Chapter 24
Introduction to Spectrochemical Methods
Measurements based on light and other
forms of electromagnetic radiation are
widely used throughout analytical chemistry.
The interactions of radiation and matter are
the subject of the science called
spectroscopy.
Spectroscopic
analytical
methods are based on measuring the amount
of radiation produced or absorbed by
molecular or atomic species of interest.
Classification
We can classify spectroscopic methods according
to the region of the electromagnetic spectrum
involved in the measurement. The regions include
–ray, X-ray, ultraviolet (UV), visible, infrared
(IR), microwave, and radio frequency (RF).
Spectrochemical methods have provided the most
widely used tools for the elucidation of molecular
structure as well as the quantitative and qualitative
determination of both inorganic and organic
compounds.
Properties of Electromagnetic Radiation
Electromagnetic radiation is a form of energy that is
transmitted through space at enormous velocities.
Electromagnetic radiation can be described as a wave
with properties of wavelength, frequency, velocity, and
amplitude. In contrast to sound waves, light requires no
supporting medium for its transmission; thus, it readily
passes through a vacuum.
Electromagnetic radiation can be treated as discrete
packets of energy or particles called photons or quanta.
These dual views of radiation as particles and waves are
not mutually exclusive but complementary.
The Speed of Light
In a vacuum, the velocity (c) of light is 2.99792 x 108 m s-1
and the velocity of light in air is about 0.03% less. Thus,
for a vacuum, or for air, the velocity of light:
c = = 3.00 x 108m s-1 = 3.00 x 1010 cm s-1
In a medium containing matter, light travels with a velocity
less than c because of interaction between the
electromagnetic field and electrons in the atoms or
molecules of the medium. Since the frequency of the
radiation is constant, the wavelength must decrease as the
light passes from a vacuum to a medium containing matter.
The wavenumber  is another way to describe
electromagnetic radiation. It is defined as the number of
waves per centimeter and is equal to 1/. The  has the
units of reciprocal centimeters (cm-1)
The particle Nature of Light: Photons
In many radiation/matter interactions, it is useful to
consider light as consisting of photons or quanta. We
can relate the energy of photon to its wavelength,
frequency, and wavenumber by
E = h = hc/ = hc
where, h is Planck’s constant (6.63 x 10-34 J s). The
wavenumber  and frequency , in contrast to the
wavelength , are directly proportional to the photon
energy E. The radiant power of a beam of radiation
is directly proportional to the number of photons per
second.
The Electromagnetic Spectrum
The electromagnetic spectrum covers an
enormous range of energies (frequencies) and
thus wavelengths. Useful frequencies vary from >
1019 Hz (-ray) to 103 Hz (radio waves). An X-ray
photon (  3 x 1018 Hz,   10-10 m), for
example, is approximately 10,000 times as
energetic as a photon emitted by an ordinary light
bulb (  3 x 1014 Hz,   10-6 m) and 1015 times
as energetic as a radio-frequency photon (  3 x
103 Hz,   105 m).
Spectroscopic Measurements
Spectroscopists use the interactions of radiation
with mater to obtain information about a sample.
The sample is stimulated by applying energy in the
form of heat, electrical energy, light, particles, or a
chemical reaction. The analyte is predominately in
its lowest-energy or ground state. The stimulus
then causes some analyte species to undergo a
transition to a higher-energy or excited state. We
obtain information about the analyte by measuring
the electromagnetic radiation emitted as it returns
to the ground state or by measuring the amount of
electromagnetic radiation absorbed as a result of
excitation.
…continued…
In emission the analyte is stimulated by the
application of heat, electrical energy, or a chemical
reaction. Emission spectroscopy usually refers to
methods in which the stimulus is heat or electrical
energy, whereas chemiluminescence spectroscopy
refers to excitation of the analyte by a chemical
reaction. Measurement of the radiant power
emitted as the analyte returns to the ground state
can give information about its identity and
concentration. The results of such a measurement
are often expressed graphically by a spectrum,
which is a plot of the emitted radiation as a
function of frequency or wavelength.
…continued…
When the sample is stimulated by application of an
external electromagnetic radiation source, several
processes are possible. Some of the incident
radiation can be absorbed and promote some of the
analyte species to an excited state. In absorption
spectroscopy, the amount of light absorbed as a
function of wavelength is measured, which can
give qualitative and quantitative information about
the sample. In photoluminescence spectroscopy the
emission of photons is measured following
absorption. The most important forms of
photoluminescence for analytical purposes are
fluorescence and phosphorescence spectroscopy.
The Absorption Process
The absorption law, also known as the Beer-Lambert law
or just Beer’s law, tells us quantitatively how the amount
of attenuation depends on the concentration of the
absorbing molecules and the pathlength over which
absorption occurs. As light traverses a medium containing
an absorbing analyte, decreases in intensity occur as the
analyte becomes excited. For an analyte solution of a
given concentration, the longer the length of the medium
through which the light passes (pathlength of light), the
more absorbers are in the path and the greater the
attenuation. Also for a given pathlength of light, the higher
the concentration of absorbers, the stronger the
attenuation.
The Absorption Process
The attenuation of a parallel beam of monochromatic
radiation as it passes through an absorbing solution of
thickness b cm and concentration c moles per liter.
Because of interactions between the photons and
absorbing particles, the radiant power of the beam
decreases from P0 to P. The transmittance T of the
solution is the fraction of incident radiation
transmitted by the solution. Transmittance is often
expressed as a percentage and called the percent
transmittance.
T = P / P0
The absorbance A of a solution is related to the
transmittance in a logarithmic manner.
A= -logT= log(P0/P)
Measuring Transmittance and Absorbance
Ordinarily, transmittance and absorbance, cannot
be measured as shown because the solution to be
studied must be held in some sort of container
(cell or cuvette). Reflection and scattering losses
can occur at the cell walls. These losses can be
substantial. Light can also be scattered in all
directions from the surface of large molecules or
particles, such as dust, in the solvent, and this can
also cause further attenuation of the beam as it
passes through the solution.
…continued…
To compensate for these effects, the power of the
beam transmitted through a cell containing the
analyte solution is compared with one that
traverses an identical cell containing only the
solvent or a reagent blank. An experimental
absorbance that closely approximates the true
absorbance for the solution is thus obtained; that
is
A = log P0 / P  log Psolvent / Psolution
Beer’s Law
According to Beer’s law, absorbance A is directly
proportional to the concentration of the absorbing
species c and the pathlength b of the absorbing
medium
A = log P0 / P = abc
Here, a is a proportionality constant called the
absorptivity. Because absorbance is a unitless
quantity, the absorptivity must have units that
cancel the units of b and c. If, for example, c has
the units of grams per liter (g L-1) and b has the
units of centimeters (cm), absorptivity has the units
of liters per gram centimeter (L g-1 cm-1).
…continued…
When we express the concentration in moles
per liter and b in centimeters, the
proportionality constant, called the molar
absorptivity, is given the special symbol .
Thus,
A = bc
where,  has the units of liters per mole
centimeter (L mol-1 cm-1).
Applying Beer’s Law to Mixture
Beer’s law also applies to solutions containing
more than one kind of absorbing substance.
Provided that there are no interactions among
the various species, the total absorbance for a
multicomponent system is the sum of the
individual absorbances. In other words,
Atotal = A1 + A2 + … An
= 1bc1 + 2bc2 + … + nbcn
where the subscripts refer to absorbing
componets 1, 2, …, n.
Limits to Beer’s Law
There are few exception to the linear relationship
between absorbance and pathlength at a fixed
concentration. We frequently observe deviations
from the direct proportionality between absorbance
and concentration where b is a constant. Some of
these deviations, called real deviations, are
fundamental and represent real limitations to the
law. Others occur as a consequence of the manner
in which the absorbance measurements are made
or as a result of chemical changes associated with
concentration changes. These deviations are called
instrumental deviations and chemical deviation
respectively.
Real Limitations to Beer’s Law
Beer’s law describes the absorption behavior of
dilute solutions only and is a limiting law. At
concentrations exceeding about 0.01 M, the average
distances between ions or molecules are diminished
to the point where each particle affects the charge
distribution, and thus the extent of absorption of its
neighbors. The occurrence of this phenomenon
causes deviations from the linear relationship
between absorbance and concentration. When ions
are in close proximity, the molar absorptivity of the
analyte can be altered because of electrostatic
interactions, which can lead to departures from
Beer’s law.
Chemical Deviations
Deviations from Beer’s law appear when the absorbing
species undergoes association, dissociation, or reaction
with the solvent to give products that absorb differently
from the analyte. The extent of such departures can be
predicted from the molar absorptivities of the absorbing
species and the equilibrium constants for the equilibria
involved. Unfortunately, we are usually unaware that
such processes are affecting the analyte, so compensation
is often impossible. Typical equilibria that give rise to
this effect include monomer dimer equilibria, metal
complexation equilibria where more than one complex is
present, acid/base equilibria, and solvent-analyte
association equilibria.
Instrumental Deviations
The need for monochromatic radiation and the
absence of stray radiation are practical factors that
limit the applicability of Beer’s law. Beer’s law
strictly applies only when measurements are made
with monochromatic source radiation. If the band
selected corresponds to a region in which the
absorptivity of the analyte is essentially constant,
departures from Beer’s law will be minimal. Many
molecular bands in the UV/visible region fit this
description. To avoid deviation, it is advisable to
select a wavelength band near the wavelength of
maximum absorption where the analyte
absorptivity changes little with wavelength.
…continued…
Stray radiation, commonly called stray light, is
defined as radiation from the instrument that is
outside the nominal wavelength band chosen for
the determination. This stray radiation is often the
result of scattering and reflection off the surfaces
of gratings, lenses or mirrors, filters, and windows.
When measurements are made in the presence of
stray light, the observed absorbance is given by
A` =
P 0  Ps
log
P  Ps
where Ps is the radiant power of the stray light.
…continued…
Stray light always causes the apparent absorbance to be
lower than the true absorbance. The deviations due to stray
light are most significant at high absorbance values.
Because stray radiation levels can be as high as 0.5% in
modern instruments, absorbance levels above 2.0 are
rarely measured unless special precautions are taken or
special instruments with extremely low stray light levels
are used.
Another deviation is caused by mismatched cells. If the
cells holding the analyte and blank solutions are not of
equal pathlength and equivalent in optical characteristics,
and intercept will occur in the calibration curve. This error
can be avoided either by using matched cells or by using a
linear regression procedure to calculate both the slope and
intercept of the calibration curve.
Absorption spectra
An absorption spectrum is a plot of absorbance
versus wavelength. Absorbance could also be
plotted against wavenumber or frequency. Most
modern scanning instruments can produce such
an absorption spectrum directly. Older
instruments often display transmittance and
produce plots of %T versus wavelength.
Occasionally, plots with logA as the ordinate are
used. A plot of molar absorptivity  as a function
of wavelength is independent of concentration.
Atomic Absorption
When a beam of polychromatic uv/visible
radiation passes through a medium
containing atoms, only a few frequencies are
attenuated by absorption. The spectrum
consists of a number of very narrow
absorption lines. Transition between two
different orbitals are termed electronic
transitions. Atomic absorption is measured at
a single wavelength using a very narrow
monochromatic source.
Molecular Absorption
Three types of energy changes occur when
molecules are excited by ultraviolet, visible,and
infrared radiation. For UV/visible radiation, when
we excite a molecule, an electron residing in a lowenergy molecular or atomic orbital is promoted to a
higher-energy orbital. The change in energy levels is
called a transition. We can only get such a transition
when the energy h of the photon is exactly the
same as the energy difference between the two
orbital energies. The transition of an electron
between different energy levels is called an
electronic transition, and the absorption process is
called electronic absorption.
…continued…
Molecules exhibit two additional types of radiationinduced transitions: vibrational transitions and rotational
transitions. The vibrational energy of a molecule is
associated with the bonds that hold the molecule together.
The vibrational energy of a molecule is quantized and can
only assume certain discrete levels. Transitions between
vibrational levels are vibrational transitions.
The overall energy E associated with a molecule in a given
state can be written as
E = Eelectronic + Evibrational + Erotaitonal
where Eelectronic is the electronic energy of the molecule,
Evibrational is its vibrational energy, and Erotaitonal is its
rotational energy.
Energy-Level Diagrams for Molecule
A partial energy-level diagram depicting typical
processes that occur when a polyatomic molecule
absorbs infrared, visible and ultraviolet radiation is
shown. The energies E1 and E2 of the first two of
the several electronically excited states of a
molecule are shown relative to the energy of its
ground state associated with each electronic state
are indicated by the lighter horizontal lines labeled
1, 2, 3, and 4. The lowest vibrational levels are
labeled 0.
Infrared Absorption
Infrared radiation is generally not of sufficient
energy to cause electronic transitions but can
induce transitions in the vibrational and rotational
states associated with the ground electronic state
of the molecule. For absorption to occur, the
analyte must be irradiated with frequencies
corresponding exactly to the energies indicated by
the lengths of the four arrows (wavelengths 1 –4
as shown).
Ultraviolet and Visible Absorption
The center arrows in the energy diagram suggest
that the molecules under consideration absorb
visible radiation of five wavelengths (1 to 5),
thereby promoting electrons to the five vibrational
levels of the excited electronic level E1. Ultraviolet
photons that are more energetic are required to
produce the absorption to level E2 shown by the
five arrows on the right (wavelengths 1 to 5).