Problem 20 - Chemistry The Science in Context

Question

Which of the following processes would not result in an entropy increase for the indicated system? a. Melting of an ice cube b. Evaporation of a sample of an alcohol c. Sublimation of a mothball d. Cooling of hot water to room temperature

Step-by-Step Solution

Answer

A) Melting of an ice cube B) Evaporation of a sample of an alcohol C) Sublimation of a mothball D) Cooling of hot water to room temperature Answer: D) Cooling of hot water to room temperature

Step 1: Process A: Melting of an ice cube

Melting of an ice cube involves a transition from the solid phase to the liquid phase. Since a liquid is more disordered than a solid, the entropy of the system should increase during this process.

Step 2: Process B: Evaporation of a sample of an alcohol

Evaporation of an alcohol involves a transition from the liquid phase to the gas phase. Gases are more disordered than liquids, so the entropy of the system should increase during the evaporation process.

Step 3: Process C: Sublimation of a mothball

Sublimation of a mothball is a process where a solid transitions directly to the gas phase without passing through the liquid phase. Gases have higher entropy than solids, so the entropy of the system should increase during sublimation.

Step 4: Process D: Cooling of hot water to room temperature

Cooling of hot water to room temperature is a process where the system loses heat to the surroundings and the water molecules slow down. As the water cools down, its molecules become more ordered, which results in a decrease in entropy for the system. Based on our evaluation, process D, cooling of hot water to room temperature, would not result in an entropy increase for the system.

Key Concepts

Entropy Increase

The principle of entropy is central to understanding not just thermodynamics, but the nature of the universe itself. In simple terms, entropy measures the level of disorder within a system; the higher the entropy, the greater the disorder and randomness.

When we apply heat to a substance or allow particles more freedom to move, we increase entropy. For example, heating a solid, like an ice cube, confers energy to the molecules, causing them to vibrate more vigorously and, when enough energy is provided, to break free from their fixed positions, transitioning to a liquid state. This is inherently a more chaotic state of affairs, representing an increase in entropy.

However, not all processes result in entropy increase. When systems lose energy, such as cooling hot water, the molecules slow down and the disorder decreases, thus reducing entropy. This aligns with the second law of thermodynamics stating that for a closed system, the total entropy can never decrease over time. It either increases or remains constant, given that no energy enters or leaves the system.

Phase Transitions

Phase transitions are transformative processes where matter changes from one state to another such as from solid to liquid, liquid to gas, or directly from solid to gas. During these transitions, the structure and the energy of a system undergo significant changes.

For instance, melting (solid to liquid), evaporation (liquid to gas), and sublimation (solid to gas) are all endothermic processes, meaning they absorb heat. As matter absorbs energy during these transitions, particles move more freely, which increases the entropy or disorder of the system.

The energy needed to induce these phase changes is known as latent heat. This heat doesn't raise the temperature but is instead used to break intermolecular forces holding the particles in their current state. The phase transition point is a physical embodiment of a balance (or imbalance) in entropy within the different states of matter.

Thermodynamics

Thermodynamics is a field of physics that deals with the relationships between heat, work, temperature, and energy. The laws of thermodynamics govern how these quantities interact and lay the groundwork for understanding phenomena such as entropy and phase transitions.

The first law of thermodynamics, often known as the law of energy conservation, dictates that energy can neither be created nor destroyed, only transformed from one form to another. When we heat water on a stove, we convert chemical energy from the stove's fuel into thermal energy within the water.

The second law, which deals with entropy, tells us that the total entropy of an isolated system can never decrease over time. This law is a statistical one, explaining why certain processes like cooling hot water to room temperature will naturally lead to decreased entropy, making it a spontaneous process in thermodynamics.

States of Matter

Matter exists in several different states, most commonly solid, liquid, and gas. Each state is defined by its unique set of physical properties determined by the arrangement and energy of its constituent particles.

Solids have a fixed shape and volume with tightly packed particles that vibrate in place, having the lowest entropy among the three states. As we move to liquids, we see an increase in entropy: liquids have a definite volume, but their shape can change as the particles are less tightly packed and can move past each other.

Gases have the most disordered state with particles that are widely spaced, move quickly, and exhibit high entropy. The changes in matter's states directly impact the entropy of a system, with increased movement and space between particles leading to higher entropy. Transitions between these states—melting, evaporating, condensing, freezing, and sublimating—each have implications for the entropy of a system, frequently increasing it in line with the spontaneous tendencies described by thermodynamics.