Question

Indicate whether each statement is true or false. (a) The third law of thermedynamics says that the entropy of a perfect, pure crystal at absolute zere 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

(a) False, (b) True, (c) False, (d) True

Step-by-step solution

Define entropy and the Third Law of Thermodynamics

Entropy is a measure of the number of possible microstates or the level of disorder within a system. The Third Law of Thermodynamics states that the entropy of a perfect, pure crystal approaches zero as the temperature approaches absolute zero.

Evaluate the truth of statement (a)

Comparing the given statement and the Third Law of Thermodynamics, we can notice that the statement mentions the entropy increases with the mass of the crystal, which is incorrect. The Third Law focuses on the entropy approaching zero as temperature approaches absolute zero. Therefore, statement (a) is false. #Statement b#

Define translational motion

Translational motion refers to the movement of a molecule or object from one position to another in space or its change in spatial location as a function of time.

Evaluate the truth of statement (b)

Given the definition of translational motion, statement (b) is accurately described, so it is true. #Statement c#

Define rotational and vibrational motions

Rotational motion refers to the spinning of molecules around their axis, while vibrational motion occurs when atoms within a molecule move back and forth along the bond.

Evaluate the truth of statement (c)

Rotational and vibrational motions contribute to the entropy of diatomic and polyatomic molecules, as they create multiple microstates. However, in atomic gases like He and Xe, only translational motion contributes to entropy as there are no molecular bonds for rotation or vibration to occur. Therefore, statement (c) is false. #Statement d#

Degrees of freedom for molecules

In general, the larger the number of atoms in a molecule, the higher the number of degrees of freedom (i.e., different ways the molecule can store energy). These include translational, rotational, and vibrational motions.

Evaluate the truth of statement (d)

Based on the general concept that larger molecules tend to have more degrees of freedom due to a higher number of atoms and bonds, statement (d) is true.

Key concepts

Entropy

Entropy is a fascinating concept in thermodynamics, often described as a measure of disorder or randomness in a system. It is fundamentally linked to the number of microscopic configurations or "microstates" that correspond to a macroscopic state. The higher the entropy, the greater the disorder.

One important aspect of entropy is its behavior as temperature changes. According to the Third Law of Thermodynamics, the entropy of a perfect, pure crystal approaches zero as the temperature approaches absolute zero. This means that at absolute zero, a system is in its most ordered state, with only one possible microstate.

It's important to understand that entropy doesn't increase with the mass of the crystal. Instead, it is dependent on the number of available microstates. In essence, entropy connects the macroscopic observation of disorder to the microscopic complexity of positions and energies within a system.

Translational Motion

Translational motion is a simple yet crucial type of molecular movement. It involves the linear movement of a molecule from one place to another over time. This movement can be thought of as the molecule traveling through space, changing its position.

For example, when a gas molecule like nitrogen moves across a room, it is displaying translational motion. This motion is key to how gases behave, influencing how they spread out and fill a container.

Translational motion is closely linked to entropy in gases. As molecules move freely and fill spaces, the number of possible microstates increases, thereby increasing entropy. Unlike other types of motion, every molecule, even atomic gases like helium, exhibits translational motion.

Rotational and Vibrational Motion

Rotational and vibrational motions are other forms of molecular movements that significantly impact the entropy of molecules.

**Rotational motion** involves a molecule spinning about its axis. Imagine a water molecule twirling in space. This type of movement is more relevant in diatomic or larger molecules where there is enough structure to allow spinning.

**Vibrational motion**, on the other hand, occurs when atoms within a molecule oscillate back and forth along the bonds. Think of it like a spring stretching and compressing, which happens along the bonds connecting the atoms in a molecule.

Both rotational and vibrational motions contribute to the entropy of molecules by expanding the range of possible microstates. However, for monoatomic gases, like He and Xe, these motions do not exist since there are no bonds to rotate or vibrate. Thus, only translational motion contributes to their entropy.

Degrees of Freedom

The concept of degrees of freedom in molecules refers to the number of independent ways in which the molecule can move or store energy. This can include translational, rotational, and vibrational motions.

**Translational degrees of freedom** pertain to movement along the three spatial axes (x, y, and z). Every molecule, regardless of complexity, supports these motions.

**Rotational degrees of freedom** are applicable to molecules with sufficient complexity, such as diatomic and polyatomic molecules. These degrees allow the molecule to spin around different axes.

**Vibrational degrees of freedom** appear in polyatomic molecules where multiple directions of oscillations can occur.

Larger molecules typically have a greater number of atoms and bonds, thereby increasing their degrees of freedom. This means they can store more energy in various movements, leading to an increase in entropy.