Environmental Engineering Reference
In-Depth Information
tive for the H atom and negative for the Cl atom)
multiplied by the charge spacing (Colthup
et al.
1975). Therefore, only those bonds that have a
dipole moment that changes as a function of time
are able to absorb infrared radiation (Pavia
et al.
2001).
In summary, the origin of the infrared absorption
by molecules is related to their vibrational and rota-
tional motions. The molecule can absorb incident
infrared radiation if it has a frequency equal to that
of a specifi c molecular vibration and if it results in a
change in the dipole moment of the molecule (Ewing
1985; Hsu 1997). Nearly all molecules, whether
organic and inorganic, absorb various frequencies of
radiation in the infrared region of the electromag-
netic spectrum. The only exceptions are diatomic
homonuclear molecules such as H
2
, N
2
, and O
2
,
because only in these can no vibration or rotation be
found that will produce a dipole moment (Ewing
1985).
Generally, the total number of fundamental vibra-
tions does not coincide with the total number of
observed absorption bands. The reason for this dif-
ference is the fact (already mentioned) that when the
vibration does not causes a net change in the dipole
moment of the molecule, its fundamental mode is
infrared inactive. On the other hand, additional
bands are generated by the appearance of overtones
at frequencies approximately two or three times that
of the fundamental line. Overtones result from exci-
tation from the ground state to higher energy states,
which correspond to integral multiples of the fre-
quency of the fundamental mode. Another phenom-
enon, called combination bands, can occur when the
energy of a photon is absorbed by two bonds rather
than one, exciting two vibrational modes simultane-
ously. Combination bands are the consequence of a
coupling of these two vibrational frequencies in a
molecule, which gives rise to the vibration of a new
infrared active frequency within the molecule. A
combination band usually occurs at a frequency that
corresponds to approximately the sum of the two
fundamental frequencies. Difference bands are anal-
ogous to combination bands, but the observed fre-
quency in this case is the difference between the two
coupling bands. The intensities of overtone, combi-
nation, and difference bands are less than those of
fundamental bands (Hsu 1997; Skoog
et al.
1998;
Pavia
et al.
2001).
frequencies by the red end of the visible region and
at low frequencies by the microwave region (Hsu
1997; Skoog
et al.
1998).
A linear wavenumber scale is usually preferred in
infrared spectroscopy because wavenumber is
directly proportional to both frequency and energy
of infrared absorption (Pavia
et al.
2001).
The energy of a molecule encompasses transla-
tional, rotational, vibrational, and electronic ener-
gies. Electronic transitions occur when the molecule
absorbs radiation in the ultraviolet (UV)-visible
region of the electromagnetic spectrum. Infrared
radiation is less energetic than visible radiation and
therefore cannot bring about electronic transitions.
However, the energy differences between various
vibrational and rotational states of molecular species
are in the infrared region of the electromagnetic
spectrum (Colthup
et al.
1975).
The translational, rotational, and vibrational ener-
gies of the molecule are related to each atom in their
structure. Above absolute zero temperature, all the
atoms in the molecules are continually vibrating with
respect to each other. Each atom can be described by
its own cartesian coordinate system with the origin
defi ned by the equilibrium position of the atom. An
atom can move along any of the three coordinate
axes (
x
,
y
,
z
) and each coordinate corresponds to one
degree of freedom. Thus, a polyatomic molecule of
n
atoms has 3
n
total degrees of freedom. However,
the motion of the entire molecule through space
(translation) corresponds to three degrees of freedom;
another three degrees of freedom are needed to
describe the rotation of the entire molecule around
its center of gravity. Therefore, for a nonlinear mol-
ecule, the true (fundamental) vibrations are the
remaining 3
n
6 degrees of freedom. To describe
rotation of linear molecules two degrees of freedom
are suffi cient, because rotation about the bond axis
is not possible. Thus, the number of fundamental
vibrations for a linear molecule is given by 3
n
−
5.
These fundamental vibrations are also called normal
modes of vibration (Hsu 1997; Skoog
et al.
1998).
However, not all the fundamental modes of the
molecule have infrared activity. Only those vibra-
tions that promote a net change in the dipole moment
of the molecule may give rise to infrared absorption
by the molecule. In the case of a simple dipole (such
as the HCl molecule), the dipole moment is defi ned
as the magnitude of either charge in the dipole (posi-
−
