Problem 39 - Introductory Chemistry Atoms First

Question

The water in a beaker of water left in a room will slowly evaporate until the beaker is dry. However, place that same beaker in a sealed box and the water level in the beaker will drop a bit but then remain constant. Is the latter case an example of equilibrium? Explain your answer.

Step-by-Step Solution

Answer

The latter case, where the beaker of water is placed inside a sealed box, is an example of equilibrium. In this scenario, the opposing processes of evaporation and condensation are balanced, and there is no net change in the system, leading to a constant water level in the beaker and a constant amount of water vapor in the sealed box.

Step 1: Define Equilibrium

In a general sense, equilibrium is a state in which opposing forces or processes are balanced, and there is no net change. In a chemical context, chemical equilibrium occurs when the rate of the forward reaction is equal to the rate of the reverse reaction, and the concentrations of the reactants and products remain constant over time.

Step 2: Open System: Beaker of Water in a Room

In this case, the water in the beaker is exposed to the air in the room. When water molecules in the liquid phase gain enough energy to escape into the gas phase, this is known as evaporation. Over time, the water level in the beaker will drop as more and more water molecules evaporate. Since there is no source of additional water molecules to replace the lost ones through the reverse process called condensation, the water in the beaker will eventually evaporate completely. This is not an example of equilibrium, as there is a net change in the system.

Step 3: Closed System: Beaker of Water in a Sealed Box

In this scenario, the beaker of water is placed inside a sealed box. Initially, the water will begin to evaporate just like in the open system. However, since the box is sealed, the vapor molecules have nowhere to go. When the air inside the box becomes saturated with water vapor, the rate of evaporation will equal the rate of condensation - the reverse process, where water molecules in the gas phase lose energy and return to the liquid phase. At this point, there is no net change in the water level of the beaker or the amount of water vapor in the box, which means that the system has reached equilibrium.

Step 4: Conclusion

The latter case, where the beaker of water is placed inside a sealed box, is an example of equilibrium. In this scenario, the opposing processes of evaporation and condensation are balanced, and there is no net change in the system, leading to a constant water level in the beaker and a constant amount of water vapor in the sealed box.

Key Concepts

Evaporation

Evaporation is a surface phenomenon in which molecules of a liquid gain enough energy to transition into the gaseous state. This process occurs when the individual molecules of a substance, like water, absorb energy from their surroundings, typically in the form of heat. Once they reach a certain energy threshold, these molecules are able to overcome the attractive forces holding them in the liquid and escape into the air as vapor.

It's important to understand that evaporation is a cooling process, as the highest energy molecules are the ones most likely to evaporate, leaving the remaining liquid with a lower average kinetic energy and thus a lower temperature. An everyday example of evaporation is the drying of wet clothes in the air. The rate at which evaporation happens depends on several factors, including temperature, surface area, humidity, and air movement.

Condensation

Condensation is the opposite process of evaporation, where water vapor in the air loses energy and changes back into liquid form. This occurs when the temperature of the vapor falls below its dew point, or when it comes into contact with a surface that is cooler than the air around it. In a sealed system, condensation plays a critical role in achieving equilibrium.

One familiar example of condensation is the formation of dew on grass in the early morning. As the grass cools overnight, it cools the air around it to below the dew point, causing water vapor in the air to condense into tiny droplets on the surface of the grass. Inside a closed system, the condensed vapor returns to the liquid state, thereby preventing the loss of molecules that would otherwise result in a dry beaker.

Closed System

A closed system is a concept critical to understanding chemical equilibrium. In such a system, matter is not allowed to enter or leave, although energy in the form of heat or work may be exchanged with the surroundings. This containment of matter is what enables the establishment of equilibrium, as seen in the example of a beaker of water in a sealed box.

The concept of a closed system is key in many scientific and engineering disciplines. In thermodynamics, it helps us understand how energy is conserved and transferred. In our beaker example, the contained water vapor can't escape, and so the rates of evaporation and condensation eventually balance each other out—no net loss of water occurs, and the water level stabilizes, illustrating the dynamic balance of a system in equilibrium.