In the Classroom
Some Insights Regarding a Popular Introductory Gas Law Experiment Ed DePierro and Fred Garafalo* School of Arts and Sciences, Massachusetts College of Pharmacy and Health Sciences, Boston, MA 02115; *
[email protected] Determining the molar mass of gases or easily vaporized liquids is described in virtually all first-year college chemistry texts to a greater or lesser extent, and is an appropriate activity to engage students once they have been exposed to the gas laws. The Dumas method provides a relatively simple way to determine the molar mass of volatile chemical compounds, and has been described in various places (1–6). This report alerts readers to a potential source of error in one approach to the Dumas method as it is often practiced in introductory chemistry laboratories. Specifically, the room-temperature vapor pressures of volatile compounds that might be considered as unknowns for the experiment lead to determined molar masses that are too low. The greater the vapor pressure of the compound, the lower the determined molar mass will be, when compared to the accepted value.
vapor fills flask
empty flask
step 1 room temperature and pressure
sample condenses
step 2 higher temperature, room pressure
step 3 room temperature and pressure
Figure 1. Flask conditions during the three steps in this version of the Dumas method.
Table 1. Expected and Obtained Results for Two Dumas Molar Mass Determinations
Amount (moles) of vapora Mass expected, step 3 Molar mass expected Mass obtained, step 3 Molar mass obtained Observed error
Cyclohexane (363 K)
Pentane (323 K)
5.03 ⫻ 10᎑3 mol
5.66 ⫻ 10᎑3 mol
0.424 g
0.408 g
84.2 g mol
᎑1
72.1 g mol᎑1
0.406 g 80.7 g mol
0.307 g ᎑1
54.2 g mol᎑1
᎑4%
᎑25%
a
Determined with the ideal gas law, using the given temperature, p ⫽ 1.00 atm, V ⫽ 0.150 L and R ⫽ 0.0821 L atm/K mol.
1194
Journal of Chemical Education
•
Experimental Procedure The experimental steps in this version of the Dumas molar mass determination include: 1. Determining the mass of the empty apparatus. This is often an Erlenmeyer flask, covered with a piece of foil in which a pinhole has been made. 2. Placing several milliliters of the unknown volatile compound into the flask, and then inserting the apparatus into a beaker of water. The water is then slowly heated to some temperature above the boiling point of the unknown. (Alternatively, the flask is placed in a bath at a temperature about 20 °C above the boiling point of the unknown.) This results in the volatile compound filling the flask, pushing the air out in the process. The excess vapor escapes through the pinhole until the pressure inside the flask is equal to the external air pressure in the laboratory. 3. Cooling the flask to condense the remaining vapor, and again determining the apparatus mass, which now includes the volatile compound that remained behind in the flask.
The flask conditions during these three steps are represented in Figure 1. The mass of the volatile compound occupying the flask under the conditions in step 2 is determined by subtracting the mass measured in step 1 from that measured in step 3. The amount (moles) of the volatile compound present under the conditions in step 2 above is determined from the ideal gas law by setting the volume, V, equal to that of the Erlenmeyer flask, the pressure, p, equal to the atmospheric pressure in the room, the temperature, T, equal to that of the water in the beaker when the vapor stopped exiting through the pinhole in step 2, and the gas constant, R, equal to 0.0821 L atm K᎑1 mol᎑1. Flask volume can be measured by filling the flask with water and then emptying it into a graduated cylinder. Once the number of moles has been determined by solving for n in pV ⫽ nRT, the ratio of mass of compound/ moles of compound gives the value of the molar mass. When this procedure is used with a compound like cyclohexane, a result that is fairly close to the actual molar mass can be obtained, barring other potential sources of experimental error. (See, for example, ref 4 ). However, when pentane is used, the calculated molar mass will be too low by about 25%, no matter how carefully the experimental procedure is followed. Table 1 summarizes some expected and obtained results using these two compounds. The temperatures were chosen to reflect values that might actually be measured in each
Vol. 82 No. 8 August 2005
•
www.JCE.DivCHED.org
In the Classroom
experiment, ones that are not very far above the respective boiling points of pentane and cyclohexane. In each case, the mass expected in step 3 was determined using the moles of vapor, and the known molar mass. The low molar mass value that is actually obtained arises from a measured mass of compound that is too low. The error does not arise from a loss of the volatile compound, but rather from an assumption that is made about the conditions existing in the flask. Since the only thing that appears to happen going from step 2 to step 3 is the condensation of the vapor, it is assumed that the apparatus mass in step 1 is less than that in step 3 by the amount of condensed vapor. If no liquid escapes, then it is true that the mass of compound in the flask does not change in going from step 2 to step 3. Also, the total pressure in the flask is 1 atm in step 3, just as it was in step 1. However, the air pressure in the flask in step 3 is no longer 1 atm. Now a portion of the 1 atm pressure is due to the vapor pressure of the liquid. Therefore, an error arises when the liquid mass is determined by subtracting the mass in step 1 from that in step 3. To see this, consider the data in Table 2.
One can determine that there are 6.24 ⫻ 10᎑3 mol of air in the “empty” flask at room temperature in step 1 by setting p ⫽ 1.00 atm, T ⫽ 293 K, V ⫽ 0.150 L, and R ⫽ 0.0821 L atm K᎑1 mol᎑1, using the ideal gas law, and solving for n. Taking the average molar mass of air to be 29.0 g/mol (8), there are 0.181 g of air in the flask in step 1. When the volatile liquid occupies the flask, the pressure of air is reduced by a quantity equal to the vapor pressure of the liquid. As a result, the moles of air and grams of air take on the values shown in Table 2. Table 3 shows how the low values for the pentane mass (0.307 g) and cyclohexane mass (0.406 g) that are experimentally observed and shown in Table 1 arise using the data from Table 2. Note that the above discussion ignores the small decrease in container volume going from step 1 to step 3 caused by the addition of the condensed liquid. The mass of pentane vapor in step 3 can be determied from the vapor pressure given in Table 2, the ideal gas law, and the true molar mass of pentane. The value is 0.251 g. The mass of liquid pentane can then be determined by difference using this value and
Table 2. Comparative Flask Conditions for Two Dumas Molar Mass Determinations
Total flask pressure Vapor pressure at 293 K
Cyclohexane (293 K)
Pentane (293 K)
Air Only (293 K)
1.00 atm (step 3)
1.00 atm (step 3)
1.00 atm (step 1)
0.0987 atm
0.559 atm
0.00 atm
0.9013 atm
0.441 atm
1.00 atm
a
Flask air pressure, step 3
᎑3
᎑3
Actual moles of air, step 3
5.62 ⫻ 10 mol
2.75 ⫻ 10 mol
6.24 ⫻ 10᎑3 mol
Actual mass of air, step 3
0.163 g
0.0797 g
0.181 g
aThe vapor pressures of pentane and cyclohexane were estimated by preparing plots of vapor pressure values versus temperature values with data from ref 7.
Table 3. Comparative Change in Mass Values Following a Dumas Molar Mass Determination Expected Mass Values, in grams
Actual Mass Values, in grams
Cyclohexane ⫹ 0.181 g
Flask contents (cyclohexane ⫹ air), step 3
0.424 g
⫺ Flask contents (air), step 1
0.181 g
0.181 g
Mass of liquid
0.424 g
0.406 g
0.424 g
⫹ 0.163 g
Pentane ⫹ 0.181 g
Flask contents (pentane ⫹ air), step 3
0.408 g
⫺ Flask contents (air), step 1
0.181 g
0.181 g
Mass of liquid
0.408 g
0.307 g
www.JCE.DivCHED.org
•
Vol. 82 No. 8 August 2005
0.408 g
•
⫹ 0.0797 g
Journal of Chemical Education
1195
In the Classroom
the total mass of pentane, 0.408 g. Then using 0.626 g mL᎑1 as the density of liquid pentane at 293 K, the decrease in container volume turns out to be only about 0.2%. Similarly, the container volume reduction is about 0.3% for cyclohexane. These reductions contribute slightly to obtaining a lower molar mass by further reducing the amount of air that reenters the flask. The above analysis suggests that when instructors select unknowns for experiments conducted in this fashion, roomtemperature vapor pressure should also be a consideration as well as the other usual factors, such as toxicity and boiling point. In an alternative approach, the partial pressure of the volatile liquid can be given, so students can determine the mass of the air lost in step three and use this to correct the calculation. If the flask is sealed after the excess vapor has escaped and prior to condensation, the problem described in this report disappears, since air can no longer return to the flask once the vapor is condensed (1). Other ways around the problem described in this paper include drawing a sample gas into a vacuum so that air is never present (9), and maintaining a constant amount of air in the apparatus at constant pressure by allowing the volume to change (10). Although these approaches eliminate the problem described in this report, they also add an increased level of complexity to the experimental procedure. In many situations, this is not prohibitive, but for large classes, the simpler experimental setup may be desireable. Finally, for readers who may not have considered why a liquid compound sitting at the bottom of a vessel and the same amount of the corresponding vapor—only a frac-
1196
Journal of Chemical Education
•
tion of whose particles are in contact with the vessel walls at a given time—can produce the same response when placed on a balance, an article by Nicholson (11) may prove enlightening. Literature Cited 1. Grider, D.; Tobiason, J.; Tobiason, F.; J. Chem. Educ. 1988, 65, 641–643. 2. Kaya, J. J.; Campbell, J. A.; J. Chem. Educ. 1967, 44, 394. 3. Steinback, O. F.; King, C. J.; Experiments in Physical Chemistry; American Book: New York, 1950; pp 20-37. 4. Alcock, J.; Gillette, M. Determining the Molar Mass of a Volatile Liquid by the Dumas Method (Laboratory Separate 481). In Modular Laboratory Program in Chemistry; C. Stanitski, Ed.; Chem. Ed. Resources, Inc.: Palmyra, PA, 1996. 5. Ebbing, D. General Chemistry, 4th ed.; Houghton Mifflin: Boston, 1987; pp 119–121. 6. Berin, J.; Brady, J. Second Edition Laboratory Manual for General Chemistry; Wiley: New York, 1982; pp 169–176. 7. The Merck Index: An Encyclopedia of Chemicals, Drugs, and Biologicals, 10th ed., M. Windholz, Ed.; Merck & Co.: Rahway, NJ, 1983. 8. Harris, A. J. Chem. Educ. 1984, 61, 74–75. 9. Pickering, M. The Rediscovery Book; Scott, Foresman / Little, Brown Higher Education: Glenview, IL, 1990; pp 65–66. 10. Peck, L.; Irgolic, K. Measurement and Synthesis in the Chemistry Laboratory, 2nd ed.; Prentice Hall: Upper Saddle River, NJ, 1992; pp 171. 11. Nicholson, L. J. Chem. Educ. 1988, 65, 808–811.
Vol. 82 No. 8 August 2005
•
www.JCE.DivCHED.org
