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Ch.19 - Chemical Thermodynamics
All textbooksBrown 14th EditionCh.19 - Chemical ThermodynamicsProblem 37
Chapter 19, Problem 37

Indicate whether each statement is true or false. (a) The third law of thermodynamics says that the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) “Translational motion” of molecules refers to their change in spatial location as a function of time. (c) “Rotational” and “vibrational” motions contribute to the entropy in atomic gases like He and Xe. (d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.

Verified step by step guidance
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Step 1: Analyze statement (a) regarding the third law of thermodynamics. The third law states that the entropy of a perfect crystal at absolute zero is exactly zero. Consider whether mass affects this entropy value.
Step 2: Evaluate statement (b) about translational motion. Understand that translational motion refers to the movement of the entire molecule through space, which indeed involves a change in spatial location over time.
Step 3: Consider statement (c) about rotational and vibrational motions in atomic gases. Recognize that atomic gases like He and Xe are monoatomic and do not have rotational or vibrational motions, which are characteristic of polyatomic molecules.
Step 4: Examine statement (d) regarding the degrees of freedom in molecules. Recall that the degrees of freedom, including rotational and vibrational, increase with the complexity and number of atoms in a molecule.
Step 5: For each statement, determine if the explanation aligns with the statement being true or false based on the analysis conducted in the previous steps.

Key Concepts

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

Third Law of Thermodynamics

The Third Law of Thermodynamics states that as the temperature of a perfect crystal approaches absolute zero, its entropy approaches a minimum value, which is typically zero. This law implies that at absolute zero, a perfect crystal has no disorder, and thus, its entropy does not increase with mass. Therefore, the statement in the question is false.
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Translational Motion

Translational motion refers to the movement of molecules from one location to another in space. It is a fundamental type of motion that contributes to the kinetic energy of a substance. In the context of gases, translational motion is significant as it affects pressure and temperature, making the statement true.
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Degrees of Freedom

Degrees of freedom in molecular motion refer to the independent ways in which a molecule can move or rotate. Larger molecules typically have more atoms, which allows for greater complexity in motion, including rotational and vibrational modes. Thus, the statement regarding the relationship between the number of atoms and degrees of freedom is true.
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Related Practice
Textbook Question

(b) How does the entropy of the system change in the processes described in Exercise 19.12?

Textbook Question

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.

Textbook Question

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