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 determined 2 to be PbO 2. 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 cassiterite 4 contains tin(iv) oxide, the mineral cuprite 5 contains copper(ii) oxide, and the mineral hematite 6 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) M (s) + CO 2 (g) (1) In this particular experiment, 2 the chemical formula of an unknown lead oxide (Pb x O y ) was discovered by smelting the lead oxide to form elemental lead. Rather than using charcoal as the reducing agent, methane gas (CH 4 ) was used. Both elements in CH 4 are oxidized in this process yielding carbon dioxide (CO 2 ) and water (H 2 O) as products, while the metal cation is reduced to its elemental form. Thus, the unbalanced chemical reaction is given in Equation 2. Pb x O y (s) + CH 4 (g) Pb (s) + CO 2 (g) + H 2 O (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 / Materials 2 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. Trial #1 Trial #2 Trial #3 Initial Mass of Unknown Lead Oxide 1.012 g 0.997 g 1.215 g Final Mass of Residue 0.877 g 0.861 g 1.060 g Mass Lost Upon Heating 0.135 g 0.136 g 0.155 g Calculated Moles of Lead in Sample 0.00423 mol 0.00416 mol 0.00512 mol Calculated Moles of Oxygen in Sample 0.00843 mol 0.00850 mol 0.00969 mol Mass Percent of Lead in Sample 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+pb x O y ) 2.036 g (empty tube) = 1.012 g Pb x O y (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 Pb x O y 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 Mass of Element = Molof Element Molar Mass of Element 1mol Pb 0.877g Pb = 0.00423mol Pb 207.2g Pb (5) (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. Massof Residue Initial Massof Sample 100% (6) 0.877 g 100% = 86.7% (6) 1.012 g 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:
Molesof O 2 (7) Molesof Pb This implies that the empirical formula of the unknown lead oxide is PbO 2. Thus, the unknown lead oxide is identified as lead(iv) oxide. The balanced chemical equation for this reaction is given in Equation 8. 2 PbO 2 (s) + CH 4 (g) 2 Pb (s) + CO 2 (g) + 2 H 2 O (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 in Mass% % Error = 100% (9) Theoretical Mass% 86.8% 86.62% 100% = 0.2% 86.62% (9) Discussion / Conclusions This experiment successfully identified the unknown lead oxide as lead(iv) oxide (with an empirical formula of PbO 2 ), 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 PbO 2. 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.