Question

Which two statements about gas mixtures are true? [Section 13.1] (a) Gases always mix with other gases because the gas particles are too far apart to feel significant intermolecular attractions or repulsions. (b) Just like water and oil don't mix in the liquid phase, two gases can be immiscible and not mix in the gas phase. (c) If you cool a gaseous mixture, you will liquefy all the gases at the same temperature. (d) Gases mix in all proportions in part because the entropy of the system increases upon doing so.

Short answer

The correct two statements about gas mixtures are: (a) Gases always mix with other gases because the gas particles are too far apart to feel significant intermolecular attractions or repulsions. (d) Gases mix in all proportions in part because the entropy of the system increases upon doing so.

Step-by-step solution

Statement (a) Analysis

: Gases always mix with other gases because the gas particles are too far apart to feel significant intermolecular attractions or repulsions. This statement is true. Gases consist of particles that are widely spaced apart and mostly do not interact with each other. Thus, gas particles are unaffected by any significant forces of attraction or repulsion, easily mixing together.

Statement (b) Analysis

: Just like water and oil don't mix in the liquid phase, two gases can be immiscible and not mix in the gas phase. This statement is false. In the liquid phase, water and oil don't mix due to the differences in polarities. However, gas particles are far more spaced out and interact minimally with other particles, allowing them to easily mix with other gases.

Statement (c) Analysis

: If you cool a gaseous mixture, you will liquefy all the gases at the same temperature. This statement is false. Different gases will have different critical temperatures and boiling points, which means that they generally won't liquefy at the same temperature when cooled together.

Statement (d) Analysis

: Gases mix in all proportions, in part because the entropy of the system increases upon doing so. This statement is true. Mixing gases increases the randomness or disorder of the system, according to the second law of thermodynamics. This increase in entropy is a primary factor contributing to the spontaneous mixing of gases in all proportions. In conclusion, the correct two statements about gas mixtures are: (a) Gases always mix with other gases because the gas particles are too far apart to feel significant intermolecular attractions or repulsions. (d) Gases mix in all proportions in part because the entropy of the system increases upon doing so.

Key concepts

Intermolecular Forces

Intermolecular forces are the forces that mediate interaction between molecules, including attractions and repulsions. In gases, these forces are exceedingly weak. This is because gas molecules are spread out over large distances, weakening the impacts of these forces.

These forces play a more significant role in liquids and solids, where molecules are closer together. Therefore, they can lead to behaviors like the immiscibility of certain liquids (e.g., water and oil).

• Weak Intermolecular Forces in Gases: Gas molecules rarely experience strong forces, which allows them to mix freely despite differences in polarity.
• Implication for Mixing: Because intermolecular forces are negligible in gases, gases tend to mix evenly when combined.

Entropy

Entropy measures the degree of randomness or disorder in a system. It's a crucial concept in understanding why gases mix so readily. When gases mix, the overall entropy of the system increases. This is aligned with the second law of thermodynamics, which states that systems tend to move toward a state of maximum entropy.

Gases seek to increase entropy by spreading out and mixing with other gases. This is why statement (d) from our exercise is true—gases mix in all proportions because the mixing leads to increased entropy.

• Spontaneous Mixing: Gases mix spontaneously to achieve higher entropy.
• Energy Dispersion: When gases mix, energy is dispersed, facilitating greater disorder and randomness.

Phase Transition

Phase transitions occur when a substance changes from one state of matter to another, such as from gas to liquid. During a phase transition, the intermolecular forces become more significant as molecules come closer together.

In the context of cooling a gas mixture (as described in statement c of our exercise), different gases will liquefy at different temperatures. This is due to their unique boiling points and critical temperatures. Not all gases will transition from gas to liquid at the same conditions because of these differences.

• Defined Temperatures for Liquefaction: Each gas has its unique temperature range for transitioning to liquid.
• Magnitude of Forces: As gases cool, intermolecular forces increase, eventually leading to liquefaction.

Thermodynamics

Thermodynamics is the study of energy transformations that affect physical systems. It relates closely to both entropy and phase transitions in gases.

The laws of thermodynamics describe how gases behave and interact, especially when mixing. According to the second law, the entropy of an isolated system will always increase over time.

When considering mixtures of gases, thermodynamic principles explain why gases mix spontaneously (as seen in statement d). They also help predict how and when phase transitions will occur based on changes in pressure, temperature, and volume.

• Second Law of Thermodynamics: Emphasizes that entropy tends to increase, leading to spontaneous mixing.
• Energy and Phase Changes: Thermodynamics explains energy use in changing states, such as gas to liquid.