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Ch.19 - Chemical Thermodynamics
All textbooksBrown 15th EditionCh.19 - Chemical ThermodynamicsProblem 89
Chapter 19, Problem 89

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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Step 1: Understand the reaction. The reaction given is 2 Mg(s) + O_2(g) ⟶ 2 MgO(s). This is a synthesis reaction where magnesium reacts with oxygen to form magnesium oxide.
Step 2: Consider the states of matter. In the reaction, we have solid magnesium and gaseous oxygen as reactants, and solid magnesium oxide as the product.
Step 3: Analyze the entropy change. Entropy (S) is a measure of disorder or randomness. Gases have higher entropy than solids because gas particles are more disordered.
Step 4: Predict the sign of ΔS°. Since the reaction involves a gas (O_2) being converted into a solid (MgO), the system becomes more ordered, leading to a decrease in entropy. Therefore, ΔS° should be negative.
Step 5: Conclusion. Your classmate's calculation of a large negative value for ΔS° is consistent with the expected decrease in entropy for this reaction, so they likely did not make a mistake.

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Key Concepts

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

Spontaneity of Reactions

A reaction is considered spontaneous if it occurs without external intervention. The spontaneity is often determined by the change in Gibbs free energy (ΔG), which is influenced by both enthalpy (ΔH) and entropy (ΔS). For a reaction to be spontaneous at constant temperature and pressure, ΔG must be negative, which can occur even if ΔS is negative, provided that ΔH is sufficiently negative.
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Entropy (ΔS)

Entropy is a measure of the disorder or randomness in a system. A negative change in entropy (ΔS < 0) indicates that the products of a reaction are more ordered than the reactants. In the case of the reaction 2 Mg(s) + O2(g) ⟶ 2 MgO(s), the formation of a solid from gaseous and solid reactants results in a decrease in entropy, which is expected and does not necessarily indicate an error in calculation.
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Gibbs Free Energy (ΔG)

Gibbs free energy combines the effects of enthalpy and entropy to predict the spontaneity of a reaction. It is defined as ΔG = ΔH - TΔS, where T is the temperature in Kelvin. A reaction can be spontaneous (ΔG < 0) even with a large negative ΔS if the enthalpy change (ΔH) is significantly negative, indicating that the energy released during the reaction outweighs the decrease in entropy.
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Related Practice
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?

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?

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).

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.

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

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. (e) Suppose that a house and its exterior are both initially at 31 °C. Some time after the air conditioner is turned on, the house is cooled to 24 °C. Is this process spontaneous or nonspontaneous?

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