Question

Why is \(\Delta S_{\text {vap }}\) of a substance always larger than \(\Delta S_{\text {fus }} ?\)

Short answer

\(\boldsymbol{ \Delta S_{\text {vap }} }\) is larger than \(\boldsymbol{ \Delta S_{\text {fus }} }\) because vaporization increases disorder more than fusion.

Step-by-step solution

- Define \(\boldsymbol{ \Delta S_{\text {vap }}}\)\ and \(\boldsymbol{\Delta S_{\text {fus }}}\)

\( \Delta S_{\text {vap }} \) is the change in entropy when a substance undergoes vaporization (liquid to gas), and \(\boldsymbol{ \Delta S_{\text {fus }} }\) is the change in entropy when a substance undergoes fusion (solid to liquid).

- Understand Entropy Change

Entropy \(\boldsymbol{(S)}\) is a measure of disorder or randomness in a system. When a substance changes state, its entropy changes.

- Analyze Entropy in Fusion

During fusion (solid to liquid), particles gain more freedom and disorder increases, but the change is relatively moderate as the solid becomes a liquid.

- Analyze Entropy in Vaporization

In vaporization (liquid to gas), particles gain a significantly larger amount of freedom and randomness because the gas phase has much more disorder than the liquid phase.

- Compare Magnitude of Entropy Changes

Since the transition from liquid to gas entails a much larger increase in particle freedom and disorder, the entropy change during vaporization (\( \Delta S_{\text {vap }} \)) is always larger than the entropy change during fusion (\( \Delta S_{\text {fus }} \)).

Key concepts

Entropy

Entropy, represented by the symbol S, is a fundamental concept in thermodynamics. It measures the amount of disorder or randomness in a system. High entropy means high disorder, while low entropy signifies more order.
When a substance undergoes a phase transition, its entropy changes. This change reflects the difference in the degree of disorder between the two phases.
Understanding entropy helps us predict the direction of natural processes. Systems tend to move from a state of lower entropy (more order) to higher entropy (more disorder).

Vaporization

Vaporization is the phase transition from a liquid to a gas. This process requires energy, known as the heat of vaporization.
During vaporization, molecules in the liquid state gain enough energy to overcome intermolecular forces and enter the gas phase.
Because gas molecules are much further apart and move more freely, the entropy (disorder) of the system significantly increases during vaporization. This large increase in freedom explains why the entropy change during vaporization (\( \Delta S_{\text {vap }} \)) is substantial.

Fusion

Fusion, also known as melting, is the phase transition from solid to liquid. It also requires energy, called the heat of fusion.
During fusion, molecules in the solid phase vibrate more vigorously until they can move freely as a liquid.
While the entropy increases because the liquid phase has more disorder than the solid phase, this increase is not as large as in vaporization. This is why the entropy change during fusion (\( \ Delta S_{\text {fus }} \)) is smaller compared to vaporization.

Disorder in Systems

Disorder in thermodynamic systems is a crucial concept. It helps explain why certain processes occur naturally.
When substances transition between phases, the level of disorder changes. In solids, molecules are in fixed positions, representing low entropy or disorder.
Liquids have more disorder as molecules can slide past each other. Gases have the highest disorder since molecules move freely and occupy more space.

• Solid to Liquid: Moderate increase in disorder (Fusion)
• Liquid to Gas: Large increase in disorder (Vaporization)

Phase Transitions

Phase transitions involve substances changing from one state of matter to another. Common transitions include melting (solid to liquid), freezing (liquid to solid), boiling or vaporization (liquid to gas), and condensation (gas to liquid).
Each transition involves changes in energy and entropy.
The transition from solid to liquid (fusion) leads to a moderate increase in entropy, while the transition from liquid to gas (vaporization) results in a significant jump in entropy.
Understanding these changes helps explain why Volume \( \Delta S_{\text {vap }} \)) is always larger than \( \Delta S_{\text {fus }} \).