Exp. 3: Beer's Law

Theory:
Graphs of absorbance vs. concentration, or -log %T vs. concentration are known as Beer's Law plots. They are made by measuring the light absorbed by solutions of varying concentration. The cell width and wavelength of the light are maintained constant. If a linear plot can be obtained (showing that the Beer-Lambert relationship holds for the solution at that wavelength) the plot (or working curve) may then be used in determining the concentration of unknown solutions.

Unfortunately, however, the condition of monochromatic light upon which the Beer-Lambert Law is based is not obtainable in the laboratory. Since more than one wavelength of light passes through a solution at the same moment, deviations from the law are observed over much of the available spectrum, and non-linearity is observed in the Beer's Law plots. An absorbance reading in such a case will indicate a concentration which may be quite different from the actual concentration of the solution. The object, therefore, of much preliminary laboratory work in optical analysis is to find a suitable wavelength band where the deviation from the law will beonly slight or negligible. The spectral curve, obtained in Exp 2, serves as a guide in our search for a desirable wavelength for Cr(III) analysis. The Beer's Law plots, to be obtained in the present experiment, will show the relative desirability of different wavelengths chosen from various portions of the spectrum. From these plots it can be seen that the choice of a wavelength for analysis is to some extent dependent upon the approximate concentration of the solution.

Procedure
The Spec 20 should be turned on at least twenty minutes before any measurements are taken.

Obtain approximately 75 mL of the Cr(III) stock solution (.0500 M) in a small beaker. Make up solutions that are 0.0100, 0.0200, 0.0300, and 0.0400 M in chromium(III) by pipetting 5, 10, 15, and 20 mL respectively into four 25 mL volumetric flasks and diluting each to the mark with distilled water.

By referring to your plot of %T vs. wavelength for the 0.0200 M chromium(III) solution (from Exp 2), select six wavelengths at which to study absorbance as a function of concentration. Include in your selection:

1 and 2. wavelengths at the minima of the curve.

3. a wavelength where %T is at a maximum

4. a wavelength corresponding to a steeply rising portion of the curve.

5. a wavelength corresponding to a steeply descending portion of the curve.

6. the 625 nm wavelength.

Obtain absorbances for Cr(NO3)3 solution for each of the selected wavelengths, in the following manner.

First, turn the wavelength dial to one of the chosen wavelengths. (It is usually easiest to start with the shortest wavelength.)

Then adjust the colorimeter for 0 and 100%T, using the same cuvette for the distilled water "blank" as in Exp. 2. Remove the cuvette from the sample holder and see if the meter returns to "0" (after 10 seconds). If not, reset the "0" and then repeat the adjustment for 100%T. Continue this until "0" and "100" are obtained with the cuvette out, and in, respectively. Next, measure and record the %T and absorbance of the 0.0200 M Cr(III) solution at the six selected wavelengths, using the same cuvette with this solution as you used in Exp. 2. (The spectral curve obtained in Exp. 2 should indicate similar %T values for the wavelengths of light selected above.) BE SURE to set the instrument at 0 and 100% with the "blank" after each change of wavelength setting, as described previously.

Now, discard the 0.0200 M sample in the container provided by the instructor, and rinse the cuvette several times with small portions of your 0.0100 M solution. Pour the 0.0100 M in the cuvette to just below the white circle and record %T and absorbance at each of the 6 wavelengths. Do this also for the other 2 prepared solutions (0.0300 and 0.0400 M Cr(III)) and for the 0.0500 M stock solution, rinsing the cuvette thoroughly with the next solution before making a measurement.

Obtain an unknown Cr(III) solution. Determine the %T and A of this solution at each of the 6 wavelengths.

Finally rinse the cuvettes thoroughly with water and turn OFF the Spec 20. Before leaving the lab, consider your answer to question 3 below.

Treatment of Results
Plot two graphs, (1) %T versus wavelengths, and (2) absorbance versus concentration (Beer's Law Plots ) for each set of data obtained at each of the six wavelengths. The first one should be done by hand and the second using Excel. Although absorbance readings are made directly from the colorimeter dial, it is better to convert the %T readings to absorbance by using your calculator, and then to use the plotting if you are using one of the analog Spec 20's.

Draw a horizontal line across your Beer's Law plots at absorbances equal to 80%T and 20%T. Measurements should be restricted within these two limits, because %T readings greater than "80" and less than "20" allow too large an error in concentration, in comparison with the actual concentration of the substance being measured.

From an appropriate Beer's Law curve, determine the concentration (in moles per liter) of your unknown Cr(III) solution. You should use both the graph itself, as well as the equation of the line to find this concentration.

Also, calculate the concentration of the unknown solution by using Beer's Law, A = abc.

Questions
1. Briefly account for the appearance of the Beer's Law plots obtained in this experiment; i.e., where do the plots appear to deviate from Beer's Law, and why? Summarize for each of the six wavelengths.

2. At which of the six wavelengths is the absorptivity (extinction coefficient) the smallest?

3. Estimate how accurately you can read %T off the colorimeter dial; i.e., ?%T. Estimate how accurately you can determine the wavelength of light passing through the sample; i.e. ? nm.

4. What wavelengths would be most desirable to use in analyzing a solution approximately 0.015 M and a solution approximately 0.055 M in Cr(III), and why? Consider both adherence to Beer's Law and inherent error in the final concentration reported?

Gwen Sibert
Roanoke Valley Governor's School
gsibert@rvgs.k12.va.us