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}

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 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.

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.