Question

Why is \(\Delta H_{\text {vap }}\) usually larger than \(\Delta H_{\text {fusion }}\) ?

Short answer

\(\Delta H_{\text{vap}}\) is larger than \(\Delta H_{\text{fusion}}\) because more intermolecular forces are broken during vaporization.

Step-by-step solution

Understanding Enthalpy of Vaporization and Fusion

The enthalpy change for vaporization, \(\Delta H_{\text {vap }}\), is the energy required to convert one mole of a substance from liquid to gas. The enthalpy change for fusion, \(\Delta H_{\text {fusion }}\), is the energy required to change one mole of a substance from solid to liquid.

Analyzing Molecular Changes

During fusion, molecules move from a structured solid phase to a less structured liquid phase. In contrast, during vaporization, molecules move from a liquid phase to a completely free gaseous phase. This transition involves breaking more intermolecular forces than fusion.

Comparing Energy Requirements

Breaking the additional intermolecular forces during vaporization requires more energy. Thus, \(\Delta H_{\text {vap }}\) is greater than \(\Delta H_{\text {fusion }}\) because vaporization requires breaking all intermolecular forces, while fusion only requires partial disruption.

Key concepts

Enthalpy of Fusion

Enthalpy of fusion is the amount of energy required for a phase transition from solid to liquid. This process involves heating the substance to its melting point and making it change state without altering its temperature. During fusion, the structured arrangement of a solid's molecules are loosened enough to flow more freely as a liquid. Each molecule in the substance absorbs a specific amount of energy, leading to this transitional movement. However, it is important to note that while the structure shifts, not all molecular connections, known as intermolecular forces, are completely broken. Instead, these forces are weakened, allowing the molecules to rearrange into a looser form. In comparison to vaporization, fusion requires less energy because the phase change doesn't require complete disruption of molecular interactions. Thus, the enthalpy of fusion is generally lower than that of vaporization.

Intermolecular Forces

Intermolecular forces are the forces that hold molecules together, playing a crucial role in phase changes between solid, liquid, and gas phases. Common types include hydrogen bonds, dipole-dipole interactions, and London dispersion forces. These forces determine the strength of cohesion within a substance and subsequently the energy necessary for phase changes:

• In the solid phase: Molecules are closely packed with strong intermolecular forces.
• In the liquid phase: These forces are weaker, allowing molecules to move more freely.
• In the gaseous phase: Molecules are far apart with negligible intermolecular forces.

The energy needed to change phases is directly linked to breaking these intermolecular forces. As you transition from one phase to another, especially moving to a gas, more energy is needed to overcome these forces. This is why the enthalpy of vaporization typically surpasses the enthalpy of fusion.

Molecular Phase Changes

Molecular phase changes occur when a substance transitions between solid, liquid, and gaseous states. These changes happen when thermal energy is added or removed, altering the energy of individual molecules. During these transitions, the spatial arrangement and freedom of movement of molecules are altered:

• Solid to liquid (fusion): Molecules switch from a fixed, ordered structure to one where they can slide past each other.
• Liquid to gas (vaporization): Molecules gain enough energy to separate completely and move independently.
• Gas to liquid (condensation): Molecules lose energy and come closer to each other, strengthening intermolecular forces.

Each phase change has its specific energy requirements indicated by specific enthalpy values like fusion or vaporization. Understanding these shifts in molecular structure helps us comprehend why different phase changes require varying amounts of energy.