Question

What are the signs \((+,-\), or 0\()\) of \(\Delta H, \Delta S\), and \(\Delta G\) for the spontaneous sublimation of a crystalline solid? Explain.

Short answer

\( \Delta H > 0, \Delta S > 0, \Delta G < 0 \).

Step-by-step solution

Understand Sublimation

Sublimation is the phase transition from a solid to a gas. This process involves breaking the ordered structure of the solid, resulting in more disorder in the gas phase.

Analyze Entropy Change \( (\Delta S) \)

When a solid sublimates into a gas, the entropy increases because gases have more disorder than solids. Therefore, \( \Delta S \) is positive.

Consider Enthalpy Change \( (\Delta H) \)

Sublimation requires energy to overcome intermolecular forces in the solid. This means heat is absorbed, so \( \Delta H \) is positive.

Determine Gibbs Free Energy Change \( (\Delta G) \)

For a spontaneous process, the Gibbs free energy change must be negative. This is given by the equation \( \Delta G = \Delta H - T\Delta S \). Since sublimation is spontaneous, \( \Delta G \) is negative.

Key concepts

Phase Transition

A phase transition refers to the change of a substance from one state of matter to another. For instance, when a crystalline solid sublimates, it transitions directly to a gas without passing through the liquid phase.

During this transformation, the substance absorbs energy because molecules need to overcome the forces holding them in a solid structure. This energy absorption is essential for altering the state of the molecules to allow them to move freely as a gas.

Common phase transitions include:

• Melting: solid to liquid
• Freezing: liquid to solid
• Evaporation: liquid to gas
• Condensation: gas to liquid
• Sublimation: solid to gas
• Deposition: gas to solid

Phase transitions occur at specific temperatures and can vary based on pressure conditions. Understanding phase transitions helps explain phenomena such as the formation of frost, drying of clothes, and even the function of freeze-drying food.

Entropy

Entropy, often symbolized as 'S', is a thermodynamic property that measures the degree of disorder or randomness in a system. During sublimation, the ordered arrangement of molecules in a solid becomes disordered as they enter the gas phase.

Gases have higher entropy compared to solids because gas molecules move freely and spread out over a larger volume. As a result, the sublimation of a solid to a gas results in an increase in entropy, making \[\Delta S > 0\]An increase in entropy is typically associated with a process becoming more spontaneous. In essence, nature favors disorder, and systems naturally evolve towards states of higher entropy under constant conditions.

This principle is crucial for predicting the spontaneity of reactions and the natural tendency of systems to progress towards equilibrium.

Enthalpy

Enthalpy, denoted by 'H', is the measure of total energy in a thermodynamic system and includes internal energy plus the product of pressure and volume. When a solid sublimates, it absorbs energy to weaken and break the intermolecular forces within its crystalline structure.

The absorption of energy during this process causes an increase in enthalpy. Therefore, the change in enthalpy for sublimation is positive:\[\Delta H > 0\]This energy is necessary to change the phase because it disrupts the stable, ordered structure of the solid, allowing it to become a gas.

Understanding enthalpy changes is vital in areas such as chemical reactions, where knowing whether a reaction absorbs or releases heat helps determine feasibility and safety measures.

Gibbs Free Energy

Gibbs Free Energy, denoted as 'G', combines enthalpy and entropy, capturing the total 'useful' work achievable from a thermodynamic process. It is a vital indicator of a system's spontaneity. The change in Gibbs Free Energy during a process can be calculated by the equation:\[\Delta G = \Delta H - T\Delta S\]where:

• \(\Delta G\) is the change in Gibbs Free Energy
• \(\Delta H\) is the change in enthalpy
• \(T\) is the absolute temperature
• \(\Delta S\) is the change in entropy

For a process to be spontaneous, \(\Delta G\) must be negative, indicating the process can occur without external input of energy.

In the sublimation of solids, although entropy increases and enthalpy is positive, the large positive \(T\Delta S\) term often outweighs \(\Delta H\), making \(\Delta G\) negative. This explains why certain solids can spontaneously sublimate under the right conditions, such as dry ice turning into carbon dioxide gas at room temperature.