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Ch.19 - Free Energy & Thermodynamics
All textbooksTro 6th EditionCh.19 - Free Energy & ThermodynamicsProblem 53e
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Chapter 19, Problem 53e

For each pair of substances, choose the one that you expect to have the higher standard molar entropy (S°) at 25 °C. Explain your choices. a. CO(g); CO2(g) b. CH3OH(l); CH3OH(g) c. Ar(g); CO2(g) d. CH4(g); SiH4(g) e. NO2(g); CH3CH2CH3(g) f. NaBr(s); NaBr(aq)

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Identify the substances involved: NO_2(g) and CH_3CH_2CH_3(g).
Recall that standard molar entropy (S°) is a measure of the amount of disorder or randomness in a system.
Consider the molecular complexity: CH_3CH_2CH_3 (propane) is a larger and more complex molecule than NO_2, which generally leads to higher entropy due to more possible molecular motions.
Consider the number of atoms: CH_3CH_2CH_3 has more atoms (8) compared to NO_2 (3), which typically increases the number of possible microstates and thus the entropy.
Conclude that CH_3CH_2CH_3(g) is expected to have a higher standard molar entropy (S°) at 25 °C than NO_2(g) due to its greater molecular complexity and number of atoms.

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Key Concepts

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

Standard Molar Entropy (S°)

Standard molar entropy (S°) is a measure of the randomness or disorder of a substance at a standard temperature of 25 °C and 1 atm pressure. It reflects the number of accessible microstates for a given amount of substance, with higher values indicating greater disorder. Entropy is influenced by factors such as molecular complexity, phase of matter, and temperature.
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Molecular Complexity

Molecular complexity refers to the number of atoms and the structural arrangement within a molecule. More complex molecules, which have larger numbers of atoms and more degrees of freedom (such as rotational and vibrational modes), typically exhibit higher entropy. In comparing substances, the one with a more intricate structure is likely to have a higher standard molar entropy.
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Gas Phase Behavior

In the gas phase, the behavior of molecules is characterized by greater freedom of movement compared to solids and liquids. Gases have higher entropy due to the increased distance between molecules and the ability to occupy a larger volume. When comparing gases, factors such as molecular size and shape can significantly affect their standard molar entropy, with larger or more branched molecules generally having higher entropy.
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