In the Classroom
A Simple Demonstration for Introducing the Metric System to Introductory Chemistry Classes Clarke W. Earley Department of Chemistry, Kent State University Stark Campus, Canton, OH 44720;
[email protected] The following is a simple exercise that can be used to demonstrate the concepts of SI units, experimental design, and significant digits in a manner that holds the attention of students who already understand these concepts but is still instructive for students who are less well prepared. An advantage of this demonstration is that it takes material that is too easily treated in an abstract manner and turns it into a concept students can visually interpret. Linear measurement (length) is a very simple and easily understood concept. Students are already familiar with several different units of length, such as inches, feet, and miles. A short discussion on when use of each of these is most appropriate should illustrate why different standards are useful. For example, students can be asked how tall they are in miles or how many inches are driven in the Indianapolis 500. While students obviously know the definitions of most familiar units of length in terms of each other (e.g., 12 inches = 1 foot), most of them will probably not be as comfortable with the concept that all these units are based on some rather arbitrary standard. This is an important point, but the previous illustrations show that none of the commonly used units are intrinsically any better than any other unit. To demonstrate how a system of measurement can be generated, the width of the lecture hall can be defined as a “room”. Choice of this standard as a base unit instead of a more conventional length (such as a meter or a foot) is designed to place all students on a more equal footing. Solicit volunteers to unroll a paper streamer the width of the lecture hall and cut it to prepare a length one room long. Discuss the fact that while this unit of measurement is convenient for some distances, it is too long for measuring smaller lengths. Have a volunteer hold each end of the streamer and have nine additional volunteers place themselves so they can mark ten approximately equal segments. Once everyone is satisfied that they are spread as evenly apart as possible, cut the streamer into ten pieces and tape one of these pieces to the front wall in clear view of all students. This unit is defined as a deciroom and is equal to 1⁄10 of a room. The emphasis at this point is on the fact that the SI prefix deci means 1⁄10. A suggestion to add a little fun to the required memorization of these prefixes has been made (1). Have several pairs of students hold up some of the deciroom pieces, which will illustrate that these pieces are not all the same length. Give the students an opportunity to come up with a better method for dividing these pieces into ten equal lengths. Typically, most students have already figured out that folding into ten pieces should be much more accurate. This provides an obvious opportunity to discuss the importance of carefully designing experiments and it can be used to introduce discussion about the laboratory portion of the course. Next, have students take one of the deciroom
pieces, divide it into ten centiroom lengths, and compare the length of these pieces. Tape one of these centiroom pieces below the deciroom length. Seeing the different lengths displayed gives students a physical picture of how much an order of magnitude changes a measurement. If desired, one of the centiroom pieces can be given to a volunteer to make ten milliroom lengths. None of the students should have any trouble understanding that ten decirooms is equal to one room and that a deciroom is the same length as ten centirooms. Perhaps the most common source of error in conversion between units is confusion over whether units are to be multiplied or divided by the conversion factor. For example, do you take the number of decirooms and multiply by 10 to get to rooms (after all, the deciroom is smaller), or do you divide by 10 (correct, because it takes fewer of the larger unit)? General chemistry textbooks typically emphasize the meaning of the SI prefixes (for example, deci = 10{1) and would show conversion factors for the units used as: 1 centiroom = 1⁄10 deciroom = 1⁄10(1⁄10 room) = 1⁄100 room 1 centiroom = 10{1 deciroom = 10{2 room Alternatively, the following conversion factors can be used, which are probably more intuitive for most students: 1 room = 10 decirooms = 100 centirooms 1 room = 101 decirooms = 102 centirooms Conversion between different units can also be demonstrated. Measure the length of the centiroom piece using a ruler or yard stick, and then ask the students how wide the room is in inches. Most students’ initial thought appears to be that you can’t tell because you haven’t measured the room. However, at least a few students will realize rather quickly that the width of the room must by 100 times longer than the length of the centiroom piece. The conversion relationship for this problem is given by 1 centiroom = x inches where x is the measured length of a centiroom piece. While this problem can be solved intuitively, it can also be used to introduce dimensional analysis (factor-label method) (2, 3). In this case:
1 room × 100 centirooms × x inches = 100x inches room centiroom More difficult problems can also be created. Have several volunteers measure the length of a convenient object in the room (a table, chalkboard, etc.) using the streamer pieces. It is best to choose an object that will require use of both centiroom and deciroom units to illustrate the need to convert
JChemEd.chem.wisc.edu • Vol. 76 No. 9 September 1999 • Journal of Chemical Education
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In the Classroom
to a common unit before adding values. For example, if the object is 1 deciroom plus 3.6 centirooms, the length is 13.6 centirooms, not 4.6. Given the length of the object in centirooms, the length in inches can be calculated using the factor-label method. After calculating the width of the room in inches, have one or two volunteers measure the width of the room using a tape measure. The measured value obtained will almost certainly be significantly different from the value calculated using the centiroom piece. This can lead quite naturally into a discussion of the difference between precision and accuracy (4–6 ). Although the length of the centiroom piece and thus the width of the room can be determined rather precisely, the accuracy of this measurement can be quite poor. To further demonstrate this, several of the centiroom pieces can be measured. These values should be consistent, which indicates high precision. The poor accuracy is due to the variability of different deciroom pieces. This exercise has several important benefits. First, it incorporates a number of important concepts (SI prefixes, dimensional analysis, experimental design, etc.) as a cohesive
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unit. The approach can be extended to include volume calculations. A second benefit is the use of a physical model to illustrate what can too easily become abstract; the physical model makes these topics less intimidating for many students. Moreover, requiring active participation within the first one or two lectures appears to make students more receptive to answering questions and participating in other ways throughout the semester. Finally, the “demonstration” is quite inexpensive and easy to prepare, requiring only a streamer roll, a tape measure, a ruler, scissors, and tape. It has been used successfully in classes ranging in size from as few as 20 students and to more than 300 students. Literature Cited 1. 2. 3. 4.
Campbell, M. L. J. Chem. Educ. 1991, 68, 1043. McClure, J. R. J. Chem. Educ. 1995, 72, 1093–1094. DeLorenzo, R. J. Chem. Educ. 1980, 57, 302. Kimbrough, D. R.; Meglen, R. R. J. Chem. Educ. 1994, 71, 519–520. 5. Guare, C. J. J. Chem. Educ. 1991, 68, 649–652. 6. O’Reilly, J. E. J. Chem. Educ. 1986, 63, 894–896.
Journal of Chemical Education • Vol. 76 No. 9 September 1999 • JChemEd.chem.wisc.edu
