BeerLambert
Equation
The
BeerLambert equation is one of the fundamental equations
of chemistry. It is used in hundreds of laboratory procedures
across a the large variety of chemical disciplines.
It is based on the absorption of light by a solution:
Figure
1. The light beam enters from the left with an intensity
of Io. Some of the light is absorbed by the sample
in the cuvette, and the light beam exits with a
lower intensity I.
The ratio of I/Io is called the transmittance, abbreviated
as "T":
For
example, if the intensity of the light is reduced to
25% of the incident beam, T = 25/100 = 0.25.
Transmittance
is a useful number, but it is not linearly related to
the concentration of the lightabsorbing species, and
concentration is what we are after. It turns out that
the concentration of the lightabsorbing species is
linearly related to the logarithm of the inverse of
the transmittance:
In words, Equation
2 says the concentration is proportional to the
log to the base 10 of the ratio of the strength
of incoming light "Io" over the outgoing
light, "I". This sounds complicated, but
it really just depends on getting two numbers, I
and Io, which is relatively straightforward.
Since the value for the
log of the ratio Io/I is so useful, it has its own name:
Absorbance, or "A":
Where:
The
absorbance is related to the concentration as shown
in Equation 4:
Where:

A = the absorbance.
It has no units.

e = molar
absorption coefficient, with units of M1 cm1.

C = concentration
of the solute (molar, M).

l = length of the path of light
through the sample, in centimeters. For most cuvettes
this is 1.0 cm.
The
equations says that the absorbance A equals the product
of the molar absorption coefficient, the path length
of the light in the sample, and the concentration of
the solute.
Here
are the steps typically used to apply the BeerLambert
equation to find the concentration of a test species
in an unknown sample:

A set of standards with known
concentrations of the test species are evaluated
in the photometer at a specific wavelength of
light, to obtain I and Io.
Figure 2. A set of
standards with known concentrations can be used
to make a standard curve. In this case the blue
color is a measure of the protein concentration
in the sample.

Equation 3 is used
to calculate A for each solution.

Equation 4 is applied
to graph the absorbance for each of the standards
vs the known concentrations, to make a standard
curve.

The absorbances of
the "unknowns" are placed on the graph
to determine the corresponding concentrations.
Figure 3. The straight
line standard curve is used to determine the concentration
of the unknown sample based on its absorbance. In
this case the unknown had an absorbance of 0.57
which corresponds to a concentration of 18.8 mM.
1) Beer's
Law, from Robert F. Schneider at Stonybrook.edu

Terms and definitions
Solute  chemical that is dissolved in a solution.
Molar absorption coefficient, ε  a measurement of how strongly a chemical species absorbs light at a given wavelength. ε is the Greek letter epsilon.
M  molar concentration
Blank  a sample with no solute. It is used to correct for light that is absorbed or scattered by the solvent, the sample tube, etc.
Standard solutions  solutions with known concentrations of the solute. Used to make a standard curve.
Standard curve  a graph showing the concentration of standard solutions on the xaxis and the absorbance on the yaxis. Used to determine the concentration of the unknown.
