Dynamic Systems and Equilibrium

There is a common misconception that the rate of evaporation of water is slower when the relative humidity is high. But that is actually not true. How would the amount of water vapor in the air affect how often a water molecule at the surface of a liquid state breaks away and enters a gas state? One of the keys to developing a deeper understanding of science is to be able to visualize and analyze atoms and molecules as physical objects, and to not accept explanations unless you can understand them on a physical level. The only way water molecules in the air would possibly slow down the rate of evaporation of liquid water is because they contribute to the overall air pressure above the liquid surface (knocking some of the water molecules breaking away from the liquid state back into the liquid state). But it does not make any difference if the molecules in the air above the liquid surface are water molecules, carbon dioxide molecules, oxygen molecules, or some other kind of molecule.

But doesn’t water evaporate more slowly on extremely humid days? Isn’t that what we observe in the real world? This is where we have to be really precise with our observations and our language. Liquid water will “dry” more slowly on a humid day, but that is not the same as saying that water is “evaporating” more slowly. Evaporation and condensation are always happening simultaneously. At the same time that water molecules are breaking away from the liquid state and entering a gas state, water molecules in the gas state are getting “captured” and entering the liquid state. Students often have difficulty understanding that both processes are happening at the same time; they struggle to understand when evaporation takes over and when condensation takes over, without realizing that evaporation and condensation are never just turned on or off. When a towel is drying, water molecules are still condensing on the towel. When water is beading up on the outside of an ice-cold glass on a hot summer day, water molecules are still evaporating from those beads of water.

Probability on a Molecular Scale

When we introduced the concepts of evaporation and condensation, we were very careful to keep them separated for clarity. But now it is time to update our simulations to better reflect the real world.

Rate of Evaporation:
molecules/s
Rate of Condensation:
molecules/s

Is this simulation modeling evaporation or condensation? Actually, it is modeling both. Overall, the liquid water at the bottom of the container ends up “drying” because the rate of evaporation is faster than the rate of condensation.

Rate of Evaporation:
molecules/s
Rate of Condensation:
molecules/s

If we double the humidity (the amount of water vapor in the air), then the liquid water at the bottom of the container does take much more time to dry. But is the rate of evaporation any slower? No. Water molecules are still evaporating at the same rate; it is just that the rate of condensation has increased. When water condenses on the outside of an ice-cold glass on a hot summer day, evaporation and condensation are both occurring. Condensation is just happening faster, so the net result is a build up of liquid water on the outside of the glass.

When the rate of evaporation equals the rate of condensation, then we have reached a state of equilibrium where the amount of liquid water at the bottom of the container will stay the same. However, even though the overall amount of liquid water is not changing, water molecules are still evaporating and condensing. This is called a dynamic system because things are changing over time. When a dynamic system reaches equilibrium, it looks like nothing is changing from the outside, but if you look closer, things are still changing but the changes are balanced so the net effect is zero.

Thermodynamics and Kinetics

Here is an interesting thought experiment for you to consider. Imagine a container with a layer of liquid water at the bottom. However, if instead of an open container (which is what we have been simulating so far), the container is sealed so that water molecules cannot get in or out of the container. The air above the liquid water is completely dry (there are no water molecules in the air) and at standard atmospheric pressure. The water, the container, and the air are all at room temperature (20 °C). What will happen over time?

Rate of Evaporation:
molecules/s
Rate of Condensation:
molecules/s

Water molecules will begin evaporating from the liquid state. The rate of evaporation will depend on the attraction between water molecules, the surface area, the temperature, and the air pressure. There will be no condensation at first because there are no water molecules in the air to condense. But once evaporation begins (and water molecules enter a gas state), condensation will begin as well. The rate of condensation will depend on the attraction between water molecules, the surface area, the temperature, and the concentration of water molecules in the air above the liquid water.

The rate of evaporation stays the same in our simulation (actually, in real life, it would slow down a little bit because the addition of water vapor into the air will increase the air pressure slightly), but the rate of condensation speeds up as the amount of water molecules in the air increases. At some point, this dynamic system will reach a state of equilibrium where the rate of evaporation will equal the rate of condensation. When that happens, we say that the air is “saturated” and cannot “hold” any more water… relative humidity is now 100%.

The Importance of Precise Language

Once the system modeled in the simulation above has reached equilibrium, what would happen if we lowered the temperature of the water, the container, and the air to 5 °C (41 °F)? Changing the temperature of the system would disrupt the equilibrium of the system. The rate of evaporation would change and the rate of condensation would change (both depend on the temperature), and the two rates would no longer be in balance. As a second interesting thought experiment, predict what will happen after the temperature is lowered and explain why it happens. The system would eventually find a new equilibrium: what would that second equilibrium state look like compared to the first equilibrium state?

Investigating Dynamic Systems

After we lower the temperature in our thought experiment, the rate of evaporation will slow down and the rate of condensation will speed up. The net effect will be an increase in the amount of water in the liquid state and a decrease in the amount of water in the gas state. Will this continue until there is no more water in the gas state and all of the water is in the liquid state? No. The system will find a new equilibrium state before that happens. As the amount of water in the gas state decreases, the rate of condensation will also slow down. At some point (before the amount of water in the gas state is zero), the rate of condensation will slow down to the same speed as the rate of evaporation. Lowering the temperature has driven the system to a new equilibrium where the percentage of water in the gas state is lower.

This is a graph of what our data might look like if we could collect it from our thought experiment. The blue and red bars represent how much water (in grams) is in the liquid and gas states. The total amount of water in the entire system is 200 g. The blue and red lines show the rates of evaporation and condensation (in grams per second). You can see that the system starts out in equilibrium (the rate of evaporation and the rate of condensation are balanced, both at 0.24 g/s), the equilibrium gets disrupted (the rate of condensation jumps to 0.3 g/s and the rate of evaporation drops to 0.2 g/s), and then the system gradually moves to a new equilibrium. In real life, measuring the rate of evaporation separately from the rate of condensation would be very difficult.