Question

(a) State the third law of thermodynamics. (b) Distinguish between translational motion, vibrational motion, and rotational motion of a molecule. (c) Illustrate these three kinds of motion with sketches for the HCl molecule.

Short answer

(a) The third law of thermodynamics states that the entropy of a perfect crystal approaches zero as the temperature approaches absolute zero, meaning the perfect crystal becomes more ordered at absolute zero temperature. (b) Translational motion is the movement of a molecule in a straight line through space, vibrational motion is the oscillation of atoms within a molecule in a regular pattern, and rotational motion refers to the movement of a molecule around an axis. (c) In HCl molecule: (i) Translational motion has the molecule moving in a straight line, maintaining the bond between H and Cl atoms. (ii) Vibrational motion has H and Cl atoms oscillating along the bond axis, causing the bond length to vary periodically. (iii) Rotational motion has the molecule revolving around an axis, usually perpendicular to the bond, while maintaining their relative positions.

Step-by-step solution

(a) State 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. In other words, as a perfect crystal cools down to absolute zero, it becomes more ordered and its entropy decreases to zero.

(b) Explain translational, vibrational, and rotational motion of a molecule.

Translational motion is the movement of a molecule through space in a straight line, like a car driving along a straight road. Vibrational motion is the oscillation of atoms within a molecule, causing them to move in a regular pattern, similarly to a vibrating guitar string. Lastly, rotational motion refers to the movement of a molecule around an axis, similar to how the Earth rotates on its axis.

(c) Illustrate translational, vibrational, and rotational motion with HCl molecule sketches.

To visualize the HCl molecule and its motion, imagine a molecule composed of hydrogen (H) and chlorine (Cl) atoms connected by a single bond. (i) Translational motion: In this case, the entire HCl molecule moves in a straight line, maintaining the bond between H and Cl atoms. (ii) Vibrational motion: During vibrational motion, the H and Cl atoms move back and forth along the bond axis, oscillating around a central position, causing the bond length between them to vary periodically. (iii) Rotational motion: For rotational motion, the HCl molecule revolves around an axis, which can be a line perpendicular to the bond between the H and Cl atoms. H and Cl atoms maintain their relative positions while the molecule spins around the chosen axis.

Key concepts

Third Law of Thermodynamics

The third law of thermodynamics plays a crucial role in understanding how substances behave at very low temperatures. At the heart of this law is the concept of entropy, which is a measure of disorder in a system. Entropy increases as the system becomes more disordered. The third law, as stated in the exercise, indicates that as a perfect crystal is cooled to absolute zero (0 Kelvin), its entropy approaches zero because the atoms in the crystal are arranged in a perfectly ordered state. However, reaching absolute zero is not possible according to the laws of physics as we know them.

This concept has profound implications in various fields, including quantum mechanics, cryogenics, and materials science. It implies that it's not possible to extract absolute all energy from a substance, and as the crystal cools, it releases less and less energy, eventually reaching a point where it can't lose any more entropy. A practical understanding of this concept can be seen in the design of ultra-low temperature refrigeration systems and in predicting the behavior of materials close to absolute zero.

Translational Motion

Translational motion refers to the straightforward movement of a molecule from one location to another. For a molecule like HCl, this means it would travel in a straight line, moving the entire molecule, hydrogen and chlorine together, as if it were a single particle gliding through space. It's the same kind of motion that we observe in everyday objects, like a car driving down the highway or a person walking across a room.

In scientific terms, translational motion corresponds to three degrees of freedom - movement along the x, y, and z axes in three-dimensional space. Importantly, this type of motion plays a significant role in the diffusion of gases and can affect the rate of chemical reactions by bringing reactive molecules into contact with one another.

Vibrational Motion

In contrast to translational motion, vibrational motion is all about the rhythmic oscillating movement of atoms within a molecule, such as the HCl molecule. Here's how it works: the hydrogen and chlorine atoms are constantly vibrating, moving towards and away from each other along the bond that connects them. This is analogous to two children on a seesaw, where the bond between the atoms acts like a spring, storing and releasing energy as it stretches and compresses.

Vibrational motion is more quantifiable at the molecular level, as it involves specific frequencies and energy levels. Understanding these vibrations is essential for spectroscopic methods, which allow scientists to study molecular structures and the forces between atoms. Vibrational motion also contributes to the heat capacity of substances, as it is a mechanism for storing thermal energy.

Rotational Motion

Lastly, rotational motion is when the molecule spins or rotates around an axis. For the HCl molecule, imagine a line drawn perpendicular to the bond holding the hydrogen and chlorine atoms together; the molecule can spin around this axis. This spinning movement can be likened to the way the Earth rotates on its axis or a spinning top.

Rotational motion is characterized by angular momentum and is affected by the distribution of mass around the axis of rotation. In the case of molecules, the rotational energy levels are quantized, meaning that they can only rotate at certain discrete speeds. This concept is important for understanding phenomena like the microwave absorption in gases and the behavior of rotating diatomic molecules in gas phase.