Maps of Phase Equilibrium - Unary Phase Diagrams

In the previous section, we alluded to something very important regarding phase behavior when talking about $\ce{H2O}$. If we control some thermodynamic parameter of a system of $\ce{H2O}$ molecules, we can control its phase. At standard pressure, you can heat water and get water vapor, you can cool it and get water ice. We can, therefore, see that the phase we observe is dependent on the temperature of the system.

Perhaps less familiar - but if the pressure of a system of water molecules changes, you this phase behavior differs. Many folks know that the boiling temperature for water is $100 ^{\circ}\text{C}$. That's true, but only at 1 atm pressure. If you live high in the mountains - for example El Alto in Bolivia (4,000 m), water boils around $86^{\circ}\text{C}$!

It's clear that it might be useful to have a map of the phases that exist at equilibrium at different temperatures and pressures: or a phase diagram. Many of you have seen the well-known phase diagram for $\ce{H2O}$ in high school or first-year chemistry courses. We've reproduced it in Figure 10.4.1.

The phase diagram in Figure 10.4.1 is tremendously useful. If I know the temperature and pressure, I can tell you the equilibrium phase of $\ce{H2O}$. This type of phase diagram is called a unary phase diagram because it plots phase equilibrium for a single chemical component - in this case $\ce{H2O}$ is acting like a single chemical entity. This unary phase diagram is also called pressure-temperature phase diagram because those are the thermodynamic variables we are plotting on either axis. Note, I could choose many different types of thermodynamics variables beyond temperature and pressure to plot (e.g., electric field, magnetic field, etc.), but for unary phase diagrams, we'll limit ourselves to pressure and temperature.

At this point, let's identify a few key features. Colored and labeled "fields" show us the phase we expect to see at that combination of temperature and pressure. These fields are called phase fields because they show the region in which we expect to find a specific equilibrium phase. Seperating the phase fields are phase boundaries. These boundaries are where phase transitions occur. For example, at 1 atm, we can heat the water molecules from $-200 ^{\circ}\text{C}$ to $0 ^{\circ}\text{C}$, at which point we'll encounter a phase boundary between the solid water phase field and the liquid water phase field. This is the point that, upon heating, the solid melts. If we continue to $100 ^{\circ}\text{C}$ we encounter another phase boundary: the liquid|gas phase boundary, or the boiling point.

In these types of unary phase diagrams we also often observe the so-called triple point. This is the point on the diagram in which three phases - here, the liquid, solid, and gas phases - are in thermodynamic equilibrium. We also call this a invariant point on the phase diagram because it represents a point on the phase diagram for which - in order to maintain the equilibrium condition at that point - you cannot vary the thermodynamics conditions. Or, you cannot vary the pressure or temperature from (e.g.) $0.0098 ^{\circ}\text{C}$ and $0.00603 \text{atm}$ and maintain three-phase equilibrium. The point is invariant.

Now, the terminology we use here, unary phase diagram implies that we might be able to have binary, ternary, quaternary, etc. phase diagrams in which we have more than one chemical component. We can. In this class, we'll only cover binary phase diagrams, but further study in MSE will lead you to higher-order phase diagrams. These can be difficult to visualize (although there are ways, but let's save that for another day), and we often use computers to help us navigate them. Let's proceed to our first binary phase diagram in the next section.