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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 ℓ is the distance the light travels, c is the concentration of the solution, and ε is an attenuation constant that describes the decreasing of transmitted light as increased light is absorbed for a given 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.

Required materials

  • Spectrometer
  • Cuvettes (SE-8739)
  • 6× cuvettes and lids
  • 2× 50-mL glass beakers
  • 4× 100-mL volumetric flasks
  • 250-mL volumetric flask
  • 19.975 g copper(II) sulfate pentahydrate (CuSO4∙5H2O)
  • Distilled water

Prepare the samples

  1. Prepare 250 mL of 0.32 M copper(II) sulfate (CuSO4). To do so, fill a 250-mL volumetric flask 1/3 full of distilled water, then add 19.975 g of copper(II) sulfate pentahydrate (CuSO4∙5H2O) to the flask and swirl to dissolve. Fill the flask to the line with distilled water.
  2. Prepare 100 mL of 0.16 M copper(II) sulfate. To do so, add 50.0 mL of the 0.32 M copper(II) sulfate stock solution to a 100-mL flask, then fill the flask to the line with distilled water and swirl to dissolve.
  3. Use a similar procedure to Step 2, replacing the 0.32 M stock solution with the 0.16 M solution, to prepare 100 mL of a 0.08 M copper(II) sulfate solution.
  4. Use a similar procedure to Step 2, replacing the 0.32 M stock solution with the 0.08 M solution, to prepare 100 mL of a 0.04 M copper(II) sulfate solution.
  5. Use a similar procedure to Step 2, replacing the 0.32 M stock solution with the 0.04 M solution, to prepare 100 mL of a 0.02 M copper(II) sulfate solution.

Connect and calibrate the spectrometer

Before the experiment, your chosen spectrometer needs to be properly calibrated to both the absence of light and a reference solution. To do this:

  1. Prepare a reference solution by filling a cuvette ¾ full with distilled water. Handle this cuvette only by the lined sides and wipe the smooth sides clean with a lint-free cloth.
  2. Start Chemvue, then connect the spectrometer to the program. The Spectrometry Module should automatically open to the solution spectra page .
  3. Cover the spectrometer's sample chamber to block out ambient light, then select Calibrate Dark at the bottom of the screen. The spectrometer will turn off light sources to perform a calibration. The icon will change to a new appearance when the calibration is complete.
  4. Place the cuvette containing the reference solution into the spectrometer so that one of the clear sides is facing towards the white light source icon.
  5. Select Calibrate Reference to begin the reference calibration. The icon will change to a new appearance when the calibration is complete.

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, and wipe off any fingerprints with a lint-free wipe.
  2. Place the cuvette into the spectrometer's sample chamber, then select Start to begin analysis of the solution.
  3. When you are satisfied with the results, select Stop to end analysis.
  4. Select Scale to Fit to automatically fit the entirety of the collected data on the screen.

  5. Click Select Wavelength to create a coordinates data target. Drag this data target across the curve until it snaps into place on a wavelength you wish to analyze. This will usually be a high point on the curve.

    Note

    If your curve plateaus near the top of the graph, the absorbance in that area is too large to be used for analysis. Select a different wavelength outside of the plateau area.

  6. Once you have found your desired wavelength, select the data target, then click the floating Select Wavelength button to set the currently selected wavelength as the analysis wavelength.

Collect data

  1. Switch to the solution concentration page using the navigation bar.
  2. In the table on the left, select the cells in the column titled Concentration and enter the concentration values for the prepared samples.
  3. Select Start to begin recording data with the highest-concentration sample still in the spectrometer.

  4. Select the cell in the Absorbance column corresponding to the current concentration. Once the Absorbance value stabilizes, select Keep next to the value to record it.

    Note

    A value of 3 indicates that the solution is too concentrated for the selected wavelength.

  5. Remove the previous sample cuvette from the chamber, then replace it with the cuvette containing the next-highest concentration and repeat Step 4.

  6. Repeat Step 5 for each of your samples until you have recorded an Absorbance value for each Concentration value.
  7. Once you have all required Absorbance values, select Stop to end data collection.

Analyze data

  1. In the graph toolbar on the right, select Toggle Live Scan Display to remove the live scan display from the graph, then select Scale to Fit to ensure all of your data is clearly visible on screen.
  2. Select Linear Fit to create a best fit line and display the equation for the line.
  3. Select Unknown Solutions in the bottom left to switch to the Determine Unknown Concentration table.
  4. Place the cuvette containing a solution of unknown concentration into the spectrometer.
  5. Select the Absorbance cell in the table, then select Start to start analyzing the solution.
  6. Once the Absorbance value stabilizes, select Keep to save the recorded value.
  7. Select Stop to end data collection.
  8. Use either the graph or the equation of the line to determine the concentration of the unknown sample. In the table, select the Concentration cell and enter the calculated concentration value.