A. Vapor Pressure
In Section 9.2 we discussed the kinetic energy in a collection of molecules and showed (in Figure 9.3) how the kinetic energy of the molecules were distributed. Figure 10.5 is similar in shape to Figure 9.3 but refers to the distribution of kinetic energies in a liquid.

FIGURE 10.5 Distribution of kinetic energies among the molecules of a liquid at two different temperatures.

Let us assume that a molecule with kinetic energy greater than A in Figure 10.5 has enough energy to overcome the attraction of its neighboring molecules. If the molecule is on the surface of the liquid, it can escape from the body of the liquid and become a gaseous molecule. The number of molecules that have at least this much energy is represented by the area under the curve to the right of A. When these molecules escape the liquid, we say that they have evaporated or vaporized; the process is called evaporation. We can show this process by the equation

Liquid + energy gas

If these gaseous molecules are confined in the space above the liquid - that is, if the liquid sample is in a closed container - some of them, in their random gaseous motion, strike the surface of the liquid and are recaptured by it. This recapturing is called condensation.

When the rate of condensation equals the rate of evaporation, the molecules are in a state of dynamic equilibrium. When a system is in a state of dynamic equilibrium, two opposing processes are going on at the same rate. In this equilibrium, the opposing processes are evaporation and condensation, and

Rate of evaporation = Rate of condensation

For this equilibrium to be established, the system (the closed flask containing both liquid and vapor) must be at constant pressure. The molecules that have escaped are in the atmosphere over the liquid and, like all gases, exert a pressure. The partial pressure (see Section 9.6) they exert is known as the vapor pressure of the liquid.

Note that this equilibrium can take place only in a closed container or closed system. The vapor must accumulate enough to allow a normal distribution of energies before the rate of condensation will equal the rate of vaporization. In an open container, the vapor can escape and equilibrium will not be reached (see Figure 10.6). We recognize this fact when we store liquids in closed containers. Even ethyl ether, with a boiling point (bp 34.5°C) slightly above room temperature, can be stored at room temperature in a tightly closed container. Figure 10.6 shows the two processes of evaporation from an open container and equilibrium in a closed container.

Vapor pressure increases with temperature. Figure 10.5 shows why. At higher temperatures, more molecules have sufficient energy to escape the body of the liquid. Figure 10.7 illustrates how the vapor pressure of a liquid changes with temperature. In that figure, the vapor pressure of water (bp 100°C) and of carbon tetrachloride (bp 78°C) is plotted against temperature (°C). Notice how rapidly the vapor pressure increases. Notice too that, for each, the vapor pressure equals 760 torr at the boiling point. This fact then defines the normal boiling point of a liquid: the temperature at which the vapor pressure of a liquid equals 1 atm.

FIGURE 10.6 (a) Equilibrium between vapor and liquid in a closed container. (b) Nonequilibrium (evaporation) in an open container; equilibrium cannot be established because the vapor does not collect.

FIGURE 10.7 A plot of vapor pressure versus temperature for carbon tetrachloride (CCl4) and for water (H2O). Notice that the vapor pressure of these two liquids equals 760 torr (1 atm) at their normal boiling points (78°C for carbon tetrachloride and 100°C for water).

Although the normal boiling point of a substance is defined as the temperature at which its vapor pressure equals 1 atm, a liquid will boil whenever its vapor pressure equals the gaseous pressure in the space over the liquid. At high altitudes, such as on a mountain, liquids boil at lower temperatures than normal because the atmospheric pressure is less than 1 atm. Foods take longer to cook because the water boils at a lower temperature. Conversely, in a pressure cooker, the vapor is confined and builds up a pressure greater than that of the atmosphere. The boiling point of water in a pressure cooker is above 100°C because of this greater pressure, which means that the water can be hotter than 100°C and still remain a liquid. Foods cook in a shorter time because they are cooking in water that is at a temperature above 100°C.

B. The Specific Heat of Liquids
At the molecular level, the temperature of a liquid is proportional to the average kinetic energy of the molecules within the liquid; any change in temperature corresponds to a change in the average kinetic energy of the molecules.
The specific heat of a liquid is the amount of energy necessary to change the temperature of a one-gram sample by one degree Celsius (review Section 2.5B). The amount of energy necessary to cause this change differs between liquids. This difference means that each liquid has a unique specific heat. Given data for the mass of the sample, its temperature change (T), and the energy added, the specific heat of the sample can be calculated:

Specific heat =

energy change (mass of sample)(T)

 

Example: Calculate the specific heat of ethyl alcohol if 402 J are required to change the temperature of a 9.63 g sample from 21°C to 38°C. Solution Wanted Specific heat (in J/g°C) of ethyl alcohol Given 9.63 g alcohol, 402 J, T = 17°C (temperature change from 21°C to 38°C) Equation Answer 2.46 J/g°C

Example: Suppose 655 J of energy are added to 16.5 g water at 25.0°C. Calculate the final temperature of the sample. Solution Wanted Final temperature. [Note: the final temperature will be 25.0°C + T), therefore we must calculate T.] Given 16.5 g water, 655 J Conversion factors Specific heat of water = 4.184 J/g°C Specific heat = (energy)/(mass x T) Rearranging this equation gives: T = (energy)/(mass x specific heat) Equation

C. The Molar Heat of Vaporization
When energy is added to a liquid, its temperature rises to the boiling point at a rate that is dependent on its specific heat. Energy added to a liquid at its boiling point does not change the temperature. Instead, this added energy counteracts the intermolecular forces in the liquid, and the molecules break apart one by one to vaporize and become gaseous. The amount of energy required to vaporize one mole of a liquid at its boiling point is its molar heat of vaporization ( H_vap). Table 10.1 shows the molecular weight, boiling point, specific heat, and molar heat of vaporization for several liquids. The liquids are listed in order of increasing polarity. Notice that this order is independent of molecular weight.

The molar heat of vaporization of a liquid can be calculated from experimental data, as the following example shows.

TABLE 10.1 Physical properties of liquids

Liquid	Molecular weight	bp (°C)	Hvap (kJ/mol)	Specific heat (J/g°C)
carbon disulfide (CS2)	76.1	46°	28.4	1.000
chloroform (CHCl3)	119.4	61.7°	31.4	0.966
ethyl alcohol (C2H5OH)	46.1	78.5°	40.4	2.45
water (H2O)	18	100°	40.7	4.18

Example: To vaporize 13.6 g benzene at its boiling point, 7.47 kJ are required. Calculate the molar heat of vaporization of benzene. Solution Wanted The molar heat of vaporization in joules per mole (Hvap = ? J/mol) Given 7.47 kJ are required to vaporize 13.6 g benzene Conversion factor 1 mol benzene = 78.1 g benzene Equation Answer 42.9 kJ/mol

Example: The molar heat of vaporization of octane (C8H18) is 38.8 kJ/mol. Calculate the energy in joules necessary to vaporize 83.7 g octane at its boiling point.. Solution Wanted ? J Given 83.7 g octane Conversion factors 1 mol octane = 114.2 g octane Hvap of octane = 38.8 kJ/mol = 38.8 x 103 J/mol Equation Answer 28.4 x 103 J

D. Surface Tension and Viscosity
The surface tension of liquid is the property that causes a liquid to have the smallest possible surface area. Within a liquid, attractive forces operate all around a molecule; on the surface, attraction is only into the body of the liquid (see Figure 10.8). This attraction into the liquid causes the molecules on the surface to minimize surface area, becoming more tightly bound together than those within the liquid.

FIGURE 10.8 Attractive forces (a) within a liquid and (b) at the surface.

Surface tension measures this surface binding. Between different liquids of similar molecular weight, the difference in surface tension can be observed by comparing the different-sized drops formed by the liquids being compared. Large drops mean large intermolecular forces and large surface tension. Surface tension decreases as the temperature and kinetic energy of the molecules increase. The resistance to flow, or the viscosity of a liquid, is another measure of the strength of its intermolecular forces. All liquids flow; some (like gasoline) flow easily, others (like diesel oil) flow very slowly. Resistance to flow means high viscosity and strong intermolecular forces just as did high surface tension. Viscosity decreases as temperature increases; recall the difference in rate of flow between cold and warm diesel oil.