Problem 112 - General Chemistry: Principles and Modern Applications

Question

At room temperature and normal atmospheric pressure, is the entropy of the universe positive, negative, or zero for the transition of carbon dioxide solid to liquid?

Step-by-Step Solution

Answer

The entropy of the universe for the transition of carbon dioxide from solid to liquid at room temperature and normal atmospheric pressure is positive.

Step 1: The Nature of the Process

We're dealing with a phase transition process, carbon dioxide going from solid state to liquid state. In this transition, the molecules' freedom of motion increases, leading to higher entropy.

Step 2: The Second Law of Thermodynamics

According to the second law of thermodynamics, any spontaneous change in a closed system will always lead to either an increase or no change in the system's entropy.

Step 3: Correlation with the Universe's Entropy

In this case, the question refers to the universe's entropy. The universe consists of the system (here, the carbon dioxide undergoing phase change) and the surroundings. The second law of thermodynamics applies to the universe too, meaning the total entropy of the universe can never decrease.

Step 4: Entropy Change in the Given Process

Since the solid-to-liquid phase transition increases the system's entropy, and considering the overall entropy of the universe can't decrease, it’s logical to conclude that entropy of the universe must increase in this process.

Key Concepts

Understanding Entropy

Entropy is a measure of the randomness or disorder within a system. In simple terms, it represents how energy is spread out among the possible states a system can be in. When molecules like those in carbon dioxide transition from being tightly packed in a solid to more freely moving in a liquid, the overall entropy of the system increases. This is because the molecules have more freedom to move around and occupy various positions, leading to more disorder.

The Second Law of Thermodynamics tells us that in any natural thermodynamic process, the total entropy of the universe tends to increase. This means that spontaneous changes typically result in increased entropy. Even in cases where a system's entropy decreases, the entropy of the surrounding environment increases by a greater amount, ensuring the overall increase in universal entropy.

Phase Transition: From Solid to Liquid

A phase transition refers to the change of one state of matter to another, such as solid to liquid or liquid to gas. In the case of carbon dioxide, the transition from solid to liquid involves an increase in molecular motion and entropy.

• In a solid, particles are closely packed together in a structured lattice, limiting their movement.
• During melting, energy is absorbed, allowing particles to move more freely. This energy absorption leads to an increased disorder or randomness, which we measure as an increase in entropy.

This increased disorder is why ice (solid water) absorbs heat and turns into liquid water at higher temperatures. In the context of carbon dioxide's phase transition at room temperature and normal atmospheric pressure, the entropy increases as it melts, contributing to a broader increase in the universe's entropy.

The Role of Carbon Dioxide

Carbon dioxide (CO₂) is a colorless gas under typical atmospheric conditions but can exist as a solid, known as dry ice, at certain pressures and temperatures. Understanding its behavior in different phases helps us comprehend the entropy changes during phase transitions.

• In its solid state, CO₂ molecules are immobilized within a rigid lattice structure, resulting in low entropy due to limited molecular movement.
• When CO₂ transitions from solid to liquid (or gas under certain conditions), the molecules gain energy, move more freely, and increase their entropy.

This process aligns with the Second Law of Thermodynamics, as the increase in disorder from a solid to a liquid increases the universe's total entropy. When studying such transitions, it's essential to consider the behavior and properties of molecules in various phases to understand entropy changes fully.