Introduction:
Pennies
minted prior to 1982 were composed of 95% 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. With a good pair of metal shears, you can cut away a piece of the penny and see that this copper
clad is very thin:
How thin is it? Well, that is the
purpose of this lab isn't it! Here is a link to make hollow pennies at home: Making hollow pennies
Theory:
Note: I have added two videos from the Khan Academy which should give you a better understanding of the theory and practice of spectrophotometry. The first video covers the theory of how spectrophotometry works using both an intuitive and algebraic approach. The second video
works through a standard spectrophotometry problem.
Warning: both videos are approximately 13 minutes long. The
first video is 16MB, and the second is 20MB.
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 NO_{3}^{}_{(aq)} 3 Cu(H_{2}O)_{4}^{
2+}_{(aq)
}+ 2
NO_{(g) }+ 4 H_{2}O_{(l)}
Zn_{(s)}
+ 2 HNO_{3}_{(aq)} Zn(H_{2}O)_{4}^{
2+}_{(aq) } + 2 NO_{3}^{}_{(aq)
}+ H_{2(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,
I_{0}.
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 / I_{0}

A = log
(I_{0}
/ 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 you have access to a "STOCK SOLUTION" of 0.134 M
copper (II) tetraammonia solution. Unfortunately, this solution
is
too concentrated and so you will have to make several dilutions.
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" to 100 mL with water. The concentration of
copper in solution "A" can be found using the relationship:
M_{1}V_{1}
=
M_{2}V_{2}
where M_{1}
is
the
molarity of the "STOCK SOLUTION", M_{2} is the molarity
of the solution "A", V_{1} is the volume of the "STOCK SOLUTION",
and V_{2} is the volume of the solution "A":
(10.0 mL) (1.34 x 10^{1}
M) = (100.0 mL) (M_{2})
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 'XY 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 'Trend line'.
The plot is fairly straight and has a 'goodness' of fit (R^{2})
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 yintercept. 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 r^{2})
+ (π x r^{2}) + (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
mm^{2} + 284.88 mm^{2} + 92.72 mm^{2
}
surface area = 662.48
mm^{2} = 6.62 cm^{2}
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}
cm^{3} / 6.62 cm^{2}
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 (post1982)
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: NOTE: You need to bring your own penny for this lab. It needs to be the newest, shiniest penny you can find!
Hints for using the cuvette and colorimeter:
 A cuvette have two clear sides (the light passes through these), and two ribbed sides, perpendicular to each other.
 Always handle the cuvette using the ribbed sides. You must avoid fingerprints on the clear sides.
 The cuvette must be clean and dry on the outside. Use a ChemWipe for this. DO NOT use a regular paper towel. This will scratch the clear sides.
 After filling with solution, make sure there are no bubbles. You may have to tap it vigorously to remove them.
 Make sure you check that the colorimeter is working properly by
putting in a cuvette of distilled water. It should have an absorbance
of zero. It is is larger than 0.002, let your instructor know so it
can be recalibrated.
 Make sure you put the cuvette in the colorimeter with the ribbed
side facing you. The light beam travels from right to left in the
colorimeter.
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).
 Thoroughly clean your 100 mL beaker with
soap and water. Rinse it with deionized water and then completely
dry it with a paper
towel.
 On
the back bench will be a container labeled "STOCK SOLUTION" that
contains a known concentration of the copper (II) tetraammonia
complex. It is fitted with a repipetter that will give you exactly 50.0 mL of the "STOCK SOLUTION". Make sure you write down the concentration of this solution!!!!
 Since
you do not know what your 10mL graduated pipette was used for last,
you will need to rinse it out with the "STOCK SOLUTION". Just
attach your pipette pump and fill the pipette up to near the top.
Then discard this solution down the drain. Your graduated pipette
is now ready.
 Using your freshly rinsed 10mL graduated
pipette,
transfer
a 10.0 mL aliquot of this "STOCK
SOLUTION" into a 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".
 Rinse your cuvette with
"Solution A"
and then discard. Refill the cuvette with "Solution A" and
measure
its absorbance.
 Discard any remaining
"Solution A" down the drain and rinse the 100 mL volumetric flask with
510 mL of distilled water.
 Using your 10mL graduated
pipette,
transfer
a 8.0 mL aliquot of this "STOCK
SOLUTION" into a 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".
 Rinse your cuvette with
"Solution B"
and then discard. Refill the cuvette with "Solution B" and
measure
its absorbance.
 Discard any remaining
"Solution B" down the drain and rinse the 100 mL volumetric flask with
510 mL of distilled water.
 Using your 10mL
graduated
pipette,
transfer
a 6.0 mL aliquot of this "STOCK
SOLUTION" into a 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".
 Rinse your cuvette with
"Solution C"
and then discard. Refill the cuvette with "Solution C" and
measure
its absorbance.
 Discard any remaining
"Solution C" down the drain and rinse the 100 mL volumetric flask with
510 mL of distilled water.
 Using your 10mL graduated
pipette,
transfer
a 4.0 mL aliquot of this "STOCK
SOLUTION" into a 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".
 Rinse your cuvette with
"Solution D"
and then discard. Refill the cuvette with "Solution D" and
measure
its absorbance.
 Discard any remaining
"Solution D" down the drain and rinse the 100 mL volumetric flask with
510 mL of distilled water.
 Using your 10mL graduated
pipette,
transfer
a 2.0 mL aliquot of this "STOCK
SOLUTION" into a 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".
 Rinse your cuvette with
"Solution E"
and then discard. Refill the cuvette with "Solution E" and
measure
its absorbance.
 Discard any remaining
"Solution E" down the drain and rinse the 100 mL volumetric flask with
5 10 mL of distilled water.
 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:
 Thoroughly clean your 150 mL beaker with
soap and water. Rinse it with deionized water and then completely
dry it with a paper
towel.
 Weigh the post1982 penny you brought to lab to
the nearest 0.001 g.
 Place the penny into your
clean
150 mL beaker. Place the beaker under your snorkel hood.
 Use a clean, dry graduated
cylinder to obtain 15 mL of concentrated nitric acid. Care
should be exercised to avoid splattering. CAUTION! HNO_{3}
is harmful
to
the skin and eyes.
 Add the nitric acid to the beaker and note any changes.
 After the reaction is complete, carefully add 15 mL of distilled
water to the beaker.
 Use a clean, dry graduated cylinder to obtain 25 mL of
concentrated ammonium hydroxide. Care
should be exercised to avoid splattering. CAUTION! NH_{4}OH
is harmful
to
the skin and eyes.
 Carefully,
add the ammonium hydroxide in portions to the nitric acid
solution.
Use your glass stirring rod to continually stir the solution. You
should notice that the solution turns a much darker shade of blue
(almost purple). You will also notice the formation of white zinc
hydroxide precipitate (solid). However, as you add more of the
ammonium hydroxide, the solid should redissolve. It is important
that all of the zinc hydroxide redissolves. If you notice any
white solid after adding all of your ammonium hydroxide, carefully add
another 5 mL. If there is still solid present after this, ask
your lab instructor for guidance.
 Allow the
solution to cool
to
room temperature. While the solution cools, obtain a 100 mL
volumetric
flask and clean it by rinsing several times with distilled water (Note: DO NOT
use soap to clean it.)
 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."
 Rinse your cuvette with
"PENNY SOLUTION"
and then discard. Refill the cuvette with "PENNY SOLUTION" and
measure
its absorbance.
 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:
 Calculate the molarity of
each
of your
standard solutions, "A", "B", "C", "D", and "E".
 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'.
 Convert the concentration of
copper in your penny to grams of copper.
 Use the example above to
calculate the thickness of the copper cladding, both in cm and in atoms.
(Updated 9/26/13 by C.R. Snelling)