Thermochemical data equilibrium constants

Based on JANAF or equivalent thermochemical data, equilibrium constants were calculated for the gas-phase equilibria ... 

Thermochemical Data. Equilibrium considerations significantly limit alcohol yield at low pressures in the vapor-phase process (116). Consequently, conditions controlling equilibrium constants have been determined and give the following relation, where Tis in K (116,117) ... 

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. 

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). 

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. 

From the standard thermochemical data ArG° = (—371.3 — 379.9 + 733.9) kJ mol-1 = —17.3 kJmol-1, corresponding to an equilibrium constant K = 1.1 x 103 M-1. This is a worrying result because all peptides in solution at 298 K should spontaneously fall apart to the monomers and hence all proteins are subject to degradation due to spontaneous hydrolysis. Fortunately, the reaction is kinetically hindered, which means that it occurs very slowly. Kinetics always control the rate at which equilibrium is achieved, relating the ratio of the forward and backward rate constants to the equilibrium constant ... 

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. 

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

The forces of a number of expls were detd experimentally when they deflagrated or burned, but no reliable direct measurements of forces produced on detonation have been obtd. However, it is possible to calculate the forces from thermochemical data. Some of these data were obtd by an analysis of die band spectra of the various molecules concerned by quantum-mechanical methods, which permitted one to calculate die specific heats and equilibrium constants as functions of the temperature. Others obtd by direct measurements of the heats of formation of the various substances from their elements. 

On the basis of the following thermochemical data, (a) calculate the equilibrium constant K° for the formation of gaseous nickel tetracar-bonyl from Ni and CO under standard conditions (b) estimate the temperature at which K° becomes unity and (c) explain how this and other related information can be applied in the refining of nickel. 

Determine the equilibrium constants Kp and Kc and the rate constant for the reverse reaction kr at 1200 K. Express any factors involving species concentrations in the units implied by kf (i.e., mole/cm3). You may use thermochemical data from Table 9.1. 

Thermochemical properties of gas-phase, surface, and bulk species are assumed to be available. This information is used in the calculation of the equilibrium constant, Eq. 11.110, and thus the reverse rate constant, Eq. 11.108. There is not a great deal of thermochemical data for species on surfaces, but techniques are becoming available for their calculation (e.g., Pederson et al. [310]). If surface reactions are specified to be irreversible, or if Arrhenius coefficients for the reverse rate constant are explicitly supplied, then the thermochemical data are not actually used. 

Since this review was completed a paper by Coomber and Whittle4111 has appeared in which they measured the equilibrium constant for C2F6 plus Br2 with CF3Br between 621 and 722°C. From a third law method they deduced the enthalpy of reaction. When combined with other thermochemical data, this result led to D CF3—CF3 = 96.5+1.0 kcal/mole or = —321.7 kcal/mole. 

In previous chapters, we discussed two different ways to determine the value of an equilibrium constant K from concentration data (Section 13.2) and from thermochemical data (Section 17.11). In this section, we ve added a third way from electrochemical data. The following are the key relationships needed for each approach ... 

Figure 8. Temperature dependence of the equilibrium constant, Kp = p(HtO)/ p(Ht) for the reduction of several metal oxides often present in Tokamak walls. The Kp values are calculated from thermochemical data listed in Ref. 51. The reduction curve for NiO, the most prevalent metal oxide on Inconel alloys, lies above the FeO curve, and thus is more easily reduced in hydrogen than the oxides shown. (Reproduced, with permission, from Ref. 37. Copyright 1980, North-...

Kerr and Parsonage (1972a, b) in their invaluable compendium of kinetic data have used the A-factor of the reverse decomposition reaction A, together with the equilibrium constant and thermochemical data to estimate the A-factors of the addition reactions. Thus, for reaction (17) it can readily be shown that the overall enthalpy and entropy changes in the reaction are given by (18) and (19) respectively. From (19) A, can be calculated if A, and AS° are... 

Based upon experimentally observed spectroscopic data, statistical thermodynamic calculations provide thermodynamic data which would not be obtained readily from direct experimental measurements for the species and temperature of interest to rocket propulsion. If the results of the calculations are summarized in terms of specific heat as a function of temperature, the other required properties for a particular specie, for example, enthalpy, entropy, the Gibb s function, and equilibrium constant may be obtained in relation to an arbitrary reference state, usually a pressure of one atmosphere and a temperature of 298.15°K. Or alternately these quantities may be calculated directly. Significant inaccuracies in the thermochemical data are not associated generaUy with the results of such calculations for a particular species, but arise in establishing a valid basis for comparison of different species. 

It should be kept in mind that the calculation of the equilibrium constant is subject to high sensitivity to small errors in thermochemical data due to its exponential dependency to the standard Gibbs free energy variation, as expressed by the relation ... 

The thermodynamic analysis of a system of stoichiometric equations is directed to the calculation of reaction enthalpies whose knowledge is necessary for energy balances and to the determination of equilibrium constants in order to evaluate the limitations of the yield and selectivity enforced by thermodynamic laws. There are numerous standard or advanced textbooks dealing with these questions, as well as many authoritative reviews of thermochemical data. Thus, only two points will be mentioned here. 

In molecular reaction schemes, only stable molecular reactants and products appear short-lived intermediates, such as free radicals, are not mentioned. Nearly all the reactions written are considered as pseudo-elementary processes, so that the reaction orders are equal to the mol-ecularities. For some special reactions (such as cocking) first order or an arbitrary order is assumed. Pseudo-rate coefficients are written in Arrhenius form. A systematic use of equilibrium constants, calculated from thermochemical data, is made for relating the rate coefficients of direct and reverse reactions. Generally, the net rate of the reversible reaction... 

To estimate the isomerization rate coefficients, eqn 5.8 is applied to the time required for close approach to the straight-line behavior of the first-order curves. Judging this time to be about 25 minutes for a 90% approach to the steady-state isomer distribution, eqn 5.8 yields k 0.1 min-1. With this value and an isomerization equilibrium constant Kn = 20 at 150°C calculated from thermochemical data [5,6] (with 2-cis and 2-trans pentene lumped into a single pseudo-component), eqns 5.40 give as rough estimates... 

Key words critically evaluated data enthalpy enthalpy of formation entropy equilibrium constant of formation Gibbs energy function Gibbs energy of formation heat capacity thermochemical tables. 

The reverse rate constants for the elementary reactions used in the present work were caJculated from the forward rate constants and the equilibrium constant by assuming microscopic reversibility. Standard states used in tabulations of thermodynamic data are invariably at 1 atm and the temperature of the system. Since concentration units were required for rate constant calculations, a conversion between Kp and Kc was necessary. Values of Kp were taken from the JANAF Thermochemical tables (1984). Kc was calculated from the expression ... 

In the field of radioactive waste management, the hazardous material consists to a large extent of actinides and fission and activation products from nuclear reactors (such is the case of the fission product Se). The scientific literature on thermodynamic data, mainly on equilibrium constants and redox potentials in aqueous solution, has been contradictory in a number of cases. A critical and comprehensive review of the available literature is necessary in order to establish a reliable thermochemical database that fulfils the requirements of a proper modelling of the behaviour of the actinide and fission and activation products in the environment. 

---