I'm confused with how the Gibbs Phase Rule works for pure substances in liquid-vapor mixtures. According to the phase rule, there should only be one degree of freedom for a two-phase mixture with a pure substance. For example, if we pick a temperature for two phases to exist, there will only be one pressure that satisfies this condition. But how is the amount of vapor in the mixture, defined?

Looking at the figure below, it appears as if the pressure and specific volume are both independent of the two-phase region. Does this contradict the phase rule? If I wanted to obtain a vessel containing a mixture of water with 50% vapor and 50% liquid, could it be done by changing the pressure and temperature alone?

enter image description here


1 Answer 1


Note that the phase rule is qualitative. It says nothing about the particular amounts. It simply enumerates the theoretical number of independent parameters needed to determine amounts and compositions for the given number of components and phases.

The definition of a system, like total amounts of components, does not count among degrees of freedom.

The number of degrees of freedom of a system is the number of independent parameters, that are needed for the given system to determine its state.

For the given container volume and the substance amount, a given temperature determines the equilibrium pressure and vice versa. So there is 1 degree of freedom.

Amounts of particular phases are determined by the temperature as the single degree of freedom.

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    $\begingroup$ What determines the amounts of each phase are the physical constraints. There simply must be enough liquid to produce gas at the vapor pressure. If not enough liquid the system is below the liquid-gas equilibrium line. If the pressure of the gas is increased [with no inert gas present ie. a pure substance] Gas will condense until the gas phase vanishes. The phase rule describes what happens at equilibrium and isn't concerned about how to attain equilibrium that is the chemists job. The graph shown describes situations where both phases exist except at high P below Tc $\endgroup$
    – jimchmst
    May 19, 2022 at 22:38
  • $\begingroup$ @jimchmst Sure, I was addressing the qualitative rule aspect. I should include note about this too. $\endgroup$
    – Poutnik
    May 20, 2022 at 6:18

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