Purpose

To determine the concentration of allura red (FD&C Red 40) in a sports drink.

Expected Learning Outcomes

After completing this experiment, students are expected to be able to

• Relate the color of a solution to its absorption spectrum. (LO 5)
• Measure the absorption spectrum of a substance. (LO 3)
• Make Beer’s Law plots and use the plot to find the concentration of a sample. (LO 3, 4, 6)

Textbook Reference

Tro, Chemistry: Structures and Properties, 2nd Ed, Ch. 8.2.

Introduction

Absorption of Light

When light passes through a sample, some proportion of the light will be absorbed, depending on the electronic structure of the molecule^[1] and the wavelength of the incoming light, while the rest of the light is transmitted.  In the figure below, the incident (incoming) light intensity is [latex]I_0[/latex] and the transmitted light intensity (the light that is able to make it through the sample and out the other side) is [latex]I_t[/latex].

To quantify this, we note that – at a particular wavelength – given that the intensity of incident light is [latex]I_0[/latex], the intensity of light that goes through the sample is [latex]I_1[/latex]; the rest of this light is absorbed by the sample:

To quantify the amount of light that is absorbed, we define the absorbance ([latex]A[/latex]) as

\begin{equation}
\frac{I_1}{I_0} = 10^{-A} \to A = -\log_{10}\left(\frac{I_1}{I_0}\right)
\end{equation}

Note that the absorbance is unitless.

In this case, we can plot an absorption spectrum – a graph of the absorbance ([latex]A[/latex]) as a function of the wavelength of a sample:

The color of the solution will be the complementary color of the color of light being absorbed – which is the color opposite the wavelength of light in the color wheel:

Examples

Methylene blue absorbs primarily at around 620 nm, which corresponds to orange on the visible spectrum.  This is opposite to blue on the color wheel, and aligns with the solution.

The visible spectrum is as follows:

The absorbance of a solution can be measured using a spectrophotometer; details on how to use this is explained in Using Laboratory Equipment.

Beer-Lambert Law

It can be shown that for a solution with a concentration (molarity) of [latex]c[/latex],^[2] the absorbance is related to this by

[latex]A = \varepsilon cl[/latex]

where [latex]l[/latex] is the path length (the thickness of the solution through which the light travels; this is typically reported in centimeters) and [latex]\varepsilon[/latex] is the molar absorptivity (with units of [latex]\mbox{M}^{-1}\mbox{cm}^{-1}[/latex]). The molar absorptivity varies with wavelength, and is a property of a particular substance at a given wavelength.

The molar absorptivity at a given wavelength can be found by producing a Beer’s Law plot (like on the right hand side of the figure above). To do this, solutions of different concentrations of the compound being studied are prepared and their absorbances at the chosen wavelength are plotted (along the y-axis) against the concentrations of these solutions (along the x-axis).

Based on this, the molar absorptivity ε can be found from the slope of the Beer’s Law plot. The slope of the Beer’s Law plot is equal to [latex]\varepsilon l[/latex]. Most cuvettes used in the laboratory have a 1 cm pathlength, and therefore in your experiment you can use this to find the molar absorptivity.  Remember that typically Beer’s Law is set up with units such that the path length is in cm.

Using the molar absorptivity, we can determine the concentration of an unknown solution of the same compound^[3] by measuring the absorbance of the sample at the same wavelength as was done for the standard solutions. Given the molar absorptivity found from the Beer’s Law plot, one can solve Beer’s Law to find the absorbance.^[4]

This technique is very widely used in modern analytical chemistry and is one of the primary ways, for example, by which proteins and nucleic acids are quantified in the biochemical laboratory.

Dilution Calculations

Often, in chemistry, we start with more concentrated stock solutions and dilute these to get the concentration we want. This is a key skill that you should acquire. We do this quite often with concentrated drinks as well.

When we dilute a stock solution with a volume [latex]V_1[/latex] by a molarity [latex]M_1[/latex] with the solvent such that the final volume of the solution is [latex]V_2[/latex], the molarity of the diluted solution can be related to the other quantities by

\begin{equation}
M_1 V_1 = M_2 V_2 \label{306A:dilution}
\end{equation}

This equation could also be used to back-solve the concentration of a stock solution from that of a diluted solution. Be aware that this equation can only be used when you are diluting something (i.e. when you add water to a SOLUTION to decrease that solutions concentration). It cannot be used to calculate the concentration when you dissolve a SOLID (or a pure liquid instead of a solution) in water.

Procedures

Chemicals Needed

Please pour the following amounts of chemicals into your own glassware.

• Stock solution of allura red: 35 mL.  You will need to record the concentration of the stock solution from the bottle.
• Sports drink: 3 mL

Obtaining the Absorption Spectrum for Allura Red

In this part of the experiment, you will use the standard allura red stock solution to obtain the overall absorption spectrum of allura red.

1. Observe and describe the color and appearance of the solution.
2. Following the directions in Using Laboratory Equipment, measure the absorption spectrum of the stock solution (using water to calibrate the spectrophotometer).

3. Determine the best wavelength at which you should measure the absorption values for the Beer’s Law plot, and record this wavelength in your notebook.
4. Save the absorption spectrum by selecting from the menu for the file name at the top left hand corner and enter “Export”.  Save an image of the graph.

Preparation of Solutions for Beer’s Law plot

In this part of the experiment, you will prepare a series of diluted solutions to prepare a Beer’s Law plot.

5. Rinse the buret with small portions of deionized water and then rinse with small portions of the stock solution. Fill the buret to the 25 mL mark (approximately) with the stock solution provided.
6. Select “New Experiment” from the file name at the top left hand corner of your screen, and then select Absorbance vs Concentration (Beer’s Law).  You will need to recalibrate the spectrophotometer using a blank solution (get your instructors help with this to make sure you have the cuvette oriented correctly).
7. Enter the wavelength you selected in step 3 above.
8. Measure the absorbance of your stock solution, and enter the concentration of the stock solution (found on the stock bottle).
9. You will now make several measurements at 5 different concentrations of allura red by first making these solutions using dilution and then doing the measurement.  You will need to use your results in the previous part of the lab on collecting the absorption spectrum of allura red to come up with the approximate volumes of solution you want to use so that the 5 solutions range from ~0.2 to ~1.0 in their absorbance.
   1. Record the initial volume of solution in the buret, being sure to estimate the hundredths place.
   2. Carefully rinse your 10 mL graduated cylinder and empty it as best you can (just like you did in the Week 3 experiment on determining the density of water), but you may not be able to empty it completely; this will be okay as long as you have rinsed it carefully.
   3. Calculate the amount of stock solution you need to make 10 mL of the solution with approximately the desired absorbance.  Deliver this volume of the stock solution into the 10 mL graduated cylinder using the buret.
   4. Record the final volume in the buret, being sure to estimate the hundredths place.  The difference in the initial and final volumes is the volume delivered.
   5. Fill the graduated cylinder carefully with deionized water such that the final volume is 10.0 mL
   6. Use a piece of Parafilm to seal the top of the graduated cylinder. Invert the graduated cylinder about twenty times until the mixture is completely mixed.
   7. Calculate the exact concentration created using your measured result from sub-step 4.
   8. Measure the absorbance of this solution, entering the correct concentration from sub-step 7.  Check that the graph matches what you would expect from Beer’s Law.

Obtaining the Molar Absorbtivity

10. On Vernier Spectral Analysis, click on the Graph tool icon on the bottom left of the graph and select Apply curve fit.  Find an appropriate function (i.e. one where all the points are relatively close to the line that function creates) and apply that fit.
11. It will show the parameters for the fit.  Record the information in the box that pops up.
12. In preparation for exporting an image of the plot, either remove the box containing the curve fit data or move it to somewhere that won’t affect you viewing the graph.
13. Export the plot as you did in step 4.

Determining the Concentration of Allura Red in a Sports Drink

Write down the identity of the sports drink (brand, flavor/type) and determine the concentration of allura red in this drink.  If the absorbance is greater than 1, then dilute the solution appropriately so that the resulting solution has an absorbance of less than 1 and greater than 0.1 and record (a) how you diluted it and (b) what the concentration was at the end (i.e. in the cuvette).

Waste Disposal

All solutions from this experiment can be disposed of down the drain.