Chemical equilibrium Gibbs energy relationship

Calculation of equilibrium conversions is based on the fundamental equations of chemical-reaction equilibrium, which in application require data for the standard Gibbs energy of reaction. The basic equations are developed in Secs. 15.1 through 15.4. These provide the relationship between the standard Gibbs energy change of reaction and the equilibrium constant. Evaluation of the equilibrium constant from thermodynamic data is considered in Sec. 15.5. Application of this information to the calculation of equilibrium conversions for single reactions is taken up in Sec. 15.7. In Sec. 15.8, the phase role is reconsidered finally, multireaction equilibrium is treated in Sec. I5.9.t... 

The relationship between the equilibrium constant Kc of a chemical reaction and the standard free energy (Gibbs energy)... 

Linear free energy relationship (LFER) — For various series of similar chemical reactions it has been empirically found that linear relationships hold between the series of free energies (-> Gibbs energy) of activation AG and the series of the standard free energies of reactions AGf, i.e., between the series of log fc (k -rate constants) and log K (Kt - equilibrium constants) (z labels the compounds of a series). Such relations correlate the - kinetics and -> thermodynamics of these reactions, and thus they are of fundamental importance. The LFER s can be formulated with the so-called Leffler-Grunwald operator dR ... 

This chapter introduces the second law of thermodynamics and THE Gibbs free-energy function. It also discusses the relationship BETWEEN Gibbs free energy and chemical equilibrium. 

The relationship between the chemical equilibrium constant K and the Gibbs free energy is... 

For two or more phases in equilibrium there is a separate equilibrium relationship for each of the chemical species present, and that relationship is that the partial molar Gibbs energy, called the chemical potential, for species i is the same in all of the phases (1, 2,. ..). The same statement applies to species j, k, and so on. 

K can often be calculated from the relationships of thermodynamics, if the Gibbs free energy for the chemical reaction can be obtained. For a gaseous reaction in which the equilibrium constant Kp is determined from equilibrium pressures of each component, the following expressions may be written ... 

Engineering systems mainly involve a single-phase fluid mixture with n components, subject to fluid friction, heat transfer, mass transfer, and a number of / chemical reactions. A local thermodynamic state of the fluid is specified by two intensive parameters, for example, velocity of the fluid and the chemical composition in terms of component mass fractions wr For a unique description of the system, balance equations must be derived for the mass, momentum, energy, and entropy. The balance equations, considered on a per unit volume basis, can be written in terms of the partial time derivative with an observer at rest, and in terms of the substantial derivative with an observer moving along with the fluid. Later, the balance equations are used in the Gibbs relation to determine the rate of entropy production. The balance equations allow us to clearly identify the importance of the local thermodynamic equilibrium postulate in deriving the relationships for entropy production. 

Understand the relationships among Gibbs free energy, chemical potential, reaction quotients (Q), the equilibrium constant, and the saturation index SI). 

An equation that describes the quantitative relationship between the enthalpy, the entropy and the equilibrium constant was developed by J. Willard Gibbs, a professor of mathematical physics at Yale in the late nineteeth century. He defined a new quantity, now called the Gibbs free energy (G), which describes the balance between the enthalpy and entropy factors for a chemical reaction. 

---