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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.

Short Answer

Expert verified
(a) False: The entropy of a perfect, pure crystal at absolute zero is constant and does not depend on the mass of the crystal. (b) True: Translational motion refers to the change in spatial location of molecules as a function of time. (c) False: Atomic gases like He and Xe do not possess rotational and vibrational motions, only translational motion. (d) True: The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.

Step by step solution

01

Statement (a) - The third law of thermodynamics

The third law of thermodynamics states that the entropy of a perfect crystal approaches zero as the temperature approaches absolute zero. That is, the entropy of a perfect, pure crystal at absolute zero is constant and does not depend on the mass of the crystal. Therefore, statement (a) is false.
02

Statement (b) - Translational motion of molecules

Translational motion refers to the movement of molecules in a way that their position in space changes with time. So, the given statement is a correct definition of translational motion, and statement (b) is true.
03

Statement (c) - Rotational and vibrational motions in atomic gases

Although both rotational and vibrational motions contribute to the total entropy of a molecule, atomic gases like helium (He) and xenon (Xe) do not possess these motions. They only undergo translational motion since they are individual atoms and not molecules. Hence, statement (c) is false.
04

Statement (d) - Degrees of freedom in molecules

The degrees of freedom are related to the ways a molecule can store energy. In general, more complex molecules (i.e., those with a larger number of atoms) have more degrees of freedom since they can undergo a greater number of rotational and vibrational motions. Therefore, statement (d) is true.

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Most popular questions from this chapter

(a) Is the standard free-energy change, \(\Delta G^{\circ}\), always larger than \(\Delta G ?\) (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0 ?\) (c) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process necessarily has a low activation barrier?

Predict which member of each of the following pairs has the greater standard entropy at \(25^{\circ} \mathrm{C}:\) (a) \(\mathrm{HNO}_{3}(g)\) or \(\mathrm{HNO}_{3}(a q)\) (b) \(\mathrm{PCl}_{3}(l)\) or \(\mathrm{PCl}_{3}(g)\), (c) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) or \(\mathrm{Fe}_{3} \mathrm{O}_{4}(s),(\mathbf{d}) \mathrm{Li}(s)\) or \(\mathrm{Li}(g)\). Use Appendix \(\mathrm{C}\) to find the stan- dard entropy of each substance.

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 .(\mathbf{b})\( If you heat a gas such as \)\mathrm{CO}_{2}$, you will increase its degrees of translational, rotational and vibrational motions. (c) \(\mathrm{CO}_{2}(g)\) and \(\mathrm{Ar}(g)\) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

A system goes from state 1 to state 2 and back to state \(1 .\) (a) Is \(\Delta E\) the same in magnitude for both the forward and reverse processes? (b) Without further information, can you conclude that the amount of heat transferred to the system as it goes from state 1 to state 2 is the same or different as compared to that upon going from state 2 back to state $1 ?(\mathbf{c})$ Suppose the changes in state are reversible processes. Is the work done by the system upon going from state 1 to state 2 the same or different as compared to that upon going from state 2 back to state \(1 ?\)

When most elastomeric polymers (e.g., a rubber band) are stretched, the molecules become more ordered, as illustrated here: Suppose you stretch a rubber band. (a) Do you expect the entropy of the system to increase or decrease? (b) If the rubber band were stretched isothermally, would heat need to be absorbed or emitted to maintain constant temperature? (c) Try this experiment: Stretch a rubber band and wait a moment. Then place the stretched rubber band on your upper lip, and let it return suddenly to its unstretched state (remember to keep holding on!). What do you observe? Are your observations consistent with your answer to part (b)?
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