Phase rule application

The phase rule (applicable to intensive properties) as discussed in Secs. 2.8 and 12.2 for nonreacting systems of tt phases and N chemical species is... 

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). 

Where does one travel next at the intersection There were comers notably untouched third-law consequences, phase rule applications, and critical phenomena, to name three. These justihably warrant full-scale treatments. By the third law of thermodynamics, the entropy and heat capacity of a crystalline system converge to zero in the limit of zero absolute temperature. According to Boltzmann ... 

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

Derive from first principles the form of the phase rule applicable to a system containing N species between which there are R independent chemical reactions. 

The general XT E problem involves a multicomponent system of N constituent species for which the independent variables are T, P, N — 1 liquid-phase mole fractions, and N — 1 vapor-phase mole fractions. (Note that Xi = 1 and y = 1, where x, and y, represent liquid and vapor mole fractions respectively.) Thus there are 2N independent variables, and application of the phase rule shows that exactly N of these variables must be fixed to estabhsh the intensive state of the system. This means that once N variables have been specified, the remaining N variables can be determined by siiTUiltaneous solution of the N equihbrium relations ... 

The material in this section is divided into three parts. The first subsection deals with the general characteristics of chemical substances. The second subsection is concerned with the chemistry of petroleum it contains a brief review of the nature, composition, and chemical constituents of crude oil and natural gases. The final subsection touches upon selected topics in physical chemistry, including ideal gas behavior, the phase rule and its applications, physical properties of pure substances, ideal solution behavior in binary and multicomponent systems, standard heats of reaction, and combustion of fuels. Examples are provided to illustrate fundamental ideas and principles. Nevertheless, the reader is urged to refer to the recommended bibliography [47-52] or other standard textbooks to obtain a clearer understanding of the subject material. Topics not covered here owing to limitations of space may be readily found in appropriate technical literature. 

The system, therefore, is at equilibrium at a given temperature when the partial pressure of carbon dioxide present has the required fixed value. This result is confirmed by experiment which shows that there is a certain fixed dissociation pressure of carbon dioxide for each temperature. The same conclusion can be deduced from the application of phase rule. In this case, there are two components occurring in three phases hence F=2-3 + 2 = l, or the system has one degree of freedom. It may thus legitimately be concluded that the assumption made in applying the law of mass action to a heterogeneous system is justified, and hence that in such systems the active mass of a solid is constant. 

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 ... 

Findlay, A. and Campbell, A. N. The Phase Rule and its Applications 9th. edition. (Longman, London, 1951). 

Most discussions, such as those cited above, of monolayer films are presented within the context of equilibrium thermodynamics. The applications of the two-dimensional gas law, ttA = kT, the phase rule, and relations between surface tension and surface pressure to free energy all assume reversibility. Perhaps it seems odd to... 

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. 

In terms of the phase rule, we must utilize Eq. (2.24) instead of (2.23), since we have only one noncompositional intensive variable, T (pressure is fixed), so A = 1. Application of Eq. (2.24) to points A and C in Figure 2.4 indicates that the liquid and solid regions (0 = 1 C = 2) correspond to F = 2, which means that both temperature and composition can be altered independently in these regions. Point B is in the liquid -b solid two-phase region (0 = 2 C = 2), so that F = 1. Temperature and composition are not independent in this region any change in temperature necessarily results in a... 

As a simple application of the phase rule, let us consider the M-O system described in Section 1.1, in which the number of components, c, is equal to... 

Application of the phase rule to the binary (M-O) and ternary oxide system (M1-M2-O) in a closed system ... 

The phase rule applies to true equilibrium systems, where the equilibrium can be reached from either side, and. furthermore, lakes no accoum of the lime involved to attain equilibrium. The phase rule is a qualitative statement., whereas the law of mass action (concentration effect I is quantitatively applicable to those equilibrium systems where the reaction which occurs may be considered to take place in a homogeneous system, e.g gas phase, or. solution phase. (See also Chemicnl Reaction Rate.). 

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. 

Since we have briefly introduced the consideration of mixed systems, we will mention, in passing, Gibbs1 famed Phase Rule. Its basic equation, which is generally applicable, is ... 

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. 

Modifications of the phase rule are required when restrictions are placed on the system. The changes are obtained from the conditions of equilibrium expressed in Equations (5.25)-(5.29). When there are several groups of phases separated by adiabatic membranes, Equation (5.25) is valid for the phases in each group however, an additional set of equations must be written for each group. We then find that the number of condition equations is decreased by one and the number of degrees of freedom is increased by one for each adiabatic membrane introduced into the system. The same arguments are applicable to Equations (5.26)-(5.29). We thus observe that the number of degrees of freedom is increased by one for each restriction that is introduced into the system. 

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