Question

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

(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

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.

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.

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.

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.

Key concepts

Third Law of Thermodynamics

The Third Law of Thermodynamics is a fundamental principle in physics that addresses the behavior of systems as they approach absolute zero, the lowest possible temperature.
This law states that the entropy of a perfect, pure crystal is exactly zero at absolute zero temperature (\(0\, \text{K}\)).
This means that as you cool down a crystal to absolute zero, its entropy, or the amount of disorder, decreases to a minimal state where it's ideally ordered.

• The entropy at absolute zero is constant and does not increase with factors like mass.
• This law helps scientists understand the thermodynamic properties by providing a reference point of zero entropy.

Knowing this, the statement that the entropy of a perfect, pure crystal at absolute zero increases with mass is false.
Mass does nothing to alter the entropy value when the temperature is zero because entropy measures disorder, not anything related to mass.

Translational Motion

Translational motion pertains to the straightforward movement of molecules through space. This type of motion is quite intuitive; it's the kind of motion we're most familiar with in everyday life.
Think about how a person might walk from one side of a room to the other or a train moving along its tracks.
In molecular terms, translational motion means that the molecule's position changes over time, moving from one point in space to another.

• Molecules can move along three perpendicular axes (x, y, and z), representing three distinct directions in space.
• In gases, this motion is more prominent because molecules are free to move around more than in solids or liquids.

Thus, the explanation of translational motion is true—molecules shift positions in space over time as they move about.

Rotational Motion

Rotational motion occurs when molecules spin around an axis.
This could be compared to how planets rotate on their axes or how a wheel turns on its axle.
In chemistry, this rotation can occur in different planes, providing multiple axes around which a molecule can rotate.

• Only molecules, not individual atoms, experience rotational motion because twisting requires multiple bonds between atoms.
• Examples include how water molecules spin around an axis that goes through the oxygen atom.

In atomic gases like helium (He) and xenon (Xe), rotational motion isn't a factor, because these are single atoms.
Hence, they do not take part in the rotation or contribute to entropy through rotational movement.
This makes the statement about rotational motion in atomic gases false.

Vibrational Motion

Vibrational motion is another fascinating type of motion exhibited primarily by molecules having more than one atom.
This involves the periodic oscillation of atoms within a molecule around their equilibrium positions.
When we imagine vibrational motion, it's like picturing two masses connected by a spring, oscillating back and forth.

• Vibrational energy levels can be excited with heat, contributing to a molecule's overall energy and entropy.
• This type of motion often comes into play in complex molecules with multiple bonds.

More atoms in a molecule usually mean more vibrational modes since each additional bond allows for more oscillations.
As a result, the larger the molecule, the greater the degrees of freedom for vibrational and, also rotational, motion.
This makes the statement about increased degrees of freedom in larger molecules true.