Of state. Contents and Concepts 1. Comparison of Gases, Liquids, and Solids Changes of State

Vapor-Pressure Curves for the Liquid and the Solid

The curve AC that divides the liquid region from the gaseous region gives the vapor pressures of the liquid at various temperatures. It also gives the boiling points of the liquid for various pressures. The boiling point of water at 1 atm is shown on the phase diagram (Figure 11.11). The curve AD that divides the solid region from the gaseous region gives the vapor pressures of the solid at various temperatures. This curve intersects the other curves at point A, the triple point, which is the point on a phase diagram representing the temperature and pressure at which three phases of a substance coexist in equilibrium. For water, the triple point occurs at 0.01°C, 0.00603 atm (4.58 mmHg), and the solid, liquid, and vapor phases coexist.

Because the triple point for water occurs at a definite temperature, it is used to define the Kelvin temperature scale. The temperature of water at its triple point is defined to be 273.16 K (0.01°C).

Suppose a solid is warmed at a pressure below the pressure at the triple point. In a phase diagram, this corresponds to moving along a horizontal line below the triple point. You can see from Figure 11.11 that such a line will intersect curve AD, the vapor-pressure curve for the solid. Thus, the solid will pass directly into the gas; that is, the solid will sublime. Freeze-drying of a food (or brewed coffee) is accomplished by placing the frozen food in a vacuum (below 0.00603 atm) so that the ice in it sublimes. Because the food can be dried at a lower temperature than if heat-dried, it retains more flavor and can often be reconstituted by simply adding water. The triple point of carbon dioxide is at -57°C and 5.1 atm (Figure 11.12 top). Therefore, the solid sublimes if warmed at any pressure below 5.1 atm. This is why solid carbon dioxide sublimes at normal atmospheric pressure (1 atm). Above 5.1 atm, however, the solid melts if warmed. Sulfur has a more complicated phase diagram (Figure 11.12 bottom). It displays three triple points, one of them involving two different solid forms of sulfur (called rhombic sulfur and monoclinic sulfur), as well as the vapor.