Physical Chemistry Third Edition

940 22 Translational, Rotational, and Vibrational States of Atoms and Molecules

PROBLEMS

Section 22.4: The Rotation and Vibration of Polyatomic
Molecules

22.21The equilibrium CO bond length in carbon dioxide
is 116.15 pm. Find the moment of inertia of CO 2.

22.22Consider the SF 6 molecule.

a. Specify the shape of the molecule in its equilibrium

conformation. List as many of the symmetry

operators that belong to the molecule as

you can.

b.Assign the principal rotational axes of the molecule. Is

the molecule a symmetric top, an asymmetric top, or a

spherical top? Estimate the three principal moments of

inertia of the molecule. Assume that the bond lengths

are equal to 1.82 Å182 pm.

c.Write a formula for the rotational energy levels of the

molecule in joules and in electron volts. Specify the

degeneracies of the levels.

d.How many vibrational normal modes does the

molecule have?

22.23Find the symmetry numbers of the molecules in their
equilibrium conformations:
a.Dichloromethane, CH 2 Cl 2

b.Toluene, C 6 H 5 CH 3

c.Sulfur hexafluoride, SF 6

22.24Classify each of the following molecules in its
equilibrium conformation as linear, spherical top, prolate
symmetric top, oblate symmetric top, or asymmetric top.
Give the symmetry number for each molecule.
a.H 2 O

b.CO 2

c.CH 3 Cl

22.25Classify each of the following molecules in its
equilibrium conformation as linear, spherical top, prolate
symmetric top, oblate symmetric top, or asymmetric top.
Give the symmetry number for each molecule.
a.CHCl 3

b.CH 2 Cl 2

c.CCl 4

22.26Classify each of the following molecules in its

equilibrium conformation as linear, spherical top,

prolate symmetric top, oblate symmetric top, or

asymmetric top. Give the symmetry number for each

molecule.

a.C 6 H 6

b.C 2 H 6 (staggered)

c.C 2 H 5 Cl

d.C 2 H 4

e.C 2 H 2

f. trans-C 2 H 2 F 2

22.27Classify each of the following molecules in its

equilibrium conformation as linear, spherical top, prolate

symmetric top, oblate symmetric top, or asymmetric top.

Give the symmetry number for each molecule.

a.CH 2 O

b.HCN

c.1,1-Dichloroethene

d.cis-C 2 H 2 F 2

e.C 2 H 6 (eclipsed)

f. 1,1,1-Trichloroethane (eclipsed)

22.28Determine the number of vibrational normal modes for

each of the molecules in Problem 22.24.

22.29Determine the number of vibrational normal modes for

each of the molecules in Problem 22.27.

22.30Determine the number of vibrational normal modes for

each of the molecules in Problem 22.25.

22.31Determine the number of vibrational normal modes for

each of the molecules in Problem 22.26.

22.32Without doing any calculations, assign principal axes for

the molecules in parts a–c of Problem 22.27.

22.33Without doing any calculations, assign principal axes for

the molecules in parts d–f of Problem 22.27.

22.34Without doing any calculations, assign principal axes for

the molecules in parts a, b, d, and e of Problem 22.26.

22.35At high temperatures, the two methyl groups making

up the ethane molecule rotate nearly freely with respect to

each other about the C–C bond instead of undergoing a