CHEM 161: Beer’s Law and Analysis of a Sports Drink
Introduction Although sunlight appears white, it contains a spectrum of colors. A rainbow actually
shows this range of colors in visible light: violet, blue, green, yellow, orange, and red.
What we see as the color of an object depends on the particles present in the object and
how they interact with white light. An object absorbs specific wavelengths or colors of
visible light and transmits the remaining colors. Consider the following examples:
Figure 1: Light Absorption and Emission
(a) If the particles/molecules do not absorb any light, the reflected light is white,
and the object appears white.
(b) If the particles/molecules absorb all light, no light is reflected, and the object
appears black.
(c) If the particles/molecules selectively absorb some colors but reflect other, the
object appears to be the color that is reflected. In the example below, the object
absorbs red-orange light and appears to be blue-green in color.
In the same way the colors of solutions depend on the solute and solvent particles
present. For colored solutions, the more concentrated the solution, the more light it
absorbs and the darker its color. In everyday life this can be observed when soda from a
dispenser seems unusually light in color. The light shade of the soda indicates the
dispenser is low in syrup (or even missing syrup altogether), so the light color indicates
the low concentration of syrup in the soda.
Because people expect specific colors for certain drinks or food, color additives are
often used to enhance their natural color. For example, yellow food coloring may be
added to lemonade or oranges that appear dull or brownish may be sprayed with Citrus
Red No. 2 to give them brighter orange color and make them more appealing.1
In 1900, there were about 80 man-made food dyes available to consumers. However,
some of them proved to be dangerous. For example, Amaranth (also known as Red No.
2) was banned for use in the US by the Food and Drug Administration (FDA) in 1976
because it was a suspected carcinogen. Fear about the dye even caused red M&M’s to
be discontinued from 1976 until 1985 even though red M&M’s never used Red No. 2.
(Red Nos. 3 and 40 were always used for red M&M’s.) Improved food safety standards
1
From the U.S. FDA/IFIC brochure,“Food Color Facts” (Jan 1993) http://www.cfsan.fda.gov/~lrd/colorfac.html
CHEM 161 Lab Manual S2012
page 69
resulted in FDA approval of seven color additives for use in foods. One of these is the
Food, Drug and Cosmetic (FD&C) certified additive Allura Red (also known as FD&C
Red No. 40), the same food coloring used for M&M’s. The image below shows the balland-stick model for the molecule superimposed over the space-filling model, as well as
the Kekule structure (in which hydrogen atoms and lone pairs of electrons are not
shown).
Figure 2: FD&C Red No. 40, Allura Red (Na2C18H14N2O8S2)
In this experiment, a sample of a sports drink will be analyzed to determine the molar
concentration of Allura Red present. This will be done using spectrophotometric
analysis, a method that determines the concentration of colored substances in solution
based on the light absorbed.
SpectroPhotometric
Analysis
A spectrophotometer (often called a Spec-20 or UV-Vis) is an instrument that measures
the intensity of a light beam of a given wavelength that passes through a sample. Light
of a given wavelength passes through a sample, which absorbs some of the light, and the
light not absorbed continues to the detector (see schematic below):
When more colored molecules are present, they can absorb more light, and less light
goes through to the detector; thus, the concentration of the solution can be determined
by calculating the amount of light passing through a sample and hitting the detector.
This amount of light absorbed by the substance is called the absorbance (A) of the
solution.
A solution containing a colored substance absorbs specific wavelengths (or colors) of
2
from http:// http://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law
CHEM 161 Lab Manual S2012
page 70
Wavelength
of Maximum
Absorption
(λmax)
visible light and transmits the remaining wavelengths (or colors), so there is often an
optimal color (and corresponding wavelength) of light at which a solution would absorb
the most light. The selection of this optimal wavelength, called the wavelength of
maximum absorption (λmax), is critical to ensure the sample absorbs the most light to
make an accurate measurement. The λmax is determined by measuring the absorbance of
a sample at various wavelengths then preparing a plot of wavelength (x-axis) versus
absorbance (y-axis), as shown below. For the example above, λmax is about 610 nm.
Figure 3: Absorbance versus Wavelength Plot to determine λmax
λmax
The relationship between concentration and absorbance can be summarized by using the
Beer-Lambert Law2 (known more commonly as Beer’s Law), which relates the
amount of light absorbed by a material with the properties of that material.
The transmission of light through a substance
is measured as a mathematical quantity called
transmittance, T, which is defined as
follows:
T= I
I0
(1)
where I0 and I are the intensity of the incident
light and the transmitted light, respectively.
Percent transmittance (%T) is defined as
follows:
%T = I ×100%
I0
(2)
The absorbance, A, is then defined as follows:
A = −log T
⎛
⎜ I
= −log ⎜
⎜I
⎝ 0
⎞
⎟
⎟
⎟
⎠
or
A = 2 − log %T
(3)
Thus, the absorbance has a linear relationship with the concentration of the colorabsorbing molecules or particles in the solution, which can be shown as follows:
A= εlc
(3)
where c is concentration, l is the path length (the length of solution the light moves
CHEM 161 Lab Manual S2012
page 71
through), and ε is the molar absorptivity (the measure of how much light the sample
absorbs at a given wavelength).
Beer’s Law This linear correlation between absorbance and concentration for a colored substance or
Plot solution is often represented as a Beer’s Law plot of the absorbance versus
concentration. In the Beer’s Law plot below, concentration is in units of molar (M).
Beer's Law Plot Example
0.700
0.600
0.500
Absorbance
y = 111.63x
0.400
0.300
0.200
0.100
0.000
0.000E+00
1.000E-03
2.000E-03
3.000E-03
4.000E-03
5.000E-03
6.000E-03
Concentration (M)
To prepare a Beer’s Law plot, a set of solutions of known concentration (called
standards) must be prepared by diluting a stock solution to make less concentrated
solutions. The absorbance for each solution is then measured at the wavelength of
maximum absorbance, and the data is used to prepare the plot.
A regression line for the data is generated, and points giving a linear plot with a positive
slope indicate a direct correlation between the absorbance and the concentration. The
absorbance of a solution of unknown concentration is then measured, and if the
absorbance is within the range plotted for the the Beer’s Law plot, the concentration
corresponding to that absorbance can be determined.
The best straight-line fit obtained from the plot has the form y = mx + b, for which the
y-intercept, b=0, since a solution with a zero concentration would have an absorbance of
zero. Thus, rewriting the line equation in terms of Beer’s Law,
y= m x
A= εlc
(4)
shows the slope, m, is equal to the product of ε×l and can be used to calculate the
concentration of a solution given its absorbance. For example, the Beer’s Law plot bestfit line equation above (y = 111.63x), has a slope equal to 111.63M-1, where the units of
CHEM 161 Lab Manual S2012
page 72
M-1 result from absorbance being unitless and concentration having units of molar (M).
The concentration for a solution with a measured absorbance of 0.359 would then be
calculated as follows:
A = 111.63 c
c=
A
111.63 M
-1
=
0.359
111.63 M
-1
= 3.22 × 10 -5 M
The calculated concentration can also be checked using the Beer’s Law plot on the
previous page, where the broken red line shows the calculated concentration can be
estimated to be between 3.2×10-5M or 3.3×10-5M. However, the concentration can be
calculated with more significant figures using the line equation generated from the
regression line.
Because the direct correlation between absorbance and concentration cannot be assumed
outside the range for the absorbance values measured, one cannot extrapolate a
concentration corresponding to an absorbance greater than the highest measured
absorbance for the standards used. In this case, the sample solution must be diluted until
the measured absorbance is within the range of absorbance values for the measured
standards.
In this experiment, you will use a spectrophotometer to analyze a sample of a red
sports drink to determine its molar concentration of Allura Red. A set of four standards
will be prepared by diluting a sample of Allura Red, and the absorbance for each
sample will be measured, so a Beer’s Law plot can be prepared. Finally, the absorbance
for a red sports drink will be measured. If the absorbance for the sports drink is outside
of the range of absorbance values measured for the standards, the solution will be
diluted until an appropriate absorbance is measured. Finally, the concentration of
Allura Red in the drink will be calculated using the line equation obtained from the
Beer’s Law plot and accounting for any dilutions carried out.
Using a Laboratory Techniques
Volumetric
Flask Using a Volumetric Flask: Volumetric Flasks are calibrated to hold an exact volume
of liquid when the bottom of the meniscus is exactly on the line at the neck of the flask.
In this lab, 50 mL volumetric flasks are used to prepare the standard solutions. These
volumetric flasks are calibrated to prepare 50.00 mL (±0.01 mL). To prepare a
solution, transfer the indicated volume of the standard solution to the volumetric flask,
fill the flask about halfway with DI water, stopper the flask, then swirl the solution to
thoroughly mix it. Next, slowly fill the flask to just below the line with DI water. If
your water bottle cannot be controlled to deliver DI water drop by drop, use a dropper
or disposable pipet to add the last few drops. If you add water above the line marked
on the neck of the flask, you will have to make a new solution. Again, stopper the
flask, and invert it several times to get a uniform solution.
CHEM 161 Lab Manual S2012
page 73
Procedure Part I: Preparing the Standard Solutions
Work in pairs.
Turn on the spectrophotometer before preparing the solutions since it requires about
15 minutes to warm up.
Check out the following from the stockroom: a 25.00 mL pipet, four 50.00-mL
volumetric flasks, and two cuvettes.
Each student should prepare at least one solution (in Part I) and take at least one
absorbance reading (in Parts II and III). Each pair will make four Allura Red standard
solutions, labeled #’s 1-4. Solution #1 is the stock solution prepared by the Chemistry
stockroom. Record the concentration of the stock solution in your lab notebook.
To prepare solutions #2-4, students will carry out a serial dilution.
1. Make sure the volumetric flasks are clean. If they appear dirty, wash them with soap
and water, and do a final rinse with DI water. Dry the outside completely. The inside
may remain wet since DI water will be added to the flask. Label three of the
volumetric flasks #2-4.
Serial 2. Obtain about 50 mL of the stock solution in a 100 mL beaker. Transfer about half of
the solution to a large test tube labeled #1. Use only about 10 mL of solution to
Dilution
condition a 25.00 mL volumetric pipet, then use the pipet to transfer 25.00 mL of the
stock solution to the clean volumetric flask #2. Add deionized (DI) water from your
water bottle to half fill the flask, stopper the flask or use parafilm to cap it, and swirl
to get a uniform solution, then add more DI water to just below the line on the
narrow neck of the flask. Add DI water drop by drop to the mark. Be sure the
bottom of the meniscus does not go above the line, or you will have to remake
that solution! Stopper the flask and invert it several times to thoroughly mix the
solution.
3. Transfer half of Solution #2 from the volumetric flask to a clean, dry beaker. Rinse
and condition the 5.00 mL volumetric pipet and use it to transfer the Solution #2 to
the clean volumetric flask #3. Fill the flask with DI water to obtain a total volume of
50.00 mL of Solution #3. Repeat this process for Solution #4.
4. Stopper all your labeled flasks, inverting them several times to thoroughly mix the
solutions, then set them aside for Part III.
Part II: Finding the λmax for the Allura Red Solutions
Each pair will use Solution #1 (the most concentrated stock solution) to determine the
wavelength of maximum absorption (λmax) . Before taking each absorbance reading, be
sure to recalibrate the Spec-20 using DI water.
Note: Use only the cuvettes in the Spec-20. Cuvettes are made from spectroscopicgrade glass, which allows the maximum of light to pass through.
CHEM 161 Lab Manual S2012
page 74
Using a 1) Prepare a blank by using a disposable pipet to fill one cuvette 2/3 full with DI water
then fill a second cuvette 2/3 full with your most concentrated solution (Solution #1).
Spec-20
Remove any air bubbles clinging to the walls of a cuvette by tapping the cuvette
gently to get the bubbles to rise to the top of the solution and escape. Use a “Kimwipe” to wipe off the outside of each cuvette to remove all fingerprints. Hold the
cuvette by the top to avoid marking the glass with fingerprints.
2) Use the toggle to switch the Spec-20 from Absorbance (A) to Transmittance (T).
(Note that as you switch the toggle, the red indicator light will move back and forth
from A to T on the display on the Spec-20.)
Note: The Spec-20 must be reset to read the maximum absorbance for the solution
being analyzed at different wavelengths. Thus, the instrument must be rezeroed and the transmittance must be adjusted to 100% whenever the
wavelength is changed.
3) Follow steps a–e below to determine the absorbance for each wavelength.
a) Use the dial on the top-right to set the wavelength to 400 nm.
b) Make sure the cover of the sample holder is closed and empty and use the left
knob on the front of the Spec-20 to set the T to 0%.
c) Clean the cuvette containing the DI water with a Kimwipe to remove all prints.
Open the sample holder, and note the line at the front by the cuvette holder. Place
the cuvette with the blank (DI water) in the holder by lining up the line on the
cuvette with the line on the Spec-20 to ensure that the light shines through the
clear sides of the cuvette. Use the right knob to set the T to 100%. This ensures
that any light absorbed by the blank (i.e., DI water in this experiment) is ignored,
so only the light absorbed by the Allura red is measured.
d) Use the toggle to switch the Spec-20 from Transmittance (T) to Absorbance (A).
The Spec-20 is now set to read the absorbance of your sample. DO NOT change
any settings!!! Clean the cuvette containing Solution #1 with a Kimwipe to
remove all prints. Remove the cuvette with water, and replace it with the cuvette
containing Solution #1.
e) Record the absorbance on the display. If it reads a small negative number, record
an absorbance of 0 for that reading.
Determining 4) Repeat steps a-e for a wavelength of 425 nm. Record the absorbance value for
λmax
Solution #1 at this new wavelength, then repeat steps a-e to obtain absorbance
readings at wavelengths every 25 nm between 400 and 600 nm.
5) Repeat steps a-e in 5-nm increments for three wavelengths above and three
wavelengths below the maximum. For example, if you found the highest absorbance
at 450 nm, repeat steps a-e for wavelengths of 455, 460, 465, 445, 440, and 435 nm.
6) The wavelength that gives the maximum absorbance for these readings is the λmax to
use for Part III below.
7) Have your instructor approve your chosen λmax before you continue to Part III.
CHEM 161 Lab Manual S2012
page 75
Measuring
Absorbance
for the
Standard
Solutions
Part III: Measuring Absorbance Values for the Standard Solutions and Sports
Drink
Using the λmax found in Part II you will determine the absorbance for each solution
made in Part I. You wil also analyze the sports drink sample for its Allura Red content.
1) Set the wavelength setting to the λmax found in Part II, then place the blank (DI
water) cuvette in the Spec-20. Use the A/T switch to display absorbance (A), and
check that the A reads zero for the water sample. If not, repeat step 3, parts a-e, from
Part II to re-calibrate the Spec-20 for the λmax. Do NOT change any settings again
for the remainder of Part III.
2) Empty the cuvette with DI water, and condition (rinse) it twice with small amounts
of Solution #4 (least concentrated solution prepared). Fill the cuvette 2/3 full with
that solution. Wipe the cuvette off with a Kim-Wipe before placing it in the sample
holder. Close the lid, then read and record the absorbance of that solution. Do not
change the wavelength or change any other settings on the Spec-20 while you
obtain absorbance readings for the standard solutions!
3) Repeat step 3 and record the absorbance at the λmax for all of the standard solutions
made in Part I.
Note: Save the standard solutions until after your Beer’s Law plot has been
completed and approved by the instructor.
4) Obtain about 15 mL of the sports drink to be analyzed in a 50 mL beaker. Record the
name of the sport drink in your lab notebook.
the cuvette used to read absorbance values for the standards in step 3, then
Analyzing a 5) Empty
rinse it several times with DI water. Condition the cuvette with a small portion of the
Sports
sports drink, then fill the cuvette 2/3 full. Wipe the cuvette off with a Kim-Wipe
before placing it in the sample holder. Close the lid, then read and record the
Drink
absorbance of the solution.
6) The linear correlation between absorbance and concentration cannot be assumed
outside the range for the absorbance values measured. Thus, if the absorbance of the
sports drink is higher than the absorbance for Solution #1, it must be diluted until its
absorbance is within the range of measured absorbance values for the standards. If
the sports drink is outside the range, check out a 10.00 mL volumetric flask and a
5.00 mL pipet from the stockroom.
7) Condition the 5.00 mL pipet, and use it to transfer 5.00 mL of the drink to the clean
10.00-mL volumetric flask. (The flask does not need to be dry since DI water will be
added to the flask, but the volumetric pipet must be conditioned.) Add DI water to
fill the flask, inverting and mixing to insure a uniform solution.
8) Rinse a cuvette with DI water then condition it with the dilute sports drink. If the
absorbance is still higher than the absorbance measured for Solution #1, continue
diluting the solution until the absorbance measured is lower than the absorbance for
Solution #1.
CHEM 161 Lab Manual S2012
page 76
9) Have your instructor approve the absorbance for your sports drink before disposing
of any solutions.
Waste Disposal: After you have recorded and graphed all of your concentration and
absorbance data from your standards and unknowns, discard your solutions down the
drain with plenty of water.
10) Rinse the cuvettes with a few portions of DI water then wipe them dry using KimWipes. Wash and rinse the volumetric flasks and pipet used, including one final rinse
with DI water, then shake out any excess DI water before drying the outside of the
glassware and returning all of the equipment to the stockroom.
Post-Lab DATA ANALYSIS
Analysis Concentration of standard solutions:
and
Calculations Use the dilution equation,
M1 V1 = M2 V2
(5)
where:
M1
V1
M2
V2
is the initial concentration of the solution before it was diluted (in M)
is the volume of the initial solution used (in mL)
is the final concentration of the standard solution after it was prepared
is the total volume of solution prepared (in mL) in the volumetric flask.
Note: Because serial dilutions were carried out, M1 will change with each successive
dilution.
You will use Excel to enter and graph the data you obtain in this lab.
Data •
Analysis
using Excel
Set up the two columns of data, with the concentration of Allura Red in the first
column and the absorbance values in the second, as shown below. Enter the data for
the four standards and the sports drink in the worksheet, as well as the concentration
and absorbance for the blank.
Allura Red Concentration (in M)
0.000M
Absorbance
0.000
•
Prepare a chart/plot, including a descriptive title for the plot and proper labels for
the axes with units: “Allura Red Concentration (in M)” for the x-axis and
“Absorbance” on the y-axis. (Note that absorbance is unitless.)
•
Add a regression line for the data points to find the best-fit linear equation to the
data. Be sure to choose “Display equation on chart” and “Display R-squared value
on chart”. Also check the “Set intercept=” box, and set it to zero, so the regression
CHEM 161 Lab Manual S2012
page 77
line goes through the origin.
• The equation option will provide the equation for the line (y = mx + b) that best
fits your data points.
• The R-squared value will indicate how close your data points are to a straight
line. A value close to 1.00 indicates your data is very close to linear.
•
Clean up the formatting of the graph before printing. Right-click the background to
clear it. You can also select and delete the legend to the right of the graph since
there is only one set of data. Move the equation box if sits on any part of the
regression line or on any points.
•
Maximize the plot, so it will fill an 8” x 11” page. Print your Beer’s Law Plot. The
plot will be submitted with the rest of your lab report.
Use the linear equation (y = mx + b) from your Beer’s Law plot to determine the
concentration of Allura Red in the sports drink. If you diluted the sports drink to get the
absorbance within the appropriate range, calculate the concentration of Allura Red for
the undiluted sports drink.
• Also use Excel to prepare a plot of Absorbance versus Wavelength (similar to
Figure 3 on p. 87) using your data from Part II. Include the plot with your lab
report.
CHEM 161 Lab Manual S2012
page 78
CHEM 161: Beer’s Law and
Analysis of a Sports Drink
Name: _________________________
Partner: ________________________
DATA
Part I: Solution Concentrations and Absorbance
LAB REPORT
Use the dilution equation, M1 V1 = M2 V2 to calculate the molarities for Solutions 2-4.
Solution #
1 (Stock)
2
3
4
Molarity
Show the calculation for the molarity of Solution #2 below:
Part II: Determining the λmax
Wavelength
Absorbance
Wavelength (nm)
400 nm
Max -15 = _________
425 nm
Max -10 = _________
450 nm
Max -5 = _________
475 nm
Max = _________
500 nm
Max +5 = _________
525 nm
Max +10 = _________
550 nm
Max +15 = _________
Absorbance
575 nm
600 nm
What is the maximum absorbance value for your Solution #1? _____________
What wavelength gave this reading (i.e., the λmax)? ________________
Instructor Initials for λmax:_____________
CHEM 161 Lab Manual S2012
page 79
Part III: Measuring Absorbance Values for Standard Solutions and Sports Drink
Solution
Molar Concentration of
Allura Red (in M)
Absorbance
DI water (blank)
1
2
3
4
Absorbance
Sports drink (original concentration)
Sports drink diluted to ________% of original concentration
Sports drink diluted to ________% of original concentration
Sports drink diluted to ________% of original concentration
Post-lab Post-Laboratory Calculations and Analysis
Calculations
and Analysis 1. Linear equation: Provide the equation for the best-fit
regression line obtained for your Beer’s Law plot: _________________________
2. Use Beer’s Law (A = ε l c) and your line equation in Question #1 to calculate the
concentration of the diluted sports drink sample with an absorbance value within the
range of measured absorbance values for the standard solutions prepared.
CHEM 161 Lab Manual S2012
page 80
3. Next, mark on your Beer’s Law plot the absorbance value for the diluted sports drink
sample, and draw lines to approximate the concentration from the plot (see example
plot on p. 88).
a. Molar Concentration of Allura Red in Gatorate from plot: ___________________
b. How does your calculated concentration from Question #2 above compare to the
estimate value from your plot?
4. Calculate the concentration of Allura Red in the original sports drink sample,
accounting for any dilutions carried out to get the absorbance value in the
appropriate range.
5.
The LD50 for Allura Red ingested orally was determined for rats and rabbits to be
10,000 mg/kg—i.e., about 10,000 mg of Allura Red consumed per kg of a rat’s or
rabbit’s mass proved lethal for 50% of test subjects. Assuming the LD50 would
be about the same for humans, use the concentration you determined in Question
#4 to calculate how many gallons of red Sports drink consumed all at once by a
150-lb. person could potentially kill the person.
CHEM 161 Lab Manual S2012
page 81
CHEM 161 Lab Manual S2012
page 82