The crystalline hydrate Cd(NO₃)₂⋅4 H₂O(s) loses water when placed in a large, closed, dry vessel at room temperature: Cd(NO₃)₂⋅4 H₂O(s) → Cd(NO₃)₂(s) + 4  H₂O(g) This process is spontaneous and ΔH° is positive at room temperature. (b) If the hydrated compound is placed in a large, closed vessel that already contains a large amount of water vapor, does ΔS° change for this reaction at room temperature?

Verified step by step guidance

1. Identify the reaction: The decomposition of the hydrate Cd(NO_3)_2·4H_2O(s) into Cd(NO_3)_2(s) and 4 H_2O(g) is given.
2. Understand the spontaneity: The process is spontaneous, meaning the overall change in Gibbs free energy (ΔG°) is negative.
3. Consider the enthalpy change: ΔH° is positive, indicating the reaction is endothermic, absorbing heat from the surroundings.
4. Analyze the entropy change: Since the reaction involves the conversion of solid hydrate to solid and gaseous water, the entropy (ΔS°) increases due to the increase in disorder from solid to gas.
5. Evaluate the effect of water vapor: In a vessel with a large amount of water vapor, the increase in entropy (ΔS°) might be less pronounced because the system already has high entropy due to the existing water vapor.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a process at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous process, while a positive ΔG suggests non-spontaneity.

Entropy (ΔS)

Entropy (S) is a measure of the disorder or randomness in a system. The change in entropy (ΔS) during a reaction indicates how the distribution of energy states changes. In the context of the given reaction, the formation of water vapor from a solid hydrate increases the disorder of the system, leading to a positive ΔS, which contributes to the spontaneity of the reaction.

Phase Equilibrium

Phase equilibrium refers to the state in which the phases of a substance (solid, liquid, gas) coexist at equilibrium conditions. In the context of the question, when the hydrated compound is placed in a vessel with existing water vapor, the equilibrium between the solid and gaseous phases may shift. This can affect the overall entropy change (ΔS) of the system, as the presence of water vapor influences the potential for further evaporation or condensation.