Question

Which of the following statements is false? (a) Gases are far less dense than liquids. (b) Gases are far more compressible than liquids. (c) Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors. (d) The volume occupied by a gas is determined by the volume of its container.

Short answer

The false statement is (c) "Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors." The solubility of liquids does not necessarily apply to their vapor phase, so their vapors can still mix even if the liquids do not.

Step-by-step solution

Statement (a) Analysis

Gases are far less dense than liquids. This statement is true because, in gases, particles are more widely spaced compared to liquids. This leads to a much lower density for gases compared to liquids.

Statement (b) Analysis

Gases are far more compressible than liquids. This statement is also true. The reason for gases being more compressible than liquids is the relatively large distance between gas particles. When pressure is applied, these particles can be brought closer, allowing a gas to occupy less space (known as compression).

Statement (c) Analysis

Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors. This statement is false. The solubility of liquids does not necessarily apply to their vapor phase. When liquids evaporate, they form gaseous particles that can interact with other gaseous particles. In this case, the fact that liquid water and liquid carbon tetrachloride do not mix does not guarantee that their vapors will not mix.

Statement (d) Analysis

The volume occupied by a gas is determined by the volume of its container. This statement is true. According to the gas laws, the volume of a gas depends on the volume of its container since gas particles will uniformly distribute themselves throughout the available space, irrespective of the size of the container. So, the false statement among the given options is (c) "Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors."

Key concepts

Gas Density

Gas density is a measure of how much mass is contained in a given volume of gas. Unlike solids and liquids, gases have a much lower density. This is because the particles in a gas are spread out, occupying more space and resulting in fewer particles per unit volume.

In practical terms, this means that for the same volume of substance, a gas will weigh much less than a liquid or a solid. This low density is why gases rise and spread in the air, filling up any space available to them.

Comparison with liquids helps clarify this concept. For instance, when you inflate a balloon with air, the air particles are much more spread out than the particles in a filled water balloon, which is why the balloon feels light. Recognizing the differences in density between gases and liquids is crucial for understanding their individual behaviors and applications.

Gas Compressibility

Gases are highly compressible, which means their volume can be significantly reduced when pressure is applied. This property is due to the wide spaces between gas molecules. When a force is exerted on the gas, these spaces allow the molecules to be packed closer together, making the gas occupy less volume.

Unlike liquids, which have molecules closely packed and are only slightly compressible, gases can easily change their volume under pressure. This characteristic is useful in various technologies.

For example, in natural gas storage or in an air compressor, gases are compressed to reduce their volume, making them easier to store and transport. Understanding gas compressibility helps in fields like aviation, where the cabin air is controlled to provide comfort by modifying the pressure and volume of the air inside.

Vapor Mixing

Vapor mixing describes how different vapors interact and combine when they occupy the same space. As outlined in the exercise, the mixing behavior of vapors can differ significantly from the properties of their liquid phase.

Even if two liquids are immiscible, meaning they do not mix, their vapors may mix freely in the gaseous state. This is because gaseous particles are more mobile and can diffuse easily in the available space.

The false statement from the exercise highlights this concept, noting that just because liquid water and liquid carbon tetrachloride don’t mix, it doesn't mean that their vapors won't mix. Understanding this concept is essential in industries such as chemical engineering, where vapors from various substances are managed in complex processes.

Gas Laws

Gas laws form the foundation for understanding the behavior of gases. These laws describe relationships between volume, temperature, pressure, and the amount of gas. A key principle is that the volume of a gas is determined by its container. This means that a gas will expand to fill the container it is in, adopting its shape and size.

Important gas laws include:

• Boyle's Law: At constant temperature, the volume of a gas is inversely proportional to its pressure.
• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its temperature.
• Avogadro's Law: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

These principles explain why gases behave as they do in different situations, such as expanding when heated or reducing in volume when compressed. Grasping the gas laws is essential for significant practical applications, including the functioning of engines, weather prediction, and many industrial processes.