For each of the following pairs, predict which substance possesses the larger entropy per mole: (a) 1 mol of O₂(g) at 300 °C, 0.01 atm, or 1 mol of O₃(g) at 300 °C, 0.01 atm

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Identify the molecular structures of the substances involved: O₂ (oxygen) is a diatomic molecule, while O₃ (ozone) is a triatomic molecule.

Consider the degrees of freedom for each molecule. O₂ has translational, rotational, and vibrational modes, while O₃, being a larger molecule, has more vibrational modes due to its additional atom and bent structure.

Recall that entropy is a measure of the randomness or disorder in a system. More complex molecules with more degrees of freedom typically have higher entropy.

Compare the conditions given: both gases are at the same temperature and pressure. These conditions allow us to focus solely on the molecular complexity and degrees of freedom without considering the effects of differing external conditions.

Predict that O₃ (ozone), having more degrees of freedom and a more complex molecular structure than O₂ (oxygen), possesses a larger entropy per mole under the same conditions.

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Key Concepts

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

Entropy

Entropy is a measure of the disorder or randomness in a system. It quantifies the number of possible microstates that correspond to a given macrostate, with higher entropy indicating greater disorder. In gases, entropy increases with the number of molecules and the complexity of the molecular structure, as more arrangements are possible.

Molecular Structure and Complexity

The molecular structure and complexity of a substance significantly influence its entropy. For example, O<sub>2</sub> is a diatomic molecule, while O<sub>3</sub> (ozone) is a triatomic molecule with a more complex structure. Generally, more complex molecules have higher entropy due to the increased number of vibrational and rotational modes available.

Effect of Temperature and Pressure on Entropy

Temperature and pressure are critical factors affecting entropy. At higher temperatures, molecules have more kinetic energy, leading to increased molecular motion and higher entropy. Conversely, lower pressures can lead to higher entropy in gases, as there is more space for the molecules to occupy, allowing for greater disorder.

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Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in H, we can know absolute values of S. (b) If you heat a gas such as CO₂, you will increase its degrees of translational, rotational and vibrational motions. (c) CO₂(g) and Ar(g) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

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Predict the sign of the entropy change of the system for each of the following reactions: (a) N₂(g) + 3 H₂(g) → 2 NH₃(g)

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Predict the sign of the entropy change of the system for each of the following reactions: (b) CaCO₃(s) → CaO(s) + CO₂(g)

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For each of the following pairs, predict which substance possesses the larger entropy per mole: (a) 1 mol of O2(g) at 300 °C, 0.01 atm, or 1 mol of O3(g) at 300 °C, 0.01 atm

Verified video answer for a similar problem:

Key Concepts

Entropy

Molecular Structure and Complexity

Effect of Temperature and Pressure on Entropy

For each of the following pairs, predict which substance possesses the larger entropy per mole: (a) 1 mol of O₂(g) at 300 °C, 0.01 atm, or 1 mol of O₃(g) at 300 °C, 0.01 atm