Phase rule power

The power of the phase rule is immediately evident in that the solid/liquid/vapor system is characterized by the same amount of variance as was the solid/vapor system. As a result, the arguments made regarding the pressure-temperature curves of the former system can be extended to apply to the latter system, except that the liquid phase takes the place of the anhydrate phase. 

Nevertheless, the phase rule is extremely useful for yielding a physical understanding of polymorphic systems and for providing a physical interpretation of phase transformation phenomena. Its greatest power is in its ability to rule out the existence of simultaneous multiple equilibria that violate its fundamental equation, permitting more quantitative investigations to focus on the possible aspects of such systems. 

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... 

A great deal of the power and usefulness of the phase rule in geochemistry comes from its demonstration of which systems are divariant, and which therefore have all their properties fixed at a given T and P. Changing the concentration of any component of a trivariant or multivariant solution will change all the properties of the solution, even if T and P do not change. However, consider a divariant system at fixed values of T and P. 

This example shows the power and the limitations of the phase rule. It does not tell us how many mols of CO2 must be admitted, the pressure or any of the phase compositions. It does not tell us if the solid that actually appears is NaHC03 or one of its hydrates, such as sodium sesquicarbonate (Na2C03 NaHC03 2H2O). But it does tell us, without benefit of any experiment, what is possible in this system and what is not. Often that is of great value. 

One rarely sees the phase rule even mentioned in books and articles on biochemistry. The main reason is that the phase rule deals with systems at physical and chemical equilibrium, and biological systems are almost never at or very near to physical and chemical equilibrium, (See Figure 1.4). In addition, the phases in biological systems are mostly even more complex physically and chemically than the adsorption case considered here. For clear, simple and well-defined phases and ordinary chemical reactions, the phase rule has explanatory and predictive power. For complex phases and complex biochemical reactions (see Chapter 16) it apparently has less such power. 

An example of a binary eutectic system AB is shown in Figure 15.3a where the eutectic is the mixture of components that has the lowest crystallisation temperature in the system. When a melt at X is cooled along XZ, crystals, theoretically of pure B, will start to be deposited at point Y. On further cooling, more crystals of pure component B will be deposited until, at the eutectic point E, the system solidifies completely. At Z, the crystals C are of pure B and the liquid L is a mixture of A and B where the mass proportion of solid phase (crystal) to liquid phase (residual melt) is given by ratio of the lengths LZ to CZ a relationship known as the lever arm rule. Mixtures represented by points above AE perform in a similar way, although here the crystals are of pure A. A liquid of the eutectic composition, cooled to the eutectic temperature, crystallises with unchanged composition and continues to deposit crystals until the whole system solidifies. Whilst a eutectic has a fixed composition, it is not a chemical compound, but is simply a physical mixture of the individual components, as may often be visible under a low-power microscope. 

As an 11th suggestion, multivalued magnetic potentials arise naturally in magnetics theory [60,61] as well as in other potential theory. This is particularly true during phase transitions, where multivalued potentials seem to be the rule rather than the exception [62]. Theoreticians do all in their power to minimize or eliminate their consideration [61]. However, if deliberately used and optimized, the multivalued magnetic potential... 

When evaluating whether or not an aqueous and organic (solvent) pair is suitable for carrying out a solvent extraction, the most important characteristic is the distribution ratios of the components to be extracted and of those to be left in the fluid. Once the distribution ratios are found to be favorable, the immiscible liquid-liquid pair must be characterized to determine if the pair can be used in commercial solvent-extraction equipment. This characterization is best done by the batch dispersion-number test (Leonard, 1995). This test can be performed easily and quickly with no special equipment. If the results are favorable, the densities of the two phases need to be considered. If the difference is less than 10%, plant operation could be difficult. As a rule of thumb, the density difference should be 15% or greater. The liquid viscosity is important in that more power will be required to turn the rotor if the viscosity is higher. The liquids also need to be able to flow easily from stage to stage. 

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