Equilibrium constant Gibbs function from

It is this calorimetric form of this equation (and the more complex equations that can be developed and used to describe sequential, parallel and more complex reacting systems) that can be analysed to yield values for the target parameters, n, k, H, K, G, S and E. References 6 and 7 provide details on the derivation of calorimetric kinetic equations and describe how to manipulate calorimetric data to determine equilibrium constants, Gibbs functions, entropies and activation energies. The approach described shows that, under normal storage conditions ( room temperature i.e. 298 K and ambient humidity), it is possible, from only 50 h of power time (the calorimetric output is of W vs. t) data, through these techniques, to distinguish between a... 

Let us apply Equation (6.8) to the two-phase liquid-vapor equilibrium requirement for a pure substance, namely p = p T) only. This applies to the mixed-phase region under the dome in Figure 6.5. In that region along a p-constant line, we must also have T constant. Then for all state changes along this horizontal line, under the p—v dome, dg = 0 from Equation (6.8b). The pure end states must then have equal Gibbs functions ... 

Figure 2.11 Equilibrium constant for the formation of DEG from EG as a function of temperature, calculated by using the Gibbs Reactor model of the commercial process simulator Chemcad (Chemstations)...

Now that we have considered the calculation of entropy from thermal data, we can obtain values of the change in the Gibbs function for chemical reactions from thermal data alone as well as from equilibrium data. From this function, we can calculate equilibrium constants, as in Equations (10.22) and (10.90.). We shall also consider the results of statistical thermodynamic calculations, although the theory is beyond the scope of this work. We restrict our discussion to the Gibbs function since most chemical reactions are carried out at constant temperature and pressure. 

The condition of Equation (13.7) can be met only if p,j = p,n, which is the condition of transfer equilibrium between phases. Or, to put the argument differently, if the chemical potentials (escaping tendencies) of a substance in two phases differ, spontaneous transfer will occur from the phase of higher chemical potential to the phase of lower chemical potential, with a decrease in the Gibbs function of the system, until the chemical potentials are equal (see Section 10.5). For each component present in aU p phases, (p 1) equations of the form of Equation (13.7) provide constraints at transfer equilibrium. Furthermore, an equation of the form of Equation (13.7) can be written for each one of the C components in the system in transfer equUibrium between any two phases. Thus, C(p — 1) independent relationships among the chemical potentials can be written. As chemical potentials are functions of the mole fractions at constant temperamre and pressure, C(p — 1) relationships exist among the mole fractions. If we sum the independent relationships for temperature. 

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. 

The critical thermochemical quantities for prediction of propeUant performance are the enthalpies of formation of the product and to a degree the reactant species. The enthalpy of formation is essential to the calculation of the enthalpy of reaction and since it also appears in the expression for the equilibrium constant, as it is the basis for relating the Gibbs functions of different species, influences the calculated product equilibrium compositions. It is most desirable to measure enthalpies of formation directly from calorimetric experiments, but often the enthalpies must be... 

The Gibbs energy function change for this reaction was calculated at 100 K invervals from 500 to 1100 K. At e ch temperature, the equilibrium constant was assumed to be 1, and A H(298.15 K) accordingly calculated. These values a d th enthalpy of formation of ZrBr (g) [see ZrBr table] were used to compute a series of values for the standard enthalpy ofJ... 

When processes are conducted at constant T and P, the criteria for spontaneity and for equilibrium are stated more conveniently in terms of another state function called the Gibbs free energy (denoted by G), which is derived from S. Because chemical reactions are usually conducted at constant T and constant P, their thermodynamic description is based on AG rather than AS. This chapter concludes by restating the criteria for spontaneity of chemical reactions in terms of AG. Chapter 14 shows how to identify the equilibrium state of a reaction, and calculate the equilibrium constant from AG. 

The most important thermodynamic property of a substance is the standard Gibbs energy of formation as a function of temperature as this information allows equilibrium constants for chemical reactions to be calculated. The standard Gibbs energy of formation A ° at 298.15 K ean be derived from the enthalpy of formation Aff° at 298.15 K and the standard entropy AS° at 298.15 K from... 

We take the reaction CH4 -I- H2O CO -F 3H2 as an example to calculate the equilibrium constants Kp and Ky (This reaction is important for syngas production from natural gas by steam reforming. Section 6.2.) The standard Gibbs function of reaction is ... 

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