0.15 Phase transitions and phase equilibrium  (Page 7/7)

It is interesting that the vapor pressure does not depend on the surface area of the liquid, even though the rate at which gas molecules condense must be greater when there is more liquid surface to strike. With a constant vapor pressure for larger surface area and greater rate of condensation, it must be that the evaporation rate is also greater for a larger surface area. This makes sense and agrees with everyday observation: when a liquid is spread out over a larger area, it evaporates more quickly.

This explanation begs another question: what determines the rate of evaporation? It appears that the rate of evaporation does not change when the temperature is unchanged, so let’s change the temperature. This leads us back to the experimental data in Figure 5, which shows that the vapor pressure always increases as we increase the temperature. It is important to realize that this increase is not due solely to the relationship between pressure and temperature in the Ideal Gas Law. That relationship is proportional. The pressure increases in Figure 5 are much, much larger than proportional to the temperature increases.

At higher temperature for a specific liquid, the vapor pressure increases. This means that there are more molecules in the vapor phase at the higher temperature, and as such, the rate of condensation must be higher at the higher temperature. But at equilibrium the rate of condensation must equal the rate of evaporation. This means that the rate of evaporation is also larger at the higher temperature. Furthermore, the rate of evaporation must depend on what the substance of the liquid is, since we get a different vapor pressure for each liquid, and therefore a different rate of condensation and a different rate of evaporation.

We need to develop a model that accounts for these observations, that a higher temperature must mean a higher rate of evaporation and that different substances have different rates of evaporation. We recall that for gases, temperature is a measure of the kinetic energy of the molecules. We can easily believe that the same is true for the kinetic energy of the molecules in the liquid phase. In fact, our vapor pressure data indicate that this is true, because at higher temperatures, more molecules are able to escape the liquid. The rate of evaporation must be determined by the number of molecules in the liquid that have sufficient kinetic energy to escape the intermolecular forces in the liquid. By increasing the temperature, we increase this number, so the rate of evaporation goes up. Therefore, the temperature of the liquid is a measure of the kinetic energy of the molecules in the liquid.

We are left only to understand why the rate of evaporation varies from substance to substance. For a substance with a lower vapor pressure and therefore lower rates of condensation and evaporation, it must be that that substance has fewer molecules with sufficient kinetic energy to escape the liquid at a given temperature. This strongly indicates that the forces of attraction between the molecules in the liquid are greater for that substance.

In combination, these two conclusions give us a kinetic molecular model for liquids. The molecules in the liquid are in constant motion in close proximity to each other with attractive forces between them. The strength of the attractive force depends on the type of molecule.

This model also reveals the dynamic equilibrium to us. At a given temperature, a fraction of the liquid molecules have sufficient kinetic energy to evaporate, and this fixes the rate of evaporation. The rate of condensation must match this rate of evaporation at equilibrium, and this can only be true at a specific pressure of the gas. Therefore, at a given temperature, only a single pressure will result in phase equilibrium for that substance. As we change the substance, we change the intermolecular attractions, and this changes the rate of evaporation and therefore changes the vapor pressure at equilibrium.

In the next study, we will examine the phase equilibrium in greater detail, and in particular we will take a much closer look at these intermolecular attractions.

Review and discussion questions

1. We observe that, when the applied pressure is less than the vapor pressure of a liquid, all of the liquid will spontaneously evaporate. In terms of dynamic equilibrium, explain why no liquid can be present under these conditions.
2. Using arguments from the Kinetic Molecular Theory and the concept of dynamic equilibrium, explain why, at a given applied pressure, there can be one and only one temperature, the boiling point, at which a specific liquid and its vapor can be in equilibrium.
3. Using dynamic equilibrium arguments, explain why the vapor pressure of a liquid is independent of the amount of liquid present.
4. Using dynamic equilibrium arguments, explain why the vapor pressure of a liquid is independent of the volume available for the vapor above the liquid.
5. The text describes dynamic equilibrium between a liquid and its vapor at the boiling point. Describe the dynamic equilibrium between a liquid and its solid at the melting point. Using this description, explain why the melting point of a solid varies very little as the pressure increases.
6. We observed that, without exceptions, substances with high vapor pressures have low boiling points, and substances with low vapor pressures have high boiling points. Using dynamic equilibrium, explain this correlation.