Question

A gaseous sample of a substance is cooled at constant pressure. Which of the following diagrams best represents the situation if the final temperature is (a) above the boiling point of the substance and (b) below the boiling point but above the freezing point of the substance?

Short answer

(a) Gas remains gas; (b) Gas condenses to liquid.

Step-by-step solution

Understanding the Situation

There are two scenarios: one where the final temperature is above the boiling point of the substance, and one where the final temperature is below the boiling point but above the freezing point. Keeping pressure constant is key in understanding how the phase changes occur.

Scenario (a) - Above Boiling Point

If the final temperature is above the boiling point of the substance, the sample will remain in its gaseous state. Cooling at constant pressure means the gas will not condense into a liquid as long as the temperature remains above the boiling point. We are looking for a diagram where the gaseous state is maintained.

Scenario (b) - Below Boiling Point but Above Freezing Point

Here, the final temperature is below the boiling point but above the freezing point. This means the gas will condense into a liquid since it is below the boiling point but will not freeze into a solid because it is above the freezing point. The diagram should show a gas turning into a liquid while maintaining constant pressure.

Key concepts

Cooling at Constant Pressure

When a substance is cooled at constant pressure, the phase change it undergoes depends not only on the pressure but also significantly on the temperature.
This means that the substance can change from one state of matter to another without altering its pressure.
At constant pressure, temperature decreases can lead to:

• A gaseous state turning into a liquid (condensation) once the temperature falls below the boiling point.
• A liquid turning into a solid (freezing) when it reaches the freezing point.
• Remaining in the same state if no phase transition temperature is crossed, like staying gaseous above the boiling point.

This concept is essential because it shows how substances react to temperature changes in a predictable way. By maintaining constant pressure, we can focus solely on how temperature influences phase changes.

Boiling Point

The boiling point of a substance is the temperature at which it rapidly changes from a liquid to a gas at a given pressure.
At this point, the substance will absorb energy without changing its temperature until all of it turns into a gaseous state.
The boiling point is crucial because:

• Above this temperature, a liquid is a gas.
• Below this temperature, it can coexist in liquid and gas form, but predominantly in liquid form.

Understanding the boiling point helps in visualizing how a gaseous sample stays gaseous if cooled but remains above this threshold, as it will neither liquefy nor solidify.

Freezing Point

The freezing point is the temperature at which a liquid turns into a solid.
It's the counterpart to the melting point, where a solid becomes a liquid.
At the freezing point, the substance must release energy, known as latent heat, to transition to a solid state.

• Above the freezing point, the substance remains liquid.
• Below this point, the substance becomes a solid.

When considering phase changes, understanding the freezing point tells us if a substance will solidify as it cools. In cooling processes, like in the original scenario, if the temperature stays above the freezing point, the substance can remain in its liquid form even when cooled.

Gaseous State

The gaseous state is one of the phases or states of matter where the substance has no fixed volume or shape.
It consists of particles that move rapidly and freely.

• Gases expand to fill their containers.
• They have lower densities compared to liquids and solids.
• They are highly compressible.

When cooled at constant pressure, the gaseous state will persist until the temperature reaches the boiling point.
Only then does condensation to a liquid potentially occur if the temperature continues to drop below the boiling point.

Condensation

Condensation is the process where a gas becomes a liquid.
It occurs when a gas is cooled to a temperature below its boiling point.
This phase change is essential in understanding natural processes like the water cycle and man-made applications such as refrigerants.

• During condensation, gas releases energy resulting in a temperature drop.
• This process occurs at a constant temperature.
• It plays a vital role in refrigeration and air conditioning systems.

In the exercise's context, when the temperature falls below the boiling point but remains above the freezing point, condensation will transform a gas into a liquid at constant pressure.