Question

Which set of conditions represent easiest way to liquefy a gas? (a) Low temperature and high pressure (b) High temperature and low pressure (c) Low temperature and low pressure (d) High temperature and high pressure

Short answer

The easiest way to liquefy a gas is under conditions of low temperature and high pressure (option (a)).

Step-by-step solution

Assess each option with regards to how temperature and pressure might impact the state of a gas

Option (a) suggests low temperature and high pressure, which aligns with our understanding that low temperature slows down gas molecules and high pressure brings them closer together. Option (b) suggests high temperature and low pressure, which would likely make it difficult to liquefy the gas as the high temperature would increase the kinetic energy of the gas molecules, making them move faster and the low pressure wouldn't force them closer together. Option (c) suggests low temperature and low pressure. While the low temperature would slow down the gas molecules, the low pressure would not help bring them closer together. Option (d) suggests high temperature and high pressure. The high pressure might help bring the molecules closer together, but the high temperature would likely increase their kinetic energy, making them move more and potentially making it difficult to liquefy the gas.

Choose the option that would most likely facilitate the liquefaction of a gas

Given our understanding of how temperature and pressure influence the state of a gas, option (a) - low temperature and high pressure - seems to represent the easiest way to liquefy a gas.

Key concepts

Temperature and Pressure Effects on Gases

Understanding the relationship between temperature, pressure, and the behavior of gases is crucial for grasping the concept of gas liquefaction. The state of a gas can greatly alter when subjected to changes in temperature and pressure.

When we discuss temperature in the context of gases, we're looking at a measure of the average kinetic energy of the gas molecules. Reducing the temperature slows down these molecules. Consequently, the interaction between molecules increases as their kinetic energy decreases, making it more likely for them to stick together and transition into a liquid state. This slow down is why a low temperature is a favorable condition for liquefaction.

On the other hand, pressure is related to how much force is exerted on the gas molecules. High pressure compresses the gas, reducing the space available for particles to move and thereby increasing their interaction. This increased pressure is another condition that favors the transition from gas to liquid. In the context of our exercise, combining low temperature with high pressure (option a) offers the ideal scenario for the liquefaction of a gas because it involves cooling the gas (reducing kinetic energy) and applying significant pressure (increasing particle interaction).

Kinetic Energy of Gas Molecules

The kinetic energy of gas molecules determines how they move and at what speed. It is intimately tied to temperature; as the temperature rises, so does the kinetic energy of the gas molecules, causing them to move more rapidly. This is described by the kinetic molecular theory, which explains the energy, movement, and properties of a substance's particles in relation to temperature.

A higher kinetic energy implies that the molecules are moving faster, making them less likely to coalesce and form a liquid. This is why option (b), high temperature and low pressure, is unfavorable for liquefaction of a gas. The fast-moving, energetic molecules resist coming together and condensing into a liquid. Whereas, in a colder environment, with lower kinetic energy, as suggested by option (a), molecules move slower, facilitating their coming together and liquefaction.

States of Matter

Matter exists fundamentally in three states: solid, liquid, and gas. These states are dictated by the arrangement and energy of molecules within the substance. Liquids and gases are closely related in that both have molecules that are in motion. However, in a gas, the molecules are far apart and move rapidly, whereas, in a liquid, they are closer together and move less freely.

Liquefaction is the process of turning a gas into a liquid, which requires manipulation of temperature and pressure to encourage gas molecules to get close enough to form a liquid. This can be achieved by cooling the gas (to slow down the molecules) and compressing it (to reduce the space between molecules), as our optimal conditions, low temperature and high pressure (option a), would achieve. Understanding this interplay between the three states of matter and the conditions necessary to shift between them is essential in various scientific applications, emphasizing the value in grasping this essential concept.