as 27 and 38, which have much more extended --systems. 

The first key factor, energy, is involved in the production of any chemical. Design of a safe process requires an understanding of the inherent energy (exothermic release/endothermic absorption) during chemical reactions. This information can come from the literature, from thermochemical calculations, or from proper use of testing equipment and procedures. The potential pressure that may be developed in the process is also a very important design consideration. 

Despite the many successes in the thermochemical modeling of energetic materials, several significant limitations exist. One such limitation is that real systems do not always obtain chemical equilibrium during the relatively short (nanoseconds-microseconds) time scales of detonation. When this occurs, quantities such as the energy of detonation and the detonation velocity are commonly predicted to be 10-20% higher than experiment by a thermochemical calculation. 

When can a set of data be regarded as a database Guidelines such as the number of records or the publication medium may not be useful. CODATA values, for example, which are the recommended starting point for any database (or any thermochemical calculation, for that matter), involve only about 150 species. Also, the CODATA reports have been printed in regular scientific journals before the final set was released as a book and later posted on the Internet. Second, we could have distinguished between databases and data compilations. The former involve recalculation of quantities such as standard enthalpies of formation to ensure a consistent set of values (see section 2.5). Databases may also include data assessment, leading to recommended values. Data compilations, on the other hand, are just collections of literature values. Although this distinction is important (see table Bl), a data compilation can be rather useful for the expert user and save many hours of literature search. 

Near the equilibrium geometry, dependence of the energy on geometric displacements is approximately quadratic. As a result, small errors in the reference geometry will insignificantly affect computed energies, but more substantial errors (say, several hundredths of an A in covalent bond lengths) will compromise the reliability of a thermochemical calculation. 

The semiempirical molecular orbital (MO) methods of quantum chemistry [1-12] are widely used in computational studies of large molecules. A number of such methods are available for calculating thermochemical properties of ground state molecules in the gas phase, including MNDO [13], MNDOC [14], MNDO/d [15-18], AMI [19], PM3 [20], SAMI [21,22], OM1 [23], OM2 [24,25] MINDO/3 [26], SINDOl [27,28], and MSINDO [29-31]. MNDO, AMI, and PM3 are widely distributed in a number of software packages, and they are probably the most popular semiempirical methods for thermochemical calculations. We shall therefore concentrate on these methods, but shall also address other NDDO-based approaches with orthogonalization corrections [23-25],... 

Most thermochemical calculations are made for closed thermodynamic systems, and the stoichiometry is most conveniently represented in terms of the molar quantities as determined from statistical calculations. In dealing with compressible flow problems in which it is essential to work with open thermodynamic systems, it is best to employ mass quantities. Throughout this text uppercase symbols will be used for molar quantities and lowercase symbols for mass quantities. 

In calculating the lattice energy of a crystal, we adopt an arbitrary reference condition (two isolated ions in the gaseous state and at infinite distance) to which we assign a zero potential. It is worth stressing that this condition is not equivalent to the standard state commonly adopted in thermochemical calculations, which is normally that of element at stable state at reference P, T. 

It is uncertain to what extent thermal equilibria are achieved in different parts of the flames. — A number of procedures are (in principle) available to determine flame temperatures The immediate measurement, for example by thermocouples, the thermochemical calculation, line reversal methods for electronic excitation temperatures, determination of vibrational or rotational temperatures. In addition more recent methods like advanced Raman techniques may be applied. 

The molecular mass of the combustion products in the ramburner is increased by the formation of the oxidized metal particles. However, the temperature in the ramburner is also increased by the oxidation. The results of thermochemical calculations indicate that the specific impulse generated by the combustion in the ramburner is more dependent on the average combustion temperature than the average molecular mass of the products when metal particles are added. Table 15.4 shows the heats of combustion and the major oxidized products of the soHd particles used in ducted rockets. 

The direction of long-term changes in rock composition due to the action of groundwater can be determined by thermochemical calculations of the equilibria between various possible constituents (8). Appropriate thermochemical data are required. Exper-... 

Additional BDEno-h data for a few other R2NOH compounds were calculated in compliance with the thermochemical cycle reported in equation l 3,69 on the basis of available p fa (RiNOH) and E° (R2NO /R2NO ) data (cf. Scheme 4), and are listed in Table 2. The thermochemical calculation reproduces the experimental BDEno-h value (i.e. 88.1 kcalmoG ) of Af-hydroxyphthalimide (HPI) exactly, so that these calculated values can be confidently compared with the experimental ones in Table 1. DFT calculations of BDEno-h also provide reliable results ... 

The Hartree-Fock approximation also provided the basis for what are now commonly referred to as semi-empirical models. These introduce additional approximations as well as empirical parameters to greatly simplify the calculations, with minimal adverse effect on the results. While this goal has yet to be fully realized, several useful schemes have resulted, including the popular AMI and PM3 models. Semi-empirical models have proven to be successful for the calculation of equilibrium geometries, including the geometries of transition-metal compounds. They are, however, not satisfactory for thermochemical calculations or for conformational assignments. Discussion is provided in Section n. 

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