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Chapter 10: Problem 137

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

Expert verified
Using the phase diagram for water, when the vacuum pump is turned on, it lowers the pressure inside the container, causing the water to boil at room temperature. As boiling is an endothermic process, it absorbs heat and lowers the temperature of the remaining liquid, eventually causing it to freeze. If the vacuum pump is left on indefinitely, the ice will undergo sublimation, gradually transitioning from solid to gas phase, reducing the overall mass of water in the container.

Step by step solution

01

Understanding the phase diagram for water

A phase diagram represents the stable phase (solid, liquid or gas) of a substance as a function of temperature and pressure. For water, the phase diagram includes the following regions: 1. Solid (ice): Low temperatures and high pressure. 2. Liquid (water): Moderate temperatures and pressures. 3. Gas (steam): High temperatures and low pressures. In addition, there are lines on the diagram that represent phase transitions, such as: 1. Solid-liquid boundary: Melting, freezing. 2. Liquid-gas boundary: Boiling, condensing. 3. Solid-gas boundary: Sublimation, deposition. The triple point is the unique condition where all three phases coexist in equilibrium.
02

Initial state: water in the container

Initially, we have a container with some water in it. The initial state of the water is liquid at room temperature and atmospheric pressure.
03

Applying the vacuum pump

When the vacuum pump is turned on, it starts to remove the air and other gases from the container. Consequently, the pressure in the container reduces, which affects the water's phase equilibrium. As the pressure drops, the water's boiling point also decreases. When the pressure inside the container is low enough, the water will start boiling at room temperature.
04

Boiling and freezing

The boiling of water is an endothermic process, meaning it absorbs heat from the surroundings. As the water continues to boil under the reduced pressure, it takes heat from the remaining liquid, which causes the temperature of the liquid to drop. Eventually, the temperature drops to the point where water freezes, leading to the observed formation of ice.
05

Outcome if the vacuum pump is left on indefinitely

If the vacuum pump is left on indefinitely, it will continue to remove gas particles and maintain a low pressure inside the container. The ice formed in the last step will not melt at this low pressure, but it can undergo sublimation, where it directly transitions from the solid phase to the gas phase. This process will be slow at room temperature, but over time, the amount of ice in the container will decrease, and the overall mass of water in the container will be reduced.

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