Problem 19 - Chemistry The Molecular Science

Question

For each process, tell whether the entropy change of the system is positive or negative. (a) Water vapor (the system) deposits as ice crystals on a cold windowpane. (b) A can of carbonated beverage loses its fizz. (Consider the beverage but not the can as the system. What happens to the entropy of the dissolved gas?) (c) A glassblower heats glass (the system) to its softening temperature.

Step-by-Step Solution

Answer

(a) Negative, (b) Positive, (c) Positive.

Step 1: Understanding Entropy and Phase Change

Entropy is a measure of the disorder or randomness of a system. In process (a), we are dealing with a phase transition from gas (water vapor) to solid (ice crystals). Generally, when a substance changes from a gas to a solid, the entropy decreases because the molecules become more ordered. Thus, for water vapor depositing as ice, the entropy change of the system is negative.

Step 2: Gas Dissolution and Entropy

For process (b), we consider the entropy change in the carbonated beverage when it loses its fizz. The loss of fizz means that the gas (likely CO₂) is escaping from the liquid. This transition from a dissolved state to an exit from the liquid increases disorder, as gas molecules spread out more than when they are dissolved. Therefore, the entropy change of the dissolved gas in the beverage is positive.

Step 3: Heating and Entropy Change

In process (c), a glassblower heats glass to its softening point. As the glass temperature increases, its molecules gain kinetic energy and move more freely, increasing disorder. Hence, the entropy of the glass system increases. Thus, the heating process results in a positive entropy change.

Key Concepts

Phase Change

When a substance undergoes a phase change, its physical state changes, leading to variations in molecular arrangement. For example, consider water vapor turning into ice. In this transition, molecules move from a less ordered state (gas) to a more ordered state (solid). Because of this increased order, the entropy of the system generally decreases. This means the entropy change is negative during the phase change from gas to solid. Conversely, during melting or vaporization, solids or liquids become more unordered, leading to a positive entropy change. Understanding these behaviors helps predict how systems respond when conditions like pressure or temperature shift.

Disorder

Disorder in a system refers to the randomness and unpredictability of molecular motion. Higher disorder means the molecules have more possible positions or arrangements, while lower disorder signifies a more structured or predictable arrangement. Entropy is a quantitative measure of disorder. More disorder equates to higher entropy, and less disorder equates to lower entropy.

• In gases, particles move freely, leading to high disorder.
• Solids, with tightly packed structures, exhibit low disorder.

When assessing processes such as a carbonated beverage losing its fizz, the escaping gas molecules become more disordered as they spread in the air, increasing entropy.

Entropy Change

Entropy change describes the variation in disorder within a system as it undergoes a process. Positive entropy change occurs when disorder increases, like when heating leads atoms to move more freely. This is seen in process (c), where heating glass results in greater molecular motion and increased entropy. Similarly, when a gas is dissolved in a liquid and subsequently escapes, the system sees a boost in disorder, marking a positive entropy change. However, in phase changes, such as gas condensing into a solid, a negative entropy change occurs because molecules settle into a less disordered, more ordered structure.

System Analysis

Performing a system analysis involves understanding how different processes affect the entropy of a system. For each transition, examining the initial and final states of the system provides insight into changes in entropy. In step-by-step analysis:

• Identify the phase or state of matter transition.
• Determine if the change increases or decreases molecular disorder.
• Assess the corresponding change in entropy.

Detailed analyses help to predict the impact of external factors upon a system's entropy. This is crucial for understanding behavior during processes like heating, cooling, dissolving, and phase transitions.