Learning Objectives Use phase diagrams to identify stable phases at given temperatures and pressures Identify the following on a phase diagram: solid, liquid, gas, triple point, critical point A phase diagram is a plot of pressure versus temperature for a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature, and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). A typical phase diagram for a pure substance is shown in Figure \(\PageIndex{1}\). Consider the phase diagram for water shown in Figure \(\PageIndex{2}\). We can use the phase diagram to identify the physical state of a sample of water under specified conditions of pressure and temperature. For example, a pressure of 50 kPa and a temperature of −10 °C correspond to the region of the diagram labeled “ice.” Under these conditions, water exists only as a solid (ice). A pressure of 50 kPa and a temperature of 50 °C correspond to the “water” region—here, water exists only as a liquid. At 25 kPa and 200 °C, water exists only in the gaseous state. Note that on the H 2 O phase diagram, the pressure and temperature axes are not drawn to a constant scale in order to permit the illustration of several important features as described here. The curve BC in Figure \(\PageIndex{2}\) is the plot of vapor pressure versus temperature as described in the previous module of this chapter. This “liquid-vapor” curve separates the liquid and gaseous regions of the phase diagram and provides the boiling point for water at any pressure. For example, at 1 atm, the boiling point is 100 °C. Notice that the liquid-vapor curve terminates at a temperature of 374 °C and a pressure of 218 atm, indicating that water cannot exist as a liquid above this temperature, regardless of the pressure. The physical properties of water under these conditions are intermediate between those of its liquid and gaseous phases. This unique state of matter is called a supercritical fluid, a topic that will be described in the next section of this module. The solid-vapor curve, labeled AB in Figure \(\PageIndex{2}\), indicates the temperatures and pressures at which ice and water vapor are in equilibrium. These temperature-pressure data pairs correspond to the sublimation, or deposition, points for water. If we could zoom in on the solid-gas line in Figure \(\PageIndex{2}\), we would see that ice has a vapor pressure of about 0.20 kPa at −10 °C. Thus, if we place a frozen sample in a vacuum with a pressure less than 0.20 kPa, ice will sublime. This is the basis for the “freeze-drying” process often used to preserve foods, such as the ice cream shown in Figure \(\PageIndex{3}\). The solid-liquid curve labeled BD shows the temperatures and pressures at which ice and liquid water are in equilibrium, representing the melting/freezing points for water. Note that this curve exhibits a slight negative slope (greatly exaggerated for clarity), indicating that the melting point for water decreases slightly as pressure increases. Water is an unusual substance in this regard, as most substances exhibit an increase in melting point with increasing pressure. This behavior is partly responsible for the movement of glaciers, like the one shown in Figure \(\PageIndex{4}\). The bottom of a glacier experiences an immense pressure due to its weight that can melt some of the ice, forming a layer of liquid water on which the glacier may more easily slide. The point of intersection of all three curves is labeled B in Figure \(\PageIndex{2}\). At the pressure and temperature represented by this point, three phases of water coexist in equilibrium. This temperature-pressure data pair is called the triple point . At pressures lower than the triple point, water cannot exist as a liquid, regardless of the temperature. Example \(\PageIndex{1}\): Determining the State of Water Using the phase diagram for water given in Figure \(\PageIndex{2}\), determine the state of water at the following temperatures and pressures: −10 °C and 50 kPa 25 °C and 90 kPa 50 °C and 40 kPa 80 °C and 5 kPa −10 °C and 0.3 kPa 50 °C and 0.3 kPa Solution Using the phase diagram for water, we can determine that the state of water at each temperature and pressure given are as follows: (a) solid; (b) liquid; (c) liquid; (d) gas; (e) solid; (f) gas. Consider the phase diagram for carbon dioxide shown in Figure \(\PageIndex{5}\) as another example. The solid-liquid curve exhibits a positive slope, indicating that the melting point for CO 2 increases with pressure as it does for most substances (water being a notable exception as described previously). Notice that the triple point is well above 1 atm, indicating that carbon dioxide cannot exist as a liquid under ambient pressure conditions. Instead, cooling gaseous carbon dioxide at 1 atm results in its deposition into the solid state. Likewise, solid carbon dioxide does not melt at 1 atm pressure but instead sublimes to yield gaseous CO 2 . Example \(\PageIndex{2}\): Determining the State of Carbon Dioxide Using the phase diagram for carbon dioxide shown in Figure \(\PageIndex{5}\), determine the state of CO 2 at the following temperatures and pressures: −30 °C and 2000 kPa −90 °C and 1000 kPa −60 °C and 100 kPa −40 °C and 1500 kPa 0 °C and 100 kPa 20 °C and 100 kPa Solution Using the phase diagram for carbon dioxide provided, we can determine that the state of CO 2 at each temperature and pressure given are as follows: (a) liquid; (b) solid; (c) gas; (d) liquid; (e) gas; (f) gas.