Beer's Law (Modified Vernier)

A spectrophotometer is a device that measures the amount of light (electromagnetic radiation) a solution (sample) absorbs. We will be using a simple spectrophotometer called a colorimeter to measure the amount of light your samples absorb. A sample put into the path of an electromagnetic ray absorb a quantity of energy from that ray and transmits the remaining energy. The amount of transmitted energy is always less than the amount of incident energy.

A detector within the colorimeter measures the amount of light transmitted and reports to you the percentage of light transmitted relative to the incident light. The amount of light energy a sample absorbs (not transmitted) can be found by applying Beer's law. Where the energy absorbed by a sample is a log10 function of the amount of light transmitted.

Light Absorbed = 2 - log(% Transmitted)
-or-
A = 2 - log(%T)

Following this relationship, the amount of light that a solution absorbs is directly proportional to its concentration. Record the following information for your solutions and perform the needed calculations.

You are to prepare five copper(II) sulfate solutions of known concentration (standard solutions). Each is transferred to a small, rectangular cuvette that is placed into the colorimeter. The amount of light that penetrates the solution and strikes the photocell is used to compute the absorbance of each solution.

The concentration of an unknown CuSO₄ solution is then determined by measuring its absorbance with the colorimeter. Using the skills of interpolation and/or extrapolation you should be able to determine the concentration of the unknown sample.

In a dilution the amount of dissolved matter (solute) always remains constant. What changes is the amount of solvent in which the solute is dissolved. This lowers the ratio of solute to solvent and thus the concentration. Dilution problems can be solved with the following formula:

Concentration₁ x Volume₁ = Concentration₂ x Volume₂

PROCEDURE

1. Obtain and wear goggles.

2. Obtain about 30 mL of 0.50 M CuSO₄ stock solution in a small beaker.

3. Label four clean, dry, test tubes 1-4 with the fifth solution being the beaker of 0.50 M CuSO₄). Using the materials provided, mix 10 mL of the following concentrations of solution: 0.08M, 0.16M, 0.24M, 0.32M. Thoroughly mix each solution with a stirring rod. Clean and dry the stirring rod between stirrings. Keep the remaining 0.50 M CuSO₄ in the small beaker to use in the fifth trial.

4. Plug the colorimeter into the adapter cable in Channel 1 of the CBL System. Connect the CBL System to the TI-8X calculator with the link cable using the port on the bottom edge of each unit. Firmly press in the cable ends.

5. Turn on the CBL unit and the TI-8X calculator. Press PRGM and select CHEMBIO. Press ENTER, then press ENTER again to go to the CHEM MAIN MENU.

6. Set up the calculator and CBL for the colorimeter.

• Select SET UP PROBES from the CHEM MAIN MENU.
• Enter "1" as the number of probes.
• Select COLORIMETER from the SELECT PROBE menu.
• Enter "1" as the channel number.
• PERFORM a NEW CALIBRATION.

7. You are now ready to calibrate the colorimeter. First prepare a blank by filling a cuvette 3/4 full with distilled water. To correctly use a colorimeter cuvette, remember:

• All cuvettes should be wiped clean and dry on the outside with a tissue.
• Handle cuvettes only by the top edge of the ribbed sides.
• All solutions should be free of bubbles.
• Always position the cuvette with its reference mark facing toward the white reference mark at the right of the cuvette slot on the colorimeter.

To calibrate the cuvette at 0% and 100% transmittance:

• 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. When the voltage reading displayed on the CBL screen stabilizes, press TRIGGER on the CBL and enter "0" (the "reference") in the TI-8X calculator.
• Turn the wavelength knob of the colorimeter to the Red LED position (635 nm). In this position, the colorimeter is calibrated to show 100% of the red light being transmitted through the blank cuvette. When the displayed voltage reading stabilizes, press TRIGGER and enter "100" in the TI-8X calculator. Leave the wavelength knob of the colorimeter set to the Red LED position for the remainder of the experiment.
• Press ENTER to return to the CHEM MAIN MENU.

8. Obtain about 5 mL of the unknown CuSO₄ in another clean, dry, test tube. Record the number of the unknown in the Data and Calculations table. Rinse the cuvette twice with the unknown solution and fill it about 3/4 full. Wipe the outside of the cuvette, place it into the colorimeter, and close the lid.

9. To find the absorbance of the unknown CuSO₄ solution:

• Select COLLECT DATA from the CHEM MAIN MENU.
• Select MONITOR INPUT from the DATA COLLECTION MENU. The absorbance value of the unknown is displayed on the screen of the TI-8X calculator. When the absorbance reading stabilizes, record its value in a Data and Calculations table (round to the nearest 0.001).
• Press [+] to quit MONITOR INPUT.

10. Set up the calculator and CBL for data collection.

• Select COLLECT DATA from the CHEM MAIN MENU.
• Select TRIGGER/PROMPT from the DATA COLLECTION menu.

11. You are now ready to collect absorbance-concentration data for the five standard solutions. Empty the water from the cuvette. Using the solution in Test Tube 1, rinse the cuvette twice with ~1-mL amounts and then fill it 3/4 full. Wipe the outside with a tissue and place it in the colorimeter. After closing the lid, wait for the percent transmittance value displayed on the CBL screen to stabilize. Then press TRIGGER and enter "0.080" (the concentration, in mol/L) in the TI-8X calculator. The absorbance and concentration values have now been saved for the first solution.

12. Continue collecting MORE DATA. Discard the cuvette contents as directed by your teacher. Rinse the cuvette twice with the Test Tube 2 solution, 0.16 M CuSO₄, and fill the cuvette 3/4 full. Wipe the outside, place it in the colorimeter, and close the lid. When the percent transmittance value displayed on the CBL has stabilized, press TRIGGER and enter "0.160" in the TI-8X calculator.

13. Repeat the Step 12 procedure to save the absorbance and concentration values of the remaing solutions.

14. Select STOP AND GRAPH from the DATA COLLECTION menu when you have finished collecting data. Use RIGHT ARROW to examine the data points along the displayed graph of absorbance vs. concentration. As you move the cursor right or left, the concentration (X) and absorbance (Y) values of each data point are displayed below the graph. Record the absorbance values in your data table (round to the nearest 0.001).

15. To determine if your data is consistent with Beer's law, plot a graph of absorbance vs. concentration. This graph will be similar to the graph you observed in Step 12, except that you will also calculate and plot a linear regression line on the curve. If your data is consistent with Beer's law (a direct relationship between absorbance and concentration), the regression line should closely fit the five data points and should pass through (or near) the origin of the graph.

• Press ENTER, then select NO when asked if you want to repeat. Select QUIT to quit the data collection program.
• Press STAT RIGHT ARROW to display the CALC menu and select LinReg(ax+b).
• Press [2ND] [L1] [,] [2ND] [L2] ENTER. The linear-regression statistics for these two lists are displayed for the equation in the form:

  y = ax+b

  where y is absorbance, x is concentration, a is the slope, and b is the y-intercept. Record the slope, a, in the data table. Note: One indicator of the quality of your data is the size of b. It is a very small value if the regression line passes through or near the origin. The correlation coefficient, r, indicates how closely the data points match up (or fit) the regression line-a value of 1.00 indicates a nearly perfect fit.

• To display the linear-regression curve on the graph of absorbance vs. concentration, first press [Y=]. Press CLEAR to clear the Y1= equation, then press VARS. Select Statistics and press RIGHT ARROW, RIGHT ARROW to display the EQ menu. Select RegEQ to copy the linear regression equation to Y1=.
• Press WINDOW and then set Xmin = 0 and Ymin = 0 (so both axes are scaled from 0).
• Press GRAPH to plot absorbance vs. concentration with the regression line for your data. You can now observe how closely your data comes to a direct relationship (Beer's law).

16. Discard the solutions as directed by your instructor.

Questions

1. Determine the concentration of the unknown CuSO₄ solution by interpolating from your graph.