SUBJECT SEMESTER: XXXXXXXXXXXXXXXXXXXXX

TYPE OF LAB:  Spectroscopy

 

 

 

 

 

 

 

TITLE OF LAB:  Beer-Lambert Law – Food Dye Concentration in Sports Drinks

 

Beer-Lambert Law - Food Dye Concentrations in Sports Drinks NANSLO Lab Activity in Word format last updated October 8, 2014

 

Lab format: This lab is a remote lab activity.

 

Relationship to theory (if appropriate):  This activity is designed to be done after a basic introduction to the Beer-Lambert Law.  It assumes that students will have been introduced to the concepts of chemical bonds and covalent and ionic compounds.  It introduces the idea of solving simultaneous equations for multiple unknowns.

 

Instructions for Instructors:  This protocol is written under an open source CC BY license. You may use the procedure as is or modify as necessary for your class.  Be sure to let your students know if they should complete optional exercises in this lab procedure as lab technicians will not know if you want your students to complete optional exercise.

 

Instructions for Students:  Read the complete laboratory procedure before coming to lab.  Under the experimental sections, complete all pre-lab materials before logging on to the remote lab, complete data collection sections during your on-line period, and answer questions in analysis sections after your on-line period.  Your instructor will let you know if you are required to complete any optional exercises in this lab.

 

Remote Resources:  Primary - UV/Vis Spectrometer; Secondary - Cuvette Holder

 

CONTENTS FOR THIS NANSLO LAB ACTIVITY:

 

Learning Objectives

Background Information

Estimating Error

Equipment

Preparing to Use the Remote Web-based Science Lab (RWSL

Pre-lab Questions

Experimental Procedure

 

LEARNING OBJECTIVES:

 

After completing this laboratory experiment, you should be able to do the following things:

 

1. Measure and analyze the visible light absorbance spectrum of a standard solution to determine the maximum wavelength of absorbance (λmax). 
2. Create multiple solutions of differing concentrations of a stock solution. 
3. Solve simultaneous equations for multiple unknown concentrations. 
4. Determine and report the concentrations of two food dyes in a sports drink, along with associated experimental uncertainty (error).

 

 

BACKGROUND INFORMATION:

 

Food dyes are used in many products to enhance or provide colors that make foods and drinks more appealing or unique in some way.  Sports drinks come in a wide variety of colors in an attempt to appeal to different consumer groups.  Food colorings are used in very small quantities and provide no nutritional value at all.  Because these molecules contain light-absorbing features, which absorb visible light very strongly, even a small amount of food coloring can result in very strong colors.

Anything that absorbs light can be quantified by using the Beer-Lambert Law, also sometimes just called “Beer’s Law”:

 

A=abc Where A=Absorbance (unitless); a = molar absorptivity (molarity-1∙cm-1), which is a constant for the absorbing species, b = path length, or thickness of the absorbing layer of a solution (cm), and c = concentration of the solution (molarity).

 

Beer’s law tells us that the absorbance of a particular species is directly proportional to the concentration of the absorbing species. The measurement of a reference sample (one with everything except the substance being analyzed) allows us to factor out the absorbance of light by the solvent, and by the cuvette itself.

So A = abc.  And if a and b are constant for any given species and path-length, we can see that the absorbance of a solution is directly proportional to the concentration of the absorbing species.  Because the absorbance of a solution is easy to measure, this technique is frequently used to measure concentrations of unknown solutions, and this is what you will be doing in this experiment.

Food dyes absorb light because of conjugated systems of double bonds, which means double bonds are alternating with single bonds in either a long chain or one or more rings.  For example, a food dye called FD&C Blue #1 (Food, Drug and Cosmetics) looks like this:

 

Figure 1:  FD&C Blue #1 (Public Domain)

 

 

Notice the alternating single and double bonds in the rings?  See Figure 1.  Having a lot of these alternating bonds is what allows this molecule to absorb light very strongly.  

The other dye we will be working with in this activity is called FD&C Yellow #5.  It looks like Figure 2.

Figure 2:  FD&C Yellow #5 (Public Domain)

 

 

It has a very different system of conjugated bonds, so it absorbs different wavelengths of light than Blue #1.  In fact, if you remember your color wheel (or look one up), you can probably predict what color and wavelength or frequency of visible light each of these dyes absorbs based on their names.  Of course, if only one of these two molecules is present, it is pretty easy to apply Beer’s Law and determine its concentration.  But what if both of them are present?  While each molecule has a wavelength at which it absorbs the most strongly (λmax), they also absorb light at many other wavelengths.  For example, here is the absorbance spectrum of Blue #1.  See Figure 3.

 

Figure 3:  Absorbance Spectrum of Blue #1

 

And here is the absorbance of Yellow #5.  See Figure 4.

 

Figure 4:  Absorbance Spectrum of Yellow #5

 

There are several features to take note of here.  The first is the absorbance features below 400 nm.  We aren’t interested in these peaks because they are in the ultraviolet region of the electromagnetic spectrum and therefore don’t affect the perceived color of the substance since our eyes don’t register in that range of wavelengths.  Also, notice how the absorbance of each dye is NOT zero at the λmax value of the other dye.

Therefore, each molecule will affect the absorbance of light at the λmax of the other molecule, making it impossible to just solve for the concentration of each one at its respective λmax.   In that case, we have two unknowns so we must have two equations, and we do!  The absorbance at the λmax for each molecule is composed of the absorbance of Yellow #5 and the absorbance of Blue #1.  What we need to know is how much light each of the two dyes absorbs relative to the other one.  Luckily, some folks at the Chemistry Department of Appalachian State University in Boone, NC have done that work for us (Sigmann and Wheeler).

So we can write an equation for each one like this (where B1 = Blue #1 and Y5 = Yellow #5):

 

 

Doing a little algebra, we get the following equations:

 

 

Where A₆₃₁ is the measured absorbance at 631 nm and A₄₂₇ is the measured absorbance at 427 nm.

To calculate concentrations, we will also need to know the molar absorptivity of each molecule.  This is the factor “a” in the Beer’s Law equation, and it tells us how much light a 1.00 Molar solution of it will absorb in a 1.00 cm path-length.  This is a property of the molecule, just like its mass, and it doesn’t change.  For these two molecules, the molar absorptivity values are (Sigmann and Wheeler):

 

Dye	Molar Absorptivity (m-1cm-1)
Blue #1	1.30 x 105 at 631 nm
Yellow #5	2.73 x 104 at 427 nm

 

ESTIMATING ERROR:

 

There are many sources of noise, or uncertainty, in any experimental measurement that you will ever make.  The goal of any scientific data collection is to gather data with as little noise as possible, although it can never be totally eliminated.  For example, using a spectrometer with fiber optic light transfer, as you will do in this lab activity, has noise in its measurements due to the inconsistencies in the fiber optics, interference between the light and the sample being measured, inefficiencies in the detector, etc.  Most of this noise is random, meaning that it has the same probability of resulting in a measurement that is too high as it does resulting in a measurement that is too low.  When noise is random, it can be minimized by averaging multiple measurements.  In a spectrometer such as this one, there are two methods of averaging measurements.  One is through the use of “boxcar averaging” and the other method is to average multiple complete spectra.

Boxcar averaging is a smoothing method by which multiple points on a curve are averaged into one point.  This reduces the overall number of points in the curve, but it averages out some of the random noise in those points.  One must be careful not to average too many points on the curve together, because the more points you average in each “boxcar”, the less information there is in that curve.  For example, in the extreme case where you averaged ALL the points on the curve, you would end up with just one point, which isn’t very useful.  Essentially, you specify how many points you want in the averaging function.  Let’s say that you specify 2 points for the boxcar average, and let’s further assume that the curve you are smoothing has 1000 points in it.  The process works like this:

 

•   Points #1 and #2 are averaged to become a single point.  We’ll call it NewPoint #1.
• Then, the ORIGINAL point #2 is averaged with the ORIGINAL point #3 to become the second point in the new curve which we’ll call NewPoint #2.
• The process continues with the boxcar moving ahead one point at a time until all the original points are averaged to become NewPoints in the smoothed curve.
• The original 1000 points are turned into 999 NewPoints, and you have a slightly smoother curve.

 

Figure 5 illustrates how this process would proceed for a small curve of 50 original points.  The “y” curve is the 50 original points and the “y-box” curve is the 49 “new” points.

The other type of averaging is to average the entire curve.  The spectrometer will collect one entire spectrum about once per second.  The spectrum consists of many thousands of points, and each time a spectrum is collected, these points are slightly different (due to random noise).  If you average two spectra together, you reduce the noise by a factor of √2.  If you average three spectra, you reduce the noise by a factor of √3, etc.  Of course, the more spectra you average, the longer it takes to get a result, so there is a balance between decreasing noise and collecting data in a reasonable amount of time.

In addition, you can always estimate the error in any measurement by taking several measurements of it and calculating the standard deviation of the set of results.  In other words, if you measure something several times, you are likely to end up with a set of results that are not all exactly the same number.  The standard error of that set of numbers is an estimate of how much error there is in your results, and it is equal to the standard deviation divided by the square root of the number of samples in the data set.  Here’s an example.  Let’s say we measured the absorbance of a sample at 500 nm five times, and the result was:

 

Trial #1	Absorbance
1	0.324
2	0.332
3	0.325
4	0.328
5	0.322

 

 

We would report that the absorbance at 500 nm was: average +/- standard error, which in this case is:  0.326 +/- 0.002.  This means that the uncertainty in your result (0.326) starts in the third decimal place, because that’s the first digit in your standard error.  Since the uncertainty starts in the thousandths place, we have to limit the average value to the thousandths place as well.  When reporting uncertainty in this way, you always report only one digit in the standard error.

The standard deviation can be calculated manually (you’ve probably done this in a math course), or you can perform the calculation using a spreadsheet program like Excel.  If you have fewer than 100 samples to work with, use the “stdev.s” function, which is more accurate for small samples.

 

Sources:

Sigmann, S. B., and Wheeler, D. E. The Quantitative Determination of Food Dyes W in Powdered Drink Mixes. J Chemical Education 2004, 81, 10, pp 1475-1478.

 

EQUIPMENT:

 

• Paper
• Pencil/pen
• Computer with Internet access

 

PREPARING TO USE THE REMOTE WEB-BASED SCIENCE LAB (RWSL):

 

Read and understand the information below before you proceed with the lab!

Scheduling an Appointment Using the NANSLO Scheduling System

Your instructor has reserved a block of time through the NANSLO Scheduling System for you to complete this activity. For more information on how to set up a time to access this NANSLO lab activity, see
www.wiche.edu/nanslo/scheduling-software.  

Students Accessing a NANSLO Lab Activity for the First Time

You must install software on your computer before accessing a NANSLO lab activity for the first time. Use this link to access instructions on how to install this software based on the NANSLO lab listed below that you will use to access your lab activity – www.wiche.edu/nanslo/lab-tutorials

 

1. NANSLO Colorado Node -- all Colorado colleges.
2. NANSLO Montana Node -- Great Falls College Montana State University, Flathead Valley Community College, Lake Area Technical Institute, and Laramie County Community College.
3. NANSLO British Columbia Node -- Kodiak College.

 

Using the UV/Vis Spectrometer and Cuvette Holder for a NANSLO Lab Activity

View this short video on the Beer-Lambert Law Lab Activity found at http://www.wiche.edu/nanslo/lab-tutorials for brief instructions on using this scientific equipment.  

 

 

NOTE:   The conference number in this video tutorial is an example.  See “Communicating with Your Lab Partners” below to determine the toll free number and pin to use for your NANSLO lab activity.

 

PRE-LAB QUESTIONS:

 

1.  How are the dyes called Blue #1 and Yellow #5 similar to each other?  How are they different?
2. What ionic group does Yellow #5 have that Blue #1 does not?
3. Describe in your own words what the “molar absorptivity” of a molecule is.
4. If you have a mixture of solutions containing Blue #1 and Yellow #5, what data will you need to determine the concentration of each dye using Beer’s Law?
5. Create a table to record the data you will need for question #4.
6. Complete the following sentences: 
1. When solutions containing Blue #1 and Yellow #5 are mixed together, the value of the molar absorptivity for each dye will _____________________.   (increase, stay the same, decrease)
2. When solutions containing Blue #1 and Yellow #5 are mixed together, the color of each dye will ________________________.   (get lighter, stay the same, get darker)
7. Explain your answers to question 6.
1.  
2.  
8. What information does the standard deviation convey about a set of numbers?

 

EXPERIMENTAL PROCEDURE:

 

Read and understand these instructions BEFORE starting the actual lab procedure and collecting data.  Feel free to “play around” a little bit and explore the capabilities of the equipment before you start the actual procedure.

Once you have logged on to the Remote Lab, you will perform the following Laboratory procedures.  

Set-up Spectrometer

 

1. Turn on temperature controller.  Ensure the temperature of the system is adjusted to 25.0 degrees C.
2. Ensure that the stirring control is turned on and ensure that cuvette 0 (the reference sample) is selected. 
3. Turn on the spectrometer light, and you will see the spectrum of the light source.
4. Play around with the Boxcar Width and # Spectra to Average to get the least noisy (“jumpy”) spectrum that you can. Make sure that you don’t smooth it out TOO much, because then you lose valuable information in the signal.  Boxcar width should be somewhere in the range of 2 to 6.
5. Turn off the light and store the Dark Spectrum.
6. Turn the light back on and store the Reference spectrum.
7. Click on the Show Absorbance Spectrum button to view the Absorbance Spectrum.

 
Determine Concentrations for Experiment

 

8. Select cuvette 1 in the Qpod.  This cuvette will be empty.
9. Inject 4.0 mL of stock solution (a mixture of solutions containing Blue #1 and Yellow #5) from Pump #1.
10. Measure the absorbance at the two values of λmax for the two dyes.  If each absorbance value is less than 0.8, you can proceed.
11. Assuming that the absorbance is linear with respect to concentration, figure out how much you need to dilute the stock solution to bring the absorbance values into the appropriate range.

 

Collect Data

 

12. Advance the carousel to select the next cuvette.
13. Use the pumps to deliver appropriate volumes of water and stock solution.
14. After allowing the mixture to stir in the cuvette for a couple minutes, record the absorbance values at both λmax locations, unless the absorbance values are still too high.  In that case, you will need to come up with a different dilution to use for the next one.
15. Another student should take control of the interface.
16. Repeat steps 12 through 15 to collect at least three measurements where both absorbance readings at each λmax is lower than 0.8.
17. After each student has collected some data (and everyone has recorded the full data set), you can log out of the lab and work on the data analysis portion.  If you have time left in your scheduled lab period, you can continue working with your lab partners to analyze the data.

 

Data Analysis (to be done offline if necessary)

 

1. Using the data you collected, along with information in the Background section above, calculate the absorbance of Blue #1 and Yellow #5 in each solution that you worked with.
2. Use Beer’s Law to calculate the concentration of Blue #1 and Yellow #5 in each of the solutions you worked with.
3. Taking into account the dilutions you made, calculate the concentration of Blue #1 and Yellow #5 in the stock solution.  You should now have at least three measurements of Blue #1 and Yellow #5 concentrations (one for each solution you made).
4. Calculate the average and standard deviation of your set of measurements for Blue #1 from step 3. The concentration of Blue #1 in the stock solution is:  _______ M ± _______
5. Calculate the average and standard deviation of your set of measurements for Yellow #5 from step 3. The concentration of Yellow #5 in the stock solution is:  _______ M ± _______
6. Look up the molar masses of Blue #1 and Yellow #5 and properly reference your source.
7. Based on your results in steps 4, 5, and 6 calculate how many grams, each, of  Blue #1 and Yellow #5 are present in 946 mL of sport drink with the same composition as the stock solution you worked with in this lab activity.

 

 

 

For more information about NANSLO, visit www.wiche.edu/nanslo.

 

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Creative Commons Attribution 3.0 United States License 3  

 

 

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