Problem 86 - Chemistry Matter and Change

Question

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

Step-by-Step Solution

Answer

The difference in density between mercury (13.5 g/mL) and water (1.00 g/mL) at the same temperature and pressure can be explained by their intermolecular forces and atomic/molecular structures. Mercury, a metal, has strong metallic bonds and a closely packed lattice structure of atoms, which contribute to its high density. On the other hand, water, a covalent compound with polar characteristics, has weaker hydrogen bonding and a less-packed arrangement of molecules, resulting in a lower density.

Step 1: Understanding the properties of mercury and water

Mercury is a metal and has metallic bonding, while water is a covalent compound with polar characteristics. This means that they have different types of intermolecular forces: mercury has metallic bonds, whereas water molecules interact through hydrogen bonding.

Step 2: Kinetic-molecular theory

According to the kinetic-molecular theory, particles of a substance are always in motion, and the average kinetic energy of these particles is directly proportional to the temperature. At the same temperature, the average kinetic energy of mercury atoms and water molecules will be the same. However, due to the different types of intermolecular forces and atomic/molecular structures, their densities will differ.

Step 3: Metallic bonding in mercury

In mercury, atoms are packed closely together in a lattice structure, with the outer electrons delocalized and shared among the metal atoms. This creates a strong metallic bond between the atoms, which helps explain its high density. At 25°C and 760 mm Hg, the density of mercury is 13.5 g/mL.

Step 4: Hydrogen bonding in water

In water molecules, hydrogen bonding occurs between the oxygen atom of one water molecule and the hydrogen atom of another molecule. These bonds are weaker than the metallic bonds in mercury, and water molecules are not as closely packed together as mercury atoms. This results in a lower density for water, which is 1.00 g/mL at 25°C and 760 mm Hg.

Step 5: Comparison and conclusion

The difference in density between mercury and water at the same temperature and pressure can be explained by the different types of intermolecular forces, as well as their atomic/molecular structures. Mercury has strong metallic bonds and a closely packed lattice structure of atoms, while water has weaker hydrogen bonding and a less-packed arrangement of molecules. These factors contribute to the higher density of mercury (13.5 g/mL) compared to water (1.00 g/mL).

Key Concepts

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion between neighboring molecules. These forces play a central role in determining the physical properties of substances, such as density, boiling point, and melting point.

• Metallic Bonds: Found in metals like mercury, where electrons are shared in a "sea" of electrons among cations. This creates a strong bond and tightly packed structure.
• Hydrogen Bonds: A type of dipole-dipole interaction, significantly weaker than metallic bonds, occurring in polar molecules like water.

Intermolecular forces greatly influence how substances arrange themselves at the molecular level, directly affecting their density.

Kinetic-Molecular Theory

The kinetic-molecular theory provides a framework for understanding the behavior of molecules in different phases. According to this theory, particles of a substance are always in motion, with their kinetic energy proportional to temperature.

• Motion and Energy: At a given temperature, the particles of mercury and water have the same average kinetic energy.
• Density Influence: While both substances are at the same temperature, the strength of their intermolecular forces affects how densely packed the particles are.

This theory helps explain why, despite having similar kinetic energies, mercury has a much greater density than water due to its particle arrangement and bonding.

Metallic Bonding

Metallic bonding is especially important in the context of metals like mercury. In metallic bonding, electrons are not bound to any single atom but instead move freely across a lattice of positively charged ions. This creates a very strong bond:

• High Density: Electrons freely moving create a compact structure, explaining mercury's high density of 13.5 g/mL.
• Lattice Structure: The lattice configuration allows atoms to be closely packed, reinforcing the density.

This type of bonding is integral to understanding why mercury behaves as it does, especially in comparison to substances with weaker intermolecular forces like water.

Hydrogen Bonding

Hydrogen bonding is a special type of dipole-dipole interaction which plays a crucial role in the properties of water. It occurs when the slightly positive hydrogen atom in a water molecule is attracted to the slightly negative oxygen atom in another molecule. These bonds are:

• Weaker than Metallic Bonds: Resulting in less dense structures, such as water at 1.00 g/mL.
• Impact on Density: This weaker attraction means water molecules aren't packed as tightly as mercury atoms.

Hydrogen bonding significantly contributes to the lower density of water, making it a unique and important property.

Atomic Structure

Atomic structure refers to the arrangement of electrons, protons, and neutrons within an atom, influencing the chemical behavior and physical properties of a substance.

• Formation: The way electrons interact and bond with each other can create different bonding types such as metallic and hydrogen bonds.
• Influence on Density: The arrangement and type of bonds, whether metallic or hydrogen, affect how substances like mercury and water differ in density.

Knowledge of atomic structure aids in understanding how and why different substances exhibit their unique characteristics, primarily focusing on their density and state under given conditions.