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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Ch.19 - Chemical Thermodynamics
Chapter 19, Problem 88e
For each of the following processes, indicate whether the signs of ΔS and ΔH are expected to be positive, negative, or about zero. (e) A piece of charcoal is combusted to form CO2(g) and H2O(g).
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Identify the reactants and products in the combustion of charcoal. Charcoal is primarily carbon, so the reaction is C(s) + O_2(g) -> CO_2(g) + H_2O(g).
Consider the change in entropy (ΔS). Combustion typically involves a solid reactant forming gaseous products, which increases disorder. Therefore, ΔS is expected to be positive.
Consider the change in enthalpy (ΔH). Combustion reactions are exothermic, meaning they release heat. Therefore, ΔH is expected to be negative.
Summarize the expected signs: ΔS is positive due to increased disorder from solid to gas, and ΔH is negative due to the exothermic nature of combustion.
Reflect on the implications: The positive ΔS and negative ΔH indicate that the combustion of charcoal is both entropically and enthalpically favorable.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Entropy (ΔS)
Entropy, represented as ΔS, is a measure of the disorder or randomness in a system. In a combustion reaction, such as the burning of charcoal, the products (gaseous CO2 and H2O) have greater molecular freedom compared to the solid charcoal, leading to an increase in disorder. Therefore, ΔS is expected to be positive.
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Entropy in Thermodynamics
Enthalpy (ΔH)
Enthalpy, denoted as ΔH, reflects the heat content of a system at constant pressure. Combustion reactions are typically exothermic, meaning they release heat as chemical bonds are broken and formed. In the case of charcoal combustion, the reaction releases energy, resulting in a negative ΔH.
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Gibbs Free Energy (ΔG)
Gibbs Free Energy, represented as ΔG, determines the spontaneity of a reaction and is calculated using the equation ΔG = ΔH - TΔS. For a reaction to be spontaneous, ΔG must be negative. In the combustion of charcoal, the combination of a negative ΔH and a positive ΔS suggests that ΔG will be negative, indicating that the reaction occurs spontaneously.
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Related Practice
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. (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?
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Textbook Question
The reaction 2 Mg(s) + O2(g) ⟶ 2 MgO(s) is highly spontaneous. A classmate calculates the entropy change for this reaction and obtains a large negative value for ΔS°. Did your classmate make a mistake in the calculation? Explain.
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Textbook Question
Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces. (f) Calculate the absolute entropy of the two-dice system.
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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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