Blue Beer's Law and other Pirate Adventures

by Mike Perona and Koni Stone
CSU, Stanisalus

Light

White light, such as sunlight, is composed of light of several different colors. This is observed by passing white light through a spectroscope, Figure 1. The white light is decomposed into its component colors which are displayed as a continuous spectrum.  There are several spectroscopes in the lab.  Use one to observe several different light sources.  Record your observations in your lab notebook.

Figure 1.  A schematic drawing of a spectroscope, showing the spectrum of white light.

According to the wave model of light, light is energy which travels through space as a wave. The wavelength, l (pronounced "lamb-dah"), of a wave is the distance between two identical points on the wave, Figure 2. The unit of wavelength in the figure is the nanometer, nm.

Figure 2

Light of different colors has different wavelengths, as shown in Figure 3.

Figure 3.  Continuous spectrum of white light

Color

A colored solution appears colored because molecules in the solution absorb only light of certain colors (wavelengths) and not others. Red strawberry Kool-AID, for example, appears red because dye molecules in the solution absorb light of all colors except red.

Figure 4.

The ratio of  incident intensity Io to emergent intensity (I) is called transmittance.  

Therefore, %T = 100%*Io/I. EQ 1

The amount of light absorbed by the sample is expressed in terms of the absorbance, A, defined as

A = log I_o/I    EQ 2

or

A = -log %T/100%  EQ3

where I_o is the incident light intensity and I is the emergent light intensity. The smaller I is relative to I_o , the greater the fraction of light absorbed by the sample and the greater the absorbance. The absorbance depends upon: the wavelength of the incident light, the concentration of the absorbing molecules, and on the sample thickness.

Absorbance depends on wavelength:  The dependence of A on l for red KOOL- AID is shown in Figure 5.

Figure 5.  The absorption spectrum of red KOOL-AID superimposed on the continuous spectrum of white light.  Do you understand  why this KOOL-AID is red?

The maximum absorbance occurs at about 500 nm, and the absorbance is zero at wavelengths above 600 nm. This means that the dye molecules in the KOOL-AID absorb light at wavelengths below 600 nm, which correspond to the colors orange, yellow, green, blue and violet . Red light is not absorbed, and the solution appears red.

Absorbance and sample thickness:  The absorbance of a solution increases with the sample thickness. This is evident if we compare the intensity of transmitted light along the long axis of a pitcher of KOOL-AID with the intensity viewed perpendicular to the pitcher axis.

Figure 6.

Absorbance depends on concentration: The absorbance of a solution increases with the concentration of the absorbing species.   This is Beer's Law and can be represented by the following equation: 

A = ebc                      EQ 4

where A= absorbance, e = a molar absorption coefficient that is specific for each species at a certain wavelength, b = path length and c= concentration.

We can use Beer's Law to determine the amount of an unknown if we generate a standard curve first.  The absorbance of solutions with known concentrations will be measured and plotted as a function of concentration.  (Absorbance versus concentration.)  The resulting straight line can be used to determine the concentration of an unknown.

Beer's Law is only valid for absorbance values between 0.1 and 1, and measurements must be taken at a wavelength maximum.  If measurements are taken on either side of the maximum, then the data will be highly variable

Figure 7.  Sample calibration curve for determining the molarity of an unknown. For this data, if the unknown has an absorbance of .58, then the unknown concentration  is  (0.58/14.3) = 0.04M.

Stockroom: Things to borrow and return on the same day.

• 100 ml vol flask (~$75)
• 250 ml vol flask (~$20)
• 25 ml vol flask (~$15)

Procedure:  

Cu⁺² in solution:  Make a 0.6M aqueous solution of copper(II) sulfate.  Calculate how much copper(II) sulfate you will need to weigh out to make 100.00 mL of a 0.6M solution.  Show this calculation to your lab instructor before you make the solution. Weigh the solid copper(II) sulfate in a small beaker, dissolve in a small amount of water, and transfer to a 100.00 mL volumetric flask to make this stock solution.  Use this stock solution to make 25.00 mL of each of the solutions listed below (A-E).   Make the most dilute solution first. Use the same 25.00 mL volumetric flask and the same pipet for all solutions; you do not need to rinse out the flask or the pipet between solutions.  Prepare Solution A by pipeting 2 mL of the stock solution into a clean 25 mL volumetric flask. Carefully fill the flask to the mark with deionized water. Stopper the flask and mix the solution thoroughly by inverting the flask several times. Poor the solution into a labeled test tube and reuse the 25 mL volumetric flask for the next solution.  (You can pour excess solution down the drain.)

Solution A: 2.00 mL of stock solution diluted to 25 mL with distilled water. 
Solution B: 4.00 mL of stock solution diluted to 25 mL with distilled water. 
Solution C: 6.00 mL of stock solution diluted to 25 mL with distilled water. 
Solution D: 8.00 mL of stock solution diluted to 25 mL with distilled water. 
Solution E: 10.00 mL of stock solution diluted to 25 mL with distilled water. 

Calculate the molarity of each solution (A-E).

Cu⁺² in pennies:  First, place a pre-weighed pre-1982 penny in a beaker and then add 25 mL of nitric acid (6M). [Caution, this should be done with great care and WORK IN A FUME HOOD; this acid will cause tissue damage.]  Then, place a pre-weighed 1983 or older penny in a beaker and add 25 mL of 6M nitric acid to it.  Heat the beakers with a hot plate--in the hood!  Do not let the solution boil.  The reaction gives off a brown gas that is toxic so do not put your sniffer near the beakers!  

Observe the reaction and record observations in your notebook. 

What reactions have occurred?  Be sure to write these balanced equation(s) for the reaction(s) in your lab notebook and restate them in the discussion of your results.

Determination of the l_max for Cu⁺²:  Observe the color of your solutions.  Based on the color that you see, predict the  wavelength maximum for Cu⁺².  Now determine the wavelength for maximum absorbance by determining the absorbance of solution E  at these wavelengths:  400, 420, 440, 460, 480, 500, 520, 540, 560, 580, 600, 620, 640, 660, 680, 700.  Then make a plot of Absorbance versus wavelength.

Directions for measuring the absorbance of a standard solution with the Spectronic 20 spectrophotometer. (See Figure 8 below.)

1. Be sure that the instrument is turned on.  These instruments need 15 minutes to warm up!

2. Set the wavelength knob to the first wavelength on the list.

3. Using the zero adjust knob on the left side, set the needle to read 0% transmittance (% T) on the top scale of the meter. Nothing should be in the sample compartment.

4. Fill one cuvette with deionized water, wipe it with a tissue, and insert it in the sample compartment with the line on the cuvette aligned with the line on the sample holder.  Close the cover.

5. Use the 100% adjust knob on the right hand side to set the needle to read 100% T with the water-containing cuvette in the sample holder. Remove the cuvette and set it aside.  Be certain the instrument can be scaled to 100% transmittance for water (blank) at both 400 nm and 700 nm before making all measurements from 400-700 nm.

6. Rinse the other cuvette with the standard solution, and fill it with the solution. Wipe it with a tissue, and insert it in the holder. Make sure that the cuvette is properly aligned as before. Read the absorbance to three significant figures on the bottom scale of the meter.

7. For each new wavelength, you will need to repeat this procedure.  

8.  Record the wavelength and the absorbance in your notebook.  Make a plot of your data to determine the wavelength for maximum absorbance.  To find the exact value, you may want to collect more data for wavelengths that are close to the maximum on your graph.  For example, if  400 and 420 nm gave the same large amount, you may want to take a measurement at 410 nm.

Figure 8. The Spectronic 20 spectrophotometer

Determination of a calibration curve:  Once you have determined the  l_max,  measure the absorbance of each standard solution (A-E) at this single wavelength.  Make a graph of absorbance versus concentration (molarity) of Cu⁺².  There will be a linear relationship between absorbance and molarity. Find the best line through your data using linear regression.  You will use this line to determine the molarity of the Cu⁺² in your dissolved penny solution.  (See figure 7.)

Determination of %Cu in a penny:  Pour your dissolved post 1982 penny solution into a 25 mL volumetric flask and fill it to the line with distilled water.  Stopper the flask and mix thoroughly by inverting several times.  Take extreme care and wear gloves as nitric acid will cause tissue damage.  Work in the hood while you are transferring and mixing solutions.  Pour sodium bicarbonate on any spills on the bench.  Rinse affected skin immediately!  

Pour your pre1983 (1982 or earlier) penny solution into a 250 mL flask and fill it to the line with distilled water.  Stopper the flask and mix thoroughly by inverting several times. 

Measure the absorbance at the l_max for each unknown (penny) solution.  Use your standard curve to determine the molarity of Cu⁺² present in each solution.  Calculate the moles of Cu⁺²,  moles of Cu and grams of Cu in the penny.  Then, calculate the percent Cu in each of your pennies.

%Cu = 100*(Cu mass/Penny mass)           EQ5

Data/Results 

Make sure that you have the following in your report: 

1. Observations from the reactions of pennies with nitric acid
2. Graph of absorbance vs wavelength, be sure to indicate  l_max
3. Sample calculation for the energy of the electronic transition that accounts for this absorbance.
4. Graph of absorbance vs molarity of Cu⁺² with linear regression line for your standard curve.
5. Sample calculations for: molarity of standards, molarity of penny solution, moles of Cu⁺², moles of Cu, grams of Cu and %Cu in a penny.

Conclusion

Be sure to write this section with complete sentences in well organized paragraphs.  Please write the balanced equations and state your results: What did you observe for the reactions of nitric acid with pennies.  What is l_{max ,} and how does that compare with what you predicted?  What is the energy of the electronic transition that accounts for this absorbance?  What colors are being absorbed by the copper(II) sulfate solution.  What percent copper was in each penny?  How did you determine this?  What are the possible sources of error that may have affected your results.  

Special thanks to Matt Page for technical and editorial assistance as fulfillment for his service based learning requirement for CHEM 4400.

last updated 06/14/2004