The electrons in molecules can absorb and emit specific wavelengths of light, just like the electrons in atoms.  For large molecules, the absorbance patterns are often complex and, when analyzed, can reveal important information about the molecule.  Much of the absorption occurs outside of the visible region, however, so we need specialized devices to observe the spectra.

Spectrophotometry is the study of the spectra of substances in the infrared, visible, and ultraviolet regions.  A spectrophotometer is a device that can pass specific wavelengths of light through a sample and measure the absorbance of the sample at that wavelength.  Some spectrophotometers have the ability to pass a range of wavelengths through the sample and output a graph of absorbance versus wavelength.  Each substance has a unique absorption pattern and so the graphs can be used to identify the sample.

Our spectrophotometers work in the UV-Visible range.  Also, they are only capable of passing a single wavelength through a sample at a time.  While you could still work wavelength by wavelength and eventually build an absorbance graph, it would be very time consuming.  Luckily, there are other ways in which a spectrophotometer can be useful.

Part A: Beer's Law

If you have a solute dissolved in water, it turns out that the amount of absorption is proportional to the concentration of the solution.  This relationship is called Beer’s Law (or sometimes the Beer-Lambert Law) and can be stated as

	A = ebc

where A is absorbance, e is a constant for the substance called molar absorptivity, b is the path length or thickness of the sample, and c is the concentration in Molarity.  In this experiment we will be measuring concentrations in mg/mL instead of Molarity, so the constant will not technically be a molar absorptivity, but the results will still be linear.

We're going to verify Beer's Law by finding the peak absorbance for two different organic compounds and then running several solutions of different concentration through the spectrophotometer.  But as usual, there is a complicating factor to deal with first.

Spectrophotometers are extremely sensitive, so we'll need very dilute solutions.  The problem with that is the masses that we'd need to measure in order to make the dilute solutions would be so small that our balances could not accurately measure them.  What we do is make a stock solution whose concentration is as low as we can reliably make it.  Then we'll take small amounts of that stock solution and dilute it to a known larger volume.  By doing this several times, we can get as many different highly dilute solutions as we need.

Methodology

Creation of Standard Solutions

1.	Select either benzoic acid or caffeine as your substance to test.  If you are working with benzoic acid, follow instructions 2 - 4; if you are working with caffeine, jump ahead to instructions 5 - 7.  You will need to partner with another group that is doing the other substance.  Make sure that you exchange data with them.

2.	Prepare a stock solution of benzoic acid by dissolving 10 mg in distilled water using a 100 mL volumetric flask.

3.	Make a 2 mg/L solution of benzoic acid by mixing 2.00 mL of your standard solution with 10 mL of 0.1 M HCl in a 100 mL volumetric flask.  Then fill the flask to the line with distilled water.

4.	Follow a similar procedure to make 4, 6, 8, and 10 mg/L solutions of benzoic acid.

5.	Prepare a stock solution of caffeine by dissolving 20 mg in distilled water and diluting in a 100 mL volumetric flask.

6.	Make a 4 mg/L solution of caffeine by mixing 2.00 mL of your standard solution with 10 mL of 0.1 M HCl in a 100 mL volumetric flask.  Then fill the flask to the line with distilled water.

7.	Follow a similar procedure to make 8, 12, 16, and 20 mg/L solutions of caffeine.

Calibration of the Spectrophotometer

1.	You will first need to find the wavelength where your substance (either benzoic acid or caffeine) is most absorptive.  Fill a cuvette with the most dilute sample and place it into the spectrophotometer.  Do not touch the clear sides of the cuvette!

2.	Set the spectrophotometer to a wavelength of 200 nm and read the absorbance.  Increase the wavelength to 350 nm in increments of 10 nm, reading each absorbance value.  Record the wavelength where absorbance is maximum; this is the wavelength you will use throughout the rest of the experiment.

Running the Samples

1.	Since water itself may absorb some light, we first run a blank sample through the spectrophotometer at the desired wavelength.  Fill a cuvette with distilled water and place it in the spectrophotometer.  Set the wavelength to your desired wavelength and measure the absorbance.  Set this value to zero.

2.	Place each of your samples, lowest to highest concentration, in a cuvette and measure its absorbance at your maximum wavelength.  Ask your partner group (the ones using the other substance) what their maximum wavelength was and take absorbance readings for each sample at that wavelength as well.  You will need these for part B.

Analysis

Draw a graph of absorbance (y-axis) versus concentration (x-axis) for your substance at both wavelengths.  Based on the equation A = ebc, the graphs should be linear with an intercept of zero.  The slope will equal the absorptivity constant times the path length.  The path length is 1.0 cm, so you can find e for your substance at both wavelengths.

Part B: Spectrophotometric Analysis of Mountain Dew

Beer's Law, if you recall, can be stated as

A = ebc

where A is absorbance, e is a constant for the substance called molar absorptivity, b is the path length or thickness of the sample, and c is the concentration in Molarity.

In this experiment we wish to find the concentrations of two additives in a sample of Mountain Dew soda, caffeine and benzoic acid.  Both substances absorb in the ultraviolet spectrum, and when mixed their absorption patterns overlap as shown below.

The peaks you found in part A for benzoic acid and caffeine will (hopefully) agree with the peaks shown on this graph.  We will collect data at these two peak wavelengths.  The situation is complicated by the fact that, in Mountain Dew, both substances are absorbing light at the same time.  Luckily, absorbance values are additive so we can get the total absorbance by adding the absorbance values of each species at a particular wavelength:

Atotal = Aba + Acaf

Using Beer’s Law, each absorbance value is equal to ebc for the substance.  The product eb can be found from your graphs from last week.  Based on the total absorbance values for both wavelengths, we can solve simultaneously for the two unknown concentrations.

Methodology

1.	Pour approximately 20 mL of Mountain Dew into a beaker and warm gently to remove all the carbonation.  Allow the sample to cool.

2.	Add 2.00 mL of your Mountain Dew sample and 10.0 mL of 0.1 M HCl to a 100 mL volumetric flask and fill to the line with distilled water.

3.	Make a second sample using the same procedure, but this time use 4.00 mL of your Mountain Dew sample.

4.	Set the spectrophotometer to your first wavelength and insert a blank cuvette (one filled with distilled water) and zero out the absorbance value.  Place your 2 mL Mountain Dew sample into the spectrophotometer and record its absorbance.  Repeat with the 4 mL sample.

5.	Repeat step 4 at your second wavelength.

Analysis

For each wavelength we can construct an equation for the total absorbance:

Atotal = ebcba + ebccaf

Atotal is the absorbance of the Mountain Dew sample and the eb terms are just the slopes of the graphs for benzoic acid and caffeine that you made last week.  That leaves the concentrations of benzoic acid and caffeine as the unknowns.  If you construct an equation for absorbance at each wavelength, you will have two equations that you can solve simultaneously.  Solving the simultaneous equations will give you the concentration values for benzoic acid and caffeine.  

Remember that the Mountain Dew solutions were diluted before we measured their absorbance.  The first sample was diluted 50 times (2 mL of soda in 100 mL solution) so you will have to multiply your calculated concentrations by 50 to get the true values for Mountain Dew.  The second sample was twice as concentrated, so you will need to multiply the absorbance values by 25 for that sample.  Then you can find the average concentrations for benzoic acid and caffeine.

The advertised concentrations for Mountain Dew are 56.5 mg/L benzoic acid and 155 mg/L caffeine.  Find the relative errors on your results.

Questions

1.	Imagine that in part A you mix four of the five dilutions and your partner mixes only one of them.  Your solutions are perfect, of course, but you don't know if you can trust your partner to do his right.  How could you determine from the graph of your results if your partner mixed his solution incorrectly?

2.	Why does the intercept of the Beer's Law graph have to be zero?

3.	Why is it important to remove the carbonation from the Mountain Dew before reading its absorbance in the spectrophotometer?

4.	If a student's results in part B are bad, explain how an error in part A could have caused it.

5.	In part B, why couldn't we use cola instead of Mountain Dew?