Absorption spectroscopy
Summary: (Last lecture)
•
•
•
•
•
definition
electromagnetic spectroscopy
matter
absorption spectroscopy
fundamental terms
(transmittance, absorbance
absorptivity, molar absorptivity)
Absorption spectroscopy
Molar absorptivity (e)
e
A = ebc
= the molar absorptivity, L mol-1 cm-1
(the characteristic of a substance
that tells how much light is
absorbed at particular wavelength)
b = the pathlength of cell, cm
C = the concentration of absorbing
species, M
Absorption spectroscopy
Quantitative aspects of absorption
measurements
Beer’s Law
A = ebc
(The heart of spectrophotometry)
*Application of Beer’s Law to mixture
Absorption spectroscopy
A solution containing more than one kind
of absorbing substances:
Atotal = A1 + A2 + … + An
= e1bc1 + e2bc2 + … + enbcn
Conditions:
no interaction among the various
species
Absorption spectroscopy
Limitations to the Applicability of
Beer’s Law
A a c
• monochromatic radiation
• dilute solutions ( 0.01 M) only
Why?
Absorption spectroscopy
Limitations to the Applicability of
Beer’s Law
At high concentration (> 0.01M):
• in concentrated solution, solutes
molecules influence one another
as a result of their proximity.
When solute molecules get close
to one another, their properties
(including molar absorptivity)
change somewhat.
Absorption spectroscopy
Limitations to the Applicability of
Beer’s Law
At high concentration (> 0.01M):
• The solute becomes the solvent.
Properties of a molecule are not
exactly the same in different solvent.
Absorption spectroscopy
Deviations of Beer’s Law
DEVIATIONS
1. Chemical Deviations
2. Instrumental Deviations
• Polychromatic Radiation
• Stray Light
Deviations of Beer’s Law
Chemical deviations
• arise when an analyte dissociates,
associates, or reacts with a solvent
to produce having a different
absorption spectrum from the analyte.
Ex: acid/base indicators
HIn
colour 1
=
H+
+ Incolour 2
Ex:
The molar absorptivity of the weak acid
HIn (Ka=1.42 x 10-5) and its conjugate
base In- at 430 and 570 nm were determined
by measurements of strongly acidic and
strongly basic solutions of the indicator
(where essentially all of the indicator was
in HIn and In- forms respectively).
The results were
e430
e570
HIn
6.30 x 102
7.12 x 103
In
2.06 x 104
9.61 x 102
Derive absorbance data for unbuffered
solutions having total indicator concentrations
ranging from 2 x 10-5 to 16 x 10-5 M
Soln.
Calculate the [HIn] and [In-] in a solution
in which the [indicator] is 2.00 x 10-5 M
Here
HIn = H+ + In-
[ H ][ In ]
Ka 
 1 . 42  10
[ HIn ]


5
(1)
From the equation for the dissociation
process;
[ H  ]  [ In  ]
[ In ]  [ HIn ]  2 . 00 x 10

5
Substitution of these relationships into
(1) for Ka:
[ In ]
 1 . 42  10
5

( 2 . 00  10 )  [ In ]
 2
5
[ In  ]  1 . 12  10
5
[ HIn ]  2 . 00  10
5
 0 . 88  10
5
 1 . 12  10
5
From Beer’s Law:
A  e In b [ In ]  e HIn b [ HIn ]

A430  2 . 06  10  1 . 00  1 . 12  10
5

 6 . 30  10 2  1 . 00  0 . 88  10
5
4
 0 . 236
At 570 nm:
A570  9 . 61  10 2  1 . 00  1 . 12  10
5

 7 . 12  10  1 . 00  0 . 88  10
5
3
 0 . 073
Note:
The direction of
curvature is opposite
at the two
wavelengths.
Instrumental deviations
• polychromatic radiation
Consider a beam consisting of just two
wavelengths and 
at ,
P0
A  log
 e bc
P
P0
e bc
 10
P
 e bc


P  P0 10
at ,
P   P010
 e bc
When an absorbance measurement is made
with radiation composed of both wavelengths,
the measurement A, Am:
( P0  P0)
Am  log
( P   P )
( P0  P0)
Am  log
e bc

( P0 10
 P010
e bc
)
Am  log( P0  P0)  log( P010
 e bc
 P010
 e bc
)
when e   e 
Am  e bc
In experiment, deviations from Beer’s Law
resulting from the use of a polychromatic
radiation is not appreciable.
Instrumental deviations
• stray light
Causes:
scattering and reflections from various
internal surface
Characteristic:
• differs greatly in wavelength from that
of the principal radiation
• may not have passed through the sample
Instrumental deviations
• stray light
P0  Ps
A  log
P  Ps
Ps is the power of nonabsorbed
stray radiation
note
At high concentration
and at longer path
lengths, stray
radiation can also
cause deviations
from the linear
relationship between
ABS and path
length.
M.R. Share, Anal. Chem. 1984, 56, 339A
Instrumental deviations: stray light
Summary:
The instrumental deviations result in
absorbance that are smaller than
theoretical.
OR
The instrumental deviations always
lead to negative absorbance error.
Analysis of Mixtures of Absorbing Substances
:
A  e M bc M  e N bc N
:
A  eM bc M  eN bc N
• two components behave independently of one
another.
Example 1
The molar absorptivities of compounds X and Y were
measured with pure samples of each.
e
 (nm)
272
327
(M-1 cm-1)
X
Y
16440
3990
3870
6420
A mixture of compounds X and Y in a 1.000 cm cell
has an absorbance of 0.957 at 272 and 0.559 at 327 nm.
Find the concentrations of X and Y in the mixture.
Example 2
The figure shows the spectra of 1.00x10-4 M MnO4-,
1.00x10-4 M Cr2O72-, and unknown mixture mixture
of both. Absorbances at several wavelengths are given
in the table. Find the concentration of each species in
the mixture
Wavelength
(nm)
266
288
320
350
360
MnO4standard
0.042
0.082
0.168
0.125
0.056
Cr2O72standard
0.410
0.283
0.158
0.318
0.181
Mixture
0.766
0.571
0.422
0.672
0.366
Quiz 2:
สารละลายของสารอินทรีย์ตัวหนึ่งเตรียมขึน้ จากสารละลาย
0.287 mg ในเอธานอล 10 mL พบว่ าหากใช้ เซลที่มี
ความหนา 1.0 cm จะให้ ค่าการดูดกลืน 1.25 ที่ 305 nm
จงคานวณ molar absorptivity กาหนดให้ นา้ หนักโมเลกุล
ของสารเท่ ากับ 500
Summary: key terms
Beer’s Law
the relationship between a sample’s
absorbance and the concentration
of the absorbing species
Stray Light
any light reaching the detector that
does not follow the optic path from
the source to the detector
Transmittance
the ratio of the radiant power passing
through a sample to that from the
radiation’s source
Absorbance
The attenuation of photons as they
pass through a sample (A)
Absorbance spectrum
a graph of a sample’s absorbance of
electromagnetic radiation versus
wavelength (frequency or wavenumber)
photon
a particle of light carrying an amount
of energy equal to hv
Next topic:
Instruments for absorption measurements
Instrument components: UV-VIS
optical
source
hn1
signal
processor
 selector
hn2
detector
sample
Instrument components: UV-VIS
Sources:
A sources must:
• generate a beam of radiation with
sufficient power for easy detection
and measurement
• provide output power that is both
stable and intense
Types of spectroscopic sources:
1. continuous sources
2. lines sources
Instrument components: UV-VIS
continuous sources
lines sources
H2 and D2 lamp
Tungsten filament lamps
Xe arc lamp
hollow cathode lamp
Hg vapor lamp
laser
Instrument components: UV-VIS
Tungsten filament lamp: Vis/near IR source
• 320-2500 nm
Instrument components: UV-VIS
Quartz Tungsten Halogen (QTH) lamp
• 200-3000 nm
• high temperature (3500 K)
Evaporation: W(s)
W(g) + I2(g)
Redeposition:
WI2(g) + W(s)
W(g)
WI2(g)
W(s) + I2(g)
Instrument components: UV-VIS
H2 and D2 lamp
• provide continuous spectrum in the UV
region (180-375 nm) by electrical
excitation of deuterium or hydrogen
at low pressure
mechanism
H2 + Eelectrical  H2*  H(KE1) + H(KE2) + hv
KE 1  KE
2
 hn  E electrical
 BDE
‘bond dissociation energy’
Instrument components: UV-VIS
sample containers
Instrument components: UV-VIS
sample containers
Note:
• a liquid sample is usually contained
in a cell called a cuvet that has a
flat
• material
• fused silica
• glass  only Vis
• quartz
Instrument components: UV-VIS
wavelength selectors
Types
1. Filters
1.1 interference filters
1.2 absorption filters
2. Monochromators
Instrument components: UV-VIS
Filters
“a wavelength selector that uses either
absorption, or constructive and destructive
interference to control range of selected
wavelengths”
• the simplest method for isolating a
narrow band of radiation
Instrument components: UV-VIS
Absorption filters
• work by selectively absorbing radiation
from a narrow region
Interference filters
• use constructive and destructive
interference to isolate a narrow range
of wavelengths
Instrument components: UV-VIS
Absorption filters
• use coloured glass
• provide effective bandwidths, range
30-250 nm
the width of the band
of radiation passing
through a wavelength
selector measured at
half the band’s height
Instrument components: UV-VIS
Instrument components: UV-VIS
Relationship between Absorption and Observed Colour
wavelength region
removed by
absorption (nm)
400-450
450-480
480-490
490-500
500-560
560-580
580-600
600-650
650-750
colour observed
violet
blue
green-blue
blue-green
green
yellow-green
yellow
orange
red
complementary
colour of the residual
light, as seen by eye
yellow-green
yellow
orange
red
purple
violet
blue
green-blue
blue-green