Determining the Concentration of a Solution: Beer’s Law

Purpose
To determine the wavelength (color) of maximum absorbance for a copper (II) sulfate solution.
To examine the relationship between the absorbance and concentration of a copper (II) sulfate solution.
To determine the concentration of an unknown copper (II) sulfate solution.

Introduction
You will be using the Colorimeter shown in Figure 1. In this device, light from an LED light source will pass through the solution and strike a photocell. The CuSO4 solution used in this experiment has a deep blue color. A higher concentration of a colored solution will absorb more light and transmit less light than a solution of lower concentration. The colorimeter will interpret the light received by the photocell and express it both as an absorbance and a percent transmittance value. 

Figure 1 Figure 2

You will prepare five copper (II) sulfate solutions of known concentration (standard solutions). Each solution will be transferred to a small, rectangular cuvette that is placed into the colorimeter. The absorbance of each solution will be measured and recorded. When a graph of absorbance vs. concentration is plotted for the standard solutions, a direct relationship should result, as shown in Figure 2. This direct relationship is known as Beer's Law, and is shown by the equation

A = εcl

where A is the absorbance measured with a colorimeter, ε is the molar absorptivity, a constant for the particular solute you are analyzing, c is the molar concentration of the solute, and l is path length, the distance light travels through the cuvette (usually 1 cm). For a single solute, absorbance and concentration are directly proportional if the path length is constant. When a linear trendline analysis is performed on a graph of absorbance vs. concentration, the slope is equal to the molar absorptivity, ε, if the path length is 1 cm.

The concentration of an unknown CuSO4 solution will then be determined by measuring its absorbance with the colorimeter and using the molar absorptivity from your trendline equation to determine its concentration.

Materials  
computer with Logger Pro 3.2 and Interface 30 mL of 0.50 M CuSO4
Vernier Colorimeter 5 mL of an unknown CuSO4 solution
two 1-mL, two 2-mL pipets (or a micropipet) pipet pump(s) or bulb(s)
1-cm square plastic colorimeter cuvette KimWipes® or similar laboratory wipes
stirring rod two 100-mL beakers
five small, labeled test tubes test tube rack

Procedure
  1. Obtain and wear goggles! CAUTION: Be careful not to ingest any CuSO4 solution or spill any on your skin. Inform the professor immediately in the event of an accident.
         
  2. Pour about 15 mL of 0.50 M CuSO4 stock solution into a 50-mL beaker. Pour about 15 mL of deionized water into a different 50-mL beaker.
         
  3. Into five clean, dry, and labeled test tubes, prepare 5.00 mL of the following solutions by dilution, using the 0.50 M CuSO4 and the pipets available to you in the lab. (Note: If you are unsure of how to read the pipets, please ask. The most common mistake in this lab involves measurements with the pipets. Any time the pipet is used with a new solution, rinse it with that solution before measuring.) Prepare a table on Sheet 1 of an Excel spreadsheet that shows the amount of 0.50 M CuSO4 and amount of water used in each test tube. Stopper and mix the contents of each test tube thoroughly.
     

    Table 1
    Test Tube CuSO4 concentration (M)
    1 0.10
    2 0.20
    3 0.30
    4 0.40
    5 0.50
  1. Save your spreadsheet using a filename convention of: Lastname1 Lastname2 BeersLaw.
         
  2. Connect the colorimeter to the LabPro interface, using an adapter, if necessary. Next, open the Logger Pro application from the desktop or the Start menu. From within Logger Pro, open the "Probes & Sensors" folder, then select the "Colorimeter" folder, and finally the "Absorbance-Conc" file.
         
  3. You are now ready to use the colorimeter. Prepare a blank by filling a cuvette 3/4 full with deionized water. Calibrate the colorimeter at λmax for the copper (II) sulfate solution.

     

    HANDLING CUVETTES: Examine your cuvette to ensure the clear sides are free from scratches. Cuvettes should be wiped clean and dry on the outside with a KimWipe before each measurement. Do not use a paper towel! Handle the cuvettes near the top of the ribbed sides. Solutions should be free of bubbles. If you are refilling a cuvette with a different solution, a small amount of the new solution should be used to rinse the cuvette before filling. Always align the reference mark on the cuvette with the reference mark on the slot of the colorimeter. To avoid inconsistencies from different cuvettes, only one cuvette should be used for the entire experiment.

     

    CALIBRATION of SQUARE COLORIMETERS:  Click the icon on the toolbar used to calibrate the probes.  (Alternatively, select "Calibrate" from the "Experiments" menu.)  Place the blank cuvette in the cuvette slot of the colorimeter and close the lid.  Turn the wavelength knob of the colorimeter to the 0% T position.  In this position, the light source is turned off, so no light is received by the photocell.  Type "0" in the % edit box.  When the voltage stabilizes, click "Keep."  Turn the knob of the colorimeter to the desired wavelength.  In this position, the sample transmits 100% of the light.  Type "100" in the % edit box.  When the voltage stabilizes, click "Keep."  Then click "OK."

    CALIBRATION of ROUNDED COLORIMETERS:  Use the arrow buttons to select the desired wavelength.  With the blank cuvette correctly positioned in the colorimeter, press the blue "Cal" button on top of the colorimeter.  When the red light stops blinking, the colorimeter is calibrated and may be used.

     

    FINDING THE WAVELENGTH OF MAXIMUM ABSORBANCE (λmax): Before making any absorbance measurements with the colorimeter, the wavelength (color) of maximum absorbance must be determined. This may be done by first calibrating the colorimeter at one of the available wavelengths as shown above. Then, place a cuvette containing the most concentrated sample into the colorimeter and measure the absorbance. Repeat this calibration and measurement procedure for the remaining wavelengths on your colorimeter. The wavelength that yields the greatest absorbance reading for this sample is called λmax. Re-calibrate your colorimeter at this wavelength if necessary. This is the wavelength you should use for all of your future measurements. No further calibrations should be necessary.

     

  1. Once you have determined λmax and calibrated the colorimeter at λmax, measure the absorbance for each of the solutions in Table 1, as well as the absorbance of the deionized water blank, by placing them into the colorimeter, aligning the reference marks, closing the lid, and measuring their absorbances. Record the results on Sheet 2 of your spreadsheet that shows the molarity of CuSO4 in each solution and each of their absorbances. Make sure to include the value of the wavelength at which you are making your measurements.
         
  2. Using Excel, prepare a graph that plots absorbance vs. concentration. Obtain the equation of the best-fit line, setting the y-intercept to zero. (Think: why should the y-intercept be set to zero? What does the slope represent in Beer's Law?)
         
  3. Fill a cuvette about 3/4 full with your unknown sample of CuSO4. Record your unknown number. Measure the absorbance of the unknown as before. If the absorbance is greater than any of the measurements used to prepare your trendline, dilute the solution and measure the absorbance again. Take note of the volumes used in your dilution.
        
  4. Use Beer's Law and the equation of your best-fit line to determine the concentration of the unknown solution (use a formula inside a spreadsheet cell). If you diluted your unknown, calculate the concentration of the undiluted solution and report the result. Clearly label the your unknown number and its concentration.
         
  5. Discard the solutions as directed by your instructor. Clean your cuvettes. Do not use test tube brushes or paper towels, as they may scratch the surface of the cuvettes. Use KimWipes to dry the cuvettes.

Lab Report

  1. In this report, you will need to include the title, an introduction (including an introduction to Beer's Law), experimental details, results (the table and graph you made above which can be embedded into a Word document), discussion, and references.
         
  2. As a part of the discussion section, you will need to include the following:
    1. the λmax value (with correct unit), and how it was determined,
    2. the molar absorptivity, ε, of CuSO4 (with correct units) from your trendline equation, your unknown number, and its molar concentration with a brief description of how Beer's Law was used to calculate the concentration,
    3. describe the preparation of 500.0 mL of 0.50 M CuSO4, using solid CuSO4 and water,
    4. using your trendline equation and Beer's Law, calculate the absorbance for 0.25 M CuSO4 at λmax,
    5. any errors that occurred or other observations made.
           
  3. Follow your instructor's directions for submitting this lab report. If you submit electronically, submit only ONE Word file with an embedded spreadsheet, and be sure to follow the filename convention mentioned earlier. If emailing, use "Chem 1061: Beer's Law Law" as the subject line. If you turn in a paper copy, you will need to provide a sample calculation for determining the concentration of your unknown solution.

Written by Lance S. Lund, Anoka-Ramsey Community College. Portions of this lab courtesy of Kirk Boraas, Minneapolis Community and Technical College, and Vernier Software, "Chemistry With Computers".  Updated December 05, 2011.