Have you also seen my:
"Beer-Lambert Law FAQ's / Spectroscopy FAQ's"?
(FAQ's: Frequently Asked Questions)
Introduction
Many compounds absorb ultraviolet (UV: ˜190 nm -
˜370 nm) or visible (Vis.: ˜370 nm -
˜800 nm) light.
The diagram below shows a beam of monochromatic
[1]
radiation of radiant power P0, directed at a sample solution.
Absorption takes place and the beam of radiation leaving the sample has radiant power P.
 |
|
The amount of radiation absorbed may be measured in a number of ways:
Transmittance: T = P / P0
% Transmittance: %T = 100 T
Absorbance: |
A = log10 (P0 / P)
A = log10 (1 / T) = -log10 (T)
A = log10 (100 / %T)
A = 2 - log10 (%T)
|
|
The last equation, A = 2 - log10 (%T) ,
is worth remembering because it allows you to easily calculate absorbance from percentage transmittance
data.
The relationship between absorbance and transmittance is illustrated in the following diagram:
So, if all the light passes through a solution without any absorption,
then absorbance is zero, and percent transmittance is 100%. If all the light is absorbed,
then percent transmittance is zero, and absorption is infinite.
Now let us look at the Beer-Lambert law and explore it's significance.
This is important because people who use the law often don't understand it -
even though the equation representing the law is so straightforward:
The reason why we prefer to express the law with this equation is because absorbance is directly proportional
to the other parameters, as long as the law is obeyed. We are not going to deal with deviations from the law.
(Why ??)
Let's have a look at a few questions...
Now, suppose we have a solution of copper sulphate (which appears blue because
it has an absorption maximum at 600 nm). We look at the way in which the intensity of
the light (radiant power) changes as it passes through the solution in a 1 cm cuvette.
We will look at the reduction every 0.2 cm as shown in the diagram below.
The Law says that the fraction of the light absorbed by each layer of solution is the same.
For our illustration, we will suppose that this fraction is 0.5 for each 0.2 cm "layer" and
calculate the following data:
|
Total Path length [cm] |
0 |
0.2 |
0.4 |
0.6 |
0.8 |
1.0 |
|
%T |
100 |
50 |
25 |
12.5 |
6.25 |
3.125 |
|
Absorbance [AUs] |
0 |
0.3 |
0.6 |
0.9 |
1.2 |
1.5 |
A(λ, env) =
ε(λ, env)bc
tells us that absorbance depends on the total quantity of the absorbing compound in
the light path through the cuvette. If we plot absorbance against concentration,
we get a straight line passing through the origin (0,0).
 |
Note that the Law is not obeyed at high concentrations.
( THAT's NOT TRUE !!! — Do YOU know why? )
If you don't have any idea, — then you have NOT UNDERSTOOD
Beer-Lambert-Bouguer! Hint: Try to think "GENERAL" !!
[4,5,6]
This deviation from the Law is not dealt with here.
|
The linear relationship between concentration and absorbance is both simple and straightforward,
which is why we prefer to express the Beer-Lambert law (Please - Beer's Law, not Ber's Law)
using absorbance as a measure of the absorption rather than %T.
(Be told: This simple and straightforward relationship between concentration and absorbance is
only for the "Special Beer-Lambert Law" and over a restricted concentration range true! More correct ... ...
.[7][8])
Question : What is the significance of the molar absorbtivity,
ε(λ, env) ?
Answer : To begin we will rearrange the equation A(λ, env)
= ε(λ, env)bc
[*]:
ε(λ, env)
= A(λ, env) / bc
[*]
In words, this relationship can be stated as:
"ε(λ, env)
is a measure of the amount of light absorbed per unit concentration at the measuring wavelength
(λ, env)!".
Molar absorbtivity is a constant for a particular substance
at the measuring wavelength (λ, env), so if the concentration
of the solution is halved so is the absorbance, which is exactly what you would expect.
Let us take a compound with a very high value of molar absorbtivity, say 100,000 L mol
-1 cm-1, which is in a
solution in a 1 cm pathlength cuvette and gives an absorbance of 1 AU.
ε(λ, env)
= 1(λ, env) / 1 x c
Therefore, c = 1 / 100,000 = 1 x 10-5 mol L-1
Now let us take a compound with a very low value of ε(λ, env),
say 20 L mol-1 cm-1 which
is in solution in a 1 cm pathlength cuvette and gives an absorbance of 1.
ε(λ, env)
= 1(λ, env) / 1 ´ c
Therefore, c = 1 / 20 = 0.05 mol L-1
The answer is now obvious - a compound with a high molar absorbtivity is
very effective at absorbing light (of the appropriate wavelength), and hence low concentrations
of a compound with a high molar absorbtivity can be easily detected.
Question : What is the molar absorbtivity of Cu2+
ions in an aqueous solution of CuSO4 ?
It is either 20 or 100,000 L mol-1 cm-1
Answer : I am guessing that you think the higher value is correct,
because copper sulphate solutions you have seen are usually a beautiful bright blue colour.
However, the actual molar absorbtivity value is 20 L mol-1 cm-1 !
The bright blue colour is seen because the concentration of the solution is very high.
b-carotene is an organic compound found in vegatables and
is responsible for the colour of carrots. It is found at exceedingly low concentrations.
You may not be surprised to learn that the molar absorbtivity of
b-carotene is 100,000 L mol-1 cm-1 !
The "CRIB":
[german: "Die Eselsleiter"[E]
]
(for all, who likes so very much molar absorbtivity; molar absorptivity):
"Draw exactly" the picture the equation is telling you, and think of ε(λ, env.)
as of a concentration for your substance, in the manner of: Who many Litres of solvent you need for diluting ONE Mole of your
compound to measure ONE Absorption in the ONE cm Cuvette at your measuring Wavelength.
"That means", if you need a lot of Litres, that you have a strong absorber, and if you need only a few Litres, that
you have a weak absorber in your cuvette. — That's it. Now it's absolute easy to calculate all you like. |
Review your learning
You should now have a good understanding of the Beer-Lambert Law; the different ways
in which we can report absorption, and how they relate to each other. You should also understand
the importance of molar absorbtivity, and how this affects the limit of detection
of a particular compound.
References:
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Division
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