Gibbs phase rule says f = r-M+2 with f: thermodynamic degrees of freedom; r: number of components; M: number of phases I wonder whether the defintion of "phase" is restricted or almost arbitrary. For example, consider a system of H2O, O2 and H2 in a closed vessel. Let there be the contstraint that there is a gaseous state which contains all three components (H2O, O2 and H2) and a liquid state which contains only H2O and O2. From my understanding of what a phase is, one would define two phases, a gas g and a liquid l, as follows: phase 1: H2O(g), O2(g), H2(g) phase 2: H2O(l), O2(l) Gibbs rule would give f = 3-2+2=3 degrees of freedom. Couldn't we have also defined the phases as follows: phase 1: H2O(g), H2(g) phase 2: O2(g) phase 3: H2O(l) Gibbs rule would give f = 3-3+2=2 degrees of freedom. My motivation for this definition is: O2 might consists of macroscopically tiny gas regions, perhaps invisible in the liquid, but ultimately they are thermodynamic subsystems and a constant pressure and temperature is applied to these regions, no matter if they are in the "gas" or in the "liquid" or if they are tiny (invisible) or large. There might be other defintions of phases, for example: phase 1: H2O(g) phase 2: O2(g) phase 2: H2(g) phase 3: H2O(l) Gibbs rule would give f = 3-4+2=1 degree of freedom. Or how about this: phase 1: H2O(g) phase 2: O2(g) phase 3: O2(l) phase 4: H2(g) phase 5: H2O(l) Gibbs rule would give f = 3-5+2=0 degrees of freedom. Are all of these definitions of phases valid and can we almost arbitrary assign the term "phase" to a homogeneous subregion of a bigger system, or am I missing a critical point here?