Spectrophotometry - Determining the Thickness of Copper in a Penny

Introduction:

Several weeks ago in the 'Data Analysis' lab, you discovered that pennies minted prior to 1982 were composed of 100% copper.  However, pennies minted after 1982 have a clad composition consisting of 97.5% zinc and only 2.5% copper.  It is interesting to note that while the penny looks like it is made of copper, it has by far the least amount of copper of any US coin.  A nickel is composed of 75% copper, the dime, quarter and 50 cent piece are 91.67% copper, and the Susan B. Anthony dollar coin is 87.5% copper.

During the cladding process, this small amount of copper is deposited on the outside of the zinc core to make the penny look like it is completely made of copper:


If you scratch a new (post 1982) penny with a sharp object, you can actually see the silver colored zinc core.  You will also notice that this copper clad is very thin.  How thin is it?  Well, that is the purpose of this lab!

Theory:

To determine the thickness of the copper clad, we first need to determine exactly how much copper is in the penny.  To do this we will dissolve a new penny in concentrated nitric acid.  Nitric acid is so strong that it will not only dissolve the copper, but the zinc as well:

3 Cu(s)  +  8 H+(aq)  +  2 NO3-(aq)     3 Cu(H2O)4 2+(aq)  +  2 NO(g)  +  4 H2O(l)

 Zn(s)  +  2 HNO3(aq)     Zn(H2O)4 2+(aq)  +  2 NO3-(aq)  +  H2(g)

The copper (II) ions, or more precisely the copper (II) tetraaqua complex ions, have a characteristic light blue color, while the zinc tetraaqua ions are colorless.  The addition of concentrated ammonia to the copper (II) tetraaqua ions displaces the water molecules and produces a copper (II) tetraammonia complex which is a very dark blue color:



The dark blue color of the complex results from the fact that the complex strongly absorbs red light.  When this red is removed from normal white light, we observe blue (therefore, red is the compliment of blue).  This absorption of red light can be used to quantitatively determine the amount of copper present in the solution.  The more absorbance of red light, the more blue the solution, and hence, the more copper is present.  Below is the visible absorbance spectrum for the copper (II) tetraammonia complex.  You can clearly see that it most strongly absorbs light at 620 nm which is red.  Although the complex absorbs light at other frequencies as well, the absorbance curve is at its maximum at 620 nm, which will give us the best results.

If red light with a wavelength of 620 nanometer is directed into a solution that contains this copper complex, some of the red light will be absorbed:

As you can see, the intensity of the red light leaving the sample, I, is less than the original intensity of the red light, I0.  There are two ways of expressing this difference.  We can talk about the fraction of light that was transmitted through the sample,  transmittance (T); or we can talk about the amount of light that was absorbed by the sample, absorbance (A).  As you can see, one is opposite of the other:

transmittance (T)
absorbance (A)
T  =  I / I0
A  =  log (I0 / I)  =  log (1 / T)

The inverse relationship between transmittance and absorbance can best be seen in the following figure:


Notice that the %T can vary from 0 to 100% whereas the absorbance varies from 2.00 to 0.00 absorbance units.  The more light that passes through the sample,  the higher the transmittance and the lower the absorbance.  Conversely, the less light that passes through the sample, the lower the transmittance and the higher the absorbance.

Unfortunately, a plot of transmittance versus concentration does not result in a straight line.  However, a plot of absorbance, versus concentration does provide a straight line:


In a typical experiment, several solutions of known concentration of the copper complex are prepared.  Since the concentration of these solutions is known, they are called standard solutions.  The absorbance of each standard solution is measured at the wavelength of maximum absorption (620 nanometer from the spectrum above) using a spectrophotometer. A graph of these absorbance values versus the concentration of each of the standards should yield a straight line. This relationship is known as Beers' Law::

A = a b c

In this equation, A is the absorbance of the solution, a is the molar absorptivity (a constant for this complex), b is the path length of cuvette (in cm), and c is the molar concentration of the solution being measured.  If the same cuvette is used to measure all of the solutions, then a and b are constant.  This means that the absorbance of a solution is directly proportional to the concentration of that solution.  Therefore, the molar concentration, c, of a solution can be determined by simply measuring the absorbance, A, of that solution.  Although we are actually measuring the absorbance of the complex, the stoichiometry of the reaction producing the complex is 1:1. So, if we know the concentration of the complex, we know the concentration of the copper is the same.

Once we know how much copper is coating the penny, we divide by the surface area of the penny to figure out the thickness of the coating.

O.K., lets work through an example to see how all of this theory works.  Lets assume that 0.855 g of pure copper is treated as outlined in the experimental procedure below.  The concentration of the complex in the "Stock Solution" can be calculated as follows:

0.855 g copper x (1 mol copper / 63.5 g)  =  1.34 x 10-2 mol of copper in the beaker

After quantitative transfer, and dilution to 100 mL (0.1 L), the molarity of the solution is:

M  =  1.34 x 10-2 mol  / 0.1 L  =  1.34 x 10-1 M

The "Stock Solution" is then diluted in varying proportions (aliquots) to yield the standard solutions "A", "B", "C", "D", and "E".  Solution "A" is produced by diluting 10 mL of the "Stock Solution" with 100 mL of water.  The concentration of copper in solution "A" can be found using the relationship:

M1V1 =  M2V2

where M1 is the molarity of the "Stock Solution", M2 is the molarity of the solution "A", V1 is the volume of the "Stock Solution", and V2 is the volume of the solution "A":

(10.0 mL) (1.34 x 10-1 M)  =  (100.0 mL) (M2)

Therefore, the concentration of standard "A" is 1.34 x 10-2 M.  Now that you know the concentration of standard "A", you can use the spectrophotometer to measure it's absorbance.  In this example, it had an absorbance of 0.458.  Likewise, you can determine the concentration and absorbance for each of the other standard solutions:

Solution
mL of Stock
Concentration
 Absorbance
"A"
10.0
1.34 x 10-2 M
 0.458
"B"
 8.0
 1.07 x 10-2 M 0.374
"C"
 6.0
 8.04 x 10-3 M 0.288
"D"
 4.0
 5.36 x 10-3 M 0.190
"E"
 2.0
 2.68 x 10-3 M 0.089

Now you have the data you need to create your Beers' Law plot.  However, it would be a good idea to check your data to make sure it is consistent before you throw away your "Stock Solution".  Remember, the whole idea behind this experiment is that the absorbance of a given solution will be directly proportional to the concentration of the copper in that solution.  If that is the case, then the Absorbance of a solution divided by the mL of Stock used to create it should be very nearly constant.  For example, if I divide the measured Absorbance of Solution "A" (0.458) by the mLs of Stock solution (10.0 mL), I obtain a value of 0.0458 Absorbance/mL.  Likewise, I obtain values of 0.0468, 0.048, 0.0475, and 0.0445 for solutions "B", "C", "D", and "E" respectively.  Since values are all within about 10% of each other, I am confident in the data I have collected and am ready to create my Beers' Law plot.  Remember that this is sample data that I have create to make the Beers' Law plot look good.  You may notice that the higher concentration solutions don't show as much Absorbance/mL as the lower concentration solutions.  This can happen if you use a large sample of copper.  If this happens, you will have to throw out the higher concentration result and only used the lower concentration results.

Once you have determined the concentration and absorbance for all five standards, you will plot these points using an 'X-Y Scatter' plot in Excel.  Your  Beers' Law plot should look like the one below:


Note that most of the points do not fall directly on the line.  So, we have asked the software to draw the 'best' straight line through the data.  This is the 'Least Squares Fit' or 'Trendline'.  The plot is fairly straight and has a 'goodness' of fit (R2) of 0.9982, where 1.000 is a perfect fit.  It also gives us an equation for the line which we will use to calculate the concentration of your copper.

Next you will need to process a new penny.  Lets assume that your penny weighs 2.481 g and you processed it in exactly the same manner as you did the pure copper.  You will end up with 100.00 mL of a "My penny" solution.  You then measure its absorbance and obtain a value of 0.388. 

When you plotted your five standards, you obtained an equation for the linear regression equation.  In our example, that equation was:

Y = 34.27·X + 0.0032

In this equation, 'Y' is the absorbance, 'X' is the concentration of the solution, '34.27' is the slope of the line, and '0.0032' is the y-intercept.  Since we know the absorbance ('Y'), we can solve for the concentration ('X'):

X = (Y - 0.0032) /  34.27
X = (0.388 - 0.0032) / 34.27
X = 1.12 x 10-2 M

This is the actual concentration of pure copper in your penny.  But we want to know the actual amount of copper in grams, so:

1.12 x 10-2 M * 0.1 liters * 63.5 g/mol  =  0.071368 g Cu

Now that we know how much copper is in the penny, we need to calculate the volume of copper using its density.  Copper has a density of  8.94 g/mL, so:

0.071368 g Cu x 1 mL/8.94 g = 7.98 x 10-3 mL of Cu

According to the U.S. Mint, a penny has a diameter of 0.750 inches (19.05 mm), and a thickness (height) of 1.55 mm.  We can use these dimensions to calculate the surface area of the penny.  We will simply the calculation by assuming that the penny is a simple cylinder:

surface area = Area of top + Area of the bottom + Area of the side

surface area = (π x r2) + (π x r2) + (h x π x d)

surface area = (3.14 x (9.525 mm)2) + (3.14 x (9.525 mm)2) + (1.55 mm x 3.14 x 19.05 mm)

surface area = 284.88 mm2 + 284.88 mm2 + 92.72 mm2

surface area = 662.48 mm2 = 6.62 cm2 

So, if we divide the volume of copper in the penny by the surface area of the penny, we will obtain the average thickness of the copper:

thickness = 7.98 x 10-3 cm3 / 6.62 cm2

thickness = 1.205 x 10-3 cm

Now that is pretty thin.  However, we can go one step further and calculate how many atoms this represents.  A copper atom has a diameter of 2.551 x 10-8 cm.  If we divide this into the average thickness of the copper cladding, we can calculate how many copper atoms thick the copper cladding is:

thickness in atoms = 1.205 x 10-3 cm / 2.551 x 10-8 cm

thickness in atoms = 47,254 atoms

Therefore, the thickness of the copper in a new (post-1982) penny is 1.205 x 10-3 cm or 47,254 copper atoms.  To give you some perspective, the gold foil that Rutherford used in his famous experiment was only 1000 atoms thick!

Procedure:

Preparation of Standards for the Beers' Law Plot:

In this section you will produce five standards that contain a known concentration of the copper (II) tetraammonia complex.  Spectrophotometric determination of each standard's absorbance will be recorded and this data will be graphically plotted against concentrations to give a standard curve (Beers' Law Plot).

  1. Thoroughly clean your 150 mL beaker with soap and water.  Rinse it with dionized water and then completely dry it with a paper towel.
  2. Cut a piece of pure copper wire that is approximately 12 inches long.  Use one of your test tubes to wind it into a spiral.  Record its mass to the nearest 0.001g.
  3. Place the copper coil into your clean 150 mL beaker.  Place the beaker under your snorkle hood.
  4. Use a clean, dry graduated cylinder to obtain 15 mL of concentrated nitric acid.  Care should be exercised to avoid splattering.  CAUTION! HNO3 is harmful to the skin and eyes.
  5. Add the nitric acid to the beaker and note any changes.
  6. After the reaction is complete, carefully add 15 mL of distilled water to the beaker.
  7. Use a clean, dry graduated cylinder to obtain 25 mL of concentrated ammonium hydroxide.  Care should be exercised to avoid splattering.  CAUTION! NH4OH is harmful to the skin and eyes.
  8. Carefully, add the ammonium hydroxide in portions to the nitric acid solution.  Use your glass stirring rod to continually stir the solution.  Note any changes.
  9. Allow the solution to cool to room temperature.
  10. Quantitatively transfer the resulting solution of copper(II) tetraammonia complex to a clean 100 mL volumetric flask and then dilute with distilled water to the mark.  Be sure to thoroughly mix this solution by inverting the volumetric flask at least ten times.  Label the flask as "STOCK SOLUTION."
  11. Using a 10-mL graduated pipette, transfer a 10.0 mL aliquot of this "STOCK SOLUTION" into a second clean 100 mL volumetric flask and dilute to the mark with distilled water.   Be sure to thoroughly mix this solution by inverting the volumetric flask at least ten times.  Label the flask as "Solution A".
  12. Rinse your cuvette with "Solution A" and then discard.  Refill the cuvette with "Solution A" and measure its absorbance.
  13. Discard any remaining "Solution A" down the drain and rinse the 100 mL volumetric flask with distilled water.
  14. Using a 10-mL graduated pipette, transfer a 8.0 mL aliquot of this "STOCK SOLUTION" into a second clean 100 mL volumetric flask and dilute to the mark with distilled water.   Be sure to thoroughly mix this solution by inverting the volumetric flask at least ten times.  Label the flask as "Solution B".
  15. Rinse your cuvette with "Solution B" and then discard.  Refill the cuvette with "Solution B" and measure its absorbance.
  16. Discard any remaining "Solution B" down the drain and rinse the 100 mL volumetric flask with distilled water.
  17. Using a 10-mL graduated pipette, transfer a 6.0 mL aliquot of this "STOCK SOLUTION" into a second clean 100 mL volumetric flask and dilute to the mark with distilled water.   Be sure to thoroughly mix this solution by inverting the volumetric flask at least ten times.  Label the flask as "Solution C".
  18. Rinse your cuvette with "Solution C" and then discard.  Refill the cuvette with "Solution C" and measure its absorbance.
  19. Discard any remaining "Solution C" down the drain and rinse the 100 mL volumetric flask with distilled water.
  20. Using a 10-mL graduated pipette, transfer a 4.0 mL aliquot of this "STOCK SOLUTION" into a second clean 100 mL volumetric flask and dilute to the mark with distilled water.   Be sure to thoroughly mix this solution by inverting the volumetric flask at least ten times.  Label the flask as "Solution D".
  21. Rinse your cuvette with "Solution D" and then discard.  Refill the cuvette with "Solution D" and measure its absorbance.
  22. Discard any remaining "Solution D" down the drain and rinse the 100 mL volumetric flask with distilled water.
  23. Using a 10-mL graduated pipette, transfer a 2.0 mL aliquot of this "STOCK SOLUTION" into a second clean 100 mL volumetric flask and dilute to the mark with distilled water.   Be sure to thoroughly mix this solution by inverting the volumetric flask at least ten times.  Label the flask as "Solution E".
  24. Rinse your cuvette with "Solution E" and then discard.  Refill the cuvette with "Solution E" and measure its absorbance.
  25. Discard any remaining "Solution E" down the drain and rinse the 100 mL volumetric flask with distilled water.
  26. Check your data to make sure your absorbance data is decreasing relative to the decreasing concentration of each solution.  For example, the absorbance for the 4 mL solution should be half of that for the 8 mL solution and the absorbance for the 2 mL solution should be half of that for the 4 mL solution, etc.  If you find that the 10 mL solution shows significantly less absorbance that it should, it is possible that it is too concentrated and has fallen off the linear portion of the Beer's Law plot.  To correct this, you will have to run a sixth standard, "Solution F", using a 1.0 mL aliquot of the stock solution.  This will still give you 5 solutions to plot (Solutions B, C, D, E, and F) while allowing you to throw out Solution A (10 mL).
Determining the Amount of Copper in Your Penny:
  1. Thoroughly clean your 150 mL beaker with soap and water.  Rinse it with dionized water and then completely dry it with a paper towel.
  2. Obtain a post-1982 penny and weigh it to the nearest 0.001 g.
  3. Place the penny into your clean 150 mL beaker.  Place the beaker under your snorkle hood.
  4. Use a clean, dry graduated cylinder to obtain 15 mL of concentrated nitric acid.  Care should be exercised to avoid splattering.  CAUTION! HNO3 is harmful to the skin and eyes.
  5. Add the nitric acid to the beaker and note any changes.
  6. After the reaction is complete, carefully add 15 mL of distilled water to the beaker.
  7. Use a clean, dry graduated cylinder to obtain 25 mL of concentrated ammonium hydroxide.  Care should be exercised to avoid splattering.  CAUTION! NH4OH is harmful to the skin and eyes.
  8. Carefully, add the ammonium hydroxide in portions to the nitric acid solution.  Use your glass stirring rod to continually stir the solution.  Note any changes.
  9. Allow the solution to cool to room temperature.
  10. Quantitatively transfer the resulting solution of copper(II) tetraammonia complex to a clean 100 mL volumetric flask and then dilute with distilled water to the mark.  Be sure to thoroughly mix this solution by inverting the volumetric flask at least ten times.  Label the flask as "PENNY SOLUTION."
  11. Rinse your cuvette with "PENNY SOLUTION" and then discard.  Refill the cuvette with "PENNY SOLUTION" and measure its absorbance.
  12. Discard any remaining "PENNY SOLUTION" down the drain and rinse the 100 mL volumetric flask(s) with distilled water and return them to where you found them.
Waste Disposal. All materials can be washed down the sink with plenty of water to neutralize the acids and bases.

Calculations:

  1. Calculate the number of moles of pure copper used in your "Stock Solution"
  2. Calculate the molarity of your "Stock Solution"
  3. Calculate the molarity of each of your standard solutions, "A", "B", "C", "D", and "E".
  4. Use Excel to produce your Beers' Law plot, making sure to add a 'Trend Line'.  This 'Trend Line' is the least squares line through your data.  You will also want to set the plot options to show the equation of the line on the graph.  You can use this equation to calculate the concentration of your copper sample by using your absorbance value for 'y' and solving for 'x'.
  5. Convert the concentration of copper in your penny to grams of copper.
  6. Use the example above to calculate the thickness of the copper cladding, both in cm and in atoms.

(Updated 7/9/08 by C.R. Snelling)