In the Laboratory
Applying Chemical Potential and Partial Pressure Concepts To Understand the Spontaneous Mixing of Helium and Air in a Helium-Inflated Balloon
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Jee-Yon Lee and Hee-Soo Yoo Department of Chemistry, Chungbuk National University, Cheong-ju, 361-763, Korea Jong Sook Park, Kwang-Jin Hwang, and Jin Seog Kim* Division of Chemical Metrology and Materials Evaluation, Korea Research Institute of Standards and Science, Yuseong, Deajeon, 305-600, Korea;
[email protected] Introduction Balloons are widely used in the laboratory as a convenient gas reservoir and for public demonstrations (1–3). Gases such as CO2 (4), CH4 (5), NH3 (6), N2, and Ar (7) can be stored in a balloon. When a balloon is used as a gas reservoir in the chemistry laboratory, the composition of the gas inside is usually estimated as being equal to that of the initial composition, and diffusion of the gas is neglected (8, 9). If a sample gas is collected at a specific place and moved to another place, then the inner composition of the balloon gas may have changed, as an equilibrium is reached with the air in the place of storage. For the most part, this is not a serious problem. However, if a balloon inflated with an inert gas is to be used to maintain oxygen-free and moisture-free conditions, then the composition of the gas inside needs to be controlled for safety reasons, and to maintain experimental accuracy. In particular, when using balloons filled with hydrogen in the laboratory, we should try to completely avoid any air diffusing into the balloon, as it can result in an explosive mixture (2, 10). 1
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Experimental A schematic diagram of the experimental setup is shown in Figure 1. Using a rubber band, the balloon was attached to metal tubing that led to the inlet tube of the mass spectrometer. The balloon was inflated with helium gas, and then deflated three times by using a rotary vacuum pump (Edward, E2M5) to degas its inner surface. After the final inflation of the balloon with helium, the vacuum line was evacuated using a rotary and a turbo molecular pump (Balzers, TPH 602). The vacuum of the system was observed to be 1.2 ⫻ 10᎑3 torr using a Pirani gauge (Alcatel P1 2). The partial pressures of the gases in the balloon were determined from the mole fractions and the total pressure measured in the balloon. The total pressure in the balloon was measured using a capacitance gauge (MKS, 626A), and the mole fraction of the gases in the balloon was determined using a mass spectrometer (Finigan Mat, 271/45). The peak sensitivities of the mass spectrum were determined by comparison with primary standard reference gases. Hazards
Figure 1. Schematic diagram of the apparatus used to analyze the gas composition inside a helium-inflated balloon using a mass spectrometer.
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Besides these considerations for balloon usage in the laboratory, our initial motivation for the analysis of the gases in a balloon was to answer simple and basic questions: Why is it that a helium-charged balloon left in the air always drops in a few days? Is the leakage of helium the only reason? What is the composition of the gas in the balloon when it falls to the ground after it has deflated? Intrigued by these questions, we developed a lab to analyze the gases in a balloon filled with helium. The variation in the composition in a balloon inflated with helium was measured over time, and the eventual mixing of He with air was observed. This serves as a compelling model of the diffusion process and the behavior of gas molecules; thus, the results described in this article will be useful in the classroom for teaching concepts of partial pressure and chemical potential in general and physical chemistry courses.
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Although conducting this experiment entails no undue hazards, the usual safety precautions should be followed when handling high-pressure helium gas and operating a vacuum system.
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where µi° is the molar Gibbs energy of a pure ideal gas, i, at the standard state. The mole fraction, xi, is the ratio of the partial pressure, pi, to the total pressure, p. In case of an ideal gas mixture, xi, is proportional to pi (xi = pi / p). The chemical potentials of the gases contained in balloon with time are shown in Figure 3(b). The atmospheric N2 and O2 have chemical potentials of –0.55 kJ mol᎑1 and –3.99 kJ mol᎑1, respectively. Therefore, the N2 and O2 molecules outside the balloon spontaneously diffuse to inside through tiny holes. Figure 4 illustrates the diffusion processes through the tiny holes in the balloon wall. The He gas escapes quickly through the holes, and the outside gases simultaneously diffuse into the inside of the balloon. After an 11 h inflation period, the mole fractions of He, N2, and O2 were found to be 0.677, 0.194, and 0.124, respectively. The diffusion rate of N2 was 1.6 times faster than that of O2, as shown in Figure 3(A), even though the partial pressure of N2 was about
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The compositions in the balloon of He and the major components of air, N2 and O2, were analyzed using a mass spectrometer. Representative mass spectra of the gases in an inflated balloon are shown in Figure 2. The mole fraction of water was very low (< 0.1%) due to the strong affinity of water to the experimental device and the mass spectrometer. Thus, the analytical data for water is omitted in this experiment and is reported later on, when the change in the mole fraction of water will be reported after analysis using an IR spectrometer. The mole fraction of the gases versus time is plotted in Figure 3 (a). As shown in Figure 3 (a), the mole fraction of helium decreased and the mole fraction of N2 and O2 in the balloon increased. The diffusion of air into the balloon appeared immediately after the leakage of He began. This observation means that the leakage of He was clearly accompanied by the influx of air. Ultimately, the mole fraction of He in the balloon decreased to 0.346 (at 751.2 torr) from an initial mole fraction of 1.000 (at 770.3 torr), while the mole fraction of N2 and O2 increased to 0.430 and 0.210, respectively, after 24 h. In the ambient air, the partial pressures of N2 and O2 were 0.78 and 0.21 atm, respectively (11). The mole fraction of N2 and O2 was almost zero in the balloon freshly inflated with helium. Even when the total pressure of the balloon (770.3 torr) was higher than the atmosphere (748.4 torr), external N2 and O2 managed to enter the balloon. How can the diffusion of air into a balloon containing a gas at a pressure higher than the surrounding atmospheric pressure occur? The difference in the chemical potential (12) of each component inside and outside of the balloon is considered to be the driving force for this process. The chemical potential is the molar Gibbs energy derived from ∆G ⫽ ᎑S∆T ⫹ V∆P. For a given constant temperature, the chemical potential is a function of partial pressure of a substance. The chemical potential, mi, of a substance, i, is a function of its mole fraction, xi, at a given temperature, as shown in equation 1.
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Results and Discussion
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In the Laboratory
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Time / hr Figure 3. (A) The change in mole fraction of a helium-inflated balloon over time. (B) The chemical potential, mi of He, N2, and O 2 in a balloon over time.
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In the Laboratory
four times that of O2 in the ambient atmosphere. The diffusion rate can be calculated using diffusion coefficients for the experimental conditions at the beginning of the experiment. This ratio, DN2/DO2, yields a value of 0.4. The chemical potential of each substance controls the direction of the diffusion process. The diffusion rates are determined by the diffusion coefficients of the gases. The diffusion coefficient, D, is given by eq 2:
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Conclusion The diffusion of air into a balloon is observed to be a spontaneous process in a balloon filled with a given pressure of helium, since each of the gases behaves independently to reach equilibrium. Not only the diffusion of helium from the balloon, but also the diffusion of the air into the balloon was confirmed by measuring the change in mole fraction of the gases in an He-charged balloon using a precision gas mass spectrometer. The mole fraction of He in the balloon decreased to 0.346 (751.2 torr) from an initial mole fraction of 1.000 (770.3 torr), while the mole fraction of N2 and O2 increased to 0.430 and 0.210, respectively, from an initial value of zero, at an atmospheric pressure of 748.8 torr and a temperature of 25 oC over a 24 h period. The results described here provide a model for teaching concepts of partial pressure, chemical potential, and diffusion to students in general chemistry and physical chemistry classes. Supplemental Material
Instructions for the students and notes for the instructor are available in this issue of JCE Online.
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atmosphere balloon wall
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where λ is mean free path and c is mean speed. The diffusion rate is a function of many variables, such as temperature, total pressure, collision cross-section, molecular weight, and partial pressure. No further theoretical estimation of the diffusion rate will be considered. Equation 2 considers only molecule–molecule collisions, but the real process includes molecule–wall collisions as depicted in Figure 4.
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Figure 4. Proposed diffusion process of gases through the pores in the balloon wall.
Acknowledgment This work was supported by the KRISS project (Establishment of a Chemical Metrology System in Korea). Literature Cited 1. Fortman, J. J. J. Chem. Educ. 1991, 68, 937. 2. Battino, R.; Battino, B. S.; Scharlin, P. J. Chem. Educ. 1992, 69, 921. 3. McNaught, I. J. J. Chem. Educ. 1998, 75, 52. 4. Jackson, B. A.; Crouse, David J. J. Chem. Educ. 1998, 75, 997. 5. Corkern, W. H.; Hughes, E., Jr. J. Chem. Educ. 1999, 76, 794. 6. Mattson, B. J. Chem. Educ. 1992, 69, 1029. 7. Bohac, A. J. Chem. Educ. 1995, 72, 263. 8. Deese, W. C. J. Chem. Educ. 1990, 67, 672. 9. Deese, W. C; Washburn, A. M. J. Chem. Educ. 1996, 73, 539. 10. Lawrence, S. S.; Franz, D. J. Chem. Educ. 1995, 72, 177. 11. Ebbing, D. D. General Chemistry, 5th ed.; Houghton Mifflin: Boston, 1996; p 210 12. Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, 1998; p 21.
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