Beer-Lambert’s law and its usage, spectral bands qualitative
description
Measurement of absorbance
Have a look at this schematic diagram of a double-beam UV-Vis.
spectrophotometer;
Figure 1. Rough scheme of a single beam photometer.
Figure 2. A double beam photometer, detailed scheme.
Instruments for measuring the absorption of U.V. or visible radiation are made
up of the following components;
1.
2.
3.
4.
5.
Sources (UV and visible)
Wavelength selector (monochromator)
Sample containers (cuvettes)
Detector
Signal processor and readout
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Limitations of the BL. law
The linearity of the Beer-Lambert law is limited by chemical and instrumental
factors.
Chemical and physical:
 1.improper reference system,
 2.deviations in molar absorption coefficients at high concentrations
(>0.01M) due to electrostatic interactions between molecules in close
proximity,
 3.scattering of light due to particulates in the sample,
 4.fluorescence or phosphorescence of the sample,
 5.changes in refractive index at high analyte concentration,
Instrumental:
 6.non-monochromatic radiation,
 7.stray light
1.Reference system
In 1 dm3 of 0.001 molar aqueous solution you may find 0.001 moles of solute
and 55.56 moles of water. As a first approximation reference cuvette contains
pure solvent to compensate intensity attenuation caused the solvent.
Figure 3. The sources of error occur in a cuvette
Interaction between light and medium.The disturbing interactions should be
substracted by preparing proper reference solution.
Proper reference solution contains all the material in the same concentration as
in the sample solution except the optically active material/materials to be
studied.
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Fig. 4. The experimental setup and intensities of reference and sample cuvettes.
Reference cuvette:
Source intensity, Is decreases by solvent absorption, thus the outgoing intensity,
I0 is free from the influence of solvent. I0 is seen by the detector.
Sample cuvette:
Source intensity decreases by solvent and solute absorption.
I source  I solvent  I 0
I source  I solvent  I solute  I
The sum of two equations
I 0  I  I solute
1.
We get an equation containing no solvent intensity. The greatest part of Isolvent
originates from light scattering and refraction loss.
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2.Deviations in molar absorption coefficients, concentration
effect
At solute concentrations high enough the molar absorption coefficient becomes
concentration dependent.
Figure 5. Absorbance vs. concentration functions. Scattered blue: calculated
curve from ε is set to be constant, solid red: the measured graph is plotted.
High concentration results in non-linearity because:
� at high concentration,
we have strong electrostatic interactions between molecules
� at high concentrations,
we may get changes in refractive index
� if we have a system in chemical equilibrium, equilibrium may shift at high
concentrations
3.Scattering of light
Photons int he source beam may scatter on particles present in the cuvette and
instrument regard scattered photons as absorbed ones, because they do not reach
the detector.
4.Fluorescence or phosphorescence of the sample
Instruments usually detect signal by unit wavelegths e.g. by nanometers, and
Beer Lambert law is valid if we measure the intensity at constant wavelength
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one by one. This is not fulfilled when fluorscence or phosphorescenece is
present. The measured outgoing intensity will be smaller.
5.Changes in refractive index at high analyte concentration
Photons avoid the window before the detector. The higher the refractive index of
sample the deviation of direction of incoming and outgoing beams are greater,
so a part of photons are not counted by the detector.
6.non-monochromatic radiation
Monochromators do not produce a single wavelength radiation. The
“monochromatic” beam contains several wavelegths.
Figure 6. Spectral band sampled at the maximum wavelength (1) and at the side
of the band (2). BL law is better applicable in case 1.
Calibration curve is constructed at band A shows a straight line, while that is
constructed at band B is bent. There is a flat part of absorption band in the
vicinity of its maximum (band A), therefore the average wavelength has a small
standard deviation.
 7.Stray light
Stray light is light in an optical system, which was not intended in the design.
The light may be from the intended source, but follow paths other than intended,
or it may be from a source other than the intended source.
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Spectral bands qualitative description
A group of atoms (chemical groups) in a molecule (-OH, -NH2, -C=O, C=C,
etc.) accounts for a particular light absorption is called chromophore.
When a structural modification is made on to the original molecule by carrying
out a reaction a red shift can be observed refering to the λmax of original band,
The original band is shifted to higher wavelengths.
Chromophore
alkene
alkyne
Carbonyl
Amido
λmax
Example
C6H13CH=CH2
C5H11C≡C-CH3
CH3-CO- CH3
CH3- CO- NH2
177
178
186
214
εmax
13 000
10 000
1 000
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Conjugation of π bonds causes red shift of λmax
Original molecule without conjugation:
CH2=CH-CH2-CH2-CH=CH2 λmax =185 nm
Molecule with conjugation:
CH2=CH-CH2=CH-CH=CH2 λmax =217 nm
Red shift of λmax with increasing number of rings:
Benzene
λmax =204 nm
Naphthalene
λmax =286 nm
Phase and solvent effect, 1,5-triazine
Figure 7. Triazine spectra in three phases.
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Transition
type
π→π*
π→π*
n→π*
n→π*
The interactions in aqueous solution extinguish the vibration fine structure of the
band.
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