Phase Rule

For a system at equilibrium the phase rule relates:

  • P = number of phases that can coexist, to
  • C = number of components making up the phases, and
  • F = degrees of freedom.
  • Where these three variables are related in the equation
    P + F = C + 2

The degrees of freedom represent the environmental conditions which can be independantly varied without changing the number of phases in the system. Conditions include:

  • Temperature,
  • Pressure,
  • Chemical Composition,
  • pH,
  • Eh,
  • Oxygen Fugacity.

Applying the phase rule to the simplified one component H2O system.
Phase rule becomes P + F = 3, because we are dealing with a one component system (C = 1).

  1. At A
    • P = 1 – water
    • F = 2 – two degrees of freedom,
    • So to maintain equlibrium, i.e. have one phase (water) stable temperature and pressure may vary independantly.
  2. At B
    Point B lies on the boundary curve separating Ice from steam field,

    • P = 2 – Ice and Steam,
    • F = 1 – one degree of freedom,
    • To maintain equilibrium, i.e., to keep the 2 phases stable, must choose an arbitrary value for pressure or temperature, which will automatically fix either temperature or pressure.
  3. At T
    • P = 3 – Water, Ice, Steam
    • F = 0 – No degrees of freedom,
    • All three phases coexist at equilibrium. Can not change pressure or temperature without causing the system to move away from Point T, which will cause one or more of the stable phases to disappear.

Therefore the maximum number of phase which can stably coexist in a one component system is three, and they do so only if there are no degrees of freedom.

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