Vibrational SpectroscopyWhen an atom in a bond is replaced with a different isotope of the same element, the reduced mass ofthe bonded atoms change the absorption of the vibration in the infrared (vibrational) spectrum.The wavenumber of a vibration is given by v = ¹, where k = force constant of the bond, μ =2πreduced mass.Reduced Mass: μ =1"where m₁ and m2 are the mass of each attached atom.Assuming the force constant of a particular pair of atoms does not change when one or the other atomis substituted with an isotope, the magnitude of the vibrational shift can be determined from a ratio ofthe two vibrations.V₁V₂1 k₁2π √11 k₂2π√√1₂1. An O-H stretch occurs at 3650 cm¹. What is the expected vibrational wavenumber of an O-D bond?2. An NH3 stretch occurs at 3337 cm¹. At what wavenumber does the ND3 vibration occur?3. An IR spectrum of a complex containing an Ru-O bond isdepicted to the right. When 0-16 is substituted with 0-18, thevibration at 887 cm¹ appears to decrease and a new vibrationappears at 841 cm2. Show that this shift is consistent with an Ru-Obond.* Prediction based on calculation.see if the expected shift is consistant withthe calculation4. The IR spectrum to the right is also of an Ru-O complexwhich has been substituted with O-18. Determine the shiftexpected for each 0-16 labeled vibration after substitutionwith O-18. Do either agree with the new peak und 887after 0-18 substitution?30-36-10001000'b 887950950 90020wow"b887926¹941841000800 750 700Wavenumber (cm)850 800 750 700Wavenumbers (cm)

O-H stretch occurs at 3650 cm-1.To determine the expected vibrational number of an O-D bond.“Since…

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1. An O-H stretch occurs at 3650 cm³¹. What is the expected vibrational wavenumber of an O-D bond?

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter20: Molecular Spectroscopy And Photochemistry

Section: Chapter Questions

Problem 6P

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Question

Vibrational Spectroscopy
When an atom in a bond is replaced with a different isotope of the same element, the reduced mass of
the bonded atoms change the absorption of the vibration in the infrared (vibrational) spectrum.
The wavenumber of a vibration is given by v = ¹, where k = force constant of the bond, μ =
2π
reduced mass.
Reduced Mass: μ =
1
"
where m₁ and m2 are the mass of each attached atom.
Assuming the force constant of a particular pair of atoms does not change when one or the other atom
is substituted with an isotope, the magnitude of the vibrational shift can be determined from a ratio of
the two vibrations.
V₁
V₂
1 k₁
2π √1
1 k₂
2π√√1₂
1. An O-H stretch occurs at 3650 cm¹. What is the expected vibrational wavenumber of an O-D bond?
2. An NH3 stretch occurs at 3337 cm¹. At what wavenumber does the ND3 vibration occur?
3. An IR spectrum of a complex containing an Ru-O bond is
depicted to the right. When 0-16 is substituted with 0-18, the
vibration at 887 cm¹ appears to decrease and a new vibration
appears at 841 cm2. Show that this shift is consistent with an Ru-O
bond.
* Prediction based on calculation.
see if the expected shift is consistant with
the calculation
4. The IR spectrum to the right is also of an Ru-O complex
which has been substituted with O-18. Determine the shift
expected for each 0-16 labeled vibration after substitution
with O-18. Do either agree with the new peak und 887
after 0-18 substitution?
30-
36-
1000
1000
'b 887
950
950 900
20
wow
"b887
926
¹941
841
000
800 750 700
Wavenumber (cm)
850 800 750 700
Wavenumbers (cm)

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