Problem 66 - Chemistry and Chemical Reactivity

Question

A sample of liquid water is sealed in a container. Over time some of the liquid evaporates, and equilibrium is reached eventually. At this point you can measure the equilibrium vapor pressure of the water. Is the process \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftarrows\) \(\mathrm{H}_{2} \mathrm{O}(\ell)\) a dynamic equilibrium? Explain the changes that take place in reaching equilibrium in terms of the rates of the competing processes of evaporation and condensation.

Step-by-Step Solution

Answer

Yes, it's a dynamic equilibrium where evaporation and condensation occur at equal rates.

Step 1: Understanding Dynamic Equilibrium

A dynamic equilibrium occurs when two opposing processes occur at the same rate, resulting in no net change in the system. In the context of this exercise, this means that the rate of evaporation of water to vapor must equal the rate of condensation of vapor back to liquid water.

Step 2: Analyzing the Evaporation Process

Initially, the evaporation rate is higher than the condensation rate because the vapor pressure inside the container is low. Water molecules on the surface gain enough energy to overcome intermolecular forces and escape into the vapor phase.

Step 3: Examining the Condensation Process

As more water molecules enter the vapor phase, vapor pressure increases. Over time, more vapor molecules attempt to return to the liquid state by condensing. This increases the condensation rate.

Step 4: Reaching Equilibrium

Equilibrium is reached when the rate of evaporation equals the rate of condensation. At this point, the amount of liquid and vapor remains constant over time, although molecules continue to transition between the phases.

Key Concepts

Evaporation

Evaporation is a process where liquid molecules transition into the gaseous phase. This occurs when molecules at the liquid's surface gain sufficient energy to break free from the intermolecular forces holding them together. These forces are weaker on the surface, making it easier for molecules to escape. As evaporation progresses, the liquid loses some molecules into the air, increasing the vapor concentration over the liquid.

Factors that influence the rate of evaporation include:

• Temperature: Higher temperatures provide more energy for molecules to escape.
• Surface area: A larger surface area allows more molecules to evaporate.
• Air movement: Wind can remove vapor, allowing more molecules to evaporate.

Evaporation is key to reaching dynamic equilibrium in a closed system.

Condensation

Condensation is the process where gas molecules lose energy and transition back into the liquid phase. As the vapor molecules collide with the liquid surface, they lose energy and rejoin the liquid, especially as they cool down. Over time, as more and more molecules condense, the liquid level in a container can increase or stabilize, depending on equilibrium conditions.

In a sealed environment, condensation becomes crucial in balancing the liquid and gas phases. As the vapor pressure builds up, more molecules in the vapor phase will condense back into the liquid. The condensation rate eventually catches up with the evaporation rate, leading to a balanced system.

Vapor Pressure

Vapor pressure is the pressure exerted by vapor when it is in equilibrium with its liquid form in a closed system. It represents the tendency of molecules to escape from the liquid to the vapor phase. At the molecular level, vapor pressure is established by collisions of vapor molecules against the walls of the container.

Factors influencing vapor pressure include:

• Temperature: Higher temperatures increase kinetic energy, thus increasing vapor pressure.
• Nature of the liquid: Liquids with weaker intermolecular forces have higher vapor pressures as their molecules escape more easily.

Vapor pressure at equilibrium signifies a precise balance between evaporation and condensation. It remains constant once this balance is achieved.

Equilibrium

Equilibrium in a chemical context refers to a state where the forward and reverse processes occur at the same rate, leading to no net change in the system. In the case of evaporation and condensation, a dynamic equilibrium is achieved when the rate of water molecules leaving the liquid phase equals the rate of vapor molecules returning. This does not mean that the processes stop; they continue but with no overall change in the quantity of liquid or vapor.

The presence of dynamic equilibrium is critical in maintaining the vapor pressure of a liquid constant over time. Once equilibrium is reached, the system is stable, with ongoing movement of molecules between the phases but no alteration in their overall amounts. This balance allows for predictable and consistent properties within the system.