Beer’s Law Experiment
Suppose we shine a narrow beam of light through a small transparent container of a colored
solution.
Container with
transparent sides (e.g.
glass or clear plastic)
containing a colored
solution.
Light beam
???
I think that it is reasonable to expect that if the solution is dilute enough, some of the light will
get through to the other side:
Light beam
Some light gets
through
What happens to the light? It turns out that there are many complicated processes occurring. For
example there are, among other things, reflection of light at the surfaces, scattering of light in the
solution, and absorption of light:
Scattering
Light beam
Reflection at the
surfaces
However, we can control from at least some of these complicated interactions by using two
identical containers (or even better, the same container). Controlling in this way, we can ask
interesting questions about the amount of light that gets through. For example:


How does the amount of light passing through vary when we change the thickness
through which the light passes?
How does the amount of light passing through vary when we change the concentration of
the solution?
These questions were investigated by scientists in 1700’s and 1800’s (Bouger in 1729, Lambert
in 1760, and Beer 1852) and what they discovered is extremely useful to this day. In particular
the answer to the second question is extensively used in chemistry and biochemistry. For us, it is
an excellent example of linear modeling.
What Bouger and Lambert discovered was that if a quantity called the absorbance of the light in
a fairly natural way (described below), there is an approximately linear relationship between
absorbance and pathlength:
What Beer discovered was that, at low concentrations, there is an approximately linear
relationship between absorbance and concentration:
The usefulness of these relationships is that one can find determine the concentrations of
solutions whose concentrations are unknown by measuring the amount of light passing through
them (once one knows the equation of the line for the particular type of solution). We will see
how this process works below.
Technical aside: What is absorbance?
Intensity of light is generally measured in units of power per area (watts per square meter for
example). This concept corresponds exactly to our feeling of the intensity of the light of sun on
a sunny day. We can design instruments to measure intensity of light. Thus we can measure the
intensity of light before and after the light passes through the solution:
Measure Intensity Ibefore
Measure Intensity Iafter
For solutions, the absorbance is defined to be the negative of the base 10 logarithm of ratio of
intensity after to intensity before, i.e.,
A   log10
Iafter
I before
For us, what is important is that this quantity called absorbance is measurable with instruments
and corresponds in a natural way to what we think of as absorbance (namely a high absorbance
means not much light gets through while a low absorbance means a lot of light gets through, an
absorbance of 0 means no light is absorbed at all: Iafter  Ibefore ).
Activity
In this activity you will produce the absorbance curve for a food dye solution by using a simple
colorimeter which measures the absorbance. You will find the regression line that models the
relationship and determine the concentration of an unknown solution.
Materials
Colorimeter with interfacing cable
TI-84 calculator (or computer with LabPro software installed)
1 cuvette with distilled water (the blank)
5 cuvettes with standards for food dye solution
Cuvette with an unknown either A or B or C.
Steps
1. Plug the colorimeter into the calculator. Normally, the EasyData program will come up
automatically and detect the colorimeter. If not, click on Apps and arrow down to
EasyData. The interface software should give the absorbance readings. Make sure that
the colorimeter is set to 635 nm. 635nm is the wavelength of the light being used for the
measurements. Light with wavelength of 635 nm is red. The colorimeter is capable of
using four different wavelengths. More sophisticated instruments, generally called
spectrophometers, are capable of using hundreds of wavelengths. When using a
spectrophometer, one usually chooses the wavelength with the highest absorbance. Of
the four wavelengths available to us, 635 nm gives the highest absorbance, and 635 nm is
rather close the maximum absorbance for this solution.
2. Measure the absorbance for each of the solutions labeled 1 through 5 as follows. Put the
blank in first. Press Cal and wait until the instruments zeroes out. Then put the cuvette
that you want to measure into the colorimeter and take the measurement. Repeat this
procedure for each of the five standards (i.e., put the blank in each time and zero it out).
Make sure that the hatched sides of the cuvette are always parallel to the instrument
(when looking at the instrument straight on). In general, try not to touch the clear sides
of the cuvettes.
Record your data in your calculator as follows. You also can use Excel if it is available
to you.
Solution
0
1
2
3
4
5
Enter this in calculator
Concentration (mol L-1)
Absorbance
L1
L2
0.000
0
1.07835E-06
2.15670E-06
3.23505E-06
4.31340E-06
5.39175E-06
3. Make a scatter plot of the data with concentration on the x-axis and absorbance on the yaxis. Add a best fit regression line. Record the equation of the trendline and the Rsquared value.
4. You will have been given an unknown (A or B or C). Find the absorbance of the
unknown using the colorimeter.
5. Using your regression line, estimate the concentration of the unknown.
What you should hand in
1.
2.
3.
4.
5.
Your data table
Your scatter plot of the data with the linear trendline.
The equation of your trendline.
Your estimated concentration of your unknown A or B or C.
Answer the following question. You will notice that there is variance in the data. For
one thing, the data doesn’t fall exactly on a line. If you make multiple measurements with
the same cuvette over time, you will get slightly different readings. Name at least two
sources of variation in this experiment.