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 constant volume due to stronger intermolecular forces, while a gas expands to fill the entire available space due to weak intermolecular forces and high kinetic energy. (b) Water and carbon tetrachloride don't mix in the liquid phase because of differing polarities, but their vapors form a homogeneous mixture as intermolecular forces become less significant in the gas phase. (c) Different density units for gases (g/L) and liquids (g/mL) are used due to differences in packing and intermolecular forces; liquids have higher mass concentration in a given volume, whereas gases have lower mass concentration.

Step-by-step solution

a) Behavior of liquid and gas in larger containers

When a liquid and a gas are moved to larger containers, their behavior differs due to differing intermolecular forces and the amount of free space available between the molecules. For a liquid, the intermolecular forces are stronger, which maintains the liquid's constant volume. When placed in a larger container, the liquid will simply occupy the same volume as before, but in the larger container, it will seem to take up less space as it does not expand to fill the entire container. On the other hand, a gas has weak intermolecular forces, and the molecules are in constant motion. When placed in a larger container, the gas will expand to fill the entire available space due to the high kinetic energy of its molecules. Consequently, the gas becomes more spread out, decreasing its overall pressure.

b) Explanation for water and carbon tetrachloride mixing behavior

Liquid water and carbon tetrachloride do not mix because they have different types of molecules. Water is a polar molecule due to the electronegativity difference between oxygen and hydrogen atoms, while carbon tetrachloride has a nonpolar molecule with evenly distributed electron density. Since "like dissolves like," polar and nonpolar molecules don't tend to mix well because polar molecules prefer to interact with other polar molecules and nonpolar molecules prefer to interact with other nonpolar molecules. Their vapors, however, can form a homogeneous mixture because they are both in the gas phase. In the gas phase, the intermolecular forces that would prevent polar and nonpolar liquids from mixing become less significant due to the high kinetic energy of the molecules. As a result, the different types of molecules can mix freely, forming a homogeneous gaseous mixture.

c) Molecular basis for different density units of gases and liquids

The molecular basis for using different density units for gases (grams per liter) and liquids (grams per milliliter) is due to the difference in the packing of molecules and the magnitude of their intermolecular forces. In a liquid, the molecules are more closely packed together, and the intermolecular forces are stronger compared to a gas. As a result, the mass of the molecules present in a given volume is considerably higher in liquids than in gases. Therefore, expressing liquid densities in grams per milliliter (a smaller unit of volume) is more appropriate as it provides a more manageable number and better representation of this higher mass concentration. In contrast, gas molecules have much weaker intermolecular forces and are far more spread out. This results in a much lower concentration of mass per given volume. To accurately represent this less concentrated mass, gas densities are reported in grams per liter (a larger unit of volume), which is a more suitable and convenient unit for gases.

Key concepts

Gas Behavior

Gases exhibit very unique behavior due to their molecular properties. They consist of molecules that are in constant motion, meaning they move rapidly and collide with each other and the walls of their container. This physical characteristic is governed by the weak intermolecular forces present between gas molecules.
These weak forces contribute to gases possessing high kinetic energy, enabling them to expand quickly and uniformly to fill any available space in their container. If you were to place a gas in a larger container, the gas molecules would spread out evenly within the new volume.
This expansion occurs because gas molecules are constantly moving, and as they collide with each other with energy, they push those molecules outward, causing the gas to occupy the additional space. In essence, gases do not have a fixed volume or shape; they adapt to fill the entirety of any container they reside in.

Liquid Behavior

Liquids behave quite differently from gases due to their much stronger intermolecular forces. These attractive forces hold the molecules closely together, maintaining a constant volume regardless of the container size. When you place a liquid in a larger container, it does not expand as a gas does.
Instead, the liquid molecules remain closely packed and maintain their volume while adjusting their shape to fit inside the container. This behavior is due to the cohesive nature of liquid molecules, which prefer to stick together.
Consequently, as the stronger forces keep the molecules near one another, the volume occupied by the liquid appears unchanged, even in larger containers. Liquids, therefore, have a definite volume but can change shape depending on the container, unlike gases.

Density Differences

The differences in density between gases and liquids can be attributed to how tightly the molecules are packed together. In a liquid, molecules are much closer, leading to a higher mass concentrated in a smaller volume. This high packing density results in liquids having densities expressed in grams per milliliter, a smaller and more precise unit.
Conversely, gas molecules are widely spread out due to weaker intermolecular forces and the nature of their constant, high-energy movement. This results in lower concentration per unit volume. Hence, for gases, density is expressed in grams per liter, a larger unit. This makes reporting gas densities manageable given their low mass concentration compared to liquids.
Essentially, the densely packed state of liquid molecules contrasts sharply with the spread-out nature of gas molecules, leading to this notable difference in density reporting.

Polarity

Polarity is a critical concept in understanding why certain substances do not mix well. Water and carbon tetrachloride provide a classic example of this phenomenon due to their differing molecular structures. Water is polar, with its molecules having uneven charge distribution, meaning it has an area with a slight positive charge and another with a slight negative charge due to its molecular shape.
On the other hand, carbon tetrachloride is nonpolar, having an even distribution of electrical charge. The polar water molecules are attracted to other polar molecules, while nonpolar molecules like carbon tetrachloride prefer interacting with other nonpolar substances.
This mutual incompatibility comes from the principle that "like dissolves like," indicating that polar and nonpolar substances do not tend to mix due to their differing interactions at the molecular level. However, in the gas phase, these molecular interactions are less significant, allowing even polar and nonpolar substances to mix as gases.