14.46.In exercise 14.36 above, the vibrational frequency of
FeH was given as 1661 cm^1. That is the observedvibrational
frequency, not the harmonicvibrational frequency. Equation
14.39 can be used to determine that the observed frequency,
, is related to the harmonic frequency eand the anhar-
monicity xeeby the equation
e 2 xeeAssume that for a deuterated molecule, the frequency of the
shifted vibration occurs at
* e 2 ^2 xeewhere is the square root of the ratio of the reduced masses,
/*. FeD absorbs light having a frequency of 1203 cm^1.
From this information, calculate the harmonic vibrational fre-
quencies and the anharmonicity constants for FeH and FeD.
(Source:A. Dendramis, R. J. Van Zee, W. Weltner, Jr. Astrophys.
J.1979, 231: 632–36.)
14.47.Derive the two equations used to solve exercise 14.46,
using equation 14.39 and the concept of reduced mass. You
will need to consider equation 14.40 as well.
14.13 & 14.14 Symmetry and Vibrations,
Nonlinear Molecules
14.48.From Figure 14.32, label the normal modes of NH 3
with their proper irreducible representation.
14.49.Consider the following two vibrational modes of di-
acetylene, HCC–CCH:
Determine their irreducible representation labels. Which (if ei-
ther) of these vibrational modes is expected to be IR-active for
symmetry reasons, and why?
14.50.Each of the following pairs of molecules has the same
number of atoms. In each pair, which one would you expect
to have fewer differentvibrational frequencies? You may have
to determine the symmetry of each molecule before you can
make a determination. (a)HCl and Cl 2 (b)H 2 O 2 and C 2 H 2
(c)CH 4 and XeF 4 (d)PF 5 and CH 3 CN (e)Ca 3 (PO 4 ) 2 and
C 6 H 5 OH.
14.51.List the individual symmetry elements for the follow-
ing point groups as either proper rotations or improper rota-
tions. (a)C3v(b)Td(c)D6h(d)S 4 (e)Dh(f)O(not Oh!)
14.52.Determine the number of IR-active vibrations for ben-
zene, C 6 H 6. Does it agree with the material in the text?
14.53.Determine the number of IR-active vibrations for the
following molecules. You may have to determine their sym-
metry first. (a)Hydrogen peroxide, H 2 O 2 (b)Oxalic acid,
(COOH) 2 (c)Sulfur trioxide, SO 3 (d)Formaldehyde, H 2 CO
(e)Acetone, (CH 3 ) 2 CO (assume C2vsymmetry)
14.54.Determine the number of IR-active vibrations for the
following molecules. You may have to determine their sym-
metry first. (a)CH 4 (b)CH 3 Cl (c)CH 2 Cl 2 (d)CHCl 3 (e)CCl 4
Do the answers make sense as you progress from methane to
fully substituted methane?
H CH CC CC CC HC H14.55.How would you determine if KrF 4 , if it were synthe-
sized, had tetrahedral or square planar geometry?
14.56.Determine the number of IR-active vibrations for the
following molecules. You may have to determine their sym-
metry first. (a)F 2 O (b)NCl 3 (c)N(CH 3 ) 3 (assume C3vsym-
metry)
14.57.Verify that cubane, C 8 H 8 , has only three IR-active
vibrations and determine the degeneracies of each. How
many total vibrations out of the 42 vibrational degrees of free-
dom are thus represented by the three IR-active vibrational
motions?14.15 & 14.16 Nonallowed, Nonfundamental
Vibrations and Fingerprint
Regions
14.58.Carbon dioxide has the following fundamental vibra-
tional frequencies:
1 667 cm^1 2 1338 cm^1 3 2349 cm^1
According to the literature (K. E. Dierenfeldt, J. Chem. Ed.,
1995, 72: 281–83), the following combination bands appear
in the spectrum: 618, 2337, and 3715 cm^1. Assign these to
the proper combinations of the fundamental vibrations.
14.59.Would you expect the above combination absorptions
to be strong or weak in a spectrum? Why?
14.60.Why is it possible to identify fingerprint regions for
overtone transitions and hot bands but not for combination
bands?
14.61.Dioctyl sulfide, (C 8 H 17 ) 2 S, and hexadecane, C 16 H 34 ,
have very similar vibrational spectra. Use a correlation table to
explain why.
14.62.Where would you expect vibrations for ethyl alcohol,
CH 3 CH 2 OH, to appear in a vibrational spectrum?14.17 Rovibrational Spectroscopy
14.63.Silane, SiH 4 , has a tetrahedral geometry and a rovi-
brational spectrum consisting of lines spaced by 16.72 cm^1.
Calculate the Si–H bond distance in silane. Could this infor-
mation be obtained by pure rotational spectroscopy? Why or
why not?
14.64.Electronic energy level transitions typically have higher
energies than vibrational energy levels. Would the equivalent
of P, Q, or Rbranches appear in electronic spectra if vwere
1, 0, or 1? Justify your answer.
14.65.What are the forms of equations 14.41 and 14.42 if
centrifugal distortion is negligible?
14.66.The table in exercise 14.71 lists some frequencies of
absorptions in a Pbranch and an Rbranch. Why is there no
line listed as P(0)?14.18 Raman Spectroscopy
14.67.Two Raman spectra are measured on the same sam-
ple. One spectrum uses the red He-Ne laser light, at 632.8 nm,
as a source; the other uses the 568.2-nm light from a Kr^ laser.
How are the two spectra different? How are the two spectra
the same?Exercises for Chapter 14 517