Vapor Pressure & Intermolecular Forces
Dr. Perona

You have probably observed that if water is left in an open container at room temperature it will eventually evaporate completely, even though its temperature is never raised to the boiling point. The explanation for this behavior is that some of the molecules in the liquid have enough kinetic energy to overcome the intermolecular forces, which hold the molecules of the liquid together, and are able to escape into the vapor phase. The molecules in the vapor phase then diffuse away, and a net loss of liquid occurs.

The evaporative process results in a momentary loss of the most energetic molecules from the liquid sample. Heat energy is continuously absorbed from the surroundings and so the supply of energetic molecules is maintained. This continues until all of the liquid has evaporated.

If the liquid water is placed in a closed container at constant temperature, however, the amount of liquid water will at first decrease and then remain constant. It will appear as if evaporation has stopped. In fact, evaporation does not stop. What happens is that since the vapor phase molecules cannot escape, their number initially increases. This results in an increase in the frequency of their collisions with each other and with the liquid surface. Collisions with the liquid surface lead to condensation. Ultimately the rate of condensation becomes equal to the rate of evaporation, and the relative amounts of water in the two phases remains constant. This corresponds to a condition of dynamic equilibrium. The word "dynamic" emphasizes the fact that both evaporation and condensation are still occurring, but they are occurring at the same rate. The water molecules in the vapor phase exert a pressure on the container walls. This pressure is referred to as the equilibrium vapor pressure of water or just the vapor pressure.

The vapor pressure of a liquid depends upon the molecular structure of the liquid and upon the temperature. Increasing the temperature increases the average kinetic energy of the liquid molecules, and hence the fraction of molecules with sufficient energy to escape from the liquid phase. Thus, the vapor pressure increases with temperature.

The variation of the vapor pressure, P, with the absolute or Kelvin temperature, T, is given by

vap2.gif (672 bytes)

where ΔHvap is the molar enthalpy of vaporization in units of J/mol and R is the gas constant, also in units of J/mol*K. (R = 8.314 J/mol*K).

This equation can be solved for ΔHvap:

vap3.gif (641 bytes)

Thus, by measuring the vapor pressure at two different temperatures, the molar enthalpy of vaporization can be determined. As you might expect, ΔHvap increases with the strength of the intermolecular force.

The structure of the molecules in the liquid determines the strength of the intermolecular forces holding the molecules together. If the intermolecular force is strong, the fraction of molecules that have enough energy to escape into the vapor is small and the vapor pressure will be small. On the other hand, if the intermolecular force is relatively weak, a large fraction of the molecules will be able to escape into the vapor and the vapor pressure will be large. By comparing the vapor pressures of various liquids at constant temperature, we can determine the relative strengths of the intermolecular forces in the liquids.

Intermolecular Forces:

The weakest intermolecular force is the induced dipole-induced dipole or London force. It arises from the fact that the shape of the electronic cloud in a molecule fluctuates with time. This fluctuation results in an instantaneous dipole moment in the molecule, which induces momentary dipole moments in neighboring molecules. The attraction between these momentary dipoles results in the London force. This force exists between all types of molecules whether polar or nonpolar since all molecules contain electrons. It is the primary force responsible for holding together the molecules in nonpolar liquids and solids.

The strength of the London force increases with the number of electrons in the molecule. Since the number of electrons increases with molar mass, we generally find the strength of the London force increases with molar mass.

In the case of polar substances, London forces exist, but in addition, the presence of a permanent dipole moment in the molecules results in a much stronger dipole-dipole intermolecular force. Thus, polar substances will generally have lower vapor pressures than nonpolar substances with the same molar mass. For example, consider the substances butane, C4H10, and acetone, C3H6O, both of which have a molar mass of 58, and hence equally strong London forces. The vapor pressures of butane and acetone at 25C, respectively are: 1735 mm Hg and 200. mm Hg. Why is the vapor pressure of butane so much higher than that of acetone? The answer is that in butane, which contains only hydrogen and carbon, the bonds are nonpolar since hydrogen and carbon have nearly equal electronegativities. Hence the molecule as a whole is nonpolar, and the only significant intermolecular force is the London type. On the other hand, acetone is a polar molecule as shown below.

Acetone molecules experience both the London Force and the much stronger dipole-dipole force. This explanation is supported by the fact that the molar enthalpy of vaporization of acetone is greater than that of butane (32.0 kJ/mole vs. 24.3 kJ/mole). That is, more energy is required to vaporize one mole of acetone than one mole of butane.

An especially strong dipole-dipole intermolecular force, called a hydrogen bond, results when a molecule contains a hydrogen atom attached to either of the highly electronegative atoms O, N or F. This results in highly polar covalent bonds. For example, in water the O-H bond is highly polar due to the large electronegativity difference between the O and H atoms. This H atom bears a large positive partial charge and the O atom bears a large negative partial charge. The attraction between the charged ends of the water molecules results in hydrogen bond formation.  Another class of compounds in which hydrogen bonding is important are alcohols, which contain at least one -OH group.  The strength of hydrogen bonding leads to significant reduction in vapor pressure and increase in boiling point.  For example, without hydrogen bonding ethyl alcohol would be a gas at room temperature.