applications and analogies A Mole of M&M1s Carmela Merlo Educational Opportunity Program lthaca College Ithaca, NY 14850 Kathleen E. ~urner' Baker Laboratory Cornell University Ithaca, NY 14853. We were interested to read in this feature column "How To Visualize Avogadro's Number" by van Lubeck ( I ) . To help our students appreciate the magnitude of Avogadro's number we use a meaningful and memorable analogy: a with conversion of units is a side mole of M&M'~.~Practice benefit. This attractive, easily remembered analogy was relayed to us by Judith and Heinz Koch of Ithaca College, and we hope that its circulation continues. The question had initially been posed i n a tutoring session led by Gretchen Rooker, then a n Ithaca College chemistry major, now a physician.
Capturing the Attention of the Students If one were to cover the 48 contiguous United States with a mole ofM&M's, or 6.02 x 10%plain chocolate candies, the thickness of the laver of M&M's so made would be closest to: (a) 1foot (b) 1mile (c) 10 miles (dl 50 miles Brainstorm with the students possible methods for solving this prohlem. Our solution follows.
Gathering Experimental Data A king-size bag of M&M's is used along with a 100-mL graduated cylinder. I t is found that the 100-mL graduated cylinder holds 88 M&M's. Volume per candy: 100 em3/ 88 M&M's = 1.1cm3per M&M 'Author to whom correspondence s h o o~ be addressed. 2Reg~steredtrademark of Mars. Inc.
edited by
RONDELORENZO Middle Georgia College Cochran, GA31014
Performing Calculations Volume of a mole of M&M's (1.1cm3/candy)(6.02x loz3candieelmole) = 6.6 x loz3cm3/mole Convert this volume to m3: (6.6 x lou cm3/male)(lm3/106cm3) = 6.6 x 1017m3/mole Find the area of the United States in mZ: The area of the 48 contiguous states is 3.02 x lo6 square miles (2). One square mile is equal to 2.59 x lo6 square meters (3). (3.02 x 106mi2)(2.59x 1 0 ~ m ~ / m = i7.82 ~) x 10'~m~ If the volume of one mole is to cover this area, calculate the depth: x 10'~m~) = 8.4 x lo4m deep. (6.6x 10'~m~/mole)/(7.82 Convert this depth to miles: 1 milkm) = 52 miles deep. (8.4 x 1 o 4 m ~km/10~m)(0.621
Of course, the calculations can be made more challengina bv having the students derive the mi2/m2conversion from fUndam&tal linear equivalents; however, we use the approach outlined above in order to focus on the primary goal of visualizing Avogadro's number. Connecting to Molecules Having seen the large number of M&M's a mole contains, we relate this to the molecules in a mole. Show the students a mole of water, 18 g. or 18 mL of water. That small amount of water containdthe same number of molecules a s our mole of M&M's contains individual candies. Conclusion We find that our students derive considerable satisfaction in performing this straightforward and illuminating "back of the envelope" type of calculation. Literature Clted 1.van Lubek, H.J. Ckem. Edve 1963,66,162. 2. Hoffman, Mark S., Ed. The World Almaand Bmk ofFods; Pharos B o o k New Ymk, 1990; p 421. 3. The WddAlmonaeondBoob offsets, p 416.
Volume 70 Number 6 June 1993
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