Question

Some water is placed in a sealed glass container connected to a vacuum pump (a device used to pump gases from a container), and the pump is turned on. The water appears to boil and then freezes. Explain these changes using the phase diagram for water. What would happen to the ice if the vacuum pump was left on indefinitely?

Short answer

Initially, water is in a liquid state in a sealed container connected to a vacuum pump. As the vacuum pump removes gas molecules and reduces pressure inside the container, the boiling point of water decreases, causing it to boil at room temperature. Further decrease in pressure causes the remaining water to reach the solid-liquid coexistence line in the phase diagram, resulting in freezing. If the vacuum pump is left on indefinitely, the ice will enter the solid-gas coexistence region, causing it to sublimate directly into water vapor, leaving only water vapor in the container.

Step-by-step solution

Understanding the phase diagram of water

A phase diagram is a graphical representation of the physical states of a substance (solid, liquid, and gas) as a function of temperature and pressure. For water, the diagram shows the regions where solid (ice), liquid (water), and gas (water vapor) coexist and where phase transitions occur.

Initial state of water in the container

Initially, water is placed in a sealed glass container connected to a vacuum pump. At this point, the water is at room temperature and atmospheric pressure, which puts it in the liquid phase according to the phase diagram.

Turning on the vacuum pump

When the vacuum pump is turned on, it starts removing gas molecules from the container, which reduces the pressure inside. As the pressure decreases, the boiling point of water also decreases, as indicated by the leftward movement along the liquid-gas coexistence curve in the phase diagram. When the pressure gets low enough, the water begins to boil at room temperature.

Water appears to boil

The water appears to boil not because it is being heated but because the pressure inside the container is being reduced, causing the water to undergo a phase transition from liquid to gas (evaporation). If the vacuum pump keeps reducing the pressure, the water will continue to boil and produce water vapor.

Water freezes

As the pressure continues to decrease and more water evaporated, the remaining water will eventually reach the solid-liquid coexistence line in the phase diagram (triple point). At this point, any further decrease in pressure (while keeping the temperature constant) will cause the water to freeze, forming ice.

What happens when the vacuum pump is left on indefinitely?

If the vacuum pump continues to run and lower the pressure even further, the ice will enter the solid-gas coexistence region in the phase diagram. Thus, the ice will sublimate or directly turn from a solid to a gas without going through the liquid phase. Over time, all the ice will eventually turn into water vapor, and the container will be left with only water vapor in it.

Key concepts

Boiling Point

The boiling point of a substance is the temperature at which it changes from a liquid to a gas. For water, this typically occurs at 100°C under standard atmospheric pressure (1 atm). However, this boiling point is not constant and can be affected by changes in pressure.

When the pressure is reduced, as when a vacuum pump is used in a sealed container, the boiling point decreases. This is because lower pressure allows water molecules to escape the liquid phase more easily, causing it to boil at a lower temperature.

In the context of the exercise, as the vacuum pump decreases the pressure inside the container, the water starts boiling at room temperature, even though no additional heat was applied. This demonstrates the relationship between pressure and the boiling point of water.

Pressure and Temperature

Pressure and temperature are crucial factors that determine the state of water. Water can exist in three primary states: solid (ice), liquid (water), and gas (vapor).

The phase diagram of water illustrates how these states vary with changes in pressure and temperature. Water transitions between these states through processes like boiling, freezing, or sublimation.

As the pressure decreases, as seen when a vacuum pump operates, water's boiling point also decreases, causing it to boil at lower temperatures. If the pressure continues to decrease while temperature remains constant, conditions may favor freezing, transitioning the remaining water into ice. This shows how crucial the interplay between pressure and temperature is in determining water’s phase.

Phase Transitions

Phase transitions refer to the change of a substance from one state of matter to another, such as from solid to liquid, liquid to gas, or directly from solid to gas.

Water's phase transitions are depicted in its phase diagram, showcasing the conditions under which these changes occur.

In the exercise, the water first boils due to a pressure drop, transitioning from liquid to gas as the vacuum pump lowers the pressure. Eventually, with sufficient reduction in pressure and evaporation of water, the liquid can reach a temperature-pressure point where it begins freezing, involving a transition to solid (ice).

If this process is continued, the ice can further transition from solid directly into a gas, known as sublimation. Understanding these transitions is crucial for predicting the behavior of water under varying environmental conditions.