Gibbs phase rule applications

Finally, it should be pointed out that the. Gibbs phase rule, as developed in Sec. 8.9. does not apply to osmotic equilibrium. This is because (1) the total pressure need not be the same in each phase (cell), so that Eq. 8.9-2 is not satisfied, and (2) the equality of partial molar Gibbs energies in each phase (cell) does not apply to all species, only to those that can pass through the membrane. A form of the Gibbs phase rule applicable to osmotic equilibrium can be easily developed (Problem 11.5-2). 

The application of n additional thermodynamic potentials (of electric, magnetic or other origin) implies that the Gibbs phase rule must be rewritten to take these new potentials into account ... 

Cistola, D. P, Hamilton, J. A., Jackson, D., and Small, D. M. (1988). Ionization and phase-behavior of fatty-acids in water. Application of the Gibbs phase rule. Biochemistry, 27, 1881-8. 

This typical application of the second kind is the Gibbs Phase Rule (for inert systems). This rule is often stated merely for systems with only two external coordinates (n = 2, e.g., xt = P,x2 = T). There must then be no internal partitions within the system, nor may it, for instance, contain magnetic substances in the presence of external magnetic fields. 

See Section 4.1.5 for other examples of how Gibbs Phase Rule works in the methane + water phase diagram. Section 5.2 shows the application of the Gibbs Phase Rule for hydrate guests of methane, ethane, propane, and their mixtures. 

Applications of the Gibbs-Duhem equation and the Gibbs phase rule... 

The lacking special description of the Gibbs phase rule in MEIS that should be met automatically in case of its validity is very important for solution of many problems on the analysis of multiphase, multicomponent systems. Indeed, without information (at least complete enough) on the process mechanism (for coal combustion, for example, it may consist of thousands of stages), it is impossible to specify the number of independent reactions and the number of phases. Prior to calculations it is difficult to evaluate, concentrations of what substances will turn out to be negligibly low, i.e., the dimensionality of the studied system. Besides, note that the MEIS application leads to departure from the Gibbs classical definition of the notion of a system component and its interpretation not as an individual substance, but only as part of this substance that is contained in any one phase. For example, if water in the reactive mixture is in gas and liquid phases, its corresponding phase contents represent different parameters of the considered system. Such an expansion of the space of variables in the problem solved facilitates its reduction to the CP problems. 

The example that follows illustrates the application of the Gibbs phase rule to several simple systems. The remainder of the chapter presents the equilibrium relationships that are used to determine the remaining intensive system variables once the allowed number of these variables has been specified. 

The Gibbs phase rule shows that specifying temperature and pressure for a two-component system at equilibrium containing a solid solute and a liquid solution fixes the values of all other intensive variables. (Verify this statement.) Furthermore, because the properties of liquids and solids are only slightly affected by pressure, a single plot of solubility (an intensive variable) versus temperature may be applicable over a wide pressure range. 

The system is constrained to obey the Gibbs Phase Rule. In the most common application, with methane (or a fixed gas composition) and water, the two components will form the three phases of hydrates, vapor, and liquid with one degree of fi eedom. Fixing the temperature (or the pressure) determines the pressure (or the temperature) at the three-phase condition. 

The principal design and operating variables in the single-stage process are pressnre, temperature, and L/Y (liquid/vapor) ratio. Application of Gibbs phase rule shows that these three variables are not entirely independent fixing two of them automatically fixes the third. Ordinarily, two of the variables are specified, and computations are employed to determine the value of the third variable as well as the compositions of the vapor and liquid products. 

Is the problem well-posed This issue concerns whether we have enough information to compute the required unknowns. In phase and reaction-equilibrium computations, this issue is resolved by a proper application of the generalized phase rule it might not be properly resolved by a routine application of the Gibbs phase rule. In particular, we have discussed two kinds of subtleties that are often overlooked. 

In this chapter we will consider not only the traditional Gibbs phase rule, but how it becomes modified or extended when aqueous solutes are included in the phase compositions. We then have a look at buffered systems, which are essentially an application of the phase rule. 

Phase rule applications merit the same attention. According to Gibbs ... 

Gibbs phase rule, which pertains to the external intensive values and the composition variables. This law is applicable both to open and to closed... 

The application of the Gibbs phase rule to multicomponent systems containing c components may he done by extending the treatment used for the unary system in Section 1.2.1.1. Again let ip represent the number of... 

We start by extending the Gibbs phase rule to multiple-component systems, in its most general form. We will confine our development of multiple-component systems to relatively simple ones, having two or three components at most. However, the ideas we will develop are generally applicable, so there will be little need to consider more complicated systems here. One example of a simple two-component system is a mixture of two liquids. We will consider that, as well as the characteristics of the vapor phase in equilibrium with the liquid. This will lead into a more detailed study of solutions, where different phases (solid, liquid, and gas) will act as either the solute or solvent. 

Equation 7.3 is the more complete Gibbs phase rule. For a single component, it becomes equation 6.19. Note that it is applicable only to systems at equilibrium. Also note that although there can be only one gas phase, due to the mutual solubility of gases in each other, there can be multiple liquid phases (that is, immiscible liquids) and multiple solid phases (that is, independent, nonalloyed solids in the same system). 

An understanding of the Gibbs phase rule for multicomponent systems allows us to consider specific multicomponent systems. We will focus on two-component systems for illustration, although the concepts are applicable to systems with more than two components. 

Historically, one of the main contributions of J. W. Gibbs to the development of thermodynamics was his extension of G = H TS to open systems. This is an important consideration for onstream processes encountered by chemical engineers. We have already introduced the concept of the chemical potential, p., = (Gilni), in two previous applications in this chapter first in the treatment of gas species p(T, F) = p° - - RT In P and then again in the discussion of the Gibbs phase rule. So far the treatments referred to closed systems and it seemed that p is just... 

Fig. 1.6 Application of the Gibbs phase rule on three special points in a simple three-component system. The phase diagram was taken from [2].

Application of Gibbs Phase Rule to Reactions in Figure 9.1... 

The Gibbs-Duhem equation is applicable to each phase in any heterogenous system. Thus, if the system has P phases, the P equations of Gibbs-Duhem form a set of simultaneous, independent equations in terms of the temperature, the pressure, and the chemical potentials. The number of degrees of freedom available for the particular systems, no matter how complicated, can be determined by the same methods used to derive the phase rule. However, in addition, a large amount of information can be obtained by the solution of the set of simultaneous equations. 

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