The phase rule and its application

We shall derive the phase rule by use of the knowledge of thermodynamics described in Section 1.2.1. Consider a system composed of species 1,2, 3. z. c with Ui, n2 3, , moles, respectively. The free energy G of the system at constant pressure and temperature can be expressed as (see eqn (1-21)) 

The system under consideration consists of phases 1, 2, 3. p ( p means the number of coexisted phases in the system under consideration), which are in an equilibrium state. Thus it follows that 

Suppose that a process occurred by which dnP moles of species z (component) were taken from phase 1 and added to phase 2. Then the free energy change, AG, in G becomes 

This process can be regarded as a chemical reaction in a system at equilibrium, which guarantees the condition AG = 0. Then we have 

In a similar manner it can be shown that similar relations apply to all components in all phases. These relations are expressed by a set of equations 

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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. 

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

Consider a system consisting of a number of phases made up of several different components, and suppose that the number of variables and conditions of constraint is such that the system has one degree of freedom. If we assign in addition a value to any one of the variables which characterize the state of the system (such as temperature, pressure, or the concentration of one of the components in one of the phases) the system will come to a perfectly definite state of equilibrium. Such an equilibrium is called a monovariant equilibrium. Rooseboom, to whom many important investigations on the phase rule and its applications are due, used the term complete equilibrium for an equihbrium of this kind. Nemst also adopts this terminology, although he raises objections to it, since mono variant equilibria are in no way more complete than nonvariant or multivariant equilibria. It would be more appropriate to use the term complete equilibria for nonvariant equilibria in which the number of phases is a maximum. (See Nernst, LeJirhuch, 6th ed. p. 473.)... 

Figure 14.7 Bubble-cap distilling column. (By permission from Findlay, Campbell, Smith, The Phase Rule and Its Applications, 9th ed. New York Dover, 1951.)...

The following discussion of the phase rule, and its application to systems of polymorphic interest, has primarily been distilled from the several classic accounts published in the first half of this century [2-8]. It may be noted in passing that one of the most serious disagreements in the history of physical chemistry was between the proponents of computational thermodynamics and those interested in the more qualitative phase rule. Ultimately the school of exact calculations prevailed... 

A. Findlay, The Phase Rule and Its Applications, 8th ed., Longmans, Green and Co., London, 1938 reprinted by Dover Publications, New York. 

Comprehensive accounts of the phase rule and its applications have been given by Bowden (1950), Findlay and Campbell (1951), Ricci (1966), Haase and Schonert (1969) and Nyvlt (1979). 

A. N. Findlay, The Phase Rule and Its Application, 9 ed., Longman Green, London (1904) Dover, New York (1951)... 

McCrone WC (1965) In Fox D, Labes MM, Weissemberg A (eds) Polymorphism in physics and chemistry of the organic solid state, vol 2. Interscience, New York, p 726 Findlay AF (1951) The phase rule and its applications, 9th edn. Dover, New York, pp 7-16 Buerger MJ, Bloom MC (1937) Z Kristallogr 96 182-200 Sirota NN (1982) Cryst Res Technol 17 661-691 Kuhnert-Brandstatter M (1965) Pure Appl Chem 10 133-144... 

Findlay, 1951] A. Findlay. The Phase Rule and its applications. Ninth edition by A.N. Campbell and N.O. Smith ed. New York Dover (1938), 1951. 

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