In the Classroom
Unit Conversions: The Speed of Light and Blood Cholesterol Arthur M. Last Department of Chemistry, University of the Fraser Valley, 33844 King Road, Abbotsford, British Columbia, Canada V2S 7M8
[email protected] Many, if not most, textbooks intended for high school or college students who are just beginning to study chemistry discuss the interconversion of units in one of the early chapters (1, 2). The method used is variously called the unit-factor method, the factor-label method, or dimensional analysis. Finding examples from everyday life to stimulate student interest is an important consideration for most instructors. Two examples that I have used both in class and as assignment or examination questions are described. Monty Python and the Speed of Light Whenever I ask a class of students if they have ever seen a Monty Python movie or television show, I usually obtain a positive response from a number of individuals and this serves as a suitable prelude to the question: In “Galaxy Song”, which can be heard in the movie Monty Python's The Meaning of Life (3a) or on the soundtrack album from the film (3b), the speed of light is quoted as being equal to 12 million miles per minute. Is this consistent with the accepted value of 3.0 108 m/s? (note: 1 mile = 1.609 km). The answer can be obtained as follows: 12 106 mi 1 min 1:609 km 1000 m 1 min 60 s 1 mi 1 km m m ¼ 3:218 108 ¼ 3:2 108 ð2 significant figuresÞ s s Some students may argue that the agreement is not perfect, but it provides an opportunity for the concepts of uncertainty and significant figures to be reviewed. Students may also be interested to learn how the accepted value for the speed of light has changed since Fizeau obtained the first reasonably accurate value in July 1849. By coincidence, Fizeau's value of 3.15 105 km/s (4) agrees well with the value used in the Monty Python song. Blood Cholesterol Hopefully, students taking introductory chemistry are not troubled with high cholesterol levels in their blood. However,
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most of them are probably aware of the problem and some may have actually searched the Internet to find out what is an acceptable level of cholesterol in the blood. The answer that they find can depend on the country of origin of the Web site. The following problem is suitable once students are familiar with the concepts of molar mass and concentration. The U.S. National Heart Lung and Blood Institute Web site indicates that the desirable concentration of total cholesterol in blood should be less than 200 mg/dL (5). However, the Heart and Stroke Foundation of Canada states that the ideal concentration is less than 5.2 mmol/L (6). Are these two recommendations consistent or contradictory? The molar mass of cholesterol is 386.65 g/mol. The answer can be obtained as follows: 5:2 mmol 1 mol 386:65 g 1000 mg 1L 1L 1000 mmol 1 mol 1g 10 dL ¼ 201:06
mg mg ¼ 2:0 102 ð2 significant figuresÞ dL dL
Thus, the two concentrations agree to two significant figures. Literature Cited 1. Tro, N. J. Introductory Chemistry, 3rd ed.; Pearson: Upper Saddle River, NJ, 2009; Chapter 2. 2. Zundahl, S. S.; Zumdahl, S. A. Chemistry, 7th ed.; Houghton Mifflin: Boston, 2007; Chapter 1. 3. (a) Monty Python's The Meaning of Life; Terry Jones, Director; Universal Pictures: Universal City, CA, 1983. (b) Monty Python's The Meaning of Life; Original Soundtrack Recording, MCA-6121; MCA Records: Universal City, CA, 1983. 4. Aczel, A. D. Pendulum: Leon Foucault and the Triumph of Science; Washington Square Press: New York, 2003. 5. U.S. Department of Health and Human Services; National Heart Lung and Blood Institute. http://www.nhlbi.nih.gov/health/dci/ Diseases/Hbc/HBC_Diagnosis.html (accessed Jul 2010). 6. Living with Cholesterol. The Heart and Stroke Foundation of Canada http://www.heartandstroke.com/atf/cf/{99452D8B-E7F14BD6-A57D-B136CE6C95BF}/Living-with-cholesterol-en.pdf.
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Vol. 87 No. 10 October 2010 pubs.acs.org/jchemeduc r 2010 American Chemical Society and Division of Chemical Education, Inc. 10.1021/ed100359y Published on Web 07/30/2010
