Question

\(\mathrm{Oxygen}, \mathrm{O}_{2}\), has a boiling point of \(90 \mathrm{~K}\) \(\left(-183^{\circ} \mathrm{C}\right)\), and nitrogen, \(\mathrm{N}_{2}\), has a boiling point of \(77 \mathrm{~K}\left(-196^{\circ} \mathrm{C}\right)\). Which is a liquid and which is a gas at \(80 \mathrm{~K}\left(-193^{\circ} \mathrm{C}\right) ?\)

Short answer

Oxygen is a liquid at 80 K; nitrogen is a gas at 80 K.

Step-by-step solution

Understand Boiling Points

The boiling point of a substance is the temperature at which it changes from a liquid to a gas. Below this temperature, the substance is a liquid, and above it, the substance becomes a gas.

Compare Oxygen's Boiling Point to 80 K

Oxygen ( O_{2} ) has a boiling point of 90 K. At 80 K, which is below 90 K, oxygen will still be in the liquid state because it hasn't reached its boiling point yet.

Compare Nitrogen's Boiling Point to 80 K

Nitrogen ( N_{2} ) has a boiling point of 77 K. At 80 K, which is above 77 K, nitrogen will have already boiled into a gas because it is above its boiling point.

Conclusion

At 80 K, oxygen will be in the liquid state since it is below its boiling point, while nitrogen will be in the gas state since 80 K is above its boiling point.

Key concepts

Understanding Liquid State

In the liquid state, molecules are closer together compared to their arrangement in gases. This close proximity is because the intermolecular forces are strong enough to hold the molecules together, but are not strong enough to prevent them from moving at all. Thus, they can still flow and take the shape of their container.
It is important to know that the boiling point marks the highest temperature at which a liquid state can exist for a given substance. For oxygen ( O_{2} ), this means that at temperatures below 90 K, oxygen remains in a liquid state. In the given exercise, at 80 K, oxygen is below its boiling point and thus maintains its liquid form.

• Molecules vibrate and slide past each other.
• They are not in a fixed position but are closely packed.
• The liquid adapts to the shape of its container but has a fixed volume.

Understanding these aspects of the liquid state helps in comprehending how substances like oxygen behave under varying thermal conditions.

Transition to Gas State

A gas state occurs when molecules have sufficient energy to overcome intermolecular forces that hold them together in a liquid state. The boiling point represents the temperature at which this transition from liquid to gas takes place for a substance under normal atmospheric pressure.
Nitrogen ( N_{2} ), with a boiling point of 77 K, will be in a gas state at any temperature above this point. Therefore, at 80 K, nitrogen is already a gas. Its molecules have spaced far apart and move chaotically, leading to the characteristic shape of gases filling any volume they occupy.

• Molecules move freely and are far apart.
• A gas expands to fill its entire container.
• No fixed shape or volume.

This concept is critical for understanding behaviors of substances under changing thermal conditions, much like what happens with nitrogen and oxygen as in our exercise.

Role of Temperature Change

Temperature change is critical in determining the state of a substance, such as from liquid to gas. The change in temperature influences the energy levels of molecules. When a substance is heated, its molecules gain kinetic energy, which may lead to a change of state depending on how close they are to the boiling point.
The original exercise shows that at 80 K, which is below oxygen's boiling point of 90 K, there isn't enough energy for oxygen to transition to gas; it remains liquid. Conversely, 80 K is above nitrogen's boiling point of 77 K, meaning nitrogen has enough energy to exist in gas form.

• Increase in temperature raises energy in molecules.
• Higher energy can overcome intermolecular forces.
• Results in state transitions like liquid to gas.

By understanding how temperature change affects different substances, like oxygen and nitrogen, students can predict the state of a substance in varying thermal environments.