Download Determination of the Empirical Formula of an

Determination
of the
Empirical Formula
of an
Unknown Lead Oxide
by:
Student Name
Abstract
Using a process known as smelting,1 the empirical formula of an unknown lead oxide
was determined2 to be PbO2. At high temperatures, methane gas was used as a reducing
agent, to reduce the cationic lead to form neutral elemental lead metal. In turn, the
methane gas was oxidized, as it was compounded with the oxygen from the unknown
metal oxide, to form carbon dioxide and water, which were lost from the reaction vessel
as gases. The remaining residue was assumed to be lead and the mass lost was assumed
to be oxygen. By determining the number of moles of lead remaining and the number of
moles of oxygen lost, the empirical formula of the lead oxide was found. This
experiment demonstrates the important historical process known as smelting and could
theoretically be used to determine the empirical formula of other metal oxides found in
nature.
Introduction
While a few metals, such as gold and silver, can be found in their elemental forms in
nature, the majority of metals are naturally found in mineral ores in the form of
compounds.1 These metals must be extracted from their ores through a process known as
smelting.2 The first metals to be smelted, more than 8000 years ago were copper and
bronze and eventually, over 4000 years later, iron.3 The advances in materials science
that came as a result of the discoveries of smelting were so groundbreaking that scholars
divide the entirety of early human history into the “stone age” (before smelting was
discovered), the “bronze age”, and the “iron age”.
Although the name sounds similar to “melting,” the process of smelting actually involves
the use of a chemical reaction to isolate the metal in its elemental form from an ionic
compound which includes the metal as a salt.3 Most commonly, metallic elements are
found in rocks and minerals as oxides.3 For example, the mineral cassiterite4 contains
tin(IV) oxide, the mineral cuprite5 contains copper(II) oxide, and the mineral hematite6
contains iron(III) oxide. These minerals can be smelted to form metallic tin, copper, and
iron respectively. Some metals can also be isolated from sulfide salts found in nature.3
The process of smelting involves oxidation–reduction (redox) chemistry.7 In a typical
smelting reaction,1 a sacrifical reducing agent is added to the mineral ore. As the
reducing agent is oxidized, the metal cation from the ore becomes reduced, allowing the
elemental metal to be isolated. Often, the reducing agent is charcoal, which is an
allotrope of carbon.8 The unbalanced chemical reaction is shown in Equation 1, where
“M” represents the metal and “MO” represents the metal oxide. It can be seen that the
metal is reduced from a cation with a positive charge to a neutral element, while the
carbon is oxidized from the neutral element to carbon dioxide (with an oxidation state
of +4).
MO (s) + C (s) Æ M (s) + CO2 (g)
(1)
In this particular experiment,2 the chemical formula of an unknown lead oxide (PbxOy)
was discovered by smelting the lead oxide to form elemental lead. Rather than using
charcoal as the reducing agent, methane gas (CH4) was used. Both elements in CH4 are
oxidized in this process yielding carbon dioxide (CO2) and water (H2O) as products,
while the metal cation is reduced to its elemental form. Thus, the unbalanced chemical
reaction is given in Equation 2.
PbxOy (s) + CH4 (g) Æ Pb (s) + CO2 (g) + H2O (g)
(2)
By measuring the mass of the lead at the end of the experiment, the number of moles of
lead used was determined. Based on the law of conservation of mass,9 the number of
moles of oxygen in the original sample could be calculated. Taken together, the
empirical formula, and ultimately the identity of the sample were determined.
Methods / Materials2
The unknown lead oxide (1.012 g) was added to a clean, tared 200 mm ignition tube
through a funnel to ensure that all of the lead oxide was located in the lower portion of
the tube, and the tube with lead oxide was weighed. A two-holed rubber stopper covered
with aluminum foil (to prevent the rubber stopper from melting to the glass tube) was
securely inserted into the neck of the ignition tube, and the tube was clamped at a 45°
angle to a ring stand. Natural gas was then routed from the gas valve in the lab, entering
in through a glass tube passing through one hole in the stopper, then out through another
glass tube passing through the other hole in the stopper, and finally to a lit Bunsen burner,
which was used to heat the ignition tube and lead oxide externally for 20 min. As the
lead oxide was heated, it was observed to change from a black powder into a grayishsilvery powder. After heating, the Bunsen burner was moved away from the tube, which
was allowed to cool while the Bunsen burner was kept burning for a period of five
minutes, at which point it was extinguished and the tube was allowed to cool to room
temperature. The stopper was removed and the tube and resulting residue (0.879 g) was
weighed. The tube and residue were heated for an additional 10 min period and were
cooled following the above procedure to ensure that the residue (0.877 g) did not lose
very much additional mass. Due to the flammable nature of methane gas, care must be
taken to not allow the methane gas to leak from the stopper and to not allow the ignition
tube to melt during the experiment, or the methane gas may combust.
Results / Calculations
The entire procedure was repeated for three samples of the unknown lead oxide. The
results of the experiment are summarized in Table 1.
Initial Mass of
Unknown Lead Oxide
Final Mass of
Residue
Mass Lost Upon
Heating
Calculated Moles of
Lead in Sample
Calculated Moles of
Oxygen in Sample
Mass Percent of
Lead in Sample
Trial #1
Trial #2
Trial #3
1.012 g
0.997 g
1.215 g
0.877 g
0.861 g
1.060 g
0.135 g
0.136 g
0.155 g
0.00423 mol
0.00416 mol
0.00512 mol
0.00843 mol
0.00850 mol
0.00969 mol
86.7 %
86.4 %
87.2 %
Table 1: Summary of data and calculations for Trials 1–3 of the experiment.
The initial and final masses of the powder in the ignition tube are calculated by
subtracting the mass of the clean, dry, empty ignition tube from the mass of the tube
containing the powder as shown in Equation 3 and Sample Calculation 3. The calculated
masses for each trial are shown in Table 1.
Mass of Tube+Powder – Mass of Tube = Mass of Powder
(3)
3.048 g (tube+PbxOy) – 2.036 g (empty tube) = 1.012 g PbxOy
(3)
The mass lost upon heating, assumed to be elemental oxygen, is found by subtracting the
final mass of the residue, assumed to be elemental lead, from the initial mass of the lead
oxide as shown in Equation 4 and Sample Calculation 4. The calculated masses for each
trial are shown in Table 1.
Initial Mass of Powder – Final Mass of Residue = Mass Lost Upon Heating
(4)
1.012 g PbxOy – 0.877 g “Pb” = 0.135 g “O”
(4)
The moles of each element are calculated by using the mass of the element (mass of
residue is assumed to be lead; mass lost upon heating is assumed to be oxygen) and
converting using the molar mass of the element as shown in Equation 5 and Sample
Calculation 5. The moles of both elements for each trial are shown in Table 1.
⎛
⎞
1
⎟⎟ = Mol of Element
Mass of Element⎜⎜
⎝ Molar Mass of Element ⎠
(5)
⎛ 1 mol Pb ⎞
⎟⎟ = 0.00423 mol Pb
0.877 g Pb ⎜⎜
⎝ 207.2 g Pb ⎠
(5)
Finally, the mass percent of lead in the sample was calculated by dividing the mass of the
residue (assumed to be pure lead) by the mass of the original sample and then multiplying
by 100 % as shown in Equation 6 and Sample Calculation 6. The calculated mass
percents for each trial are shown in Table 1.
Mass of Re sidue
× 100%
Initial Mass of Sample
(6)
0.877 g
× 100% = 86.7 %
1.012 g
(6)
The average mass percent of lead for all three samples was 86.8 %
The empirical formula of the unknown lead oxide was determined by comparing the
number of moles of lead to the number of moles of oxygen for each of the three samples.
It can be seen that the number of moles of oxygen for each sample is almost exactly twice
the number of moles of lead. In other words, Equation 7 holds true for all three samples
of the unknown lead oxide:
Moles of O
≈2
Moles of Pb
(7)
This implies that the empirical formula of the unknown lead oxide is PbO2. Thus, the
unknown lead oxide is identified as lead(IV) oxide. The balanced chemical equation for
this reaction is given in Equation 8.
2 PbO2 (s) + CH4 (g) Æ 2 Pb (s) + CO2 (g) + 2 H2O (g)
(8)
The theoretical molar mass of lead(IV) oxide is determined to be 239.2 g / mol. Treating
this as the “initial mass of sample” and using the molar mass of lead (207.2 g / mol) as
the “mass of residue”, the theoretical mass percent of lead in the sample is determined to
be 86.62 % by using Equation 6. The average percent error for the experiment can be
calculated by dividing the error in the average mass percent of lead by the theoretical
mass percent of lead as shown in Equation 9 and Sample Calculation 9.
% Error =
Error in Mass %
× 100%
Theoretical Mass %
86.8 % − 86.62 %
× 100% = 0.2 %
86.62 %
(9)
(9)
Discussion / Conclusions
This experiment successfully identified the unknown lead oxide as lead(IV) oxide (with
an empirical formula of PbO2), with an average percent error of 0.2 %. This error is very
small and is probably caused by typical sources of experimental error including, but not
limited to, minor weighing errors caused by balance calibration and incomplete reaction
of the lead oxide.
The experiment would probably have been completed with greater relative ease if the
author had used a wing-top for the Bunsen burner. The wing-top would likely have
distributed the flame more evenly over the ignition tube, reducing the frequency of soft
spots appearing on the ignition tube. These soft spots slowed the experimental process
because they required removal of the heat source to prevent the tube from melting.
In summary, by smelting an unknown lead oxide powder to remove elemental oxygen
leaving behind elemental lead as a residue, it has been shown that the unknown lead
oxide powder is lead(IV) oxide with the empirical formula PbO2. This simple experiment
could, in theory, be used to determine the empirical formula of a variety of unknown
metal oxides, provided that methane gas can act as a reducing agent for each metal oxide.
Further exploration into the empirical formulas of naturally occurring rocks and minerals
using this method could prove particularly interesting, provided that relatively pure
samples of minerals composed of metal oxides could be acquired.
References
1) McLaughlin, E. D., Breaux, L. A., Eds. Chemical Mineralogy, Smelting, and
Mineralization; Nova Science Publishers, 2009.
2) The procedure for this experiment is adapted from Torres, O., Ed. Chemistry 1A
Laboratory Manual; Moorpark College Department of Chemistry, 2010, p 17–20.
3) Craddock, P. T. Early Metal Mining and Production; Smithsonian University Press:
Washington, D.C., 1995.
4) Wikipedia contributors, “Cassiterite,” Wikipedia, The Free Encyclopedia,
http://en.wikipedia.org/w/index.php?title=Cassiterite&oldid=339910635
(accessed
February 9, 2010).
5) Wikipedia contributors, “Cuprite,” Wikipedia, The Free Encyclopedia,
http://en.wikipedia.org/w/index.php?title=Cuprite&oldid=341878502
(accessed
February 9, 2010).
6) Wikipedia contributors, “Hematite,” Wikipedia, The Free Encyclopedia,
http://en.wikipedia.org/w/index.php?title=Hematite&oldid=340979380
(accessed
February 9, 2010).
7) McMurry, J. E., Fay, R. C. Chemistry, 5th ed. Pearson Prentice Hall: Upper Saddle
River, 2008, p 107–108, 116–119.
8) McMurry, J. E., Fay, R. C. Chemistry, 5th ed. Pearson Prentice Hall: Upper Saddle
River, 2008, p 384–385.
9) McMurry, J. E., Fay, R. C. Chemistry, 5th ed. Pearson Prentice Hall: Upper Saddle
River, 2008, p 33–35.