Chemistry Everyday for Everyone
Using Data Pooling to Measure the Density of Sodas An Introductory Discovery Experiment Richard S. Herrick,* Lisa P. Nestor, and David A. Benedetto Department of Chemistry, College of the Holy Cross, Worcester, MA 01610; *
[email protected] The chemistry department at Holy Cross has developed a series of guided-inquiry experiments for our general and organic chemistry sequence we call the Discovery Curriculum (1–7 ). In a typical discovery experiment, a question is posed in pre-lab that leads students to rediscover a scientific concept. Many discovery experiments utilize data-pooling to answer the question (1, 3–10). Data-pooling experiments have several advantages over traditional laboratory teaching methods in which all students perform the same experiment. The most important advantage is the creation, in a single laboratory period, of a database that allows the student researchers to examine different aspects of the experiment. Data-pooling experiments have the additional advantage that each student or group of students works on a unique aspect of the experiment. They learn from this experience that their work is contributing to the group effort and that an accurate value is important. Finally, we find that actively engaging students in the laboratory leads to better comprehension of the material. The first experiment chemistry students perform normally introduces them to laboratory techniques, different kinds of equipment, and the scientific method. A very successful first experiment designed at Holy Cross is the Pennies experiment, regarded by many as the signature experiment of our curriculum. It has been discussed several times in this Journal (1, 8–10), has been featured in numerous talks by our faculty, and has also been adapted for use at the Museum of Science in Boston. However, it has become a victim of its own success. Numerous high schools now use the experiment. Many of our recent first year students have already performed the Pennies experiment, removing the element of discovery from it. For this reason we have developed a new first experiment that will allow students to experience the scientific method. In this experiment students determine the density of Coke and Diet Coke. During this process they discover that the densities of the two sodas are different and that density is an intensive property. In addition, their data are used to compare the accuracy and precision of different types of glassware. The experiment was run for the first time in the fall of 1997. It was the first experiment for the 210 students taking Atoms and Molecules, our first-semester general chemistry course. The students were organized into seven laboratory sections of 30 students and into three lecture sections. All students in a particular laboratory section were assigned to the same lecture section to maintain the tie between lecture and lab.
the glassware, students measure the mass and volume of 25mL degassed samples of either Coke or Diet Coke using each type of glassware (see Experimental Methods). They perform these measurements using a 25-mL graduated cylinder, a 50mL glass buret, and a 25-mL volumetric pipet. They convert these data to densities, which are entered into a graphing software application. A plot illustrating the scatter of the values is generated (Fig. 1). The students then recongregate in the pre-lab room and examine the graph. Among the observations they make are: The graduated cylinder data have by far the most scatter. The pipet data have the least scatter. The average values for the pipet and the buret are very similar (between 1.03 and 1.04 g/mL for Coke and just under 1.00 g/mL for Diet Coke). The average values for the graduated cylinder are lower (between 1.02 and 1.03 g/mL for Coke and between 0.97 and 0.98 g/mL for Diet Coke). While most of the data for the glassware are within a specific range, occasionally there is a point well outside the range. The density values for Coke are higher than the values for Diet Coke.
A discussion of these observations leads to several conclusions: The graduated cylinder is less precise than the buret or pipet. In the students’ hands the buret is less precise than the pipet. Random error accounts for most of the scatter. Human error accounts for the occasional data point well outside the range of other values. Coke and Diet Coke have different densities.
Experimental Design and Results The experiment is divided into two parts. At the beginning of the first part, the question “Are the densities of Coke and Diet Coke different?” is posed to the students. After receiving instruction on the use of the electronic balance and
Figure 1. Student soda density data for 25-mL volumes measured with three types of glassware. The data are from one laboratory section.
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Chemistry Everyday for Everyone
Since the average densities obtained with the graduated cylinder are different from those obtained with the buret and pipet, the students suggest that the graduated cylinder is less accurate than the buret or the pipet. The class does not have true values to evaluate this suggestion. Most of the conclusions are obtained by the group, although guidance from the instructor is occasionally necessary. It is a spirited discussion as students find that there is much information to be obtained from this graph. At this point the instructor poses the second question, “Does the size of the sample affect the density?” and focuses the discussion on how that question can be answered. Since the class has already learned about graphing and the power of straight-line relationships, they are able to suggest plotting a range of masses and volumes for both Coke and Diet Coke. The discussion of which glassware to use reinforces the advantages and disadvantages of the three types of glassware. The graduated cylinder is seen as not very precise or accurate but easy to use. When measurement does not require great accuracy or precision, it will be the choice. The volumetric pipet is the most precise piece of glassware and will be of use when analytical measurement of a specific volume is required. The buret is somewhat less precise than the pipet but can used to add variable volumes. The students immediately see why it is the apparatus of choice in the next part of the experiment. At the end of this discussion, students are given the procedure for the second part of the experiment and are assigned the approximate volume and the soda they are responsible for. Fifteen volumes from 2 to 30 mL are assigned for each soda. Each student determines the mass and volume for his or her own unique assignment. Students calculate the density and finish the experiment by determining the error propagation for all density calculations, using the max/min approach, and recording this information in their laboratory notebooks. Uncertainty values of ±0.2 mL for the graduated cylinder, ±0.02 mL (per reading) for the buret, and ±0.03 mL for the pipet are assumed. Students turn in their data sheets with all the data for the experiment along with the uncertainties. The faculty plot the data. A typical example of student data for the density of Coke is shown in Figure 2. The plot of mass vs volume for each soda is shown at the beginning of the next lecture to convince the class that density is an intensive property. This leads into a general discussion of density as a characteristic property of matter. The density for each soda obtained from the slope of the line is consistent with the values measured with the buret or pipet in the first part of the experiment (Table 1). The question of why Coke is more dense is also explored. Students are quick to suggest that the reason Coke is more dense is that it has sugar and Diet Coke does not. Information from the cans can be used to support this hypothesis. For example, a 12-oz. can of Coke states that there are 39 g of sugar (as high fructose corn syrup
Figure 2. Mass vs volume plot for Coke. The line is the best-fit linear regression line. The correlation coefficient, r 2, is greater than .999 for the line. The data were obtained by one laboratory section.
and/or sucrose) in 355 mL of soda. An 11% by weight sucrose solution has a density of 1.0423 g/mL at 20 °C (the densities of 11% fructose and glucose solutions are 1.0427 and 1.0416 g mL{1 at 20 °C, respectively) (11). These values are in agreement with the experimental determinations of density by the students (see Table 1). This can be used as evidence that the buret and pipet are more accurate than the graduated cylinder—a point that could not be definitively answered earlier in the experiment. Diet Coke contains the artificial sweetener Aspartame. This compound is the dipeptide N-L-α-aspartyl-L-phenylananine-1-methyl ester. The difference in the densities becomes understandable when it is pointed out that aspartame is 160 times sweeter than sucrose in aqueous solution (12). An indication that there is much less sweetener in Diet Coke than in Coke is the observation that Aspartame is listed as the third most abundant ingredient in Diet Coke (after water and caramel color), whereas fructose/sucrose is listed second in Coke. This means that Diet Coke is essentially colored water. This is backed up by the observation that the students determine its density (Table 1) to be close to the density of water—0.99821 g/mL at 20 °C (11). Although the can of Diet Coke gives no quantitative information, it is apparent that less Aspartame than sugar is required to achieve the right degree of sweetness. An effective way to show students that they have found a real difference in the two sodas is to bring a clear container of water to class and drop in cans of Coke and Diet Coke. The Coke can sinks and the Diet Coke can floats. Assuming that all other variables affecting the mass of the can are equal in each soda, the density of the soda solution determines whether it sinks or floats. This observation has been reported previously for a variety of sugar-containing and sugar-free sodas (13).
Table 1. Data from Pooled Mass/Volume Measurements Density/g mL{1 Sample
Part 2
Cylinder
Buret
Pipet
Slope
1.02 ± 0.01
1.035 ± 0.006
1.038 ± 0.002
1.033 ± 0.003
Diet Coke 0.98 ± 0.01
0.995 ± 0.004
0.997 ± 0.007
0.995 ± 0.002
Coke
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Journal of Chemical Education • Vol. 76 No. 10 October 1999 • JChemEd.chem.wisc.edu
Chemistry Everyday for Everyone
Experimental Methods At least 24 hours before lab, Coke and Diet Coke are emptied into separate large Erlenmeyer flasks each equipped with a stir bar and a watch glass. They are stirred to remove CO2 from the solution. Approximately 3 to 4 L of each soda is required for each 30-student lab section. Coke cannot be prepared more than two days in advance of the experiment or bacteria will begin to grow in the degassed sugar solution. Student obtain a 50-mL plastic bottle with screw cap attached and tare it on the balance. They are given a 200-mL sample of Coke or Diet Coke. They measure 25 mL of soda with a 25-mL graduated cylinder, pour it into the plastic bottle, and reweigh the bottle with the lid on. They dispose of the soda down the drain and retare the bottle and lid. A 25-mL volumetric pipet is used to add 25 mL to the bottle. The procedure is then repeated with a 50-mL buret. They make an initial measurement near 10 mL and a final measurement near 35 mL. Student density data are entered into a spreadsheet program in the laboratory. After the intermediate discussion about the experiment, students make one measurement of mass and volume for their soda. They are assigned a volume between 2 and 30 mL and use a buret to deliver the soda. They copy the data and error analysis from their notebooks onto their data sheets, which they turn in as they leave the laboratory. Conclusions The most important aspect of this experiment is that it successfully introduces students to the scientific method while teaching them important concepts and techniques. It also encourages student participation in the discussions that take place during the laboratory period, even though this is their first laboratory experience at Holy Cross. This is partly due to the fact that the concept of density is somewhat familiar to them and also that the question of soda densities is interesting to them. While they are busy finding which soda is denser, they also learn about many topics, including: The use of the electronic balance, graduated cylinder, buret, and volumetric pipet The advantages and limitations of the types of glassware Uncertainties and error propagation Extensive and intensive properties Graphing of a straight line Drawing conclusions from scientific data
Our experience shows that students in their first week of lab are able to accurately distinguish densities differing by just 4%. Both the data for Coke and the data for Diet Coke are internally consistent. From this it is clear that the students’ data can be used to answer the question “Do Coke and Diet Coke have different densities?” While the Pennies experiment provides an elegant initial experience that works well with both college and high-school students, we have discovered that the Soda Densities experiment has two distinct advantages over it as an introductory experiment. First, because students deal with chemical solutions of sweeteners in water, the concept of solutions and concentrations arises in the very first week of lab. Second, this experiment provides a way to teach students about these three types of volumetric glassware and their relative advantages and disadvantages. Students find this experiment to be interesting and educational. They use all three types of volumetric glassware in subsequent experiments. They become proficient in their use and understand the reasons for using a particular item of glassware. We have limited the experiment to Coke and Diet Coke, but many other sodas could be investigated. Acknowledgment We wish to acknowledge the Coca Cola Foundation for support of this work. Literature Cited 1. Ricci, R. W.; Ditzler, M. A. J. Chem. Educ. 1991, 68, 228. 2. Ricci, R. W.; Ditzler, M. A.; Jarret, R. M.; McMaster, P. D.; Herrick, R. S. J. Chem. Educ. 1994, 71, 404. 3. Ricci, R. W.; Ditzler, M. A; Nestor, L. P. J. Chem. Educ. 1994, 71, 983. 4. Jarret, R. M.; McMaster, P. D. J. Chem. Educ. 1994, 71, 1029. 5. Ditzler, M.A.; Ricci, R. W. J. Chem. Educ. 1994, 71, 685. 6. Jarret, R. M.; New, J. Patraitis, C. J. Chem. Educ. 1995, 72, 457. 7. Jarret, R. M.; New, J.; Karaliolios, K. J. Chem. Educ. 1997, 74, 109. 8. Mauldin, R. F. J. Chem. Educ. 1997, 74, 952. 9. Sardella, D. J. J. Chem. Educ. 1992, 69, 933. 10. Lamba, R.; Sharma, S.; Lloyd, B. W. J. Chem. Educ. 1997, 74, 1095. 11. Handbook of Chemistry and Physics, 77th ed.; CRC: Boca Raton, FL, 1996. 12. The Merck Index, 11th ed.; Merck and Co.: Rahway, N.J. 1989. 13. Toepker, T. P. Phys. Teach. 1986, 24, 164.
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