Chemistry for Everyone edited by
Secondary School Chemistry
Diana S. Mason University of North Texas Denton, TX 76203-5070
Determining the Pressure inside an Unopened Carbonated Beverage
Erica K. Jacobsen University of Wisconsin–Madison Madison, WI 53706
Hans de Grys Lakeside School, 14050 1st Avenue NE, Seattle, WA 98125;
[email protected] Two things that can generate instant interest in chemistry students are the ability to see the real-life applications of chemical theory and the prospect of being able to consume sugar. This laboratory investigation gives students the opportunity to do both.1 Consider the humble 12-ounce aluminum soft drink can. When filled with a bubbly sugar solution, it provides not only liquid refreshment, but also a wonderful vehicle for studying gas laws, stoichiometry, and solubility. Perhaps even more importantly, when presented as an openended problem, this exercise inspires students to think critically and creatively about the chemistry at work in this everyday household item. In order to get carbon dioxide gas to dissolve in soft drinks, these beverages are bottled under significant pressure. Once sealed, the cans provide marvelous little black boxes to think about how gases behave and about the various ways one can “measure” a gas. After spending a few days introducing gases and discussing the simple and ideal gas laws, my students are presented with a sealed can of soda (or “pop” as many in the Pacific Northwest insist). The students are asked to break into small groups and devise a way to measure the gas pressure inside the unopened can. The students have one short period (45 minutes) to plan their strategy, and one extended period (75 minutes) to complete their investigation in the laboratory. They may use any of the standard equipment in the lab, but they are only provided with a single can. At this point the experiment could be reduced to an exercise in following directions by providing a protocol for the students to use, but experience has shown that much of the learning comes when students think about the problem and when teachers allow them to devise their own unique solutions. Over the seven years or so that I have performed this lab with students, I have been amazed at the incredible creativity and resourcefulness that my students have shown in attempting to solve this problem. I will outline several of the more common solutions that students have come up with over the years, with a brief discussion of the merits and implications of each method. As an aside, this lab is most appropriate for the high school and introductory college level, and while most of the assumptions made are quite reasonable, it does not attempt to address the more complex nonidealities of aqueous solutions introduced in an advanced course like physical chemistry. The “Ideal” Solution The first solution is ideal in two ways: when performed carefully it usually generates a fairly accurate answer, and it www.JCE.DivCHED.org
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makes good use of the familiar ideal gas law. To use the ideal gas law to calculate the pressure inside the can, one needs to know the temperature of the gas, the volume of the gas, and the number of moles of gas. Measuring the temperature is straightforward, especially if the students allow the cans to sit at room temperature and come to thermal equilibrium with the lab environment. Drinks that are still slightly cool from the refrigerator can be measured with a thermometer upon opening, although error is introduced here as the drink tends to warm up during the course of the experiment. Temperature being the only physical attribute that is easy to measure while the can is sealed, it is time to pop the top. Clever students will measure the mass of the sealed can first, then carefully open it listening for the characteristic pssssst of escaping carbon dioxide. Immediately, they find the new mass of the opened can on the balance and record their data. In this way students can measure of the mass of CO2 that escapes when the gas sitting above the drink goes from its unknown higher bottling pressure down to atmospheric pressure. Typically masses range from 0.1 to 0.2 g for the escaping gas, depending largely on the temperature. A conventional 12-oz can of soda has a mass in the range of 380– 390 g, so it is important that the balance have a capacity of at least 400 g as well as accuracy to at least ± 0.01 g (a milligram balance is preferable, but not strictly necessary). A little stoichiometry yields the moles of carbon dioxide that left the container immediately upon opening. Finally, the students need to find the volume of the gas space in the can. It is important for them to realize that only the headspace where the gas resides (and not the volume of the liquid nor the entire volume of the can) is the measurement of interest. They should also realize that at equilibrium, the carbon dioxide that is dissolved in the aqueous solution does not directly contribute to the pressure of the gas in the unopened can. With these things in mind, they set about to measure the volume of the headspace. Some students will try to empty the entire can to find the volume of the soft drink, the total capacity of the can, and volume of the headspace by subtraction. This is very messy, and not terribly accurate.2 A better way is to pop the top and then slowly and carefully add water from a very small graduated cylinder or graduated pipet. Students keep track of how much water they add and stop when the total level of the liquid rises to the top of the can. Typical volumes for the headspace are around 14–16 mL. After gathering the data they need, students can easily employ the ideal gas law to calculate the pressure that the gas was under while the container was still sealed. Thought-
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ful students will realize that the pressure calculated in this manner does not represent the total pressure inside the can before it was opened, but rather the “gauge pressure”, or the added pressure above ambient atmospheric pressure. Even after the explosive opening pssssst, there is still carbon dioxide gas occupying the headspace, exerting a pressure equal to the ambient atmospheric pressure. Thus, if one wishes to calculate the total pressure of gas in the can before it was opened, the current atmospheric pressure in the room must be added to the calculated gauge pressure. Capture the Gas A second strategy used by students is not too different from the first, but centers around trying to capture the gas that is trapped in the headspace. There are many variations of this technique, but most of them involve submerging the pop can in a container of water and constructing a gas trap of some kind to catch the escaping carbon dioxide by water displacement. The apparatus usually involves a eudiometer or graduated cylinder to measure the volume of the gas, and a funnel and rubber tubing to try to catch the escaping gas when the container is opened. This method is usually inferior for a number of reasons. First, it takes a certain degree of finesse to capture the gas without letting some escape, and many groups notice bubbles of carbon dioxide that do not make it into the eudiometer. Second, there is some subjective judgment involved as to when the gas from the headspace has all been collected and when the device is beginning to collect carbon dioxide that is outgassing from the aqueous solution. The distinction is an important one, since the gas that was dissolved when the can was sealed did not contribute directly to the pressure. Finally, the calculations are a little more complicated since the vapor pressure of water must be considered when finding the pressure of the collected carbon dioxide by water displacement. This method also does not provide the volume of the initial headspace, and therefore a second can of soda is required to get this additional information. Although I tell the students up front that their total quota is only one can of soda, I often relent and provide an additional can to students whose experiments initially go awry. Henry’s Law When this exercise is performed with my advanced chemistry class, the solutions are often more theoretically technical or simply more elegant. Over the years, a couple of groups have resorted to Henry’s law to determine the pressure: Cgas = kPgas (1) Simply put, the solubility of the gas in a solvent, Cgas, is directly related to the (partial) pressure of that gas above the liquid, Pgas. One needs only to find the solubility of carbon dioxide in the sealed can and the Henry’s law constant (k, which is approximately 3.5 × 10᎑2 M兾atm for CO2 at 25 ⬚C; ref 1), and one can solve for the pressure directly. The constant k is for the solubility of carbon dioxide in water, not in
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Diet Pepsi, but experiments have shown that the water value works well for different kinds of sodas. Unlike the previous methodologies where only the gas in the headspace was at issue and the dissolved gas was not measured, in this case the opposite is true. The solubility term refers to only the gas that is actually dissolved in the sealed can. The challenge then, is to completely degas a can of soda and measure the moles of carbon dioxide that were dissolved. There are various means to this end, some of which provide more accurate measurements than others. Simple agitation is a favorite, although care must be taken not to spill any of the liquid contents. A high frequency shaker table can be used if one is available, with the mass of the can taken before and after shaking. Another approach is to heat the can gently with a hot plate and allow the gas to escape as the solubility of carbon dioxide falls with rising temperature. If the can is heated too much, a significant quantity of water vapor also escapes, foiling the attempt at measuring the mass of the CO2 accurately. A more novel method of degassing involves the introduction of nucleation sites into the beverage. Sprinkles of salt, sugar, or even whole candies (e.g., Mentos, Life Savers, etc.) have been shown to bring about rapid outgassing of carbon dioxide in a variety of sodas. As long as the students remember to measure the mass of these added substances and to add them slowly to prevent the dreaded bubble-over, they can be an effective tool. My most nonchalant student simply opened his Coke and left it on the counter to outgas overnight. A pop can filled with water was left next to it as a control to see how much of the “lost” mass was actually evaporated water as opposed to outgassing carbon dioxide. Once the total number of moles of CO2 have been found and the solubility calculated, it is a straightforward matter to use Henry’s law to find the initial pressure that led to that level of carbonation. Farther Afield Although the three strategies outlined above represent the three basic models that most students use, there are other possible avenues to solving the problem, some that promise viable solutions and many others that do not. One group from my advanced class wanted to use an acid–base approach, since aqueous carbon dioxide forms carbonic acid. They measured the pH of a newly opened soda, thoroughly degassed it, and measured the pH again. Their plan was to use the change in pH and the Ka for carbonic acid to calculate the concentration of carbonic acid present. From these data and literature equilibrium constant values, they could in turn calculate the molarity of the aqueous CO2 dissolved in the soda, on route to a Henry’s law solution described above. Unfortunately, the change in pH between the fizzy and flat cola was so small that our pH meter could not reliably measure it. Upon further reflection, the group realized that the very weak nature of carbonic acid (Ka = 4.3 × 10᎑7 at 25 ⬚C) (2) coupled with its very dilute concentration in soda (in the neighborhood of 1 × 10᎑4 M) (3) could not possibly make any difference in the sea of stronger and more concentrated phosphoric acid already present in the cola. The result was
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that the phosphoric acid swamped any noticeable change in the [H3O+] owing to the removal of the CO2. The group could not complete the experiment using their chosen method, but I still classified their endeavor as a success since they completed a more fundamental mission: to think about chemistry on a deep level and engage the material in a thoughtful and creative way. Accuracy and Complexity No one is arguing that any of these methods will generate extremely accurate or precise figures for the pressure inside a sealed soda can. Some measurements involved are subject to relatively large uncertainty, such as 5% or more for volume measurements of the headspace owing to the constant effervescence of the drink. And even the more accurate models described above include some working assumptions or simplifications. Moreover, experience has shown that the exact pressure varies somewhat from brand to brand and even from can to can. The primary purpose of the lab is to stimulate students to think carefully and deeply about a problem, not just on the theoretical level, but also on a practical one. Some plans initially reveal deep misconceptions about gases and gas laws. Other plans sound great in theory, but prove to be hopelessly impractical in real life. Requiring students to both plan and execute a lab with very few instructions allows them to develop the critical skills necessary to become thoughtful experimentalists. Despite the focus on process over product, a little skill in the lab will generate quite reasonable values for the pressure inside the can. Most of my students typically calculate gauge pressures between 3 and 4 atmospheres of pressure for sodas at ambient temperatures of 22–24 ⬚C. A search of the Internet supports these values (4), and a call to a local soft drink bottling plant (5) confirms that we are well within experimental error. When I spoke to the production manager, he quoted me gauge pressures of 20 psi (1.4 atm) for “refrigerated” Pepsi and 55 psi (3.7 atm) for “room temperature” Pepsi. Since the solubility of carbon dioxide varies so dramatically with temperature, it is important to consider carefully the temperature of the can when evaluating the accuracy of the pressure. A graph of carbon dioxide’s solubility in water at different temperatures could be readily used in creating a rough graph of a particular soda’s gauge pressure at those temperatures. A side note to this experiment is that many students, being energetic and inquisitive young people, want to shake the can first as a way of altering the pressure inside. Interestingly, this seems to have a pretty small effect on the pressure that is measured by these different methodologies. This result seems to support the idea that while shaking a sealed can of soda may redistribute the gas inside (and consequently contribute to foamy eruptions) it does not cause much (if any) of the dissolved CO2 to come out of solution. Two interesting articles describing this conclusion more thoroughly and including ways to test it were published some years back (6, 7).
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Conclusion Many articles have been written about the wonders of soft drink chemistry as an education tool, both in this Journal (3, 8–11) and elsewhere. This fact should not be surprising since soda cans and bottles provide wonderful real-life illustrations of a multitude of chemical topics, from gas laws to equilibrium to acid–base chemistry. The investigation described in this article is one that has proved particularly worthwhile in getting students to think deeply about the concepts involved, devise novel and creative solutions to problems, and follow through on an investigation even when their initial strategy proves to be inadequate. The investigation provides flexibility in the level of sophistication demanded of the students, in terms of the number of hints or scaffolding provided and in the kind of approach chosen (e.g., ideal gas law vs Henry’s law). The soda pressure concept is also ripe for extensions or additional investigations: comparing different brands of soda or differences between diet and regular, exploring the different pressures found in soda bottles compared to soda in cans, contrasting the results achieved through different experimental methods, and so forth. While my students have uncovered many of the obvious routes to solving the problem of calculating soda pressure, there are undoubtedly many more that have not yet come up in our classes. The author would appreciate hearing about novel methodologies not described in this article. Notes 1. Common sense safety protocols dictate that drinking the beverages should occur either before or after the lab, using cans that were not subjected to experimentation. 2. An interesting observation is that despite 12-oz cans listing their net volume as 355 mL, almost all of them contain much closer to 365 mL of beverage when poured out. Perhaps the submerged bubbles account for the gain in volume.
Literature Cited 1. Sander, Rolf. Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry. http://www.mpch-mainz.mpg.de/ ~sander/res/henry.html (accessed Mar 2007). 2. CRC Handbook of Chemistry and Physics, 74th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1993; pp 8–47. 3. Howald, R. J. Chem. Educ. 1999, 76, 208–209. 4. Meraj, S. Pressure in a Soda Can. http://hypertextbook.com/facts/ 2000/SeemaMeraj.shtml (accessed Mar 2007). 5. Pepsi Bottling Group, 2300 26th Ave S, Seattle, WA 98144. 6. Deamer, D. W.; Selinger, B. K. J. Chem. Educ. 1988, 65, 518. 7. Edmiston, M. D. The Physics Teacher 1992, 30, 325. 8. Kavanah, P.; Zipp, A. P. J. Chem. Educ. 1998, 75, 1405. 9. Snyder, C. A.; Snyder, D. C. J. Chem. Educ. 1992, 69, 573. 10. Rohrig, B. J. Chem. Educ. 2000, 77, 1608A. 11. Herrick, R. S.; Nestor, L. P.; Benedetto, D. A. J. Chem. Educ. 1999, 76, 1411–1413.
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