# Beer`s Lambert ```Introduction to Spectroscopic
Methods of Analysis
(part 2)
Lecture 2
This lecture will cover:
• Molecular absorption spectroscopy
• Terms employed in absorption
spectroscopy: Absorbance &amp;
Transmittance
• Beer’s Law
Molecular Absorption Spectroscopy
- is based on measurement of the
transmittance, T or the absorbance,
A of solutions contained in
transparent cells
Molecular absorption spectroscopy
Absorption
is a measure of the decrease in
P0
P
Absorbing solution
TERMS EMPLOYED IN
ABSORPTION
SPECTROSCOPY
Transmittance - The fraction of incident
radiation transmitted through the sample medium.
b
T = P
P0
P0
P
Power of
incident
Absorbing solution of
concentration, c
Power of
transmitted
A = -log T
Commonly expressed as a percentage:
%T = P x 100
P0
Absorbance - A measurement of the amount of
radiant power absorbed by the sample defined as the
negative log of transmittance.
b
A = -log T
P0
P
Power of
incident
Absorbing solution of
concentration, c
Power of
transmitted
A = log P0
P
• Absorbance has a linear relationship with sample
concentration defined by Beer’s Law.
Questions:
1.
Convert the following percent transmittance data into
absorbance:
i) 33.6
ii) 92.1
i) 0.474
ii) 0.0357
iii) 1.76
iii) 1.75
i) %T
T
= 33.6
= 33.6 / 100
= 0.336
A
= - log T
= log 1/T
= log 1/0.336
= 0.474
Questions:
2.
Convert the following absorbance data into
percent transmittance:
i) 0.375
ii) 1.325
ii) 4.73%
iii) 97.3%
iii) 0.012
Beer’s Law
- shows linear relationship between absorbance,
concentration of the species measured, sample
path length and the absorptivity of the species.
A = bc
ε = molar absorptivity, liter mol-1 cm-1
b = sample path length, cm
c = concentration, mol per liter
Beer’s Law
A = abc
absorbance
Absorptivity
(Lg-1cm-1)
Pathlength
(cm)
Concentration
(g/liter)
The term “a” is a proportionality constant called
absorptivity.
Absorptivity is a constant for a given chemical
species at a specific wavelength.
Examples:
E.g. 1
What is the concentration of an absorbing species if its
molar absorptivity is 1500 L/mol cm and the measured
absorbance in a 1.00 cm cuvette is 0.742?
A = εbc
c = 0.742
(1.00cm) (1500L/mol.cm)
= 4.95 x 10-4 M
c = A / εb
E.g. 2 The measured absorbance of a sample in a 1.00cm
cuvette is 0.544. If the concentration is 1.40 x 10-3 M, what is
the molar absorptivity for the species?
A = εbc
ε = 0.544
(1.00cm)(1.40x10-3 mol/L)
= 389 L/mol.cm
ε=A/bc
E.g. 3 A sample in a 1.0cm cell is determined with a spectrometer to
transmit 80% light at a certain wavelength. If the absorptivity of this
substance at this wavelength is 2.0, what is the concentration of the
substance?
The percent transmittance is 80%. So, T = 0.80
A
log 1/T
= abc
= 2.0 L/g.cm x 1 cm x c
log 1/0.80 = 2.0 L/g x c
c
= 0.10
2.0 L/g
= 0.050 g/L
PARAMETERS THAT AFFECT
ABSORBANCE
A = abc
• Concentration
• Width of cuvette
• Inherent ability for the absorbing species to
absorb light
• Width of cuvette
b
Wider cuvette more
absorbing species
present in the path of
the light, hence
absorbance is greater.
b
• Inherent ability for the absorbing species to
absorb light
- Chemical species vary with respect to this
inherent ability since absorption depends on
individual electronic and vibrational transitions
available in a given species
APPLICATION OF BEER’S LAW
• Applying Beer’s Law to Mixtures
- Beer’s law also applies to solutions containing more
than one kind of absorbing substance, provided
there is no interaction among the various species
- Total absorbance for a multicomponent system at
a single wavelength is the sum of the individual
absorbances.
Atotal = A1 + A2 + ………+ An
= ε1bc1 + ε2bc2 + ……… + εnbcn
LIMITATIONS TO THE
APPLICABILITY OF BEER’S LAW
- Deviations are frequently observed
from the direct proportionality btw
absorbance, A and concentration, c
when pathlength, b is constant.
Deviations may be due to:
1. Fundamental
2. Instrumental
3. Chemical deviations
1. Fundamental deviations
- Real limitation to the law
- At high concentration (0.01M) each
particle affects the charge distribution of
its neighbours.
- Therefore, this interaction alter the
ability of analyte species to absorb a given
Causing deviation from the linear
relationship between absorbance and
concentration.
2. Instrumental deviations
- Beer’s Law strictly applies when
- In practice, polychromatic sources that
have a continuous distribution of
wavelengths are being used.
- Deviations occur if the radiation is
polychromatic since the relationship btwn
A and c is no longer linear when  is differ.
2. Instrumental deviations
- due to presence of stray radiation
- Due to instrument imperfections.
- This stray radiation is the result of
scattering and reflection off the surfaces
of gratings, lenses or mirrors, filters and
windows.
- The wavelength of stray radiation differs
greatly from the principal radiation &amp; may
not have passed thru’ the sample.
- When measurements are made in the