Minimization of Gibbs energy

Minimization of Gibbs energy and heterogeneous phase equilibria... 

The predictions of CO are based on a thermodynamic equilibrium computer program in which the chemical equilibrium compositions for assigned thermodynamic states are calculated. Most often temperature and pressure, calculated from the main CFD code, are used to specify the thermodynamic state. The method for evaluating the equilibrium compositions is based on the minimization of Gibbs energy as mentioned earlier (Wang et al., 2006). 

The fourth and final chapter in this voliune is given over to the determination, both experimentally and by computation, of the values of the parameters associated with chemical reactions. Thermochemistry for enthalpy, the determination of the entropies, specific heat capacities and Gibbs energy values ultimately lead to the determination of the equilibrium constants. Analysis of the different thermodynamic tables and methods for estimating unknown values enable us to proceed to the practical application and finally computation of the equilibria by the equilibrium constant method and minimization of Gibbs energy. 

In principle, aU chemical reactions are equilibrium reactions, but, as we shall see later, in practice, many are not. In aU chemical reactions, at equilibrium the reacting system has taken up the set of compositions that minimizes the Gibbs energy of the mixture of reactants and products, as described in Section 4.5.3 and Figure 4.12. Thus, all that we do in this chapter is apply Eq. 4.6, minimization of Gibbs energy, to chemical reaction equilibria. 

Example 12.1 Estimate the chemical equilibrium composition of a gaseous mixture of -butane and isobutane at 298.15 K and 1 bar, based on direct minimization of Gibbs energy. Assume that -butane and isobutane form an ideal solution of ideal gases at this T and P. 

In Chapter 6 we established that the criterion for spontaneity of a process is the minimization of Gibbs energy. It is interesting to look at the effect of the Margules parameter, A, on the total Gibbs energy of the system. Using Equations (7.47) and (6.22), we get ... 

ForVLE, LLE, and SLE, relate phase diagrams schematically to the Gibbs energy of each phase in the mixture using the minimization of Gibbs energy to determine the equilibrium state of the mixture. 

Given a set of species in a system, apply the Gibbs phase rule to determine how many independent reactions need to be specified to constrain the system. Write an appropriate set of reactions and solve them using the equilibrium constant formulation. Alternatively, solve for the equilibrium composition using the minimization of Gibbs energy. 

In this section, we will consider a specific example to illustrate how the same principle that we applied to solve phase equilibria problems also applies to chemical equilibria the minimization of Gibbs energy. As we have seen, Gibbs energy represents a trade-off between reducing the energy of a system and maximizing its entropy. 

Figure 9.3 Minimization of Gibbs energy for a reacting system of species 1, 2, and 3.

We can apply the general formalism developed so far to the criteria for chemical equilibrium. At constant temperature and pressure, the condition for equilibrium is the minimization of Gibbs energy. The change in Gibbs energy is given by Equation (6.16) ... 

Solution of Multiple Reaction Equilibria by Minimization of Gibbs Energy... 

Equations (9.45) and (9.47) represent a set of m + / equations that can be solved for the unknowns / and Aj. Example 9.22 shows how we solve the same problem we encountered in Example 9.19 using the minimization of Gibbs energy. Expressions similar to Equation (9.47) can be developed for real gases, liquids, and solids by using the appropriate form of the chemical potential. 

Reformulate the solution of Example 9.19 using the minimization of Gibbs energy. Compare... 

In this chapter, we learned how to calculate the equilibrium composition for a system undergoing a single chemical reaction or a set of reactions at a specified T, P, and initial composition. Our analysis was based on the principle that when a system reaches the equilibrium state, its Gibbs energy is a minimum. For a determined stoichiometry of a chemical reaction, the minimization of Gibbs energy leads to the following expression for the equilibrium constant, K ... 

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