Problem 1 - General Chemistry: Principles and Modern Applications

Question

Indicate whether each of the following changes represents an increase or a decrease in entropy in a system, and explain your reasoning: (a) the freezing of ethanol; (b) the sublimation of dry ice; (c) the burning of a rocket fuel.

Step-by-Step Solution

Answer

(a) The freezing of ethanol decreases entropy. (b) The sublimation of dry ice increases entropy. (c) The burning of rocket fuel increases entropy.

Step 1: Freezing of Ethanol

During the freezing process, particles move from a less ordered state (liquid) to a more ordered state (solid). The particles in the solid state are closely packed and have less movement compared to the liquid state. Therefore, freezing decreases the system's entropy.

Step 2: Sublimation of Dry Ice

Sublimation is the process by which a substance transitions from the solid state directly to the gaseous state, bypassing the liquid state. In the case of dry ice (solid carbon dioxide), the particles in the gas state are much more disordered and spread out than in the solid state. Therefore, the sublimation of dry ice increases the system's entropy.

Step 3: Burning of Rocket Fuel

The burning of rocket fuel is a chemical reaction that converts reactants (ordered molecules) into products in the form of various gases. These gases spread out and increase the disorder of the system. Therefore, the burning of rocket fuel increases the system's entropy.

Key Concepts

Phase Changes

Phase changes are fundamental transformations in matter that involve transitions between different states: solid, liquid, and gas. Each of these transitions either absorbs or releases energy, thereby affecting the entropy, or disorderliness, of the system.
Sublimation and freezing are two examples of phase changes that show how entropy varies with the order of particle arrangements.

• Freezing: When a substance like ethanol freezes, its molecules organize themselves into a more structured solid form. Molecules in a solid state have less freedom to move around, so the entropy decreases.
• Sublimation: Opposite to freezing, sublimation is when a solid, such as dry ice, turns directly into a gas. This process causes molecules to spread out and become more disordered, leading to an increase in entropy.

Understanding these transformations helps explain how energy exchanges affect the molecular structure and entropy of a system.

Chemical Reactions

Chemical reactions involve breaking and forming chemical bonds, resulting in the transformation of reactants into products. These reactions often lead to changes in the system’s entropy due to the variation in the number and arrangement of molecules.
For instance, consider the burning of rocket fuel, a complex chemical reaction. During this process:

• Combustion occurs, where highly ordered liquid fuel is transformed into gases. This change means increased movement and disorder because gases spread and occupy a larger volume.
• The chemical reaction releases energy, contributing to the increased randomness of particle motion in the system.

Consequently, this elevation in disorder signifies an increase in the system’s entropy. Chemical reactions are essential to everyday life, both producing energy and playing a role in natural processes like metabolism.

Thermodynamics

Thermodynamics is the branch of physics that studies the relationships between heat, work, temperature, and energy within physical systems. One of its key components is entropy, which thermodynamics notes as a measure of disorder or randomness.
Relevant to phase changes and chemical reactions, thermodynamics outlines several principles:

• The Second Law of Thermodynamics: This law states that in any isolated system, the total entropy can never decrease over time. Systems naturally evolve toward thermodynamic equilibrium, the state of maximum entropy.
• In practical terms, whether dealing with water freezing or a match burning, one can apply thermodynamics principles to predict the direction and spontaneity of processes.
• Understanding these principles allows us to manage energy resources efficiently and design better materials and processes.

Applying thermodynamic concepts helps explain why some reactions occur spontaneously while others require energy input, highlighting the critical role of entropy in these natural processes.