Question

(a) A liquid and a gas are moved to larger containers. How does their behavior differ once they are in the larger containers? Explain the difference in molecular terms. (b) Although liquid water and carbon tetrachloride, \(\mathrm{CCl}_{4}(l)\), do not mix, their vapors form a homogeneous mixture. Explain. (c) Gas densities are generally reported in grams per liter, whereas liquid densities are reported in grams per milliliter. Explain the molecular basis for this difference.

Short answer

(a) In a larger container, a liquid maintains its volume and only takes the shape of the container's bottom, while a gas expands to fill the entire container due to the difference in intermolecular forces and molecular spacing. (b) Water and carbon tetrachloride do not mix in the liquid phase because of the different intermolecular forces (polarity), but they form a homogeneous mixture in the vapor phase as the differences in intermolecular forces become less significant. (c) The molecular basis for reporting gas densities in grams per liter and liquid densities in grams per milliliter arises from the differences in molecular spacing and interaction, with gases having a much lower density due to the larger spaces between molecules and weaker intermolecular forces.

Step-by-step solution

(a) Liquid vs. Gas Behavior in Larger Containers

When a liquid and a gas are moved to larger containers, their behavior differs due to the nature of their molecular interactions. In a liquid, molecules are closer together and have strong intermolecular forces. Therefore, when a liquid is moved to a larger container, it will still occupy the same volume and take the shape of the container at the bottom. The intermolecular forces keep the molecules close to one another, and the liquid does not expand to fill the entire container. In the case of a gas, molecules are much farther apart and have weaker intermolecular forces. When a gas is moved to a larger container, it will expand and occupy the entire volume of the container. Gas molecules move freely and randomly, and their distribution becomes uniform throughout the container. This occurs due to their constant motion and the lack of significant intermolecular forces to keep them confined.

(b) Mixing Behavior of Liquid Water and Carbon Tetrachloride

Liquid water and carbon tetrachloride (\(\mathrm{CCl}_{4}(l)\)) do not mix due to the polar nature of water molecules and the nonpolar nature of carbon tetrachloride molecules. In water, the oxygen atom has a higher electronegativity than the hydrogen atoms, creating a dipole moment. This causes water molecules to form hydrogen bonds with one another. Carbon tetrachloride is a nonpolar molecule because the electronegativity difference between carbon and chlorine atoms is not significant enough to create a dipole moment. The carbon tetrachloride molecules interact through weaker London dispersion forces. Since water and carbon tetrachloride have different types of intermolecular forces, they do not mix, following the principle of "like dissolves like." However, when both substances are in the vapor phase, the differences in intermolecular forces have less effect. In the vapor phase, the molecules of both substances are farther apart and have higher kinetic energy. The interactions between water and carbon tetrachloride vapor molecules become less significant, allowing them to form a homogeneous mixture.

(c) Molecular Basis for Density Reporting Differences

The molecular basis for reporting gas densities in grams per liter and liquid densities in grams per milliliter arises from the differences in molecular spacing and interaction between the two phases. In a gas, molecules are widely spaced, and intermolecular forces are relatively weak. As a result, the overall mass of the gas is spread across a larger volume, making the density much lower than that of a liquid. On the other hand, liquid molecules are closely packed, with stronger intermolecular forces holding them together. This leads to a greater mass of substance per unit of volume, resulting in a higher density than that of a gas. Therefore, it is more convenient to report gas densities in grams per liter, which is a larger unit of volume, and liquid densities in grams per milliliter, a smaller unit of volume, to account for the significant difference in densities between the two phases.

Key concepts

Intermolecular Forces

Intermolecular forces are vital in understanding the behavior of different states of matter. They are the attractive forces that occur between molecules, influencing how substances interact and behave. For example, liquids have stronger intermolecular forces compared to gases, which help keep the molecules closer together. This is why liquids maintain a consistent volume and shape to the container they occupy at the bottom.

In contrast, gases have weaker intermolecular forces. This allows gas molecules to move freely and spread out, occupying the entire volume of a container. Due to this, gases like air or helium can fill a balloon completely, whereas a liquid, such as water, retains its larger structure and shape at the base of any vessel.

Gas Behavior

Gas behavior is unique due to the properties that define its molecular interactions and movements. Molecules in a gas are spaced far apart, leading to weak interactions. This spacing makes gases highly compressible and capable of expanding to fill any container they are placed into.

The molecules in a gas are in constant random motion, which contributes to the uniform distribution within a container. These properties explain why air evenly fills a room or why balloons can inflate to various sizes. The behavior is dictated by the kinetic energy of the molecules, which moves unrestricted due to minimal intermolecular forces.

Liquid Behavior

The behavior of liquids is shaped by their intermediate level of intermolecular forces. In a liquid, molecules are packed closely together but can still slide past each other, giving liquids a definite volume but an indefinite shape. They conform to the shape of their container but only fill the bottom, rather than expanding to fill the entire volume like a gas.

Hydrogen bonding in water exemplifies strong intermolecular forces, which is why water exhibits high surface tension and does not easily compress. Liquids can be poured and will find their level according to gravity, unlike gases that have the freedom to explore the available volume.

Molecular Interactions

Molecular interactions are foundational to the properties of materials. In liquids, these interactions are significant enough to keep molecules together but do not immobilize them, allowing for fluidity. Water's hydrogen bonds are an example of strong molecular interaction, giving water unique properties like high boiling and melting points.

Carbon tetrachloride, on the other hand, engages in weaker London dispersion forces, as it's a nonpolar molecule. Such differences in molecular interactions explain phenomena like the immiscibility of water and oil. However, in vapor form, such interactions become minimal, allowing different vapors to mix homogeneously because molecules move independently, voiding the influence of their respective forces.

Density Difference

The concept of density difference arises from how tightly packed the molecules are in different states of matter. Gases have low density due to widely spaced molecules. Their mass spreads over a larger volume, hence densities are reported in grams per liter, as this suits their expansive nature.

Liquids, however, have molecules that are much closer together, resulting in higher density. The molecules exert stronger intermolecular attractions which support this tight packing. As such, liquid densities are expressed in grams per milliliter, reflecting the smaller volume in which their mass is contained. This fundamental difference highlights why gas densities are much lower compared to that of liquids.