0.16 Phase equilibrium and intermolecular forces  (Page 3/7)

What if we start at a temperature-pressure combination on the curve and elevate the applied pressure without raising the temperature? This places us “above” the curve, which is also of course to the left of the curve. The applied pressure is now greater than the vapor pressure, and as before all of the gas will condense into the liquid. Just as before, for all points to the left of or above the curve, only liquid exists. The opposite reasoning applies if we decrease the applied pressure.

Figure 1 thus actually reveals to us what phase or phases are present at each combination of temperature and pressure: along the line, liquid and gas are in equilibrium; above or to the left of the line, only liquid is present; below or to the right of the line, only gas is present. When we label the graph with the phase or phases present in each region as in Figure 1, we refer to the graph as a “phase diagram.” In general, every substance has a liquid-vapor phase diagram like Figure 1, although the values of the pressures and temperatures along the equilibrium line differ from substance to substance.

Observation 2: solid-liquid-gas phase diagrams

Of course, Figure 1 only includes liquid, gas, and liquid-gas equilibrium. We know that, if the temperature is low enough, we expect that the water will freeze into solid. To complete the phase diagram, we need additional observations.

We go back to our apparatus we used before, with a piston in a cylinder trapping liquid water and vapor in phase equilibrium. We can start at a temperature of 25 ↓C and 23.8 torr since we know that this is the vapor pressure of liquid water at 25 ºC. If we slowly lower the temperature, the vapor pressure decreases slowly as well, as shown in Figure 1. However, if we continue to lower the temperature, we observe an interesting transition, as shown in the more detailed Figure 2. The very smooth variation in the vapor pressure shows a slight, almost unnoticeable break very near to 0 ↓C. Below this temperature, the pressure continues to vary smoothly, but along a slightly different curve.

To understand what we have observed, we examine the contents of the container. We find that, at temperatures below 0 ↓C, the water in the container is now an equilibrium mixture of water vapor and solid water (ice), and there is no liquid present. The direct transition from solid to gas, without liquid, is called “sublimation.” For pressure-temperature combinations along this new curve below 0 ↓C, the curve shows the solid-gas equilibrium conditions. As with the liquid-vapor curve, we can interpret this new curve in two ways. The solid-gas curve gives the vapor pressure of the solid water as a function of temperature, and also gives the sublimation temperature as a function of applied pressure.

Figure 2 is still not a complete phase diagram, because we have not included the combinations of temperature and pressure at which solid and liquid are at equilibrium. As a starting point for these observations, we look more carefully at the conditions near 0 ↓C. Very careful measurements reveal that the solid-gas line and the liquid-gas line intersect in Figure 2 where the temperature is 0.01 ↓C. Under these conditions, we observe inside the container that solid, liquid, and gas are all at equilibrium inside the container. As such, this unique temperature-pressure combination is called the “triple point.” At this point, the liquid and the solid have the same vapor pressure, so all three phases can be at equilibrium. If we raise the applied pressure slightly above the triple point, the vapor must disappear. We can observe that, by only slightly varying the temperature, the solid and liquid remain in equilibrium. We can further observe that the temperature at which the solid and liquid are in equilibrium varies almost imperceptibly as we increase the pressure. If we include the solid-liquid equilibrium conditions on the previous phase diagram, we get Figure 3, where the solid-liquid line is very nearly vertical.