Chemical Gibbs energy minimization

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

Two approaches to the treatment of large systems have been developed the Gibbs energy minimization method and the equilibrium constant approach. Both are based on a knowledge of the chemical potentials of species under standard conditions and under actual conditions of composition of conditions in the chemical system. In the Gibbs energy minimization approach (Clason,... 

The mathematical formulation leads to a constrained Gibbs energy minimization problem, subject to conservation of the total amounts of the individual chemical elements that make up the chemical species This constraint is incorporated into the problem via the method of Lagrange multipliers Details of the procedure are given elsewhere W ... 

To accommodate the possible chemical reactions of the ongoing corrosion process, the calculated concentrations at c (t -i- At) (cfin Fig. 32.3) must be corrected according to the local thermodynamic equilibrium. For this purpose, the concentrations c (t + At) are transferred into a thermodynamic subroutine ThermoScript [10], which contains the commercial program ChemApp [11]. ChemApp is based on a numerical Gibbs energy minimization routine in combination with tailor-made databases [12]. In order to avoid excessive calculation times, the parallel-computing system PVM (parallel virtual machine) is used, i.e., ThermoScript distributes the individual... 

Choose Chemical Reaction Equilibria from the ThermoSolver main menu, then choose the Reaction Equilibria Calculations. The reaction equilibria program solves for the composition of a reacting system at equilibrium, using the Gibbs energy minimization method discussed in Section 9.6. The software is limited to gases and solids. 

The stoichiometric coefficients i9, are positive for products and negative for reactants. The Gibbs energy of the system of products and reactants must be minimal at equilibrium. If this condition is combined with the mass balance that is imposed by eq.(2.4-3) we get the general thermodynamic condition for chemical equilibrium ... 

The calculation of the equilibrium composition of a system of chemical reactions with equcalcc is based on minimizing the Gibbs energy subject to the conservation condition An = nc. This is accomplished by using a Lagrangian L defined by... 

The study of chemical equilibrium can detect thermodynamic constraints on the achievable conversion and selectivity. In this section we make use of the Gibbs free-energy minimization method available in Aspen Plus [9], We assume that both cyclohexanone and cyclohexanol are products. The curves in Figure 5.2 show the evolution of the phenol equilibrium conversion, yield and selectivity with the ratio hydrogen/phenol at temperatures of 180, 200, 220 °C and a pressure of 3 bar. 

Inside the reactive zone, chemical and phase equilibrium occur simultaneously. The composition of phases can be found by Gibbs free-energy minimization. The UNIQUAC model is adopted for phase equilibrium, for which interaction parameters are available, except the binary fatty-ester/water handled by UNIFAC-Dortmund. 

Complex Chemical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

One approach to computing the equilibrium composition of a system involves minimizing the total Gibbs energy of the system, for example, minimizing an expression such as equation 48, subject to the material balance constraints and others of the system. Thus it is essential in applying this approach to know the bahavior of the chemical potentials as a function of system parameters, namely, p, T, and composition. 

As previously mentioned, the Gibbs free energy of a chemical system is minimized at equilibrium. At equilibrium, the forward and reverse reactions of a chemical reaction, such as given in Eq. [1-8], are necessarily occurring at the same rate, and the change in Gibbs free energy is zero ... 

Bernard et al.221, have calculated the CVD phase diagrams for several silicide systems. These phase diagrams are based on a calculation which minimizes the Gibbs energy for a certain fixed amount of chemical species. Although very helpful, we should keep in mind the following limitations ... 

In the text, we focused our attention on minimizing Gibbs energy to determine the chemical equilibrium at fixed temperature and pressure. To be fair to the other energy functions, what system function would be at an extremum (maximum or minimurn) if the following were specified. Provide a short derivation verifying your result starting with the second law, dSm > 0. 

Stability criteria are discussed within the framework of equilibrium thermodynamics. Preliminary information about state functions, Legendre transformations, natural variables for the appropriate thermodynamic potentials, Euler s integral theorem for homogeneous functions, the Gibbs-Duhem equation, and the method of Jacobians is required to make this chapter self-contained. Thermal, mechanical, and chemical stability constitute complete thermodynamic stability. Each type of stability is discussed empirically in terms of a unique thermodynamic state function. The rigorous approach to stability, which invokes energy minimization, confirms the empirical results and reveals that r - -1 conditions must be satisfied if an r-component mixture is homogeneous and does not separate into more than one phase. 

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