12.9

*Equilibrium Between Phases of Matter

Under specific conditions of temperature and pressure, a substance can exist at equilibrium in more than one phase at the same time. Consider Figure 12-32, which shows a container kept at a constant temperature by a large reservoir of heated sand. Initially the container is evacuated. Part a shows it just after it has been partially filled with a liquid and a few fast-moving molecules escape the liquid and form a vapor phase. These molecules pick up the required energy (the latent heat of vaporization) during collisions with neighboring molecules in the liquid. However, the reservoir of heated sand replenishes the energy carried away, thus maintaining the constant temperature. At first, the movement of molecules is predominantly from liquid to vapor, although some molecules in the vapor phase do reenter the liquid. As the molecules accumulate in the vapor, the number reentering the liquid eventually equals the number entering the vapor, at which point equilibrium is established, as in part b. From this point on, the concentration of molecules in the vapor phase does not change, and the vapor pressure remains constant. The pressure of the vapor that coexists in equilibrium with the liquid is called the equilibrium vapor pressure of the liquid.

Figure 12-32 (a) Some of the molecules begin entering the vapor phase in the evacuated space above the liquid. (b) Equilibrium is reached when the number of molecules entering the vapor phase equals the number returning to the liquid.

The equilibrium vapor pressure does not depend on the volume of space above the liquid. If more space were provided, more liquid would vaporize, until equilibrium was reestablished at the same vapor pressure, assuming the same temperature is maintained. In fact, the equilibrium vapor pressure depends only on the temperature of the liquid; a higher temperature causes a higher pressure, as the graph in Figure 12-33 indicates for the specific case of water. Only when the temperature and vapor pressure correspond to a point on the curved line, which is called the vapor pressure curve or the vaporization curve, do liquid and vapor phases coexist at equilibrium.

Figure 12-33 A plot of the equilibrium vapor pressure versus temperature is called the vapor pressure curve or the vaporization curve, the example shown being that for the liquid/vapor equilibrium of water.

To illustrate the use of a vaporization curve, let’s consider what happens when water boils in a pot that is open to the air. Assume that the air pressure acting on the water is (one atmosphere). When boiling occurs, bubbles of water vapor form throughout the liquid, rise to the surface, and break. For these bubbles to form and rise, the pressure of the vapor inside them must at least equal the air pressure acting on the surface of the water. According to Figure 12-33, a value of corresponds to a temperature of 100 °C. Consequently, water boils at 100 °C at one atmosphere of pressure. In general, a liquid boils at the temperature for which its vapor pressure equals the external pressure. Water will not boil, then, at sea level if the temperature is only 83 °C, because at this temperature the vapor pressure of water is only (see Figure 12-33), a value less than the external pressure of . However, water does boil at 83 °C on a mountain at an altitude of just under five kilometers, because the atmospheric pressure there is .
The fact that water can boil at a temperature less than 100 °C leads to an interesting phenomenon that Conceptual Example 16 discusses.

| Conceptual Example 16 | | | How to Boil Water That is Cooling Down

Figure 12-34a shows water boiling in an open flask. Shortly after the flask is removed from the burner, the boiling stops. A cork is then placed in the neck of the flask to seal it. To restart the boiling, should you pour hot (but not boiling) water or cold water over the neck of the flask, as in part b of the drawing?

Figure 12-34 (a) Water is boiling at a temperature of 100 °C and a pressure of one atmosphere. (b) The water boils at a temperature that is less than 100 °C, because the cool water reduces the pressure above the water in the flask.

Reasoning and Solution When the open flask is removed from the burner, the water begins to cool. Boiling stops, because water cannot boil when its temperature is less than 100 °C and the external pressure is one atmosphere (). Certainly, pouring hot water over the corked flask can rewarm the water within it to some extent. But since the water being poured is not boiling, its temperature must be less than 100 °C. Therefore, it cannot reheat the water within the flask to 100 °C and restart the boiling. However, when cold water is poured over the corked flask, it causes some of the water vapor inside to condense. Consequently, the pressure above the liquid in the flask drops. When the pressure drops to a certain level, boiling restarts. This occurs when the pressure in the flask becomes equal to the vapor pressure of the water at its current temperature (which is now less than 100 °C). Thus, it is possible to restart the boiling by pouring cold water over the neck of the flask.

It takes less heat to boil water high on a mountain, because the boiling point becomes less than 100 °C as the air pressure decreases at higher elevations. (Gregg Adams/Stone/Getty Images)

The operation of spray cans is based on the equilibrium between a liquid and its vapor. Figure 12-35a shows that a spray can contains a liquid propellant that is mixed with the product (such as hair spray). Inside the can, propellant vapor forms over the liquid. A propellant is chosen that has an equilibrium vapor pressure that is greater than atmospheric pressure at room temperature. Consequently, when the nozzle of the can is pressed, as in part b of the drawing, the vapor pressure forces the liquid propellant and product up the tube in the can and out the nozzle as a spray. When the nozzle is released, the coiled spring reseals the can and the propellant vapor builds up once again to its equilibrium value.

Figure 12-35 (a) A closed spray can containing liquid and vapor in equilibrium. (b) An open spray can.

The physics of spray cans.

As is the case for liquid/vapor equilibrium, a solid can be in equilibrium with its liquid phase only at specific conditions of temperature and pressure. For each temperature, there is a single pressure at which the two phases can coexist in equilibrium. A plot of the equilibrium pressure versus equilibrium temperature is referred to as the fusion curve, and Figure 12-36a shows a typical curve for a normal substance. A normal substance expands upon melting (e.g., carbon dioxide and sulfur). Since higher pressures make it more difficult for such materials to expand, a higher melting temperature is needed for a higher pressure, and the fusion curve slopes upward to the right. Part b of the picture illustrates the fusion curve for water, one of the few substances that contract when they melt. Higher pressures make it easier for such substances to melt. Consequently, a lower melting temperature is associated with a higher pressure, and the fusion curve slopes downward to the right.

Figure 12-36 (a) The fusion curve for a normal substance that expands on melting. (b) The fusion curve for water, one of the few substances that contract on melting.

It should be noted that just because two phases can coexist in equilibrium does not necessarily mean that they will. Other factors may prevent it. For example, water in an open bowl may never come into equilibrium with water vapor if air currents are present. Under such conditions the liquid, perhaps at a temperature of 25 °C, attempts to establish the corresponding equilibrium vapor pressure of . If air currents continually blow the water vapor away, however, equilibrium will never be established, and eventually the water will evaporate completely. Each kilogram of water that goes into the vapor phase takes along the latent heat of vaporization. Because of this heat loss, the remaining liquid would become cooler, except for the fact that the surroundings replenish the loss.
In the case of the human body, water is exuded by the sweat glands and evaporates from a much larger area than the surface of a typical bowl of water. The removal of heat along with the water vapor is called evaporative cooling and is one mechanism that the body uses to maintain its constant temperature.

The physics of evaporative cooling of the human body.

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