## Implications of the phase rule

The metal oxidation system must satisfy the phase rule, Eq (1.21a). The reaction described by Eq (9.31) involves two components: 2 elements, M and O; or 3 species, M, MO2 and O2 less the equilibrium reaction involving all three. There are three phases: the solids M and MO2, and O2 gas. The total pressure is not a degree of freedom because it is equal to the oxygen pressure, which cannot be adjusted independent of temperature. For this system, the phase rule reduces to

The single degree of freedom is temperature, which determines the oxygen pressure. Digression #1 The total pressure can be made an additional independent variable by adding an inert gas to the oxygen. However, the inert gas becomes an additional component, so the phase rule for this case is:

The two degrees of freedom are temperature and total pressure. However, total pressure has little effect on the properties of the two solids and none on the O2 pressure, so p can be ignored as an additional degree of freedom for this system.

Digression #2 The oxygen gas could be totally eliminated by completely enclosing the two solids in a tight-fitting, impervious boundary at an external pressure greater than the oxygen pressure. The resulting mixture of two immiscible solid phases would still possess a virtual O2 pressure even though no gas phase is present. This interpretation of the O2 pressure exerted by the M + MO2 mixture (often termed a couple) is the reason that RTln p0 in Eq (9.33b) is called the oxygen potential of the M + MO2 couple.

As the temperature is varied, the oxygen pressure, or equivalently, the oxygen potential, follows by either of Eqs (9.33). Thus p0 is to be interpreted as a property of the M + MO2 couple, not as a composition variable in the phase-rule sense. 