The phase rule for. reactive components

Consider a system in which there are altogether N chemical species, some of which may be inert and do not react at all, whilst the remainder are at reaction equilibrium with each other. Let R be the number of the independent reactions, as determined by the method described in 4 16. Let P be the number of phases. 

Proceeding as in 5 2, the state of the system is specified by P values of the temperature, P values of the pressure and by P(N — 1) composition variables, such as the mole fractions. Thus 

The conditions of equilibrium include P —1 equalities of temperature, P—1 equalities of pressure, jV(P—1) equalities of chemical potential of the N species between the P phases, and finally, R conditions of chemical reaction equilibrium, each of the form Thus 

Comparing with (6 4), the quantity JV-P is seen to take the place of C, which was the total number of species in the case of a non-reactive system. The two forms of the phase rule, (5 4) and (5 6), may be made formally identical if we define the number of components of the reactive system by the relation 

The number of components, in the sense of the phase rule, is therefore to be taken as the total number of chemical species less the number of independent reactions between them. In 4 16 it has already been shown (but not in complete generality) that jW—P is in fact the minimum number of substances which must be available in the laboratory in order to prepare any arbitrary equilibrium mixture of the system in question. The number of components is therefore the same in both senses in which the term is used. 

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