Question

When a molecule escapes from the surface of a liquid by evaporation, it has a kinetic energy that's much larger than the average \(\mathrm{KE}\). Why is it likely that after being in the vapor for a while its kinetic energy will be much less? If this molecule collides with the surface of the liquid, is it likely to bounce out again?

Short answer

After evaporation, the molecule's kinetic energy will likely decrease through collisions in the vapor phase, leading it to have an energy close to the average. Upon collision with the liquid surface, it is unlikely to have the necessary energy to escape again, making re-entry into the liquid more probable than bouncing out.

Step-by-step solution

Understanding Evaporation

Evaporation occurs when a molecule at the surface of a liquid gains enough kinetic energy to overcome the intermolecular forces and escape into the vapor phase. This molecule typically has a higher kinetic energy than the average because it must have enough energy to break free from the liquid's surface.

Energy Distribution in the Vapor Phase

Once in the vapor phase, the molecule will likely collide with other gas molecules. These collisions tend to redistribute the kinetic energy amongst the molecules, leading to an overall equilibrium in energy distribution. This process results in the previously high-energy molecule losing some of its kinetic energy and having kinetic energy much closer to the average of the vapor phase molecules over time.

Probability of Re-entry into the Liquid

If this molecule collides with the surface of the liquid, the likelihood of it bouncing back out again is related to its kinetic energy at the moment of collision. Due to the redistribution of energy as mentioned in the previous step, it now has kinetic energy closer to the average of the vapor phase. Therefore, unless it happens to have kinetic energy that is again above the threshold needed to escape the liquid, it is not likely to bounce out upon collision but rather be reabsorbed into the liquid.

Key concepts

Kinetic Energy in Evaporation

Kinetic energy (KE) is the energy an object possesses due to its motion. In the context of evaporation, molecules within a liquid are constantly moving and colliding with each other. To escape into the vapor phase, a molecule must have sufficient kinetic energy to overcome the attractive forces holding it within the liquid, known as intermolecular forces.

Not every molecule has the same kinetic energy; instead, there is a distribution of energies. Molecules on the surface that have higher than average kinetic energy can break these forces and evaporate. This is why, during evaporation, the escaping molecules are those with kinetic energies much larger than average. Over time, as these molecules collide with others in the vapor phase, their kinetic energies adjust to match the average energy of the system, leading to a decrease in their individual kinetic energies.

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion which act between neighboring particles (atoms, molecules, or ions). These forces dictate the physical properties of substances, like boiling points and melting points.

In a liquid, intermolecular forces hold the molecules close together. Molecules escaping the liquid during evaporation must do so by breaking these forces, which requires energy. The stronger these forces, such as hydrogen bonds or dipole-dipole interactions, the higher the necessary kinetic energy to escape. On the other hand, weaker forces like London dispersion forces require less energy to overcome. Understanding these forces helps explain why certain substances evaporate more readily than others.

Vapor Phase Equilibrium

Vapor phase equilibrium is a state where the rate of evaporation of a liquid equals the rate of condensation from its vapor.

In a closed system, molecules constantly escape the liquid and enter the vapor phase, but some vapor molecules also re-enter the liquid. Over time, the system reaches a balance where the amount of liquid and vapor remains constant, known as dynamic equilibrium. At this point, although individual molecules continue to move between phases, there is no net change in the amount of liquid or vapor. The kinetic energy of molecules in the vapor phase plays a crucial role in maintaining this equilibrium, as it influences both their ability to remain in the vapor phase and their probability of re-entering the liquid upon collision.

Energy Distribution in Gases

The distribution of kinetic energy among molecules in gases can be described by the Maxwell-Boltzmann distribution. This principle asserts that in a gas, molecules have a range of speeds and, consequently, a range of kinetic energies.

Most molecules have moderate speeds, while a few have either very high or very low speeds. This distribution is crucial for understanding phenomena like evaporation because it predicts that there will always be some molecules with enough energy to escape the liquid. After evaporation, as these molecules interact through collisions, their kinetic energies tend to redistribute until a state of equilibrium is reached where the energy distribution reflects that of the Maxwell-Boltzmann statistics.