In the Laboratory
Measuring the Density of a Sugar Solution A General Chemistry Experiment Using a Student-Prepared Unknown Karen I. Peterson Department of Chemistry, San Diego State University, San Diego, CA 92182-1030;
[email protected] In the process of taking measurements or obtaining results that can be compared with known values, students can lose sight of an important goal of scientific experimentation—to obtain new results that are reliable enough to stand on their own. The standard methods for increasing confidence in measurements are well described by Vitha and coworkers (1). Although intended for students starting research, the concepts are important even for beginners. In this article, we focus on one of those concepts—calibrating an instrument to reduce systematic error—in an experiment designed for general chemistry students. While the experiment involves a simple calibrated density measurement, it is designed in such a way that students have full control over the accuracy of their measurement. In introductory chemistry courses, students are taught how to manipulate significant figures, yet many never learn their importance. Our experience has been that even upper-level undergraduates do not always understand the real meaning of significant figures and uncertainties in measurements. This meaning can be emphasized by rewarding students for results that are correct within the experimental uncertainty. This seems simple, but for this to be fair, we must ensure that careful work guarantees an accurate result. In this article, we suggest measuring the density of an aqueous sucrose solution. Sucrose solutions of a particular weight percent1 are easily prepared by the students. Although the densities are found in some editions of the CRC Handbook of Chemistry and Physics (2), they are not given in a simple form (interpolation is needed) and they are not readily accessible to the students while they conduct the experiment. Therefore, if each student is given a different weight percent of solution to prepare, it effectively becomes a student-prepared unknown. The CRC Handbook lists the densities of aqueous sucrose solutions for concentrations 0.5% to 84% (w/w)1 (2). These can be fitted to a cubic polynomial, thereby allowing the instructor to easily determine the true value of the density (Figure 1). Students should be assigned concentrations between 20% and 40% (w/w). If the concentration is higher, the
Density / (g/mL)
1.5
sucrose takes too long to dissolve, and the viscosity makes the measurements more difficult. If the concentration is lower, the experiment is less challenging because the densities are closer to the density of water. Experiment The experimental procedure used in the general chemistry course is given in the online supplement. Briefly, each student prepares a sucrose solution with an instructor-assigned concentration. After calibrating a 10 mL graduated cylinder with water, the density of the sucrose solution is measured multiple times. Prior to this lab, our students complete experiments involving calibration of glassware and density measurement. Sample preparation is addressed in prelab exercises, so we were able to make the instructions brief. This makes for a more student-guided experiment. The entire lab, including a short report, can be finished in about 2.5 hours, provided that students prepare by completing the prelab assignment, which includes good drafts of the introduction and procedure sections of the report. An uncharacteristically large percentage of the graded report (35%) is awarded for accurate and precise results. Based on trials done by students and instructors, we found that a reported uncertainty of less than 0.5% was a reasonable expectation. Therefore, we award full credit for a result which is within 0.5% of the literature value.2 Students who obtain results that deviate by more than 2–3% from the literature value most likely have made calculation errors. In our course, about 30% of the students receive full credit for their reported result. About 20–30% either do not finish the lab or report an unrealistic value for the density, and this seems to correlate with their lack of preparation. Hazards No significant hazards are associated with the chemicals used in this lab. Goggles, however, must be worn. Sources of Error
1.4 1.3 1.2 1.1 1.0 0.9 0
20
40
60
80
Weight Percent Sucrose Figure 1. Densities of sucrose solutions. Data points were taken from the CRC Handbook of Chemistry and Physics (2). The fitted curve is a cubic polynomial; the RMS deviation is 0.002.
Even fairly large errors in the preparation of the solution do not greatly affect the final result. Using a milligram balance, the uncertainty in the weight percent of a 100 g sample is about ±0.001% (w/w), which is negligible. The literature densities (2) for the sucrose solutions were measured at 20 oC. The students know that they must take into account the effect of temperature during the calibration process by using the appropriate density of water as their standard. However, their reported solution density will be uncorrected. If the temperature dependence of the solution density is the same as that of pure water, then a difference of ±5 oC in the temperature will give an error of about 0.1% in the density. This is insignifi-
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 8 August 2008 • Journal of Chemical Education
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In the Laboratory
cant compared to the magnitude of the random error and can be corrected by either the student or the grader. The most serious potential error, and one that is hard to correct, is due to absorption of moisture from the air by the sucrose. The Merck Index (3) states that finely divided sucrose can absorb up to 1% moisture, corresponding to about 0.5% uncertainty in the density—too large for this activity. To check how much moisture our sucrose sample absorbs, we dried a sample for three days at 70 oC. The mass was reduced by less than 0.1%, insignificant for our purposes. This result is specific to our environment in which the relative humidity is only about 25%; it should be rechecked in more humid environments. Conclusion Careful laboratory work, which corrects for systematic error, should produce results that are accurate within experimental uncertainty. Our main objective was to make this fundamental idea more apparent to beginning students. This was accomplished by designing a lab in which students’ results would correlate well with the quality of their work. Since students can measure the density of sucrose solutions reliably and can prepare their own unknown samples, they can be held responsible for the accuracy and precision of their final result and evaluated objectively. Acknowledgment I would like to thank Dale Chatfield for his input in developing this experiment for the general chemistry lab.
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Notes 1. The term weight percent, or wt %, with units of % (w/w), is most commonly used. Mass percent is equivalent to weight percent and appears to be preferred in general chemistry texts, but % (w/w) is still used. See, for example: Silberberg, M. S. Chemistry, 4th ed.; McGraw Hill, Boston, 2006; p 512. 2. Students report the standard deviation of five measurements that corresponds to about a 90% confidence interval for their results (approximately two standard deviations of the mean).
Literature Cited 1. Vitha, M. F.; Carr, W. C.; Mabbott, G. A. J. Chem. Educ. 2005, 82, 901–902. 2. CRC Handbook of Chemistry and Physics, 57th ed.; Weast, R. C., Ed.; CRC Press: Cleveland, OH, 1976; p D-261. 3. The Merck Index, 11th ed.; Budavari, S., Ed.; Merck and Co., Inc.: Rahway, NJ, 1989; p 8858.
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Journal of Chemical Education • Vol. 85 No. 8 August 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
