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Ch.19 - Free Energy & Thermodynamics
All textbooksTro 6th EditionCh.19 - Free Energy & ThermodynamicsProblem 99
Chapter 19, Problem 99

All the oxides of nitrogen have positive values of ΔG°f at 298 K, but only one common oxide of nitrogen has a positive ΔS°f. Identify that oxide of nitrogen without reference to thermodynamic data and explain.

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Identify the common oxides of nitrogen: NO, NO2, N2O, N2O3, N2O4, and N2O5.
Understand that ΔS°_f refers to the standard entropy of formation, which is related to the disorder or randomness of a substance.
Consider the molecular structure and physical state of each oxide. Gases generally have higher entropy than solids or liquids due to greater molecular motion.
Recognize that N2O (dinitrogen monoxide) is a gas and has a relatively simple molecular structure, which contributes to a higher entropy compared to other nitrogen oxides that may be more complex or exist in different states.
Conclude that N2O is the oxide of nitrogen with a positive ΔS°_f due to its gaseous state and simple molecular structure, leading to higher entropy.

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Key Concepts

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

Gibbs Free Energy (ΔGf°)

Gibbs Free Energy (ΔGf°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A positive ΔGf° indicates that the formation of the compound from its elements is non-spontaneous under standard conditions. Understanding this concept is crucial for analyzing the stability and reactivity of chemical species, particularly in the context of nitrogen oxides.
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Entropy (ΔS°f)

Entropy (ΔS°f) is a measure of the disorder or randomness in a system. A positive ΔS°f suggests that the formation of the compound increases the overall disorder of the system, which is often associated with the production of gases or the breaking of strong intermolecular forces. Recognizing how entropy influences the spontaneity of reactions helps in identifying which nitrogen oxide exhibits this property.
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Nitrogen Oxides

Nitrogen oxides (NOx) are a group of gases that include various oxides of nitrogen, such as nitric oxide (NO) and nitrogen dioxide (NO2). Among these, nitrous oxide (N2O) is notable for having a positive ΔS°f, as it is a gas that contributes to increased disorder compared to its elemental forms. Understanding the characteristics and behaviors of these oxides is essential for identifying the specific oxide mentioned in the question.
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Related Practice
Textbook Question

These reactions are important in catalytic converters in automobiles. Calculate ΔG° for each at 298 K. Predict the effect of increasing temperature on the magnitude of ΔG°.

a. 2 CO(g) + 2 NO(g) → N2(g) + 2 CO2(g)

b. 5 H2(g) + 2 NO(g) → 2 NH3(g) + 2 H2O(g)

c. 2 H2(g) + 2 NO(g) → N2(g) + 2 H2O(g)

d. 2 NH3(g) + 2 O2(g) → N2O(g) + 3 H2O(g)

Textbook Question

Calculate ΔG° at 298 K for these reactions and predict the effect on ΔG° of lowering the temperature.

a. NH3(g) + HBr(g) → NH4Br(s)

b. CaCO3(s) → CaO(s) + CO2(g)

c. CH4(g) + 3 Cl2(g) → CHCl3(g) + 3 HCl(g) (ΔG°f for CHCl3(g) is -70.4 kJ/mol.)

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Textbook Question

The values of ΔG°f for the hydrogen halides become less negative with increasing atomic number. The ΔG°f of HI is slightly positive. However, the trend in ΔS°f is to become more positive with increasing atomic number. Explain.