Question

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

Short answer

The false statement is (c): "Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors." This is false because gases typically mix with one another, regardless of whether their corresponding liquids mix or not.

Step-by-step solution

Analyzing statement (a)

Statement (a) states that "Gases are far less dense than liquids." We know that gases have molecules that are widely separated compared to liquids. In liquids, molecules are closer together, which leads to a higher density. Therefore, statement (a) is true.

Analyzing statement (b)

Statement (b) states that "Gases are far more compressible than liquids." Due to the much larger distances between the molecules in gases compared to liquids, gases can be compressed more easily than liquids. As pressure is applied on a gas, its molecules come closer together, which allows for more significant changes in the gas volume. On the other hand, the molecules in liquids are already close together, so applying pressure does not cause a significant change in volume. Therefore, statement (b) is true.

Analyzing statement (c)

Statement (c) states that "Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors." This statement is incorrect. Just because two liquids don't mix, it does not mean that their vapors won't mix. Gases, unlike liquids, typically mix with one another, regardless of whether their corresponding liquids mix or not. This is due to the behavior of gas particles, which move rapidly and spread out to fill any available space. So, statement (c) is false.

Analyzing statement (d)

Statement (d) states that "The volume occupied by a gas is determined by the volume of its container." This statement is true. Gases will expand or contract to fill the entirety of a container in which they are placed. This is because gas particles move rapidly and spread out evenly throughout the available space. Hence, the volume of a gas, under constant temperature and pressure conditions, will equal the volume of its container.

Conclusion

Based on our analysis, statement (c) - "Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors." - is the false statement among the given options. The other statements accurately describe properties of gases and liquids.

Key concepts

Density of Gases Vs Liquids

Understanding the difference in density between gases and liquids is crucial when exploring the fundamental properties of matter. Density, which is the measure of mass per unit volume, typically varies significantly between the two states.

In liquids, molecules are closely packed due to intermolecular forces, leading to a higher mass in a given volume, and consequently, a higher density. For instance, water has a density of approximately 1 gram per cubic centimeter at room temperature. On the other hand, gases have molecules that are spaced considerably further apart, as these intermolecular forces are much weaker. This spacing results in less mass in the same volume, therefore, gases exhibit much lower densities. For example, dry air has a density of about 0.0012 grams per cubic centimeter.

This difference underpins many phenomena, such as why oil floats on water or why helium balloons rise in the air. The substantially lower density of gases also explains why they can be compressed into smaller spaces — a property widely utilized in various applications from filling balloons to operating pneumatic systems.

Compressibility of Gases Vs Liquids

Compressibility refers to the degree to which a substance can decrease in volume under pressure. Gases are far more compressible than liquids due to the arrangement and movement of their molecules.

Gas molecules, separated by large distances, can move closer together when pressure is applied, reducing the gas's overall volume substantially. This contrasts sharply with liquids, where molecules are already packed tightly due to stronger intermolecular forces, leaving very little space for further compression. Indeed, while gases can be compressed into a fraction of their original volume, liquids are almost incompressible, changing volume only slightly under extremely high pressures.

This property not only allows for a wide range of industrial applications, such as gas cylinders and air brakes but also affects natural processes, such as the formation of weather systems where atmospheric pressure plays a critical role.

Mixing of Gas Vapors

The behavior of gas vapors in terms of mixing is markedly different from that of liquids. Despite the mixing properties of their liquid forms, gas vapors will typically mix fully with each other. This is because gas particles move independently and rapidly, dispersing evenly in all available space, regardless of the identity of other gases present.

When we consider vapors such as those of water and carbon tetrachloride, their ability to mix in the gaseous state has little to do with whether their liquid counterparts are miscible. In the atmosphere, this leads to the formation of homogeneous mixtures, such as air, which is a mix of oxygen, nitrogen, and various other gases. This property is also fundamental in processes like industrial gas reactions and environmental air quality management, defining how different gases will interact when released into the atmosphere.