Species approach to the phase rule

This section derives an expression for the number of degrees of freedom, F, based on species. Section 13.1.3 derives an expression based on components. Both approaches yield equivalent versions of the phase rule. 

Recall that a species is an entity, uncharged or charged, distinguished from other species hy its chemical formula (Sec. 9.1.1). Thus, CO2 and C03 are different species, but COilaq) and COilg) is tbe same species in different phases. 

Consider an equilibrium system of P phases, each of which contains the same set of species. Let the number of different species be x. If we could make changes while the 

Thermodynamics and Chemistry, second edition, version 3 2011 by Howard DeVoe. Latest version www.chem.umd.edu/thermobook 

The equilibrium system is, however, in transfer equiUbrium, which requires each species to have the same chemical potential in each phase = /xf, /l] = /xf, and so on. There 

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