Phase rule of Gibbs

Two-phase equiUbria may be soHd—Hquid, Hquid—vapor, or soHd—vapor. As is evident from the phase rule of Gibbs, two-phase equiUbria are pressure-dependent ... 

This relation is known as the phase rule of Gibbs or simply the phase rule. 

Eq.(2.2-4) is the phase rule of Gibbs. According to this rule a state with II phases in a system with N components is frilly determined (all intensive thermodynamic properties can be calculated) if a number of F of the variables is chosen, provided that g of all phases as function of pressure, temperature and composition is known. 

By the phase rule of Gibbs the system has s degrees of freedom so that, if the two thermodynamic variables are chosen, only s — 2 of the remaining concentrations may be selected, and the other two are fixed by (9) and... 

The Gibbs-Duhem equation is the basis for the phase rule of Gibbs. According to the phase rule, the number of degrees of freedom F (independent intensive variables) for a system involving only PV work, but no chemical reactions, is given by... 

Equation (2.1.8) specifies the famous phase rule of Gibbs (1875—1878). Knowing the number of components and phases in a given system, and assuming that T and P for the system as a whole are uniformly adjustable, Eq. (2.1.8) indicates how many state variables may be independently adjusted without altering the number of phases of the system. The ramifications of the phase rule will be discussed in Section 2.3. 

The Phase Rule.— The Phase Rule of Gibbs, which defines the... 

The relation (9-2) is known as the phase rule of Gibbs, and/is usually called the number of degrees of freedom of the system. It is important to note that the phase rule in the form (9-2) holds only under the following assumptions ... 

One of the most powerful approaches to separations involves pairs of phases in which the component of interest transfers from one phase to the other more readily than do interfering substances. For all phase-distribution equilibria, the classical phase rule of Gibbs is applicable and useful. The phase rule... 

The first important contribution to atomic stoichiometry in this century seems to be provided by Brinkley (1946). He has shown the importance of the rank of the atomic matrix and presented a proof of the phase rule of Gibbs (1876). A systematic outline of stoichiometry was presented by Petho (sometimes Petheo) and Schay (Petheo Schay, 1954 Schay, Petho, 1962). They gave a necessary and sufficient condition for the possibility of calculating an unknown reaction heat from known ones based upon the rank of the stoichiometric matrix. They introduced the notion of independence of components and of elementary reactions, the completeness of a complex chemical reaction (see the Exercises and Problems) and gave a method to generate a complete set of independent elementary reactions with as many zeros in the stoichiometric matrix as possible (see Petho, 1964). 

One should keep in mind that for phase equilibria, such as the equilibrium between liquid and vapor, there are additional relationships between pressure and temperature. The number of degrees of freedom for the states decreases, owing to the additional relationships between temperature and pressure (phase rule of Gibbs). 

The maximmn nnmber of conditions or concentrations that can be controlled is determined by the phase rule of Gibbs (chapter 2). This rale states that the number of degrees of freedom F in a closed system is equal to two plus the number of components n minus the number of phases rthat are in equilibrium with each other (F=2 + n - jt). The number of degrees of freedom agrees with the number of controlled corrditions or components. 

In practice, a temperature controller is often used as a simple form of quality control. According to the phase rule of Gibbs, for binary mixtures the composition is fixed when the pressirre and temperature are constant. Obviously, this does not hold for multi-component mixtures. One could also try to estimate the product quality from some tray temperature measirrements and other easily measurable variables. This is called an inferential measurement. 

This equation is the phase rule of Gibbs. The number of independent intensive variables denoted by / is called the number of degrees of freedom or the variance. Try not to be confused by the fact that the term variance is also used for the square of a standard deviation of a distribution. 

Phase diagrams can be used to show the phase equilibria of multicomponent systems and can be understood through the phase rule of Gibbs. 

The variance of the adsorption equilibrium can be regarding as the number of intensive variables that must be set to know completely the thermodynamic state of the system. It can be calculated by using the well-known phase rule of Gibbs [6] ... 

There are seven thermodynamics parameters characterizing this equilibrium (p, T, rr, ya, yB, xa, andxB). In that case, the application of the phase rule of Gibbs leads to a variance equal to 3. The representation of the binary adsorption equilibrium is obviously more complicated than for the adsorption of a single component. Coadsorption equilibrium could be represented in a three dimensional space by plotting for example the amounts adsorbed as a function of the pressure in one direction and the composition of the adsorbate in another one. However, this kind of plot is not common because it requires a lot of data measured at different composition and pressure. We prefer to represent the coadsorption equilibria in a two-dimension space by maintaining constant certain variables. The representations that are the more often used and easily understandable are ... 

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