Vibrational Spectroscopy

Question 1

What is meant by vibrational spectroscopy?

Answer 1

This is the study of how EM radiation interacts with a molecule to change its vibrational energy

Question 2

What is molecular vibration?

Answer 2

Vibrations involve the motion of atoms in individual chemical bonds
The atoms in a molecule vibrate around their equilibrium positions and the bonds act like springs

Question 3

What region of the EM does vibrational spectroscopy correspond to?

Answer 3

They correspond to the IR region

Question 4

What is the purpose of vibrational spectroscopy?

Answer 4

It is used to identify functional groups in molecules, to confirm the structure of compounds and to measure concentrations
- it can also measure vibrational frequencies and force constants of chemical bonds

Question 5

What is the equation for the restoring force (Hooke’s law)?

Answer 5

F= -k (r-re)

K is the force constant which is the stiffness of spring/ strength of bond (Nm-1)
(r-re) is the distance from equilibrium (m)
PE is the potential energy= J (Nm)

Question 6

What is the equation for potential energy?

Answer 6

PE= 1/2 k(r-re) ^2
K is the force constant which is the stiffness of spring/ strength of bond (Nm-1)
(r-re) is the distance from equilibrium (m)
PE is the potential energy= J (Nm)

Question 7

What happens when a diatomic molecule vibrates?

Answer 7

• stretching or compression
• atoms are connected by a ‘spring’
• when molecule vibrates the string stretches and contracts around equilibrium position
  (Corresponds to equilibrium bond length ro)

Question 8

What is simple harmonic motion?

Answer 8

• motion of the spring
• spring vibrates because there is a restoring force that pulls it back to the equilibrium position
• restoring force is proportional to displacement

Question 9

What is the equation for vibrational frequency?

Answer 9

Vvib= 1/ 2pi {k/RM}

{}= square root
RM= reduced mass (kg)
Vvib= s-1
Vibrational wavenumber= cm-1

Question 10

What happens during the vibration of a heavy atom and a light atom?

Answer 10

During the bond vibrations, the heavy atom stays almost still with the light atom moving much larger distances

Question 11

What is the equation for reduced mass?

Answer 11

RM= m1 x m2/ m1 + m2

Units are kg

Question 12

What does quantum mechanics tell us about the vibrational energy levels?

Answer 12

-Energy levels are quantised
- moderately spaced (moderate difference in energy between levels)
- v is quantum number
Ev is the energy of the vth level
V=0 is equal to 1/2 hv
Vibrational energy levels are non degenerative

Question 13

How do you calculate the energy of vibrational level?

Answer 13

Ev= (v+ 1/2) x vibrational wavenumber
Where v= 0, 1,2,3…
V= vibrational quantum number
Vvib determines the actual energy levels for a specific molecule
You can define the energy in terms of Vvib (wavenumber)

Question 14

What is the energy at the lowest level?

Answer 14

Lowest level for v=0 is Eo= 1/2 Vvib (wavenumber)

This means the molecule is not permitted to have no vibrational energy and so atoms are always moving

Question 15

What happens to the energy levels as you increase v ?

Answer 15

The gaps between the energy levels are constant

Question 16

What is the equation for the vibrational wavenumber?

Answer 16

VW= 1/2piC x {k/RM)

VW= cm-1
Force constant is k (Nm-1)
Reduced mass is in kg
Speed of light is c = (ms-1 or cms-1)

Question 17

What is the equation for Ev ( energy of level)?

Answer 17

Ev= (v+ 1/2) VW

Question 18

For a small light molecule what would the force constant, RM, vibration wavenumber, energy and energy gap be like?

Answer 18

Force constant would be high
Reduced mass would be low
VW would be high
Energy would be large
Energy gap would be large

Question 19

For a large heavy molecule what would the force constant, RM, vibration wavenumber, energy and energy gap be like?

Answer 19

The force constant would be low
The reduced mass would be high
The VW would be low
The energy would be small 
The energy gap would be small

Question 20

What are the gross selection rules?

Answer 20

There must be a change in dipole during the vibration to give a peak
In diatomics this means it needs a permanent dipole
(Homonuclear have no dipole therefore no peak)

Question 21

What is the specific selection rule?

Answer 21

Transitions can only take place between adjacent vibrational energy levels
^V=+-1

Question 22

Vibrational energy levels are moderately spaced, what does this mean?

Answer 22

This means most molecule are in the lowest level V=0 at room temperature
Only one transition can occur ( to V=1)
( absorb photon equal to this gap)
Spectrum shows one band

Question 23

Why would you expect the same peak in the spectrum, irrespective of the level from which the transition originates?

Answer 23

This is because the energy gap is the same for all adjacent energy levels (hv)

Question 24

What is the major application for IR?

Answer 24

To determine the force constant for bonds
You can find this from experimental data by using the wavenumber equation and rearranging
FC is the stiffness of the bond (related to bond strength)