applications and analogies A Mole of Salt Crystals-Or How Big Is the Avogadro Number? William Hoyt St. Joseph's College Windham, ME 04062 Students can write the Avogadro number N and do calculations with it, but they have a hard time comprehending just how large it is. Common analogies involve numbers so large that they are hard to comprehend. For example, if a mole of dollars is evenly distributed to all the population of the world (I),each person would get about 120 trillion dollars. Alternatively, the interest for l s on a mole of dollars (5% annual interest rate) evenly distributed to the population of Earth would be around $200,000 per person (2). Smaller numbers can be obtained when astronomical analogies are used A mole of dollar bdls, laid end to end, would extend 5.9 times thc distance to the Andromeda Galaxv, our nearest large neighbor galaxy. Or, if the age of the ~ n i verse is taken a s 16 billion years, then about 5 x 1017s (83 micromoles) have passed since the Big Bang began the Universe. But students still have comprehension problems when discussing the distance to galaxies or the age of the Universe. As an alternative to the above, I ask my students to carry out the following sequence of calculations. First, they determine the volume of a mole of marbles 1cm in diameter, assuming cubic close packing, with 76% (3) of the total space occupied. For one marble,
and the molar volume is: 0.524 em3 6.02 x 10" marbles marble
mol
0.76
- 4.15 x
edited by
RONDELORENZO Middle Georgia College Cochran, GA31014
Using the area ofMaine (5),they find that the mole of sand grains would cover Maine to a depth of 4.82 m.
Students calculate the volume of a cubic NaCl crystal 0.01 mm on a side, then determine the volume of a mole of these crystals. Since the volume of a cube is equal to the cube of the edge, V = l3= (lo5 m)'
=
lo-'' m3
and m3 6.02 x loB crystals - 6.02 x 10' m3 crystal mol mol
lo-''
This volume can be used to calculate t h a t a standard American football field (6)would be covered to a depth of 113 km by a mole of these salt crystals. Area = 120 yd x 53.1 yd x 0'929 mZ - 5.33 x lo3 m2 yd2
A millimole of salt crystals would cover the field to a depth of 113 m. For a European football (soccer) field, corresponding depths are 118.8 km and 118.8 m for a mole and millimole, respectively. These calculations help students begin to appreciate the true vastness of Avogadro's number. An extension of this concept is to calculate the number of millimoles of salt crystals the largest building on your campus could hold. For exam le, a gym 100 m x 130 m x 40 . filled with NaCl crystals, m has volume of 5.2 x lo5 m8., if only 0.864 millimoles of crystals would be used.
loz3on3
mol 5'2
Converting to kilometers,
6.02 x
lo5 m3
= 0.864 mmole
lo5 (m3/mmale)
If a mole of NaCl crystals was in the shape of a cube, the length of the edge would be 844 m or 2768 R. $6.02 x 10%'
= 8.44 x
lo2 m or 844 m
Given the area of the United States (41, the students then calculate how deep the United States would be evenly covered by this mole of marbles:
Finally, the volume ratio of a single Na+ or C t ion to the volume of a n individual crystal (0.01 m on a side) is about the same a s the ratio of that individual crystal to the millimole of crystals on the football field.
The students then repeat the calculations for bird-shot 1 mm in diameter and sand grains 0.1 mm in diameter, resulting in depths of 44.3 m and 44.3 mm, respectively.
1. Hein,M.;Best,L.;Patdson,C. CollegechemisnyilnI~tmdtmdtrorota &"erol, own* ondBiochemislry,4th ed., BmoLs-Cole Pub. Co., Pacific Cmve, CA, 1988, p 193. 2. Van Lubeck, H. J. Ckm. Edue 1339.66.762. 3. &toby, D.: Naehhieb, N.; Freeman, W. Chemistry-A Seipnep of Change; Saunders,
Presented at the 198th National Meeting of the American Chemical Society.
4 N e w York PublieLibrory DoskRefenm; Webster'sNew World. 1989, p 765. 5. Collier's Encyclopedia 1988. 15, 234. 6. Ref. 4, p 580.
Literature Cited
496
Journal of Chemical Education
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