Section B 3

Question 1

restoring force eq:

Answer 1

F = -k x

x is the change in r ; k is the “force constant”, related to the bond strength

Question 2

• The reduced mass (μ) must have dimensions of …

Answer 2

kg

Question 3

• To obtain atomic masses in kg, multiply the atomic masses (e.g., H ~ 1; C = 12; O ~ 16 etc) by the
mass of a proton (i.e., one H atom (~1.67 x 10-27 kg).

Answer 3

k

Question 4

• The bond stretching force constant k is given in units of …

Answer 4

N/m or kg s^-2

Question 5

• The value of k is related to the bond strength : usually k ~… N/m

Answer 5

100-1000

Question 6

• Strong, short bonds have … k; long weak bonds have ….. k

Answer 6

high

small

Question 7

• νo … with k ; …. for heavier atoms (larger μ)

Answer 7

increases

decreases

Question 8

• If we use typical atomic masses and force constant values, we find molecular vibrational frequencies νo ~1012 - 1014 s-1

Answer 8

• These correspond to frequencies in the IR range of the electromagnetic
spectrum

Question 9

• To calculate frequency in wavenumbers (cm-1) : divide νo by ….

Answer 9

the speed of light c (3 x 1010 cm/s)

Question 10

Calculate νο for H2

1. Force constant k = 500 N/m (approx.)
2. mass of proton : m1 = m2 = 1 a.m.u. = 1.7 x 10-27 kg

Answer 10

3. Reduced mass μ = m1m2/(m1 + m2) = (1x1)/(1 + 1) = 0.5 x 1.7 x 10-27 kg = 0.85 x 10-27 kg
4. Calculate frequency in s-1:

ν o =1.22 x 10^14 s−1

5. Calculate frequency in cm-1 :

ν o (cm−1) =≈ 4070 cm−1

Question 11

H2 has the highest vibrational frequency of any molecule. In general stretching vibrations involving H occur at very high frequency, mainly because of the small mass of H, combined with relatively strong bonding (high k)

Answer 11

k

Question 12

Calculate νο for the C=O stretching vibration

1. Force constant k ~ 1200 N/m (note: double bond)
2. m1 = 12 ; m2 = 16 a.m.u.

Answer 12

3. Reduced mass μ = (12 x 16) / (12 + 16) = (6.86) x 1.7 x 10-27 kg = 11.7 x 10-27 kg
4. Calculate frequency in s-1:

ν o =5.10 x1013 s−1

5. Calculate frequency in cm-1 :

ν o (cm−1) =≈ 1700 cm−1

Question 13

This is about where we see C=O stretching vibrations occurring in different molecules :

Answer 13

aldehydes, ketones, carboxylic acids, protein peptide linkages, transition metal complexes with carbonyls ….

Question 14

• O-H stretching vibrations for a free molecule occur …

Answer 14

~3600 - 3700 cm-1

Question 15

• asymmetric stretching usually occurs at …. frequency than symmetric stretching

Answer 15

higher

Question 16

• Bending vibrations : usually …r than stretching

Answer 16

~50% lowe

Question 17

• O-H stretching vibrations can become lowered by …

Answer 17

H-bonding effects

Question 18

How Does IR Absorption Work ?

Answer 18

• If the vibration causes a change in the electric dipole moment (μo), this results in a
fluctuating electric field that can interact with the infrared light
• Homonuclear diatomic molecules (e.g. H2, O2, N2) have no dipole moment, and so μo does
not change during the vibration. These molecules do not have any IR absorption spectrum
• Heteronuclear diatomic molecules (e.g. CO, HCl etc) do have a dipole moment, and these
molecules have an IR absorption spectrum
• For more complicated molecules, even if there is no permanent dipole moment, some of the
vibrations can cause a change in μo : these vibrations are IR active (e.g., in CO2)
• If the dipole moment change is large, the IR absorption intensity is strong : if not the
absorption is weak.

Question 19

• The incident IR beam is provided by a “source” - usually a heated “Globar” (SiC ceramic)
• Nowadays, the spectrum is obtained in a single “burst”, then transformed into intensity vs cm-1 using
Fourier transform (mathematics) techniques (FTIR spectroscopy)
• The sample is mounted in different ways. If a solid, it is mixed with “Nujol” gel, or pressed in a disc with KBr ; if a
liquid it is run between two KBr plates; if a gas, it is put inside a gas cell (with a fixed length L) and KBr windows
• We measure % transmission (“transmittance”): T % = It/Io x 100 (100% transmission corresponds to no absorption)

Answer 19

k

Question 20

O-H stretching : 3700-3600 cm-1 : no H-bonding present ; lowered to 3200-2500 cm-1 when H-bonding via solvent
effects, intermolecular or internal ; usually broadening of the band
N-H stretching: ~3500-3300 cm-1 : less affected by H-bonding than O-H
C-H : Saturated (alkane : -CH2- ; -CH3) : ~2960-2800 cm-1. Intensity related to number of C-H bonds present.
Unsaturated (alkene ; olefin : C=CH- ; aromatic) : 3050-3020 cm-1 : can be weak/broad
1800-1600 cm-1 : Double bonds : C=C ; C=O ; C=N
The position (and number) of C=O stretch bands give information on bonding in organic and inorganic molecules.
2300-2100 cm-1 : Triple bonds : -C≡N (Also N≡N (N2 ) : but not IR active; -C≡C- often weakly active )
1600-400 cm-1 : Skeletal or “fingerprint” region : contains C-C stretching, bending (deformation), torsion etc
vibrations : not usually analysed in detail.
But characteristic of each substance : used in qualitative and quantitative analysis : e.g. applications in forensic
science

Answer 20

k