# 11.5 Vapor Pressure

We have seen that molecules can escape from the surface of a liquid into the gas phase by vaporization or evaporation. Suppose we conduct an experiment in which we place a quantity of ethanol, C2H5OH, in an evacuated, closed container such as that in Figure 11.20. The ethanol will quickly begin to evaporate. As a result, the pressure exerted by the vapor in the space above the liquid will begin to increase. After a short time the pressure of the vapor will attain a constant value, which we called the vapor pressure of the substance.

FIGURE 11.20 Illustration of the equilibrium vapor pressure over liquid ethanol. In (a) we imagine that no molecules exist in the gas phase; there is zero pressure in the cell. In (b) the rate at which molecules leave the surface equals the rate at which gas molecules pass into the liquid phase. These equal rates produce a stable vapor pressure that does not change as long as temperature remains constant.

## Explaining Vapor Pressure on the Molecular Level

The molecules of a liquid move at various speeds. Figure 11.21 shows the distribution of kinetic energies of the particles at the surface of a liquid at two temperatures. The distribution curves are like those shown earlier for gases (Figures 10.15 and 10.16). At any instant some of the molecules on the surface of the liquid possess sufficient energy to escape from the attractive forces of their neighbors. The weaker the attractive forces, the larger the number of molecules that are able to escape into the gas phase, and hence the higher the vapor pressure.

FIGURE 11.21 Distribution of kinetic energies of surface molecules of a hypothetical liquid at two temperatures. The fraction of molecules having sufficient kinetic energy to escape the liquid is given by the shaded area. Notice that the fraction of molecules that can escape increases with increasing temperature.

At any particular temperature the movement of molecules from the liquid to the gas phase goes on continuously. However, as the number of gas-phase molecules increases, the probability increases that a molecule in the gas phase will strike the liquid surface and stick there, as shown in Figure 11.20(b). Eventually, the rate at which molecules return to the liquid is exactly equal to the rate at which they escape. The number of molecules in the gas phase then reaches a steady value, and the pressure of the vapor at this stage becomes constant.

The condition in which two opposing processes are occurring simultaneously at equal rates is called a dynamic equilibrium. A liquid and its vapor are in equilibrium when evaporation and condensation occur at equal rates. The observer may conclude that nothing is occurring during an equilibrium because there is no net change in the system. In fact, a great deal is happening; molecules continuously pass from the liquid state to the gas state and from the gas state to the liquid state. All equilibria between different states of matter possess this dynamic character. The vapor pressure of a liquid is the pressure exerted by its vapor when the liquid and vapor states are in dynamic equilibrium.

## Volatility, Vapor Pressure, and Temperature

When vaporization occurs in an open container, as when water evaporates from a bowl, the vapor spreads away from the liquid. Little, if any, is recaptured at the surface of the liquid. Equilibrium never occurs, and the vapor continues to form until the liquid evaporates to dryness. Substances with high vapor pressure (such as gasoline) evaporate more quickly than substances with low vapor pressure (such as motor oil). Liquids that evaporate readily are said to be volatile.

Hot water evaporates more quickly than cold water because vapor pressure increases with temperature. We see this effect in Figure 11.21: As the temperature of a liquid is increased, the molecules move more energetically and a greater fraction can therefore escape more readily from their neighbors. Figure 11.22 depicts the variation in vapor pressure with temperature for four common substances that differ greatly in volatility. Note that the vapor pressure in all cases increases nonlinearly with increasing temperature.

FIGURE 11.22 Vapor pressure of four common liquids, shown as a function of temperature. The temperature at which the vapor pressure is 760 torr is the normal boiling point of each liquid.

## Vapor Pressure and Boiling Point

A liquid boils when its vapor pressure equals the external pressure acting on the surface of the liquid. At this point bubbles of vapor are able to form within the interior of the liquid. The temperature of boiling increases with increasing external pressure. The boiling point of a liquid at 1 atm pressure is called its normal boiling point. From Figure 11.22 we see that the normal boiling point of water is 100°C.

The boiling point is important to many processes that involve heating liquids, including cooking. The time required to cook food depends on the temperature. As long as water is present, the maximum temperature of the cooking food is the boiling point of water. Pressure cookers work by allowing steam to escape only when it exceeds a predetermined pressure; the pressure above the water can therefore increase above atmospheric pressure. The higher pressure causes water to boil at a higher temperature, thereby allowing the food to get hotter and so cook more rapidly. The effect of pressure on boiling point also explains why it takes longer to cook food at higher elevations than at sea level. The atmospheric pressure is lower at higher altitudes, so water boils at a lower temperature.

### Sample Exercise 11.4

Use Figure 11.22 to estimate the boiling point of diethyl ether under an external pressure of 600 torr.

SOLUTION The boiling point is the temperature at which the vapor pressure is equal to the external pressure. From Figure 11.22 we see that the boiling point at 600 torr is about 27°C, which is close to room temperature. We can make a flask of diethyl ether boil at room temperature by using a vacuum pump to lower the pressure above the liquid to about 600 torr.

### Practice Exercise

At what external pressure will ethanol have a boiling point of 60°C? Answer: about 350 torr