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Beer's law

Determine the concentration of solute in a sample using a spectrometer.

There are several ways to determine the concentration of solute in a solution. Titration is the most common technique, but this process is time-consuming and glassware-intensive. Another technique involves simply shining a light through the solution. A concentrated solution that is dark will absorb a greater amount of light than a dilute solution of a lighter color. Beer’s law states that there is a direct relationship between a solution’s absorbance of light and its concentration. Mathematically, this law states that the absorbance A is equal to the product of εℓc, where ε is an attenuation constant that describes the decreasing of transmitted light as increased light is absorbed for a given solution, ℓ is the distance the light travels, and c is the concentration of the solution. In other words:

A = εℓc

Beer’s law indicates that there is a linear relationship between Absorbance and Concentration. By plotting a calibration curve of solutions of known concentration and their respective absorbance, the concentration of an unknown sample can be determined.

Gather the materials

  • Spectrometer
  • Cuvettes and lids (6)
  • Beakers (2), glass, 50-mL
  • Volumetric flask (4), 100-mL
  • Volumetric flask, 250-mL
  • 0.32 M Copper(II) sulfate (CuSO4)
  • Distilled water

Prepare the samples

  1. Prepare 250 mL of 0.32 M copper(II) sulfate pentahydrate (CuSO4∙5H2O) by filling a 250-mL volumetric flask 1/3 full of distilled water. Add 19.975 g of copper(II) sulfate pentahydrate to the flask and swirl to dissolve. Fill flask to line with distilled water.
  2. Prepare 100 mL of 0.16 M copper(II) sulfate (CuSO4) by adding 50.0 mL of the 0.32 M copper(II) sulfate stock solution to the flask. Fill the flask to the line with distilled water and swirl to dissolve.
  3. Use a similar procedure to step 2 to prepare a 0.08 M copper(II) sulfate solution from 0.16 M copper(II) sulfate.
  4. Use a similar procedure to step 2 to prepare a 0.04 M copper(II) sulfate from 0.08 M copper(II) sulfate.
  5. Use a similar procedure to step 2 to prepare a 0.02 M copper(II) sulfate from 0.04 M copper(II) sulfate.

Calibrate the spectrometer

Before the experiment, the spectrometer needs to be properly calibrated to both the absence of light and a reference solution. To do this, follow the instructions under Two point calibration.

Select an analysis wavelength

  1. Place 4 mL of the most concentrated solution to be analyzed into a cuvette. Always handle the cuvette by the lined sides. Wipe off any fingerprints using a lint-free wipe.
  2. Place the cuvette into the spectrometer as you did in the calibration.
  3. Click Record at the bottom left of the screen to begin analyzing the solution.
  4. Click Stop when you are satisfied with the result.
  5. Click Scale To Fit to rescale your data.

  6. Use the Coordinates tool on the screen to locate a wavelength to analyze on the curve. This is usually a high point on the curve.

    1. Drag the Coordinate tool box to the curve until it snaps in place.

      Tip

      If your curve plateaus near the top of the graph, the absorbance is too large in that area to be used for analysis and another wavelength should be selected.

    2. Once you have found a desirable wavelength, click Accept to the left of the selected wavelength value.

Collect data

  1. Select the Concentration page from the menu at the top of the screen. A table will appear on the left side of the screen that has columns for Concentration and Absorbance.
  2. Select the concentration cells in the column titled Concentration and type over the given values with the concentrations of the samples prepared.
  3. Select Record to start analyzing the solution.

  4. Place the highest-concentration sample into the spectrometer and click the cell in the Absorbance column that corresponds to the respective concentration. Once the absorbance stabilizes, click Accept next to the absorbance to record the value.

    Note

    A value of three indicates that the solution is too concentrated for the selected wavelength.

  5. Repeat the previous step for the samples of lesser concentration and record each of their absorbance values.

  6. Click Stop to stop data collection.

Analyze data

  1. Click Show Live Scan Display to remove the Live Scan Display from the graph.
  2. Click Scale To Fit to rescale your data.
  3. Click Linear Fit to create a best fit line and display the equation for the line.
  4. Place the cuvette containing a solution of unknown concentration into the spectrometer.
  5. Select the Absorbance cell in the Determine Unknown Concentration table at the bottom of the screen.
  6. Click Record to start analyzing the solution.
  7. Once the absorbance stabilizes, click Accept next to the absorbance to record the value.
  8. Click Stop to end data collection.
  9. Use either the graph or the equation of the line to determine the unknown concentration. In the Determine Unknown Concentration table, select the Concentration cell and enter the concentration.