Question

Some liquid water is placed in a room-temperature container and sealed. After some time, the level of the liquid drops by a small amount. After that, the water level remains constant.

Short answer

In conclusion, the initial decrease in the liquid water level is due to evaporation, while the eventual constant water level results from the establishment of a dynamic equilibrium between evaporation and condensation in the sealed container. This equilibrium is governed by the vapor pressure of the liquid at room temperature.

Step-by-step solution

Identify the initial conditions

In the beginning, some liquid water is placed in a room-temperature container. The container has a fixed volume, and the water level is constant initially. The system is in a not fully equilibrium state as there is a transition between the liquid and gas phase.

Explain the initial decrease in water level

The liquid water molecules possess a range of energies. Some molecules will have enough energy to overcome the intermolecular forces that hold them together in the liquid state. When this happens, these molecules escape from the liquid surface to enter the gas phase, which is called evaporation. This transition causes a decrease in the liquid water level.

Describe the role of the sealed container

If the container were not sealed, the escaped water molecules would leave the container and disperse into the surrounding environment. Since the container is sealed in this case, the water molecules cannot escape, and they remain in the container's space above the liquid surface.

Discuss the establishment of equilibrium

The escaped water molecules will collide with the liquid surface and can get trapped by the intermolecular forces again, returning to the liquid phase. This process is called condensation. As more and more water molecules evaporate and enter the gas phase, the rate of condensation increases. Eventually, the rate of evaporation will equal the rate of condensation, and the system reaches a dynamic equilibrium. At this point, no net change occurs in the amount of liquid water, so the water level remains constant.

Connect the concepts to thermodynamics

This phenomenon can be explained using the concept of vapor pressure, which is the pressure exerted by vapor in equilibrium with its corresponding liquid at a given temperature. In the sealed container, the water vapor pressure rises until it reaches a value that corresponds to the liquid water's vapor pressure at room temperature. Once this happens, the equilibrium is established, and the water level remains constant. In conclusion, the initial decrease in the liquid water level is due to evaporation, while the eventual constant water level results from the establishment of a dynamic equilibrium between evaporation and condensation in the sealed container. This equilibrium is governed by the vapor pressure of the liquid at room temperature.

Key concepts

Evaporation

When liquid water is exposed to the air, some of its molecules gain enough energy to escape the liquid surface and become gas. This process is known as evaporation. During evaporation, the molecules that break free are those with higher kinetic energy.

• This means that they were moving faster than others and managed to overcome the attractive forces holding them together in the liquid state.
• Because evaporation primarily removes higher-energy molecules, the remaining liquid has a slightly lower average energy, or temperature.

In a sealed container, however, these escaping water molecules can only go so far. Eventually, they start to accumulate in the vapor space above the liquid surface.

Condensation

As water molecules accumulate in the vapor space above a liquid in a sealed container, they will eventually begin to return to the liquid phase. This process is called condensation.

• Condensation occurs when gas molecules lose energy, usually through collisions with other molecules or the container walls.
• When these gas molecules approach the liquid surface, they can be captured by the liquid's cohesive intermolecular forces and reincorporated into the liquid.

In an environment that allows condensation, the rate of gas molecules returning to the liquid can increase over time, helping establish a balance with the rate of evaporation.

Vapor Pressure

Vapor pressure is an important concept when discussing dynamic equilibrium in a sealed container. It is the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase at a given temperature.

• When evaporation and condensation occur at equal rates, the vapor pressure reaches a constant value.
• This pressure indicates the tendency of molecules to escape from the liquid to enter the gas phase.
• The higher the vapor pressure, the more 'volatile' the substance, meaning it evaporates easily.

In our sealed container scenario, water achieves a vapor pressure specific to room temperature, signifying equilibrium.

Thermodynamics

Thermodynamics is the branch of science concerned with heat and temperature and their relation to energy and work. The principles of thermodynamics help to explain phenomena like evaporation and condensation.

• In a sealed system like our container, energy remains consistent, aligning with the first law of thermodynamics - the conservation of energy.
• The dynamic equilibrium reached, where evaporation equals condensation, is an example of a system minimizing free energy.
• At equilibrium, the potential energy in the vapor phase and liquid phase balances, reflecting the concept of entropy, a measure of disorder or randomness in the system.

Understanding these concepts explains why the water level eventually remains stable in the container.