Problem 35 - Chemistry: The Central Science

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.

Step-by-Step Solution

Answer

The Third Law of Thermodynamics states that the entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero (0 Kelvin or -273.15 degrees Celsius). There are three types of molecular motion: (i) Translational Motion: The entire molecule moves in a straight line along any one of the three Cartesian planes (x, y, or z) without any change in its orientation. (ii) Vibrational Motion: Atoms oscillate about their equilibrium positions due to stretching, bending, or twisting of chemical bonds. (iii) Rotational Motion: The molecule rotates around an axis, either external or through a bond within the molecule, with each atom following a circular path around the axis of rotation. For the HCl molecule, translational motion shows the entire molecule moving in a straight line, vibrational motion shows the H and Cl atoms oscillating about their bond, and rotational motion shows the molecule rotating around an axis, either external or through the H-Cl bond.

Step 1: (A) The Third Law of Thermodynamics

The Third Law of Thermodynamics states that the entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero (0 Kelvin or -273.15 degrees Celsius). In other words, as a system becomes perfectly ordered at absolute zero, the entropy (which represents the disorder in a system) also becomes zero.

Step 2: (B) Types of Molecular Motion

(i) Translational Motion: It is the movement of a molecule in a straight line along any one of the three Cartesian planes (x, y, or z). In this motion, the entire molecule moves in the same direction without any change in its orientation. (ii) Vibrational Motion: It is the periodic movement of atoms or groups of atoms within a molecule that occurs due to the stretching, bending or twisting of chemical bonds. In this motion, the atoms oscillate about their equilibrium positions. (iii) Rotational Motion: It is the movement of a molecule around an axis. The axis can be an external axis, or it can be a bond axis within the molecule. The molecule rotates as a whole, with each atom following a circular path around the axis of rotation.

Step 3: (C) Sketches of Molecular Motion for HCl

For the HCl molecule, which consists of one hydrogen atom (H) and one chlorine atom (Cl) bonded together, the sketches of the three types of motion are as follows: (i) Translational Motion: The entire HCl molecule moves in a straight line along any one of the three Cartesian planes (x, y, or z). ``` H --> H Cl --> Cl ``` (ii) Vibrational Motion: The hydrogen and chlorine atoms oscillate about their equilibrium positions in the direction of their chemical bond. ``` _ _ H-Cl (Stretching or compressing along bond) H | (Bending motion) Cl ``` (iii) Rotational Motion: The HCl molecule rotates around an axis, either external or through the bond between the hydrogen and chlorine atoms. ``` H \ --> \ (clockwise rotation) / Cl ```