In which of the following processes will ΔS° be negative? — Thermodynamics Chemistry Question

STEPS:

1. Understand the underlying chemical concept (Entropy, $S$): Entropy is a thermodynamic measure of the positional disorder of a system and the number of microstates (spatial arrangements) available to its constituent particles.
2. Establish the sign convention for $\Delta S^\circ$:
* A positive change in entropy ($\Delta S^\circ > 0$) indicates that a process results in an increase in disorder (such as when particles gain more freedom of motion during transitions from solid to liquid, liquid to gas, or solid to gas).
* A negative change in entropy ($\Delta S^\circ < 0$) indicates that a process leads to an increase in order and restriction (such as when particles lose freedom of motion during transitions from gas to liquid, liquid to solid, or gas to solid).
3. Analyze the phase transition in Option D ($\text{Cl}_2(g) \rightarrow \text{Cl}_2(l)$): This equation represents the physical process of condensation, transitioning chlorine from a gas to a liquid.
4. Determine the entropy change for Option D: In the gaseous phase, chlorine molecules move rapidly and independently throughout a large space. When they condense into a liquid, the gas molecules become restricted to a much smaller volume. This restriction in volume and spatial movement reduces the number of available positional microstates, making the system more ordered. Therefore, $\Delta S^\circ$ is negative, identifying Option D as the correct choice.

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WHY_OTHERS_WRONG:

• Option A is incorrect: The process $\text{C}_2\text{H}_5\text{OH}(l) \rightarrow \text{C}_2\text{H}_5\text{OH}(g)$ represents vaporization (evaporation). The molecules in the gas phase can act independently and are distributed over a much greater volume than they are in the liquid phase, increasing positional disorder and resulting in a positive $\Delta S^\circ$.
• Option B is incorrect: The process $\text{NaCl}(s) \rightarrow \text{NaCl}(l)$ represents melting (fusion). Ions held in rigid, fixed positions within a solid crystalline lattice are freed to move randomly among one another in the liquid state, which increases positional disorder and yields a positive $\Delta S^\circ$.
• Option C is incorrect: The process $\text{CO}_2(s) \rightarrow \text{CO}_2(g)$ represents sublimation. Highly restricted molecules in the solid state escape to the gaseous state where they can act independently and occupy a vastly greater volume, leading to a significant increase in disorder and a positive $\Delta S^\circ$.