AP Chemistry Lab 4
Using Beer’s Law to Determine the Mass Percent of Copper in an Alloy
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PURPOSE
To determine the mass percent of copper in a penny.
DEFINITIONS
Transmittance, absorbance, Beer’s law, complementary color, calibration curve, molarity.
INTRODUCTION
There are many ways to determine concentrations of a substance in solution. For solutions that are colored, Beer’s
law relates color intensity and concentration. When colored solutions are irradiated with white light, they will
selectively absorb light of some wavelengths but not of others. This is because of the relationship between the
electrons in a molecule or atom and its energy. Electrons in molecules and atoms are restricted in energy,
occupying only certain fixed energy levels. The electrons in molecules can absorb energy to jump up to higher
energy levels if exactly the right amount of energy is supplied. This amount of energy can be provided by
electromagnetic radiation. Visible light is one form of electromagnetic radiation. When this happens, the
particular energy of light, which corresponds to a particular wavelength or color, is absorbed and disappears. A
color wheel illustrates the approximate complementary relationship between the wavelengths of light absorbed
and the wavelengths transmitted. For example, a blue substance would absorb the complementary (opposite it in
the color wheel) color of light, orange.
When light is not absorbed, it is said to be transmitted through the solution. The wavelengths that a substance
absorbs can be determined by exposing the solution to monochromatic light of different wavelengths and
recording the light transmitted.
If light of a particular wavelength is absorbed, the intensity of the beam transmitted, I, through the solution will be
less than that of the original intensity of light, Io. The ratio of I / Io indicates the fraction of incoming light
transmitted by the solution and is called transmittance, T.
T = I /Io
AP Chemistry Lab 4
Using Beer’s Law to Determine the Mass Percent of Copper in an Alloy
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A more useful quantity is related to the amount of light absorbed, called absorbance, A.
A = –log(T)
The higher the absorbance of light by a solution, the lower the transmittance. The wavelength () at which
absorbance is highest is the wavelength to which the solution is most sensitive to concentration changes. This
wavelength is called λmax. In the first part of this experiment, you will determine λmax of a standard copper(II) ion
solution. Once λmax is determined, you will construct a calibration curve based on Beer’s law:
A=abc
where a = molar absorptivity (often symbolized by ε), which depends on the substance, the solvent and
wavelength, λ.
b = pathlength of the light through the solution (also called the cell length), usually 1.00 cm
c = molar concentration
the
The molar absorptivity, a, depends on the substance, the solvent, and wavelength, λ. The units for molar
absorptivity are 1/M·cm or L/mole·cm.
Beer’s Law is useful because the absorbance is directly proportional to concentration provided the absorbing
substance, solvent, wavelength, and pathlengh are fixed. With this equation you can determine the concentration
of a substance.
It should be noted that there are conditions where deviations from Beer’s law occur. This happens when the
concentration of the absorbing substance is too high to allow significant light to be transmitted or because of lack
of sensitivity of instrumentation.
In this lab, you will study the light absorption of aqueous copper(II) ions. Copper(II) ions in water form a
complex ion with the formula Cu(H2O)6)2+ which are blue in appearance.
PROCEDURE
Spectral Curve
1. Your instructor will show you the correct use of a spectrophotometer. Each model is slightly different in the
way solutions are measured.
2. Measure the transmittance of the standard 0.40 M copper solution every 20 nanometers from 400–660 nm.
Record your data in a table. (Note: some spectrophotometers display percent transmittance rather than
transmittance. Record only transmittance.)
Calibration Curve Solutions
3. Clean and dry five large test tubes.
4. Determine what volume of 0.400 M Cu2+ solution (the stock solution) is required to make 20.00 mL of 0.200
M Cu2+ solution. Use a volumetric pipette to transfer this volume of the stock solution into a clean test tube.
Then add the proper amount of distilled water to the test tube using a separate pipette to make a total volume
of 20.00 mL. Thoroughly mix the solution. Repeat the dilution process to make 20.00 mL each of three
additional dilute solutions that are 0.100 M, 0.0500 M, and 0.0250 M, respectively. Use the process of serial
dilution, whereby each diluted solution acts as the starting solution for the next dilution. Be sure to “rinse”
the pipette each time with ~2 mL of solution before withdrawing that solution for the next dilution.
5. Seal these five solutions with Parafilm to measure transmittance in the next lab period.
AP Chemistry Lab 4
Using Beer’s Law to Determine the Mass Percent of Copper in an Alloy
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Measuring the Unknown
6. Measure the mass of five post-1983 penny to ± 0.0001 g using the analytical balance. Place the pennies in a
clean 400 mL beaker.
7. Assuming the penny is 100% copper (it is not!), use stoichiometry to determine the amount of 16 M nitric
acid to add to the penny to completely convert the copper metal to copper(II) ion. The half reactions for this
redox reaction are:
unbalanced oxidation half-reaction:
unbalanced reduction half-reaction:
Cu(s) ➝ Cu2+(aq–)
NO3–(aq) ➝ NO(g)
You will need to write the balanced equation for the overall reaction to do the stoichiometric calculation.
Show this equation and stoichiometric calculation in your lab report.
8. Under a fume hood, have your teacher add approximately 2 mL more than this volume of HNO3(aq) to the
pennies so that the HNO3 is the excess reagent, and then your teacher will cover the beaker with a watch
glass. Wait a few minutes for the reaction to proceed. Record observations. If the copper in the penny is not
completely dissolved, the teacher will add more nitric acid. After the metal dissolves completely, your teacher
will add distilled water to bring the volume to ~75 mL. Then you will remove the beaker from the fume hood
and transfer the solution to a 100 mL volumetric flask. (Caution: this solution still contains HNO3.)Rinse the
beaker three times with ~5 mL of distilled water and add the washings to the flask. Dilute to a final volume of
100.00 mL, cover with Parafilm, and mix thoroughly.
9. Measure the transmittance of this copper(II) ion solution using the spectrophotometer set at the predetermined
wavelength.
10. Measure the transmittance of each of the five calibration curve solutions.
ANALYSIS
Spectral Curve
1. Calculate the absorbance for each measured transmittance.
2. Construct a plot of absorbance vs. wavelength, and determine the wavelength where the absorbance equals
~1.0. (This will ensure that the wavelength chosen for the remainder of the lab will be done in the linear range
of the spectrophotometer.)
3. Use the absorbance value at the determined wavelength to calculate the molar absorptivity of the hydrated
copper(II) ion. For this calculation, assume the path length is 1.00 cm.
Calibration Curve
4. Convert transmittance of each of the five calibration solutions to absorbance, and construct a plot of
absorbance vs. concentration.
5. Determine the equation for the line of best fit.
Measuring the Unknown
6. Use the equation of the best fit line from the calibration curve to calculate the concentration of copper(II) ion
in the penny solution.
7. Determine the mass of Cu dissolved in the penny solution based upon the determined molarity and volume of
the volumetric flask.
8. Use this mass to calculate the mass percent copper in the penny.
9. Compare the mass percent values of copper in the penny determined by the two different experimental
methods (Lab 1 and Lab 4). Which method do you think is more accurate? Why?
EXPERIMENTAL ERROR
What would be the effect on the value of percent copper in the penny if the penny contained a colored impurity?