Question

How does the entropy of a system change for each of the following processes? (a) A solid melts. (b) A liquid freezes. (c) A liquid boils. (d) A vapor is converted to a solid. (e) A vapor condenses to a liquid. (f) A solid sublimes. (g) A solid dissolves in water.

Short answer

(a) Increase, (b) Decrease, (c) Increase, (d) Decrease, (e) Decrease, (f) Increase, (g) Increase.

Step-by-step solution

Understanding Entropy

Entropy is a measure of the disorder or randomness of a system. Generally, when a system becomes more disordered, the entropy increases.

Process Analysis: Solid Melting

(a) When a solid melts, it changes from a highly ordered state to a less ordered liquid state. This transition involves an increase in the disorder, and hence an increase in entropy.

Process Analysis: Liquid Freezing

(b) When a liquid freezes, it changes from a less ordered state to a highly ordered solid state. This transition involves a decrease in the disorder, and hence a decrease in entropy.

Process Analysis: Liquid Boiling

(c) When a liquid boils, it changes from a less ordered liquid state to a gas state, which is even less ordered. This transition results in an increase in entropy.

Process Analysis: Vapor to Solid

(d) When a vapor is converted directly to a solid, this represents a transition from a very disordered state (vapor) to a highly ordered state (solid), leading to a decrease in entropy.

Process Analysis: Vapor Condensation

(e) When a vapor condenses to a liquid, it moves from a more disordered gas state to a less disordered liquid state. This transition leads to a decrease in entropy.

Process Analysis: Solid Subliming

(f) When a solid sublimes, it changes directly from a solid to a gaseous state. Sublimation involves a move to a more disordered state, leading to an increase in entropy.

Process Analysis: Solid Dissolving

(g) When a solid dissolves in water, the solid molecules disperse in the solvent, increasing the disorder of the system. This typically results in an increase in entropy.

Key concepts

Phase Transitions

Phase transitions are processes where a substance changes its state between solid, liquid, and gas. These transitions are central to understanding entropy changes. When a solid melts, it transitions to a liquid, resulting in increased molecular motion and disorder. Look at ice turning into water. The ice molecules in a structured lattice shift to a freer, liquid form. Hence, entropy increases.

• Melting ice cubes
• Boiling water into steam

Conversely, when a liquid freezes or a vapor condenses, the molecules slow down and settle into less energetic states, creating an ordered structure. Such order leads to decreased entropy. Comparing it with syrup thickening into a solid candy.

• Freezing water into ice
• Condensing steam

Understanding phase transitions aids in predicting how entropy changes, helping appreciate the complexities in everyday phenomena.

Disorder in Chemical Systems

Disorder in chemical systems describes how molecules are arranged and move within a system. High disorder means molecules have high freedom and random distribution.

• Gaseous state has high disorder
• Solid state has low disorder

When a system like a solid dissolves in water, the molecules' freedom to move increases. This dissolving process creates more randomness as the solid particles spread within the liquid, raising the system's entropy.

• Sugar dissolving in tea
• Table salt in soup

Considering dissolution helps illustrate disorder's role in entropy, emphasizing the energetic spread of molecules when a substance dissolves.

Energy States

Energy states in a system refer to the various levels of energy that the molecules within that system can occupy. These energy levels impact their movement and arrangement.

• Low energy, lower movement in solids
• Higher energy, greater movement in gases

When analyzing entropy, consider how energy states shift during phase transitions. A subliming solid, for example, directly changes to gas, skyrocketing in both energy and disorder levels. Entropy increases significantly in this case.

• Dry ice sublimation
• Frozen carbon dioxide vaporizing

Understanding energy states helps grasp why certain states have higher entropy, as energy identifies how freely molecules can move and arrange themselves.

Thermodynamics

Thermodynamics is the branch of physics focusing on heat, energy, and their transformations. It provides key insight into a system's entropy changes. By evaluating phase transitions through thermodynamic principles, we appreciate how energy and entropy are deeply linked.

• First Law: Energy conservation
• Second Law: Entropy increase in natural processes

When applying thermodynamic principles to entropy, comprehension of everyday processes enhances. Melting, boiling, or subliming reflects energy shifts guided by thermodynamic laws. For example, the energy absorbed during melting is released in freezing.

• Water cycle processes
• Freezing and heating systems

Thus, thermodynamics not only provides a macroscale view of changes but also fine-tunes our understanding by linking energy exchanges and entropy dynamics intricately.