Problem 86 - Chemistry Matter and Change

Question

At \(25^{\circ} \mathrm{C}\) and a pressure of \(760 \mathrm{mm} \mathrm{Hg},\) the density of mercury is 13.5 \(\mathrm{g} / \mathrm{mL}\) ; water at the same temperature and pressure has a density of 1.00 \(\mathrm{g} / \mathrm{mL}\) . Explain this difference in terms of intermolecular forces and the kinetic-molecular theory.

Step-by-Step Solution

Answer

Mercury's higher density is due to strong metallic bonds, while water's lower density is due to hydrogen bonding.

Step 1: Introduction to Densities

The densities of mercury and water at the given conditions are 13.5 g/mL and 1.00 g/mL, respectively. This means that mercury is much denser than water.

Step 2: Intermolecular Forces in Mercury

Mercury has strong metallic bonds due to the presence of delocalized electrons shared among mercury atoms. These strong bonds give mercury its high density as the atoms are closely packed together.

Step 3: Intermolecular Forces in Water

In contrast, water molecules interact through hydrogen bonding, which is significant but weaker than metallic bonds. This results in a less dense structure compared to mercury.

Step 4: Kinetic-Molecular Theory Explanation

According to kinetic-molecular theory, the particles in a substance are in constant and random motion. In mercury, the strong bonds limit the movement and packing of the atoms, leading to higher density. In water, the weaker hydrogen bonds provide more freedom of motion, resulting in a lower density.

Step 5: Comparison and Conclusion

The differences in density between mercury and water can be attributed to the nature of their intermolecular forces and the implications of kinetic-molecular theory. Mercury's dense arrangement of atoms due to metallic bonding contrasts sharply with water's less packed structure influenced by hydrogen bonding.

Key Concepts

Density

Density is a measure of how much mass is contained in a given volume. In simpler terms, it tells us how "heavy" something is for its size. For example, at 25°C, mercury is denser than water because it has a density of 13.5 g/mL, compared to water's 1.00 g/mL. The higher the density, the more tightly packed the particles are in a substance.

• Denser materials have atoms or molecules that are closely packed together.
• Less dense materials have more space between their particles.

Understanding density helps us explain why some objects float while others sink. A substance with higher density than water will sink; one with lower density will float. This property is crucial in understanding how materials behave in different conditions.

Kinetic-Molecular Theory

The kinetic-molecular theory provides a framework to understand the behavior of particles in different states of matter. This theory proposes that all substances are made up of tiny particles, which are in constant motion.
- **Basic Points of the Theory:**

• Particles in a gas move rapidly and are far apart, while in liquids and solids they are closer together.
• The speed at which these particles move depends on the temperature, with higher temperatures causing faster motion.
• In a liquid like water, the movement allows molecules to break and form hydrogen bonds easily, leading to a less compact arrangement than in solids.

In mercury, metallic bonds significantly restrict particle movement, resulting in a higher density. In water, while hydrogen bonds control movement, they are far weaker, allowing more freedom and hence a lower density.

Metallic Bonds

Metallic bonds are the force that holds atoms together in metallic substances. These bonds arise from the attraction between positively charged metal ions and a "sea" of shared free-flowing electrons. This unique bonding arrangement gives metals their distinct properties.

• They are typically strong bonds, contributing to the high density observed in metals like mercury.
• These bonds provide metals with their characteristic properties, such as high electrical conductivity and malleability.
• The closely packed nature of metallic bonds means particles are tightly arranged, thus enhancing density.

In mercury, these delocalized electrons play a crucial role by allowing atoms to be packed very closely together, which contributes to its significant density compared to substances like water.

Hydrogen Bonding

Hydrogen bonding is a type of intermolecular force occurring between molecules that include hydrogen atoms attached to highly electronegative atoms like oxygen, nitrogen, or fluorine. This is a particularly strong type of dipole-dipole interaction but is generally weaker than metallic bonds.

• Hydrogen bonds are crucial for the structure and properties of water.
• These bonds are responsible for water's high surface tension and boiling points relative to other liquids with similar molar mass.
• The nature of hydrogen bonding allows for some flexibility and space between water molecules, leading to its lower density compared to metals like mercury.

Though potent, hydrogen bonds don't pack molecules as tightly as metallic bonds do, leading to the lighter density of water.