Temperature thermochemical data

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).

Since rates of arsenic redox reactions are slow at room temperature (5), it is assumed that the oxidation state data represent adjustment of arsenic species to the electron activity of the solution at 300°C. A quantitative assessment of the Eh of the basalt-water system at 300°C requires high-temperature thermochemical data for aqueous arsenic species. Such data are not available and, therefore, approximations were used to calculate Eh at 300°C. 

Structure, and the a-polymorph adopts a bcc lattice. Phases that form at high temperatures may be quenched to lower temperatures (i.e. rapidly cooled with retention of structure), allowing the structure to be determined at ambient temperatures. Thermochemical data show that there is usually very little difference in energy between different polymorphs of an element. 

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. 

The absorption wavelengtlrs quoted here are for the complete dissociation of these molecules to the atoms in their ground state. The thermochemical data also show that a temperature of nearly 4000 K is requhed before the atomic oxygen concentration is equal to that of molecular oxygen, and almost 7000 K for the nitrogen atom population to be equal to the molecular nitrogen concentration, at one atmosphere pressure. 

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.,... 

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 ... 

Most thermochemical data are reported for 25°C (more precisely, for 298.15 I<). Temperature is not part of the definition of standard states we can have a standard state at any temperature 298.15 K is simply the most common temperature used in tables of data. All reaction enthalpies used in this text are for 298.15 K unless another temperature is indicated. 

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 range of temperatures for each alteration zone can be estimated from the following chemical reactions and thermochemical data available for these reactions... 

From (1-79) it is clear that the Hg content of electrum is related to /sj and A l-vg. Using the thermochemical data for reaction (1-78) by Barton and Skinner (1979), isoactivity lines for Hg in electrum may be drawn on a log/sj-temperature diagram (Fig. 1.175). At a given temperature, the activity of Hg in electrum increases with a decrease in /sj. Therefore, the /sj for the mercurian gold of the Tsugu deposit is inferred to be relatively low. 

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).

Iso-FeS content lines for sphalerite in equilibrium with pyrite or pyrrhotite were drawn on the log/sj-temperature diagram (Figs. 1.179 and 1.180) using thermochemical data by Scott and Bames (1971) and Barton and Skinner (1979). 

The relationship between the iron content of stannite in equilibrium with sphalerite and pyrite or with sphalerite and pyrrhotite was derived based on thermochemical data by Scott and Barnes (1971), Barton and Skinner (1979) and Nakamura and Shima (1982). These types of deposits are skam-type polymetallic (Sn, W, Cu, Zn, Pb, Au, Ag) vein-type and Sn-W vein-type deposits. As shown in Fig. 1.181, the /s -temperature range for each type of deposits is different at a given temperature, /sj increases from Sn-W vein-type through skam-type to polymetallic vein-type deposits. It is interesting to note... 

Figure 1.189. The relationship between tAuCl / Au(HS)" temperature. Hatched and dotted areas represent the probable geochemical environment for typical Japanese gold-silver vein and auriferous vein deposits, respectively. A, mci- = 10, mK+ =2, qh2S = 10, K-feldspar/K-mica/quartz equilibrium B, mQ- = 1. niK+ =0.2, H2S = 10 - , K-feldspar/K-mica/quartz equilibrium C, mci- — 1, Wk+ =0.2, qh2S = 10, K-feldspar/K-mica/quartz equilibrium D, mci- =0.2, mK+ =0.04, oh2S = 10 , K-feldspar/K-mica/quartz equilibrium E, mci- =0.2, m <+ =0.04, uh s = 10 K-feldspar/K-mica/quartz equilibrium F, mci- =0.2, = 0.04, UHiS = 10 , K-feldspar/K-mica/quartz equilibrium. Thermochemical data for the calculations were taken from Helgeson (1969), Seward (1973), Drummond (1981), and Henley et al. (1984). (Shikazono and Shimizu, 1987).

This equation shows that activity of Ca + is related to pH, concentration of H2CO3 and temperature. Because pH is related to the concentration of Cl for the equilibrium curves 1 and 2 in Fig. 2.14, the relationship between the concentrations of Ca " " and Cl" can be derived for calcite-albite-sericite-K-feldspar-quartz equilibrium (curves 4 and 7 in Fig. 2.14) and calcite-albite-sericite-Na-montmorillonite-quartz equilibrium (curves 5 and 8 in Fig. 2.14) with constant w2h2C03- The range of zh2C03 in the solution in equilibrium with calcite is assumed to be 10 to 10 . The other equilibrium curves for the assemblage including Ca minerals are also drawn (Fig. 2.14). These assemblages are wairakite-albite-sericite-K-feldspar-quartz (curve 3), Ca-montmotillonite-albite-sericite-Na-montmorillonite-quartz (curve 6), Ca-montmorillonite-albite-sericite-K-feldspar-quartz (curve 9) and anhydrite (curve 10). The effect of solid solution on the equilibrium curves is not considered because of the lack of thermochemical data of solid solution. 

In order to have a consistent basis for comparing different reactions and to permit the tabulation of thermochemical data for various reaction systems, it is convenient to define enthalpy and Gibbs free energy changes for standard reaction conditions. These conditions involve the use of stoichiometric amounts of the various reactants (each in its standard state at some temperature T). The reaction proceeds by some unspecified path to end up with complete conversion of reactants to the various products (each in its standard state at the same temperature T). 

For the gas-phase, second-order reaction C2H4 + C4H6 - CgHio (or A + B - C) carried out adiabatically in a 2-liter experimental CSTR at steady-state, what should the temperature (T/K) be to achieve 40% conversion, if the (total) pressure (P) is 1.2 bar (assume constant), the feed rate (q0) is 20 cm3 s-1, and.. the reactants are equimolar in the feed. The Arrhenius parameters are EA = 115,000 J mol-1 and A =3.0x 107L mol-1s-1 (Rowley and Steiner, 1951 see Example 4-8). Thermochemical data are as follows (from Stull et al., 1969) ... 

Based on the reaction network in Example 18-8, calculate and plot the temperature (7)-volume (V) profile and the concentration (c,)-volume profiles for a set of independent species in a PFR operated adiabatically. Consult the paper by Spencer and Pereira (1987) for appropriate choice of feed conditions and for kinetics data For thermochemical data, consult the compilation of Stull et al. (1969), or an equivalent one. 

Since the reverse of the reaction Nl is the ionisation of the ester, the equilibrium position for any one system depends critically on the nature, especially the polarity, of the solvent, which determines the AHS terms. The accumulation of the necessary thermochemical data is essential to a rationalisation of the relation between cationic and pseudocationic polymerisations but the prevalence of the former at low temperatures and of the latter at high temperatures is surely related to the fact that the dielectric constant, and with it solvation energies, increases as the temperature of a polar solvent is reduced, so that decreasing temperature favours ionisation. 

Although molalities are simple experimental quantities (recall that the molality of a solute is given by the amount of substance dissolved in 1 kg of solvent) and have the additional advantage of being temperature-independent, most second law thermochemical data reported in the literature rely on equilibrium concentrations. This often stems from the fact that many analytical methods use laws that relate the measured physical parameters with concentrations, rather than molalities, as for example the Lambert-Beer law (see following discussion). As explained in section 2.9, the equilibrium constant defined in terms of concentrations (Kc) is related to Km by equation 14.3, which assumes that the solutes are present in very small amounts, so their concentrations (q) are proportional to their molalities nr, = q/p (p is the density of the solution). 

The equilibrium constants, Kj, may be evaluated as functions of temperature using readily available thermochemical data. 

The reader should refer to the original tables for the reference material on which the thermochemical data are based. The reference state used in Chapter 1 was chosen as 298 K consequently, the thermochemical values at this temperature are identified from this listing. The logarithm of the equilibrium constant is to the base 10. The unit notation (J/K/mol) is equivalent to (JK mol ). Supplemental thermochemical data for species included in the reaction listing of Appendix C, and not given in Table A2, are listed in Table A3. These data, in combination with those of Table A2, may be used to calculate heats of reaction and reverse reaction rate constants as described in Chapter 2. References for the thermochemical data cited in Table A3 may be found in the respective references for the chemical mechanisms of Appendix C. 

Thermochemical data are also available from the Internet. Some examples are the NIST Chemical Kinetics Model Database (http //kinetics.nist. gov/CKMech/), the Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion (A. Burcat and B. Ruscic, ftp //ftp. technion.ac.il/pub/supported/aetdd/thermodynamics/), and the Sandia National Laboratory high-temperature thermodynamic database (http //www.ca.sandia. gov/HiTempThermo/). 

Fei Y. and Saxena S. K. (1986). A thermochemical data base for phase equilibria in the system Fe-Mg-Si-O at high pressure and temperature. Phys. Chem. Minerals., 13 311-324. 

Though the above equations are nonlinear and complex, 1 and tij may be computed for any combustion reaction for which thermochemical data are available. In the following, the reaction -t Oj at 2 MPa is used to demonstrate a representative computation, illustrating the procedure for the determination of T)-and rij and reiterating the principles of thermochemical equilibrium and adiabatic flame temperature. Eirst, the following reaction scheme and products are assumed ... 

More and better solubility data for simple and complex oxides (glasses, UO2 matrices) at elevated temperatures and pressures and improved techniques for measuring small solubilities. Solubility data for simple oxides provide thermochemical data, free energies in particular, which allow prediction of solubilities for complex oxides. Solubility data for some complex oxides are also necessary in order to verify the methods of predictions for complex oxides and establish key points. 

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