Thermochemical data, calculating

Assuming chemical equilibrium between Kuroko-forming minerals and Kuroko ore fluids, the chemical composition of Kuroko ore fluids can be estimated, using thermochemical data. Calculations for the purposes of estimating the chemistry of Kuroko... 

Boron Monoxide and Dioxide. High temperature vapor phases of BO, B2O3, and BO2 have been the subject of a number of spectroscopic and mass spectrometric studies aimed at developiag theories of bonding, electronic stmctures, and thermochemical data (1,34). Values for the principal thermodynamic functions have been calculated and compiled for these gases (35). 

Thermodynamic calculations for reactions forming carbon disulfide from the elements are compHcated by the existence of several known molecular species of sulfur vapor (23,24). Thermochemical data have been reported (12). Although carbon disulfide is thermodynamically unstable at room temperature, the equiHbtium constant of formation increases with temperature and reaches a maximum corresponding to 91% conversion to carbon disulfide at about 700°C. Carbon disulfide decomposes extremely slowly at room temperature in the absence of oxidizing agents. 

Interatomic distances calculated from the detailed analysis of rotational fine structure of the UV spectrum of pyrazine are in close agreement with those observed in (7) and (8), with the calculated bond lengths for C—C of 1.395, C—N 1.341 and C—H 1.085 A (60DIS(20)4291). Thermochemical data have provided a figure of 75 kJ moP for the delocalization energy of the pyrazine ring (B-67MI21400). 

A modified definition of resonance energy has been introduced by Dewar (66T(S8)75, 69JA6321) in which the reference point is the corresponding open-chain polyene. In principle this overcomes the difficulties inherent in comparing observed stability with that of an idealized molecule with pure single and double bonds, as thermochemical data for the reference acyclic polyenes are capable of direct experimental determination. In practice, as the required data were not available, recourse was made to theoretical calculations using a semiempirical SCF-MO method. The pertinent Dewar Resonance Energies are listed in Table 30. 

Two now classical papers 61MI40400, 62JCS2927) contain almost all the experimental thermochemical data on pyrazole and indazole. Heats of combustion determined by Zimmerman (61MI40400) have been used by Dewar to calculate the heats of atomization (Table 25) (69JA796). Quantum mechanical calculations, carried out by Dewar (69JA796) or Olivella 81JHC1189), gave accurate empirical values. 

Table 25 Experimental and Calculated Thermochemical Data of Pyrazole and Indazole (kJ mol )...

Whether AH for a projected reaction is based on bond-energy data, tabulated thermochemical data, or MO computations, there remain some fundamental problems which prevent reaching a final conclusion about a reaction s feasibility. In the first place, most reactions of interest occur in solution, and the enthalpy, entropy, and fiee energy associated with any reaction depend strongly on the solvent medium. There is only a limited amount of tabulated thermochemical data that are directly suitable for treatment of reactions in organic solvents. Thermodynamic data usually pertain to the pure compound. MO calculations usually refer to the isolated (gas phase) molecule. Estimates of solvation effects must be made in order to apply either experimental or computational data to reactions occurring in solution. 

The heats of formation of most organic compounds are derived from heats of reaction by arithmetic manipulations similar to that shown. Chemists find a table of AH values to be convenient because it replaces many separate tables of AH° values for individual reaction types and permits AH° to be calculated for any reaction, real or imaginary, for which the heats of formation of reactants and products are available. It is more appropriate for our purposes, however, to connect thermochemical data to chemical processes as directly as possible, and therefore we will cite heats of particular reactions, such as heats of combustion and heats of hydrogenation, rather than heats of formation. 

The original paper defining the Gaussian-2 method by Curtiss, Raghavachari, Trucks and Pople tested the method s effectiveness by comparing its results to experimental thermochemical data for a set of 125 calculations 55 atomization energies, 38 ionization potentials, 25 electron affinities and 7 proton affinities. All compounds included only first and second-row heavy atoms. The specific calculations chosen were selected because of the availability of high accuracy experimental values for these thermochemical quantities. 

Standard-State Enthalpy Changes (AH°). To expedite calculations, thermochemical data are ordinarily presented in the form of standard-state enthalpy changes of the system AH°(T,P), with the requirement that materials start and end at the same temperature (T) and pressure (P) and in their standard states of aggregation, i.e.,... 

It is difficult, essentially impossible, to measure AH for this reaction because when carbon burns, the major product is always carbon dioxide, C02. It is possible, however, to calculate AH using thermochemical data for two other reactions that are readily carried out in the laboratory (Example 8.6). 

The rule for the calculation of the electromotive force of such a cell is, therefore, according to Nernst (cf. Bed. Ber., 1909,. p. 247) extrapolate the thermochemical data to the lowest possible temperature and put ... 

Sources of thermochemical data for such calculations are Vol 7, H38 Lff Heat Effects — Data for Common Explosives NBS Circular 500 (Ref 39a) Cox Pilcher (Ref 89) and the studies of Rhodes Nelson (Ref 24b) and McKinley Brown (Ref 28a) on mixed acids As an example of such a calculation we will compute the heat evolution and temp rise occurring during the mixed acid nitration of glycerol to NG. We will assume that a typical 50/50 nitric acid/sulfuric acid MA is used and that the MA/glycerol ratio is 5/1. Further assumptions are that all the glycerol is converted to NG, and that the heats of soln of NG in die. spent acid, and of spent acid in the NG, are negligibly small (cf discussion of these effects by the writer in Ref 51). The net reaction is then ... 

In the following paper of this series6 a value of about 1.7 v.e. has been found from thermochemical data for the resonance energy of benzene. Equating the negative of this quantity to 1.1055a, we calculate the value of a to be about —1.5 v.e. This value may not be very reliable, however, since it is based on the assumption that values of bond energies obtained from aliphatic compounds can be applied directly to aromatic compounds. 

The Nature of the Chemical Bond. VI. The Calculation from Thermochemical Data of the Energy of Resonance of Molecules Among Several Electronic Structures1... 

In formulating a set of bond-energy values we first calculated the energies of formation of molecules from experimental values of the heats of combustion of the compounds6 and thermochemical data pertaining to the products of combustion—carbon dioxide, water, nitrogen, etc. The same values for the latter quantities were used as previously.4... 

This study of thermochemical data for a very large number of substances has shown that in every case for which the data are reliable the observed energy of the molecule is equal to that calculated for an assumed distribution of bonds or differs from it in the direction corresponding to greater stability, in accord with the quantum-... 

Extensive quantum chemical calculations have been reported for sulfur-rich compounds in the past two decades. These calculations were used to investigate molecular structures and spectroscopic properties, as well as to understand the nature chemical bonding and reaction mechanism. Many high-level ab initio calculations were used for interpretation of experimental data and for providing accurate predictions of molecular structures and thermochemical data where no reliable experimental values are available. In recent years, density functional calculations have been extensively tested and used on many first- and second-row compounds. These proven DFT methods look promising for larger systems because for their computational efficiency. 

Calculation of thermochemical data using high-quality ab initio electronic structure calculations has been a long-standing goal. However, the availability of supercomputers and new theoretical techniques now allow the calculation of thermochemical properties with chemical accuracy, i.e., AHf to within... 

Figure 1.39. Relationship between /co2> oh2C05 and temperature for silicate-carbonate equilibria. Thermochemical data used for the calculations are taken from Helge.son (1969) (Shikazono et al., 1998).

The variations in Fe and Mg contents of the 14 A Fe-chlorite-14 A Mg-chlorite solid solution are considered here. However, structural formulae for chlorite are not as simple as those considered here. As mentioned by Walshe and Solomon (1981), Stoesell (1984), Cathelineau and Nieva (1985) and Walshe (1986), chlorite solid solution may be represented by six components, and accurate thermochemical data on each end-member component at the hydrothermal conditions of concern are necessary to provide a far more rigorous calculation of the equilibrium between chlorite and hydrothermal solution. However, the above argument demonstrates that the composition of chlorite is a highly useful indicator of physicochemical conditions of hydrothermal solution and extent of water-rock interaction. 

Figure 1.86. Variation in chemical compositions (in molal unit) of hydrothermal solution with temperature. Thermochemical data used for the calculations are from Helgeson (1969). Calculation method is given in Shikazono (1978a). Chloride concentration in hydrothermal solution is assumed to be 1 mol/kg H2O. A-B Na concentration in solution in equilibrium with low albite and adularia, C-D K concentration in solution in equilibrium with low albite and adularia, E-F HaSiOa concentration in equilibrium with quartz, G-H Ca + concentration in equilibrium with albite and anorthite (Shikazono, 1978a, 1988b).

Seward (1973) experimentally determined the solubility of Au due to this complex and equilibrium constant for the above reaction. Figure 1.102 shows the solubility of Au on log/oj-pH diagram calculated based on the thermochemical data by Seward (1973). 

Figure 1.175. Activity of S2-temperature diagram showing iso-Hg contents contours for gold. The calculations were carried out using thermochemical data of Craig and Barton (1973).

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