Problem 33 - Chemistry: The Central Science

Question

How does the entropy of the system change when (a) a solid melts, (b) a gas liquefies, (c) a solid sublimes?

Step-by-Step Solution

Answer

For each phase transition, the entropy changes are: a. Solid melts to liquid: \(ΔS > 0\) (increase in disorder) b. Gas liquefies to liquid: \(ΔS < 0\) (decrease in disorder) c. Solid sublimes to gas: \(ΔS > 0\) (increase in disorder, larger than in solid-liquid transitions).

Step 1: (a) Entropy change when a solid melts

In the case of a solid melting into a liquid, the particles in the substance gain more freedom to move and arrange themselves randomly. In other words, the disorder of the system increases. Therefore, the entropy change during a solid-liquid phase transition will be positive (\(ΔS > 0\)).

Step 2: (b) Entropy change when a gas liquefies

In the case of a gas liquefying into a liquid, the particles become more restricted in their arrangement and movement, as they are in closer proximity to each other. This results in a decrease in the disorder of the system. Therefore, the entropy change during a gas-liquid phase transition is negative (\(ΔS < 0\)).

Step 3: (c) Entropy change when a solid sublimes

In the case of a solid subliming directly into a gas (skipping the liquid phase), the particles in the substance gain significant freedom to move and arrange themselves randomly. This is an even more dramatic change in the system's disorder than in the case of melting. Therefore, the entropy change during a solid-gas phase transition (sublimation) will be positive and generally larger than in solid-liquid phase transitions (\(ΔS > 0\)). In summary, the entropy change for each phase transition is as follows: a. Solid melts to liquid: \(ΔS > 0\) (positive entropy change) b. Gas liquefies to liquid: \(ΔS < 0\) (negative entropy change) c. Solid sublimes to gas: \(ΔS > 0\) (positive entropy change, generally larger than in solid-liquid phase transitions)

Key Concepts

Solid-Liquid Phase Transition

When discussing the solid-liquid phase transition, it's crucial to focus on entropy, a measure of disorder within a thermodynamic system. As a solid melts into a liquid, its particles gain increased freedom of movement, which allows for more random arrangements. This process is akin to tidying a room only to disorganize it later; just as the room becomes less orderly, the system's entropy increases. Therefore, during the melting process, there is a positive entropy change, represented by the formula \(ΔS > 0\).

In educational terms, you might think of the particles as students in a classroom. When they are 'solid', they're seated and still. But as they 'melt' into a liquid state, they stand up and mingle, representing the increase in entropy.

Gas-Liquid Phase Transition

Conversely, a gas-liquid phase transition goes against the 'disorganization' seen in melting. Here, gas particles, which are initially free to roam, are confined within the closer quarters of the liquid state. It's like inviting the students – or gas particles – to find their seats in the classroom after playtime, effectively reducing their random movements and decreasing the system's entropy. Symbolically, this reduction in disorder or 'neatening' of the system translates to a negative entropy change: \(ΔS < 0\).

This reduction can be challenging for learners, as one might initially think all transitions lead to increased disorder. Remembering that gas has the highest entropy helps make sense of why condensation leads to decreased entropy.

Solid-Gas Phase Transition

The solid-gas phase transition, or sublimation, sees a direct shift from a highly ordered solid state to a highly disorganized gaseous state, bypassing the liquid phase entirely. This is akin to students going straight from sitting exams – a structured, solid-like situation – to a playground free-for-all without a structured class in between. Sublimation entails a significant increase in entropy, greater even than in melting, once again giving us a positive entropy change but of a larger magnitude: \(ΔS > 0\), and typically larger than in solid-liquid transitions.

Students should note that this phase change, while similar in increasing entropy to melting, creates a more extreme effect due to the greater freedom particles gain when transitioning directly to a gas.

Thermodynamics

Thermodynamics offers the framework to understand these phase transitions. It is a field of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter. The concept of entropy is a cornerstone in thermodynamics that helps us comprehend the 'disorder' within a system, which invariably changes during phase transitions.

According to the second law of thermodynamics, the total entropy of an isolated system can never decrease over time. Thus, in any spontaneous process, whether a phase change or not, the overall disorder or entropy always increases or, at best, remains constant in an ideal reversible process.

State of Matter

The state of matter is fundamental to understanding phase transitions. Matter exists in traditionally recognized states of solid, liquid, and gas, each with distinct properties. Solids have a fixed shape and volume, liquids have a fixed volume but adapt to the shape of their container, and gases have neither fixed volume nor shape. During transitions like melting, freezing, vaporization, condensation, and sublimation, matter moves between these states.

Each state has characteristic entropy levels: solids have the least entropy, liquids have more, and gases have the most due to the freedom of their particles to move. Consequently, phase transitions where the state changes from solid to liquid to gas typically involve an increase in entropy, impacting the system’s thermodynamic behavior.