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Chapter 19: Problem 35

(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

Expert verified
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 by step solution

01

(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.
02

(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.
03

(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 ```

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Most popular questions from this chapter

For a certain chemical reaction, \(\Delta H^{\circ}=-35.4 \mathrm{~kJ}\) and \(\Delta S^{\circ}=-85.5 \mathrm{~J} / \mathrm{K} .(\mathrm{a}) \mathrm{ls}\) the reaction exothermic or en- dothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (c) Calculate \(\Delta G^{\circ}\) for the reaction at \(298 \mathrm{~K}\). (d) Is the reaction spontaneous at \(298 \mathrm{~K}\) under standard conditions?

Use data from Appendix \(\mathrm{C}\) to calculate the equilibrium constant, \(K\), at \(298 \mathrm{~K}\) for each of the following reactions: (a) \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)\) (b) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (c) \(3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(g)\)

(a) Express the second law of thermodynamics in words. (b) If the entropy of the system increases during a reversible process, what can you say about the entropy change of the surroundings? (c) In a certain spontaneous process the system undergoes an entropy change, \(\Delta S=42 \mathrm{~J} / \mathrm{K} .\) What can you conclude about \(\Delta S_{\text {surr }} ?\)

Consider the decomposition of barium carbonate: $$ \mathrm{BaCO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{CO}_{2}(g) $$ Using data from Appendix \(\mathrm{C}\), calculate the equilibrium pressure of \(\mathrm{CO}_{2}\) at (a) \(298 \mathrm{~K}\) and (b) \(1100 \mathrm{~K}\).

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?
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