Gibbs free energy approach

FIGURE 8.4 The variation of the molar Gibbs free energy of an ideal gas with pressure. The Gibbs free energy has its standard value when the pressure of the gas is 1 bar. The value of the Gibbs free energy approaches minus infinity as the pressure falls to zero. 

There are two basic approaches to the solution of a species distribution problem (1) The equilibrium constant approach, and (2) the Gibbs free energy approach. Most... 

Gibbs free energy approach. The change in the Gibbs free energy for selected processes was also used to assess the stability of compounds and the dissolution sequence. For an equation such as Eq. (1) above, the free energy of the reaction is calculated as... 

Gibbs free energy of reaction depends on the composition of the reaction mixture and how it changes as the reaction approaches equilibrium. 

BrCl(g), K = 0.2. Construct a plot of the Gibbs free energy of this system as a function of partial pressure of BrCl as the reaction approaches equilibrium. 

If we were to place a piece of zinc metal into an aqueous copper(II) sulfate solution, we would see a layer of metallic copper begin to deposit on the surface of the zinc (see Fig. K.5). If we could watch the reaction at the atomic level, we would see that, as the reaction takes place, electrons are transferred from the Zn atoms to adjacent Cu2 r ions in the solution. These electrons reduce the Cu2+ ions to Cu atoms, which stick to the surface of the zinc or form a finely divided solid deposit in the beaker. The piece of zinc slowly disappears as its atoms give up electrons and form colorless Zn2+ ions that drift off into the solution. The Gibbs free energy of the system decreases as electrons are transferred and the reaction approaches equilibrium. However, although energy is released as heat, no electrical work is done. 

Naslain, R., Thebault, J., Hagenmuller, P., and Bernard, C., The Thermodynamic Approach to Boron CVD Based on the Minimization of the Total Gibbs Free Energy, J. Less Common Metals, 67(1) 85-100 (1979)... 

The equilibrium state is generated by minimizing the Gibbs free energy of the system at a given temperature and pressure. In [57], the method is described as the modified equilibrium constant approach. The reaction products are obtained from a data base that contains information on the enthalpy of formation, the heat capacity, the specific enthalpy, the specific entropy, and the specific volume of substances. The desired gaseous equation of state can be chosen. The conditions of the decomposition reaction are chosen by defining the value of a pair of variables (e.g., p and T, V and T). The requirements for input are ... 

Semianalytical mean-field theories of block copolymer micellization were formulated by Noolandi et al. [ 197] and by Leibler et al. [198]. In the approach of Noolandi et al., the micellar characteristics were obtained through a minimization of the Gibbs free energy for an isolated micelle. This was applied to PS-PB micelles, and the obtained theoretical values were in good agreement with the experimental ones. 

Typically, solving (5.151) to find fc(oo ) is not the best approach. For example, in combusting systems Srp(0 4)1 < 1 so that convergence to the equilibrium state will be very slow. Thus, equilibrium thermodynamic methods based on Gibbs free-energy minimization are preferable for most applications. 

An entirely different approach to equilibrium adsorption is to assume that adsorbed layers behave like liquid films, and that the adsorbed molecules are free to move over the surface. It is then possible to apply the equations of classical thermodynamics. The properties which determine the free energy of the film are pressure and temperature, the number of molecules contained and the area available to the film. The Gibbs free energy G may be written as ... 

So far, we have seen several ways of calculating the Gibbs free energy of a two-component mixture. To extend calculations to ternary and higher-order mixtures, we use empirical combinatory extensions of the binary properties. We summarize here only some of the most popular approaches. An extended comparative appraisal of the properties of ternary and higher-order mixtures can be found in Barron (1976), Grover (1977), Hillert (1980), Bertrand et al. (1983), Acree (1984), and Fei et al. (1986). 

Figure 5.11 Gibbs free energy of mixing in binary join Mg2Si04-Ca2Si04 dXT = 600 °C and P = bar, calculated with a static interionic potential approach. Reprinted from G. Ottonello, Geochimica et Cosmochimica Acta, 3119-3135, copyright 1987, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

A recent paper gives a method for the calculation of the Gibbs free energy changes and heats of reaction for the formation of amide bonds in the solid-to-solid approach [47]. 

For the present a, is expressed in mole fraction units. We see, therefore, that /x, approaches as a, approaches unity. Furthermore, since fi, is the partial molal Gibbs free energy, Equation (5) also applies to fx, provided we replace V with V the partial molal volume of component i ... 

---