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Ch.19 - Chemical Thermodynamics
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
All textbooksBrown 15th EditionCh.19 - Chemical ThermodynamicsProblem 86b
Chapter 19, Problem 86b

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.
Understand the spontaneity: The process is spontaneous, meaning the overall change in Gibbs free energy (ΔG°) is negative.
Consider the enthalpy change: ΔH° is positive, indicating the reaction is endothermic, absorbing heat from the surroundings.
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.
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

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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Gibbs Free Energy of Reactions

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.
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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.
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Related Practice
Textbook Question

For each of the following processes, indicate whether the signs of ΔS and ΔH are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of Co(s) is lowered from 60 °C to 25 °C. (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form CO2(g) and H2O(g).

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Textbook Question

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as CH2F2. An air-conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram).

During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber. (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why?

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Textbook Question

Trouton’s rule states that for many liquids at their normal boiling points, the standard molar entropy of vaporization is about 88 J/mol‐K. b. Look up the normal boiling point of Br2 in a chemistry handbook or at the WebElements website (www.webelements.com) and compare it to your calculation. What are the possible sources of error, or incorrect assumptions, in the calculation?

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Textbook Question

(a) Which of the thermodynamic quantities T, E, q, w, and S are state functions? (b) Which depend on the path taken from one state to another?

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Textbook Question

(d) For a reversible isothermal process, write an expression for ΔE in terms of q and w and an expression for ΔS in terms of q and T.

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Textbook Question

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.

(a) What is the sign of ΔS° at room temperature?