Beer’s Law

Beer’s Law

Lab Report Assistant

This document is not meant to be a substitute for a formal laboratory report. The Lab Report Assistant is simply a summary of the experiment’s questions, diagrams if needed, and data tables that should be addressed in a formal lab report. The intent is to facilitate students’ writing of lab reports by providing this information in an editable file which can be sent to an instructor.

Exercise 2: Beer’s Law Curve and Unknowns

Data Table 1. Concentration and Resistance.

Tube LabelConcentration of Blue Dye in Test Tube (M)Resistance Reading on Colorimeter (Ω)
B2.57 x 10-4 M27.4
125.7
222.9
320.6
417.6
513
69.6
76.7
84.2
92.6
W0 M1.7
CD 110
CD 24.1

Graph 1. Plot of Concentration vs. Resistance.

Plot

Questions

A. Describe possible sources of error in this experiment.

The remainder of these questions are based upon the following scenario:

A testing laboratory has been hired by a company called “Drug Company Q” to analyze a series of over-the-counter drugs that the company produces. In these over-the-counter drugs, the active ingredient is called “Active Ingredient M.” The laboratory technician collected the following data from samples with known concentrations of the Active Ingredient M. That data is shown below in Table 2. Convert %T to absorbance (A=2-log(%T)) and prepare a Beer’s law plot using this data.

Table 2. Known Concentration of M Drugs.

Sample Identification CodeSample Concentration (M)%T
Q50004.00 x 10-417.9
Q50013.20 x 10-425
Q50022.40 x 10-435.7
Q50031.60 x 10-450.2
Q50048.00 x 10-570.8

The technician also collected absorbance readings for the 5 over-the-counter drugs for review. The data collected for the 5 over-the-counter drugs is shown in Table 3.

Table 3. Absorbance Data for Over-the-Counter Drugs.

Sample Identification Code%T
M21050-143.7
M21050-244.1
M21050-345.8
M21050-442.1
M21050-530.1

B. Create a Beer’s law plot and best fit line for the data in Table 1.

C. Use the Beer’s law plot and best fit line to determine the concentrations for samples: M21050-1, M21050-2, M21050-3, M21050-4, M21050-5.

D. The company reported that sample M21050-2 has an M concentration of 0.0003M. Assuming that the results in Question C are 100% accurate and without error, is the company’s statement accurate? What is the percent error between the reported concentration and the concentration calculated in Question C?

E. By law, Drug Company Q must have an M concentration between 2.85 x 10-4 M and 3.15 x 10-4M. Do all samples analyzed meet the legal requirements? Use the information from Question C to explain your answer.

Beer’s Law
Hands-On Labs, Inc.
Version 42-0140-00-03

Review the safety materials and wear goggles when
working with chemicals. Read the entire exercise
before you begin. Take time to organize the materials
you will need and set aside a safe work space in
which to complete the exercise.

Experiment Summary:

In this experiment, you will learn about Beer’s law and
how it correlates absorbance with concentration. You
will be introduced to the concept of spectroscopy and
colorimetry. You will prepare a series of samples and
use a colorimeter to create a Beer’s law curve. From
that curve, you will determine the concentration of
two unknown samples.

EXPERIMENT

Learning Objectives
Upon completion of this laboratory, you will be able to:

● Discuss solutions, solutes, and solvents and their relevance to applied science.

● Define spectroscopy and describe different spectroscopic methods.

● Identify the visible and ultraviolet regions of the electromagnetic spectrum.

● Explain UV-Vis Spectroscopy and how absorbance is measured.

● Define Beer’s law.

● Calculate concentrations and produce serial dilutions of blue dye samples for colorimetry
analysis.

● Collect spectrophotomic data regarding FDC blue dye, from both known and unknown
samples, using a colorimeter.

● Create a Beer’s law plot for a series of samples with known concentrations to determine the
concentrations of unknown samples.

Time Allocation: 2.5 hours

Experiment Beer’s Law

Materials
Student Supplied Materials

Quantity Item Description
1 Bottle of distilled water
1 Dish soap
1 Pair of scissors
1 Roll of toilet paper
1 Roll of paper towels

HOL Supplied Materials

Quantity Item Description
1 Colorimeter assembly
1 Digital multimeter
2 Glass beaker, 100 mL
1 Graduated cylinder, 10 mL
2 Jumper cables
1 Pair of gloves
1 Permanent marker
1 Plastic tweezers
1 Test tube cleaning brush

13 Test tubes, 13 x 100
1 Well plate – 24
1 Experiment Bag: Beer’s Law:

1 – Commercial drink sample #1, 6 mL in dropper bottle
1 – Commercial drink sample #2, 6 mL in dropper bottle
1 – FDC blue dye #1, 2 mL in Pipet
2 – Pipets, empty, short stem

Note: To fully and accurately complete all lab exercises, you will need access to:

1. A computer to upload digital camera images.

2. Basic photo editing software, such as Microsoft Word® or PowerPoint®, to add labels, leader
lines, or text to digital photos.

3. Subject-specific textbook or appropriate reference resources from lecture content or other
suggested resources.

Note: The packaging and/or materials in this LabPaq kit may differ slightly from that which is listed
above. For an exact listing of materials, refer to the Contents List included in your LabPaq kit.

Experiment Beer’s Law

Background
A solution is composed of a solute dissolved into a solvent, with the most common solvent being
water (H2O). In contrast, there is not a most common solute that dissolves in water; rather, the
possibilities for a water soluble solute are immense, ranging from colored dye, to proteins, to
molecules, to inorganic substances. See Figure 1.

Figure 1. Unknown solutions and solutes. A. Variety of liquids containing unknown colored
dye. © Aksenova Natalya B. Molecular structure of the protein glucagon, which may be found in

solution.

Determining the components and concentrations of the solute in a solution is a daily task of
scientists in many disciplines. For example, drug chemists are constantly determining the
concentration of proteins in solutions, food chemists determine the concentrations of FDA food
dyes in beverages, medical doctors determine the concentration of hormones in urine to identify
pregnancy, and environmental chemists determine the concentration of pollutants in the water.
Identifying the components of a solution and determining the concentration of these components
is carried out through a variety of techniques known as spectroscopy.

Spectroscopy

Spectroscopy is the analysis of spectra, typically light or mass spectra, where the spectrum of a
source is used to determine the composition of a substance. There are a wide variety of different
spectroscopic methods, including circular dichroism (measures the absorption of polarized light
to determine secondary structure of proteins), mass spectrometry (vaporizes ions to determine
the chemical composition of a sample), Raman spectroscopy (uses scattered laser radiation to
determine molecular vibrational, rotational, and other energy states of a molecule), nuclear
magnetic resonance (NMR) spectroscopy (uses a magnetic field to spin and vibrate chemical
isotopes which are used to determine the structure of a protein), and ultraviolet-visible
spectroscopy. See Figure 2. Ultraviolet-visible (UV-Vis) spectroscopy uses light in visible and near
ultraviolet regions of the electromagnetic spectrum to measure the wavelength and intensity of
the light absorbed by a sample. See Figure 3.

Experiment Beer’s Law

Figure 2. NMR and Mass Spectrometry. A. 900 MHz NMR spectrometer. © Charlesy B. Mass
spectrometer.

Figure 3. Electromagnetic spectrum. The visible region of the spectrum is located in the
wavelength range between 400 nm and 700 nm. The ultraviolet region of the spectrum is

located in the wavelength range between 400 nm and 200 nm.

Light in the ultraviolet region is
the light we absorb directly from

the sun. This light is beneficial as it
provides humans with vitamin D,
and also harmful because it causes
sunburns and possibly skin cancer.

Experiment Beer’s Law

UV-Vis Spectroscopy

In UV-Vis spectroscopy, a beam of light at a specific wavelength is passed through a cuvette
containing the sample to be analyzed. The sample absorbs some of the light and the remaining
light, which is not absorbed by the sample, passes through the sample and is detected by the
spectrophotometer. The intensity of the light before it passes through the sample is referred
to as “Io,” while the intensity of light after it passes through the sample is referred to as “I”, or
transmittance. See Figure 4.

Figure 4. Measurement of spectrophotometer. The intensity of the light before passing through
the cuvette (Io) and the intensity of the light that has passed through the cuvette (I). © adapted

from mtr

A UV-Vis spectrophotometer measures absorbance, which is related to the transmittance (or
transmission) of light through a solution. Absorbance is the measure of the light intensity that
is absorbed by a sample and is calculated as shown in the equation below. Most UV-Visible
instruments carry out this calculation automatically, which allows absorbance to be read directly
from the instrument.

Experiment Beer’s Law

Beer’s Law and Colorimeter

Absorbance is a dimensionless quantity which can be used to determine the concentration of
a sample through Beer’s law. Beer’s law, also known as the Beer-Lambert-Bouguer law, math-
ematically expresses the relationship between absorbance and sample concentration:

As both the molar extinction coefficient and the path length of the cuvette are constants,
the concentration of the sample is directly proportional to absorbance. As absorbance and
concentration are directly proportional to one another, absorbance can be plotted as a function
of concentration to create a Beer’s law plot. A Beer’s law plot is a graph showing the linear
relationship between absorbance and concentration that can be fit to a straight line from which
the concentration of an unknown sample can be calculated. See Figure 5.

Figure 5. Beer’s law plot.

Experiment Beer’s Law

A colorimeter is a type of spectrophotometer which is used to measure the light transmitted
through a sample at a specific wavelength. For this experiment, a specially designed colorimeter
will be used to determine the concentration of FDC blue dye in a variety of known and unknown
samples. The colorimeter used in this experiment utilizes a red LED light at a wavelength of 650
nm. The light passes through the sample, where it is detected by a cadmium sulphide photocell,
located on the other side of the colorimeter. The darker the solution, the more light will be
absorbed by the sample and less light will be detected by the photocell. The intensity of the light
will be recorded with a multimeter as electrical resistance (in ohms Ω), and is directly proportional
to the concentration of dye in the sample. The electrical resistance functions as the absorbance in
a Beer’s law plot, as shown in Figure 5.

Experiment Beer’s Law

Exercise 1: Colorimeter and Sample Preparations
In this exercise, you will prepare the colorimeter and also prepare the samples for evaluation with
the colorimeter.

Procedure

Part 1: Colorimeter Assembly

1. Gather all of the materials needed for the experiment, as noted in the materials list.

2. Ensure the multimeter is in the “off” position. Set the multimeter dial to 200k in the Ω section.
See Figure 6.

3. Place the end of the red cable into the circular VΩmA slot of the multimeter. Place the end of
the black cable into the circular COM slot of the multimeter. See Figure 6.

Figure 6. Multimeter with black and red cables. Note that the dial is set to 200k in the Ω
section.

4. Attach an alligator clip to the end of the red cable and also attach an alligator clip to the end
of the black cable. See Figure 7.

Note: Your alligator clips may both be encased in the same color, or may be two different colors. The
color of the alligator clip does not impact the experiment and any color alligator clip can be attached
to either color (red or black) cable.

Experiment Beer’s Law

Figure 7. Alligator clips attached to red and black cables.

5. Remove the colorimeter from the box and ensure that the power switch is in the off position.
See Figure 8.

Figure 8. Colorimeter in off position. The colorimeter is in the off position when the switch is
directly over the “0.”

Experiment Beer’s Law

6. Remove the bottom cover of the colorimeter and connect the battery. Then re-snap the
bottom cover into the colorimeter. It is not necessary to insert the screws, but do keep them
in your lab kit. See Figure 9.

Figure 9. A. Battery connected. B. Bottom cover snapped into colorimeter.

7. Attach the alligator clip that is clipped to the red wire into the red hole of the colorimeter, and
attach the alligator clip that is clipped to the black wire into the black hole of the colorimeter.
See Figure 10.

Part 2: Sample Preparations:

Figure 10. Completed and labeled multimeter/colorimeter assembly.

Experiment Beer’s Law

8. Put on your safety gloves.

9. Use the graduated cylinder to measure 50.0 mL of distilled water and place it into a clean,
100-mL glass beaker.

Note: This experiment uses a 10.0-mL graduated cylinder, so you will need to measure 10.0 mL five
times to reach 50.0 mL.

10. Use scissors to snip the FDC blue dye pipet open. To the beaker containing 50.0 mL of distilled
water, add exactly 10 drops of the blue dye. Gently swirl the beaker to distribute the blue dye
throughout the water.

Note: The beaker containing the diluted blue dye is now referred to as the “standard blue dye.”

Note: 10 drops of blue dye is equal to 0.5 mL, and the initial concentration of the FDC blue dye in
the pipet is 0.026M.

11. Review the following M1V1 = M2V2 equation and Table 1 used to calculate the initial
concentration of the standard blue dye. You will use this equation in step 18 to complete Data
Table 1 in your Lab Report Assistant.

Table 1. Sample Preparations.

Tube Label Volume of Distilled
Water (mL)

Volume of Standard
Blue Dye (mL)

Total volume in Test
Tube (mL)

B 0 5.0 5.0
1 0.5 4.5 5.0
2 1.0 4.0 5.0
3 1.5 3.5 5.0
4 2.0 3.0 5.0
5 2.5 2.5 5.0
6 3.0 2.0 5.0
7 3.5 1.5 5.0
8 4.0 1.0 5.0
9 4.5 0.5 5.0
W 5.0 0 5.0

Experiment Beer’s Law

12. Fill the second clean, 100-mL glass beaker with distilled water.

13. Use the permanent marker to label 1 of the empty, short-stem pipets “distilled water,” and
place this pipet into the beaker containing the distilled water.

14. Use the permanent marker to label the second empty, short-stem pipet “blue dye” and place
this pipet into the beaker containing the standard blue dye.

15. Remove the 11 test tubes from their wrappings and use the permanent marker to label the
test tubes as follows: “W, 1, 2, 3, 4, 5, 6, 7, 8, 9, B.” It is very important that the labels be as
close to the opening of the test tube as possible. See Figure 11.

16. Place the labeled test tubes into the 24-well plate which is to be used as a test tube holder.
See Figure 11.

Figure 11. Example of labeled test tube in 24-well plate. It is important that the label be as close
to the top of the test tube as possible.

17. Fill each of the 11 test tubes with the standard blue dye and distilled water, as described
in Table 1. For example, in Tube 1, use the pipet in the standard blue dye to fill the 10-mL
graduated cylinder with 4.5 mL of the standard blue dye. Then use the pipet in the distilled
water to fill the graduated cylinder to the 5.0-mL mark with distilled water. Next, carefully
pour the contents of the graduated cylinder into the test tube labeled “1.”

Note: Rinse the graduated cylinder with distilled water and dry the graduated cylinder after each
use.

18. Use the M1V1 = M2V2 equation and example in step 10 to calculate the final concentration of
blue dye in each of the test tubes. Record the final concentrations for each test tube in Data
Table 1.

19. Leave all preparations set up for use in Exercise 2.

Experiment Beer’s Law

Exercise 2: Beer’s Law Plot and Unknowns
In this exercise, the student will use the samples prepared in Exercise 1 to create a Beer’s law
plot. The plot will be used to determine the concentration of FDC blue dye in 2 commercial drink
samples.

Procedure

1. Use the permanent marker to label one of the remaining clean test tubes “CD1” and the other
“CD2.” Again, label as close to the test tube opening as possible.

2. Fill test tube CD1 with 5 mL of the commercial drink #1 sample from the dropper bottle in the
experiment bag. See Figure 12.

Figure 12. Adding solution to test tubes.

3. Fill test tube CD2 with 5 mL of the commercial drink #2 sample from the dropper bottle in the
experiment bag.

4. Turn on the multimeter and then turn on the colorimeter by moving the switch from “0” to
“II.” This will cause a red light to appear inside of the colorimeter.

5. Pick up the test tube labeled “B,” wipe the outside with the piece of facial tissue to be sure it
is clean and to minimize error, then place the test tube into the colorimeter chamber. Place
the black cap onto the top of the chamber.

Experiment Beer’s Law

Experiment Beer’s Law

6. Read the resistance on the multimeter and record in Data Table 1.

7. Carefully use the plastic tweezers to remove the test tube from the colorimeter chamber.

8. Repeat steps 6 through 8 for all remaining samples in Data Table 1.

9. Turn off both the colorimeter and the multimeter.

10. Create a graph by plotting the Concentration of Blue Dye along the x-axis and the Resistance
along the y-axis. Add the equation for the line of best fit (y = mx +b) to the graph. Insert the
graph into Graph 1 in your Lab Report Assistant.

11. Use the equation for the line of best fit to determine the concentrations of commercial drink
samples #1 and #2. Note that in the line of best fit, the resistance equals the “y” variable and
you are solving for the “x” variable (the concentration).

12. Record the concentrations of commercial drink samples #1 and #2 in Data Table 1.

13. When you are finished uploading photos and data into your Lab Report Assistant, save and
zip your file to send to your instructor. Refer to the appendix entitled “Saving Correctly,” and
the appendix entitled “Zipping Files,” for guidance with saving the Lab Report Assistant in the
correct format.

Cleanup:

14. Disassemble the colorimeter and multimeter and clean all glassware.

15. Return all items to the kit for future use.

Questions
A. Describe possible sources of error in this experiment.

The remainder of these questions are based upon the following scenario:

A testing laboratory has been hired by a company called “Drug Company Q” to analyze a series of
over-the-counter drugs that the company produces. In these over-the-counter drugs, the active
ingredient is called “Active Ingredient M.” The laboratory technician collected the following data
from samples with known concentrations of the Active Ingredient M. That data is shown below
in Table 2. Convert %T to absorbance (A=2-log(%T)) and prepare a Beer’s law plot using this data.

Table 2. Known concentration of M drugs

Sample Identification Code Sample Concentration (M) %T
Q5000 4.00 x 10-4 17.9
Q5001 3.20 x 10-4 25
Q5002 2.40 x 10-4 35.7
Q5003 1.60 x 10-4 50.2
Q5004 8.00 x 10-5 70.8

Experiment Beer’s Law

The technician also collected absorbance readings for the 5 over-the-counter drugs for review.
The data collected for the 5 over-the-counter drugs is shown in Table 3.

Table 3. Absorbance data for over-the-counter drugs

Sample Identification Code %T
M21050-1 43.7
M21050-2 44.1
M21050-3 45.8
M21050-4 42.1
M21050-5 30.1

B. Create a Beer’s law plot and best fit line for the data in Table 2.

C. Use the Beer’s law plot and best fit line to determine the concentrations for samples: M21050-
1, M21050-2, M21050-3, M21050-4, M21050-5.

D. The company reported that sample M21050-2 has an M concentration of 0.0003M. Assuming
that the results in Question C are 100% accurate and without error, is the company’s
statement accurate? What is the percent error between the reported concentration and the
concentration calculated in Question C?

E. By law, Drug Company Q must have an M concentration between 2.85 x 10-4 M and
3.15 x 10-4M. Do all samples analyzed meet the legal requirements? Use the information from
Question C to explain your answer.

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