Thermochemical data, calculating equilibrium constant from

Substituting the balance relations into equation (4.10) and calculating the equilibrium constant from the given thermochemical data we obtain the algebraic equation... 

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. 

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 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. 

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. 

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... 

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 ... 

Calculated mostly from thermochemical data (Wagman et ah, 1982). Data for HC1 are from Fritz and Fuget (1956) data for HN03 from Schwartz and White (1981) rate coefficients were taken from the compilation of Graedel and Weschler (1981) equilibrium constant for reaction A9 from Deister et al. (1986). Powers of 10 are shown in parentheses. b M = mol/liter. c For T= 283 K. d In units of mol/liters. 

The third law of thermodynamics, like the first and second laws, is a postulate based on a large number of experiments. In this chapter we present the formulation of the third law and discuss the causes of a number of apparent deviations from this law. The foundations of the third law are firmly rooted in molecular theory, and the apparent deviations from this law can be easily explained using statistical mechanical considerations. The third law of thermodynamics is used primarily for the determination of entropy constants which, combined with thermochemical data, permit the calculation of equilibrium constants. 

Thus the equilibrium constant at temperature T can be computed from thermochemical data which determine the coefficients AT and which, with the aid of the third law, determine AS. The quantity AH is evaluated by use of an experimentally determined value of AH or K at a given temperature. We note that, at low temperatures, the coefficients of the temperature expansion of the heat capacity at constant pressure of pure component / at 1 atm pressure, rather than the zero-pressure limit, are usually used in the calculation of the equilibrium constant. 

Knowledge of the thermodynamics of HDT reactions is necessary for predicting chemical equilibrium. Detailed thermochemical data on individual reactions of complex feedstocks are generally unavailable [24]. The literature offers some generalizations about each type of reaction made from theoretical calculations and few experimental studies with model compounds. For modeling proposes, the equilibrium constants are usually approximated using group contribution methods. 

This relation is usually called detailed balance relation. The equilibrium constant may be calculated from idependent thermochemical and spectroscopic data. These calculations often utilize the following expression of statistical thermodynamics... 

For the sake of illustration we have calculated the equilibrium composition of a mixture, formed by decomposition of methane with steam at an initial ratio of 1 2 moles, 900 K and in the 10 to 1000 atm range. Thermochemical data for CH4, H2O, H2, CO will be found in Example 10, for CO2 in Example 11. The calculation was performed according to relations (6.96) — (6.102), constants of the Beattie-Bridgman equation are given in Appendix 11 for the individual pure constituents. The results are plotted in Fig. 24. It will be seen from the plot, that for all constituents 900 K is a high enough temperature for deviations from ideal behaviour to become apparent only at elevated pressure. 

We have adopted a vialue of AHS(CF2,g,298) = -44.6 kcal/mol from the data of Modica and LeGraff (16,17) and of Carlson (19). This yields values of the equilibrium constant for reaction t ) with in a factor of two of those calculated from the data of Farber et (21), which is certainly within the accuracy of both the experiment and the limits of the rigid-rotor, harmonic oscillator approximation at 2000 to 2500 K ( ). The physical and thermochemical data selected here are sumnarized in Table II and the ideal gas thermodynamic functions calculated to 1500 K from these data are summarized in Table III. 

Howard (1980) has recently determined and in the temperature range 230-1270 K using a flow reactor and laser magnetic resonance measurements of HO2, OH, NO, and NO2. The data for ki and were also used to obtain the equilibrium constant K = k /k-i). Calculated values of K together with the thermochemical data of OH, NO, and NO2 were used to obtain an improved heat of formation for H02(A// 29s(H02) = 2.5 0.6 kcal/mol) which differs significantly from the value previously suggested by JANAF (AH 29s(H02) = 5 2 kcal/mol). 

The most common thermochemical data available to calculate the equilibrium constant are in the form of the Gibbs energy of formation, Agf Appendix A.3 shows some representative values for 25°C and 1 bar. The Gibbs energy of formation is defined analogously to the enthalpy of formation, introduced in Section 2.6. It is equal to the Gibbs energy of reaction when the species of interest is formed from its pure elemental constituents, as found in nature, that is,... 

Like the equilibrium constant, is obtained from thermochemical data. Since the overall reaction in the electrochemical cell is composed of two half-reactions, we can tabulate electrochemical data in terms of half-reactions. We then simply add together the appropriate reduction and oxidation half-reactions to calculate E for the entire electrochemical cell. 

Each equilibrium constant can be found by using appropriate thermochemical data, as discussed in Section 9.4. Once values for Ki and are obtained. Equations (E9.18C) and (E9.18D) can be solved for unknowns and 2- Notice that the specific values given by will differ from that given by Equation (E9.16D) hence the value of 2 will also be different. However, the compositions that are calculated will turn out identical to those in Example 9.16. This result illustrates the magic of chemical reaction equilibria No matter what set of independent reactions we pick, the equilibrium compositions that are calculated remain the same. 

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