Spectrophometry

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Spectrophotometry Electromagnetic radiation is
characterized by its frequency (n) or its
wavelength (l). These two are related by the
velocity of light (c), n c/l. The
electromagnetic spectrum ranges from high-energy
cosmic rays (high frequency, short wavelength) to
very low-energy microwaves (low frequency, long
wavelength).
Visible light represents a very narrow section of
this range with wavelengths between 400
nanometers (nm) for blue light to around 700 nm
for red light. Shorter wavelengths fall into the
ultraviolet region and longer wavelengths are in
the infrared region.
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Visible light represents a very narrow section of
this range with wavelengths between 400
nanometers (nm) for blue light to around 700 nm
for red light. Shorter wavelengths fall into
ultraviolet region and longer wavelengths are in
the infrared region.
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White light is a mixture of all of the
wavelengths in the visible range. When light
strikes an object, it may be reflected, absorbed,
transmitted, or diffracted. A prism or a
diffraction grating separates white light into
its various colors. If some of the light is
absorbed, the reflected or transmitted light has
the complementary color of the absorbed light.
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Interaction of Electromagnetic Radiation with
Matter ? c/? Eh? ? nm   Visible
Near UV 1014 cycles/sec ? 200 700 nm
outer orbit e-1

vibrations or

bonding electrons   Far
UV 1015 cycles/sec ? 10
200 nm middle e-1   High Frequency
1016 cycles/sec ? below 10 nm inner
orbital e-1 X rays   IR (heat waves)
1013 cycles/sec ? 700 1000 nm molecular
vibrations    
transmittance input absorbance
heat    
Ein ? EA ET low energy
Lambert's Law A log 1/T
A absorbance T
transmittance    
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If sample had a Transmitted light through
sample of 80. What is the Absorbance of the
sample?
80.T .80 Transmittance Alog 1/0.80 ---
log 1.25 0.096
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Spectrophotometry and Absorbance (Optical Density)
Sample absorbance is related to the thickness of
sample container (curvet) and the concentration
of absorbing molecules
Beers Law
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Beer Lambert Law A1 A2
C1 C2
Only valid at wavelength Max
Wavelength Max is the wavelength with maximum
interaction with the sample.
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A spectrophotometer uses an arrangement of
prisms, mirrors, and slits to select light of a
desired wavelength and to direct it toward a
sample compartment and a detector.  The detector
electronically measures the intensity of the
light striking it.  A sample is placed in the
light path, and the instrument compares the
intensity of the light going through the sample
(I) to the intensity observed without the sample
(Io).
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The effect is measured either as Transmittance
(T, the percentage of light that goes through the
sample) or as the Absorbance (Abs, representing
the amount of light absorbed by the sample) T
100(I/Io)      Abs - log10(T/100)
log10(Io/I) In the example above, a single sheet
of the colored material transmits 70 of the
light I/Io 0.70         T 70        Abs
- log10(0.70) 0.155
A second sheet transmits 70 of the light it
receives, or 49 (0.70 x 70) of the original
light I/Io 0.49         T 49        Abs
- log10(0.49) 0.310 The third sheet transmits
70 of the light it receives, or 34.3 (0.70 x
49) of the original light I/Io 0.343    
    T 34.3        Abs - log10(0.343)
0.465 The Absorbance is seen to be proportional
to the number of sheets of the colored material. 
This is Lambert's Law, the absorbance is directly
proportional to the thickness or path length of
the absorbing material.
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A spectrophotometer is often used to study
solutions.  A solution containing an absorbing
material is compared to a reference solution of
the same solvent and non-absorbing materials. 
The transmittance of the reference solution is
set to 100 (Abs 0), then the relative
transmittance of the solution is measured.
In the example above, the addition of a drop of
red dye to one of the cells reduces the
transmittance to 70 (Abs 0.155).  The addition
of a drop to the second cell reduces the
transmittance to 49 (Abs 0.310) doubling the
absorbance as is expected by Lambert's Law, since
the path length of colored material is doubled.
However, the addition of the second drop to the
first cell has exactly the same effect as adding
it to the second cell.  In this case, the path
length remains the same but the concentration of
colored material is doubled, doubling the
absorbance.  This is Beer's Law at constant path
length, the absorbance is directly proportional
to the concentration of absorbing material. The
two laws are combined in the Beer-Lambert Law in
which b is the path length, C is the
concentration, and a is a constant which depends
on the wavelength of the light, the absorbing
material, and the medium (solvent and other
components).  The constant a is called the
extinction coefficient or the molar absorbtivity
coefficient. Abs abC
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If there are several absorbing materials present,
the effects are additive Abs a1b1C1 a2b2C2
. . .
A graph of Absorbance vs Wavelength for a red dye
shows a maximum at 525 nm
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For a blue dye, the maximum occurs near 625 nm
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If the both of these dyes are dissolved at the
same concentrations to form a purple solution,
the resulting graph shows both maxima and at
each wavelength, the absorbance of the purple
solution is exactly equal to the sum of the
absorbances of the red and blue solutions at that
wavelength.  This can be seen clearly by looking
at all three spectra at a wavelength of 525 nm. 
The red dye shows an absorbance of 0.233, the
blue dye has a small absorbance of 0.016, and the
mixture has an absorbance of 0.249.
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The absorbtivity coefficients can be calculated
for the two dyes at wavelengths where the other
will not interfere   At 625 nm, the blue dye
at 3.0 ppm has an absorbance of 0.318 in a cell
of path length 1.00 cm.  Therefore the
absorbtivity coefficient (a) is ablue,625
0.318/(3.0 ppm x 1.00 cm) 0.106 ppm-1cm-1 . We
will calculate the absorbtivity coefficient for
the red dye at 510 nm to minimize the inflence of
the blue dye.  (There are mathematical methods to
optimize these calculations in overlapping
regions, but that is beyond the scope of this
discussion.)   At 510 nm, the red dye at 3.0
ppm has an absorbance of 0.183 in a cell of path
length 1.00 cm.  Therefore the absorbtivity
coefficient (a) is ared,510 0.183/(3.0 ppm x
1.00 cm) 0.061 ppm-1cm-1 .  
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These values may be used to calculate the
concentrations of these red and blue dyes in
other mixtures   A different mixture of these
two dyes has Abs 0.317 at 510 nm, and Abs
0.477 at 625 nm. From the data at 510 nm, we
calculate the concentration of red dye0.317
(0.061 ppm-1cm-1 )(1.00 cm)Cred Cred
(0.317)/(0.061) 5.2 ppmFrom the data at 625
nm, we calculate the concentration of blue
dye0.477 (0.106 ppm-1cm-1 )(1.00 cm)Cblue
Cblue (0.477)/(0.106) 4.5 ppm
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Colorimetry One useful and often used way of
determining the concentration of a chemical in a
solution, if it has a color, is to measure the
intensity of the color and relate the intensity
of the color to the concentration of the
solution. Several useful factors are very
important. After discussing those important
factors and the mathematical summary of them
called Beer's Law, we will look at colorimeters,
the instruments that you will use to measure
color intensity. Next we will deal with the
problem of actually figuring out the
concentration of a solution from the absorbance
measurements that can be made using the
colorimeters by looking at Calulations for
Colorimetry. There are three methods that can be
used depending on what information is available.
They involve using proportionality, graphing and
Beer's Law.
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Beer's Law is often written in the form of this
equation A abc as a way of summarizing and
quantifying the relationship between the
absorbance, the nature of the absorbing chemical,
the path length of the solution, and the
concentration of the solution. It expresses the
ideal situation in which these factors are truly
proportional to the absorbance.
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Also, the amount of light absorbed is directly
proportional to the thickness (or path length) of
the solution.
The assumption is that the amount of light
absorbed is directly proportional to the
concentration of the chemical specie that the
light passes through.
These factors and assumptions can be summarized
as Beer's Law and written as the equation, A
abc. In this equation A is absorbance, a is a
proportionality factor called the molar
absorptivity, b is the path length, and c is the
molar concentration.