Gibb phase rule

Gibbsitic [14762-49-3] Gibbs-Kelvin equation Gibbs phase rule Gibbs s phase rule Gibbs s theorem Gibbs-Thomson equation... 

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

It was shown some time ago that one can also use a similar thermodynamic approach to explain and/or predict the composition dependence of the potential of electrodes in ternary systems [22-25], This followed from the development of the analysis methodology for the determination of the stability windows of electrolyte phases in ternary systems [26]. In these cases, one uses isothermal sections of ternary phase diagrams, the so-called Gibbs triangles, upon which to plot compositions. In ternary systems, the Gibbs Phase Rule tells us... 

Having phases together in equilibrium restricts the number of thermodynamic variables that can be varied independently and still maintain equilibrium. An expression known as the Gibbs phase rule relates the number of independent components C and number of phases P to the number of variables that can be changed independently. This number, known as the degrees of freedom f is equal to the number of independent variables present in the system minus the number of equations of constraint between the variables. 

The concept of chemical potentials, the equilibrium criterion involving chemical potentials, and the various relationships derived from it (including the Gibbs phase rule derived in Chapter 5) can be used to explain the effect of pressure and temperature on phase equilibria in both a qualitative and quantitive way. 

While the Gibbs phase rule provides for a qualitative explanation, we can apply the Clapeyron equation, derived earlier [equation (5.71)], in conjunction with studying the temperature and pressure dependences of the chemical potential, to explain quantitatively some of the features of the one-component phase diagram. 

We will be looking at first-order phase transitions in a mixture so that the Clapeyron equation, as well as the Gibbs phase rule, apply. We will describe mostly binary systems so that C = 2 and the phase rule becomes... 

The international temperature scale is based upon the assignment of temperatures to a relatively small number of fixed points , conditions where three phases, or two phases at a specified pressure, are in equilibrium, and thus are required by the Gibbs phase rule to be at constant temperature. Different types of thermometers (for example, He vapor pressure thermometers, platinum resistance thermometers, platinum/rhodium thermocouples, blackbody radiators) and interpolation equations have been developed to reproduce temperatures between the fixed points and to generate temperature scales that are continuous through the intersections at the fixed points. 

The framework for constructing such multi-component equilibrium models is the Gibbs phase rule. This rule is valid for a system that has reached equilibrium and it states that... 

When a reversible transition from one monolayer phase to another can be observed in the 11/A isotherm (usually evidenced by a sharp discontinuity or plateau in the phase diagram), a two-dimensional version of the Gibbs phase rule (Gibbs, 1948) may be applied. The transition pressure for a phase change in one or both of the film components can be monitored as a function of film composition, with an ideally miscible system following the relation (12). A completely immiscible system will not follow this ideal law, but will... 

When treated by the modified Gibbs phase rule (Crisp, 1949 Defay, 1932), these results suggest that at equilibrium, the enantiomeric monolayer system... 

A basic exposition of Gibbs phase rule is essential for understanding phase solubility analysis, and detailed presentations of theory are available [41,42]. In a system where none of the chemical species interact with each other, the number of independently variable factors (i.e., the number of degrees of freedom, F) in the system is given by... 

If solvent is added to either of the solid eutectics represented by e or e in Fig. 25a or b, the undissolved solid retains this composition while the saturated solution maintains the composition E or E, respectively. Again, Gibbs phase rule [145,146] can provide further insight into these systems. If the solid enantiomers are solvated, the compositions of the equilibrium solids are displaced symmetrically along the DS or LS axes to an extent determined by the stoichiometry of the solvates. Similarly, if the racemic compound is solvated, the stoichiometry of the equilibrium solid is displaced from R along the line RS to an extent determined by the stoichiometry of the solvate. 

The most broadly recognized theorem of chemical thermodynamics is probably the phase rule derived by Gibbs in 1875 (see Guggenheim, 1967 Denbigh, 1971). Gibbs phase rule defines the number of pieces of information needed to determine the state, but not the extent, of a chemical system at equilibrium. The result is the number of degrees of freedom Np possessed by the system. 

The relationship between the number of degrees of freedom, F, defined as the number of intensive parameters that can be changed without changing the number phases in equilibrium, and the number of phases, Ph, and components, C, in the system is expressed through Gibbs phase rule ... 

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 ... 

Binary phase diagrams from thermodynamics Gibbs phase rule... 

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