Interpretation of a Phase Diagram

Question

I am a bit confused about the correct way to interpret a phase diagram. I was told that the line separating the liquid and gas phases gives the vapor pressure of the liquid substance as a function of temperature. I am not fully sure why this must be the case as in my mind, that line represents the boiling point of the liquid as a function of pressure and I don't see clearly how this connects with vapor pressure.

Furthermore, I know that the line separating the solid and liquid phases gives the melting point as a function of temperature. I am wondering if there is an alternative interpretation of this line involving an analog of vapor pressure between the solid and liquid phases (i.e. I know that there is a vapor pressure between the solid and liquid/solid and gas phases. I am wondering if there is some analogous equilibrium pressure between the solid and liquid phases. If so, how would this be represented on the diagram and if not, why is the solid/gas, liquid/gas boundary special?)

Answer 1

Liquids and solids have vapor pressure, even though well below their boiling point. For example, the vapor pressure of solid $\ce{CO2}$ is high enough that it sublimes, i.e., goes directly from solid to gas.

In the diagram below, adapted from Wikipedia, notice that

• Water boils at 100°C, i.e., the vapor pressure is equal to atmospheric pressure, and causes bubbles to form and burst out of a container.
• At 50°C, e.g., a very hot day in Death Valley, AZ, the vapor pressure of water is ~10 kPa (about 1/10 atmospheric pressure). This pressure is still high enough to make water evaporate rapidly, though it is not visibly boiling.
• At about 180°C, perhaps the temperature of an old steam-engine boiler, the pressure is 1 MPa (about ten times atmospheric pressure). If the boiler were to burst, all the water would flash to steam. Yet, in a deep-sea hydrothermal vent, that would still be liquid water at that temperature.

Answer 2

The phase diagram for a pure substance has only one component, the substance in its phases, and describes the equilibria among the phases. The Gibbs Phase Rule: Freedoms = Components - Phases + 2; F = C- P + 2, describes the diagram. For one phase present there are 2 freedoms, T and P are independent; this is an area in the diagram.

If two phases are present there is one freedom, T and P are entangled, for each value of one there is one value of the other. This is a line in the diagram. This line is continuous and monotonic until a new phase is encountered. There are no boiling points or freezing points just continuing equilibrium. The line does not separate the phases, it is the Equilibrium between the phases. Remember boiling points and freezing points are defined at a SPECIFIC temperature and pressure; the pressure is the open atmosphere and is variable. Addition of a second component, the atmosphere adds an additional freedom, the atmospheric pressure. [Even more when the composition of the atmosphere is of concern.]

A point, the intersection of 3 lines, [This is interesting because this is nonEuclidian, the lines are not straight or continuous but end at the triple point] is invariant with no degrees of freedom; there is a distinct T and VP. Three lines are necessary because the solid and liquid have the same VP but different latent heats and volume changes. When an inert gas, an atmosphere, is introduced the change in pressure has a different effect on the liquid and solid phases changing their vapor pressures differently. The difference in vapor pressures causes a temperature change to equalize the vapor pressures and results in a new triple point at every inert gas pressure. This gives a 4 dimensional aspect to the phase diagram with a continuous overlay of triple points and the corresponding phase diagrams. This is why melting points and boiling points in an [inert] atmosphere must be defined by a temperature and an applied pressure while a one component triple point has invariant T and VP.

Answer 3

Boiling is a special mode of liquid substance evaporation (transition to its gaseous phase). In this mode, the evaporation occurs not only at the liquid surface, but also inside the liquid, where are being formed bubbles of the gaseous phase of the substance.

The curve between liquid and gaseous phases on phase diagrams have two equivalent meanings:

• The liquid vapor pressure at the given temperature at equilibrium
• The liquid boiling point at the given pressure

As at temperature of the boiling point, the liquid vapor pressure is equal to external pressure and is able to push the liquid away, against the external pressure. The formed space is filled with the vapor.

The relation of temperature and vapor pressure relates to equilibrium conditions of a closed container containing just the liquid and its vapor, reaching the particular pressure at given temperature.

The boiling is a dynamic process with ongoing on (usually) open system, that is far from equilibrium.

There are two small deviations:

• Forming of a bubble needs to overcome the liquid surface tension, so there is needed vapor pressure little higher than external pressure.
• In presence of gravity, boiling point raises with the depth due contribution of hydrostatic pressure.

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The curve between the solid and liquid phase gives primarily the dependance of the substance melting point on pressure.

There are few hidden thermodynamic relations to this (s)-(l) curve.

Chemical potentials $\mu_{i}=\left( \dfrac {\partial G}{\partial n_i}\right)_{p, T, n_j, j \ne i}$ of solid and liquid phase are equal at the melting point.

If there is 2 component system with an inert gas, coexistence of 3 phases is not limited to the triple point with given temperature and pressure, but there is still one degree of freedom = 1 parameter we can deliberately choose, usually temperature. If we keep such a system at temperature of melting point, partial vapor pressures over both condensed phases are equal and $$\mu_text{s}=\mu_text{l}=\mu_text{g}$.