Question

There is an increase in entropy as solid iodine, \(\mathrm{I}_{2}(\mathrm{~s})\), sublimes into iodine vapor, \(\mathrm{I}_{2}(\mathrm{~g})\). Is this increase in entropy necessarily balanced out by an increase in entropy elsewhere?

Short answer

No, the increase in entropy is not necessarily balanced elsewhere; total entropy must increase.

Step-by-step solution

Understanding Entropy

Entropy is a measure of the disorder or randomness in a system. When a solid sublimates, it changes into the gaseous phase, which has higher entropy due to increased molecular motion and randomness.

Analyzing the Sublimation Process

In the sublimation of iodine, \(\mathrm{I}_2(\mathrm{s}) \rightarrow \mathrm{I}_2(\mathrm{g}),\) the solid iodine absorbs energy to break intermolecular forces, resulting in increased entropy within the system.

Considering the Surroundings

For this transformation to occur, heat is absorbed from the surroundings, which can lead to a decrease in entropy in the immediate surroundings.

Applying the Second Law of Thermodynamics

The Second Law of Thermodynamics states that the total entropy of the universe (system plus surroundings) must increase for a spontaneous process. Therefore, the increase in entropy from the sublimation of iodine is not necessarily entirely balanced out by an equivalent decrease in entropy elsewhere.

Key concepts

Second Law of Thermodynamics

The Second Law of Thermodynamics is a fundamental principle in the world of physics and chemistry. It states that the total entropy, or disorder, of an isolated system always increases over time. This law helps us understand why certain processes occur spontaneously while others do not. Entropy can be viewed as a measure of randomness or the number of ways a system can be arranged.
An isolated system will seek to maximize its entropy, meaning spontaneous processes will usually result in the dispersion of energy and matter to more probable states, with no external energy input.

• Spontaneous processes increase the universe's entropy, not just within the system itself.
• This concept can be applied to a wide range of phenomena, from simple chemical reactions to complex ecological systems.

In the case of iodine sublimation, the process is spontaneous because the overall entropy of the universe increases, even if some entropy is temporarily lost from the surroundings as heat is absorbed during sublimation.

Sublimation

Sublimation is a fascinating phase change that skips the liquid phase. It occurs when a substance transitions directly from a solid to a gas. This process requires energy, typically in the form of heat, to overcome intermolecular forces.
Sublimation is endothermic because energy absorption is necessary to dissociate molecules within a solid structure. For iodine, its molecules need sufficient energy to transition from the ordered arrangement in a solid to freely moving particles in a vapor. Some essential characteristics of sublimation include:

• Energy absorption – It is essential for breaking the solid's intermolecular forces.
• Higher entropy – The gaseous phase has much higher molecular disorder compared to solids.
• No liquid phase – Direct transition from solid to gas, notably seen in dry ice and iodine.

Understanding sublimation highlights the significant changes in entropy that occur, playing a crucial role in the context of thermodynamics.

Iodine Phase Change

Iodine exemplifies sublimation beautifully as it transitions directly from a solid to a gas. At room temperature, iodine is a shiny, purple-black solid with visible vapor pressure evidenced by a faint purple gas above it.
The sublimation of iodine involves iodine crystals absorbing energy, leading to a phase change to a gas, usually resulting in purple vapors.
The process:

• Involves absorption of heat energy from surroundings, causing an increase in internal energy.
• The organized structure of iodine crystals breaks, allowing molecules to disperse widely.
• Higher molecular movement in the gaseous state indicates increased randomness or entropy.

This phase change process highlights the relationship between energy absorption, increased entropy, and system spontaneity, encapsulated by the Second Law of Thermodynamics.