In the Classroom edited by
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Harold H. Harris
Experimentally Determining the Molar Mass of Carbon Dioxide Using a Mylar Balloon
University of Missouri—St. Louis St. Louis, MO 63121
Barbara Albers Jackson and David J. Crouse Department of Chemistry, Tennessee Technological University, Cookeville, TN 38505
Does a balloon inflated with air weigh more than an empty balloon? Air has mass and so does helium. Helium balloons float in the air. Does that mean the helium balloon weighs less than zero? If helium were placed in an empty container, would the container weigh less? (1). Objects in water seem “lighter” because part of their mass is offset by the mass of water they displace. This is typically referred to as buoyant force (2). The same phenomenon occurs in air, but the mass of air displaced is usually quite small relative to the mass of the object (3, 4). In order to determine the mass of a gas in a flexible, lightweight container, the buoyant force of air must be taken into account. One of the problems in working with gases is that a given mass of gas will fill the volume of a rigid container, thereby requiring pressure measurements. Measurements of the molar volume of a gas in traditional balloons or fixed volume containers (5) requires the use of a pressure gauge. Rubber balloons, in particular, require higher pressure in order to stretch the balloon to a given volume (6). In this experiment only an internal pressure equal to that of the atmosphere is needed. Mylar balloons were used because they have a fixed, definite volume as contrasted with rubber balloons; Mylar is lightweight, requiring minimal additional pressure for inflation; and Mylar balloons are inexpensive and convenient to use. Materials and Methods A container for the solid carbon dioxide (dry ice) was made using a screw-top pint milk container and an eye dropper. A hole was drilled in the screw top, large enough to fit the glass of the eye dropper. The tapered part of the eye dropper was wedged tightly in the hole. (A hamster water A Typical Experiment Volume of balloon
1.615 L
Moles of air a
0.065 mol
Mass of air b
1.865 g
Mass of balloon
3.07 g
Mass of balloon + CO2
4.02 g
Observed mass of CO2
0.95 g
Total mass of CO2 (observed + air)
2.82 g
Moles of CO2 a
0.065 mol
Calculated molar mass of CO2
43.3 g/mol
Error
1.30%
a
Calculated using the formula PV = nRT ( P = 0.972 atm; T = 295 K, R = 0.0821 L atm/mol K).
b
Calculated using the formula moles = mass/molecular mass (molar mass of air = 28.97).
bottle from a pet shop would work equally well.) The dry ice was placed in the container and capped. The bottle was allowed to stand for a few minutes to have the carbon dioxide force out the residual air. A Mylar balloon and fastener were preweighed. The balloon was attached to the glass tube and the carbon dioxide filled the balloon. The balloon was tied with the fastener and reweighed. The carbon dioxide was let out of the balloon. Using a graduated cylinder, the balloon was filled with water and the volume of water was recorded. The room temperature was converted to kelvins. The atmospheric pressure was recorded using a barometer. The pressure in millimeters of mercury was converted to atmospheres. (If there is no access to a barometer, the barometric pressure given by the weather station in inches can be used; it can be converted to atmospheres by dividing by 29.9 inches.) The number of moles of gas in the balloon can be calculated using the ideal gas equation. The average molar mass of air (28.97 g/mol) was calculated by multiplying the molar mass of each gas by the percentage of that gas in the atmosphere, then totaling the individual masses. Results The results of a typical experiment are shown in the box. The temperature was 22 °C (295 K) and the atmospheric pressure was 739 mm Hg (0.972 atm). The empty balloons and fasteners were weighed. The balloons were filled with carbon dioxide gas and reweighed. The difference corresponds to the observed mass of the carbon dioxide. To get the true mass, we had to calculate the buoyant force contributed by an equal amount of air and add that to the observed value for the carbon dioxide. Having the volume, temperature, and atmospheric pressure, the number of moles of air in each balloon was determined. Having the number of moles of air, the mass of air was calculated. This buoyant force of air was then added to the observed mass of CO 2 to give the actual mass of CO2. Discussion The average results based on three trials gave a calculated molar mass of 43.1 g/mol with an error of 2.1%. When this experiment was done in laboratory classes by more than 200 students, the error generally ranged between 5 and 10%. All trials were performed at room temperature. Since this is a very quick experiment, there was no problem with changes in temperature or pressure. As soon as the balloon was inflated, it was capped. In the student trials, the balloons may have been over inflated, causing the higher percent error. Over-inflation of the balloons was more of a problem when
JChemEd.chem.wisc.edu • Vol. 75 No. 8 August 1998 • Journal of Chemical Education
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In the Classroom
propane and butane gases were used, since these gases came from pressurized cans. The carbon dioxide slowly sublimed. In previous experiments with larger Mylar balloons the error was 2–3%. The volume of the larger balloons was 11 L, making the experiment cumbersome and awkward. This experiment can easily be done in a general chemistry laboratory, since it takes less than two hours to perform. It gives a practical application of the ideal gas equation tied with the concept of moles. The molar mass of gases lighter than air could be done using a double pan balance. The string of the balloon would be tied to the weights on one side of the balance. The differ-
998
ence in mass would be subtracted from the mass of air. For more advanced chemistry courses, the molar mass of a gas generated by a chemical reaction could be determined. Literature Cited 1. Nicholson, L. A. J. Chem. Educ., 1988, 65, 808–811. 2. Van Nostrand’s Scientific Encyclopedia, 7th ed.; Considine, D. M., Ed.; Van Nostrand Reinhold: New York, 1989; Vol. 1, p 458. 3. Battino, R.; Williamson, A. G. J. Chem. Educ. 1984, 61, 51–52. 4. Lewis, J. E.; Woolf, L. A. J. Chem. Educ. 1971, 48, 639. 5. Bodner, G. M.; Magginnis, L. J. J. Chem. Educ. 1985, 62, 434–435. 6. Zaborowski, L. M. J. Chem. Educ. 1972, 49, 361.
Journal of Chemical Education • Vol. 75 No. 8 August 1998 • JChemEd.chem.wisc.edu
