Question

(a) Both a liquid and a gas are moved to larger containers. How does their behavior differ? Explain the difference in molecular terms. (b) Although water and carbon tetrachloride, \(\mathrm{CCl}_{4}(l)\), do not mix, their vapors form homogeneous mixtures. Explain. (c) The densities of gases are generally reported in units of \(\mathrm{g} / \mathrm{L}\), whereas those for liquids are reported as \(\mathrm{g} / \mathrm{mL}\). Explain the molecular basis for this difference.

Short answer

(a) When a liquid is moved to a larger container, it fills the base and retains its volume, as molecules are tightly packed and held together by intermolecular forces. In contrast, a gas expands to fill the entire volume of the new container due to its widely spaced molecules with negligible intermolecular forces. (b) Water and carbon tetrachloride do not mix in their liquid forms due to the difference in polarity and intermolecular forces but form homogeneous mixtures in the vapor phase as the intermolecular forces are much weaker. (c) Densities of gases and liquids are reported in different units (\(\mathrm{g} / \mathrm{L}\) and \(\mathrm{g} / \mathrm{mL}\), respectively) due to their distinct molecular arrangements, with gases having a lower molecular concentration and mass-to-volume ratio compared to liquids.

Step-by-step solution

(a) Comparing the behavior of liquids and gases in larger containers

When a liquid is moved to a larger container, it will spread out to fill the new container's base but not change its volume. In contrast, when a gas is moved to a larger container, it will expand to fill the entire volume of the new container. This difference in behavior is due to the varying molecular interaction between the liquid and gas. In liquids, molecules are tightly packed and held together by intermolecular forces like hydrogen bonding, van der Waals forces, and dipole-dipole interactions. When the liquid is poured into a larger container, the intermolecular forces prevent the liquid from spreading beyond its given volume. On the other hand, gas molecules are widely spaced apart and possess negligible intermolecular forces. When a gas is moved to a larger container, it will expand to fill the entire volume of the container as the gas molecules move randomly and spread out uniformly in all directions.

(b) Homogeneous mixtures of vapors of water and carbon tetrachloride

Although water (\(\mathrm{H}_{2}\mathrm{O}\)) and carbon tetrachloride (\(\mathrm{CCl}_{4}\)) do not mix in their liquid forms, their vapors can form homogeneous mixtures. This is because water is a polar molecule due to its bent structure and the electronegativity difference between hydrogen and oxygen atoms, while carbon tetrachloride is a non-polar molecule due to the equal distribution of electrons around its central carbon atom. In the liquid state, water molecules are held together by hydrogen bonding, and carbon tetrachloride molecules are held together by London dispersion forces, which makes it difficult for these two different molecular structures to mix or interact. However, when they become vapors, they form homogeneous mixtures since the intermolecular forces are much weaker in the gas phase. Both water molecules and carbon tetrachloride molecules can move freely and interact with each other, forming a homogeneous vapor mixture.

(c) Molecular basis for the difference in density units between gases and liquids

The densities of gases and liquids are reported differently because of their distinct molecular arrangements and concentrations. Gases have a much lower density than liquids due to their widely spaced and randomly distributed molecules. In liquids, the molecules are closely packed together and held by intermolecular forces, resulting in a higher density. Therefore, for liquids, the density is reported in units of \(\mathrm{g} / \mathrm{mL}\), which indicates a relatively high mass compared to its volume. In gases, the molecules are spaced far apart and possess very weak intermolecular forces. This leads to a significantly lower mass-to-volume ratio, and thus, the density units for gases are reported in \(\mathrm{g} / \mathrm{L}\). The use of different density units helps in distinguishing and comparing the compactness of the molecular distribution in each state of matter.

Key concepts

Molecular Interactions

When we explore why liquids and gases behave differently in larger containers, it's crucial to understand molecular interactions. In liquids, molecules are held closely by strong intermolecular forces such as hydrogen bonds and van der Waals forces. These forces keep the molecules tightly packed, so when a liquid is placed in a larger container, it only spreads along the base without changing its volume.

On the other hand, gas molecules are far apart with negligible intermolecular forces. This absence of strong binding allows them to move freely and spread out to fill the entire container. These differing forces explain why liquids remain confined while gases expand.

Density Differences

Why are density units different for gases and liquids? It all comes down to how molecules are packed. Liquids have molecules tightly arranged, leading to high density. Hence, densities of liquids are measured in \(\mathrm{g/mL}\), reflecting a relatively high mass per volume.

In contrast, gas molecules are spread far apart. This spacing results in lower density, so densities of gases are expressed in \(\mathrm{g/L}\), representing much less mass relative to their volume. These units help us easily distinguish between the mass and space occupied by substances in different states.

Homogeneous Mixtures

Even though water and carbon tetrachloride don't mix as liquids, they form homogeneous mixtures as vapors. This occurs because molecular interactions are weaker in the gas phase.

Water is polar with strong hydrogen bonds in its liquid state, while carbon tetrachloride is non-polar with London dispersion forces. These forces prevent them from mixing when both are liquids. However, once in the vapor state, these molecules can mix freely due to reduced intermolecular forces, forming a uniform mixture. The concept of homogeneous mixtures explains how different substances can blend seamlessly under certain conditions.