adllod by
WALTER A. WOLF Eisenhower College Seneca Falls, New Yo* 13148
An Illustration to Demonstrate the Smallness of Molecules David W. Kingston Northern Michigan University Marquette, M I 49855
Now, I uaually drink a glass of water in front of my class and fantasize about whom I am drinking. This concept can be approached from a numher of directions; religious counterparts, political leaders and their opposition, military opponents, villians and heroes alike, and the list just goes on and on until your grasp of history fails you. This process has to he the ultimate in recycling.
What would sou think if vou were told that coursine Dasmann, R. F., "Environmental Conservation," John Wiley & through your veins was the stuif of the genius of Newton, the Sons, Inc., New York, 1976, p. 132. musical abilityof Brahms, the beautvof Cleo~atra?It miaht he true. ~ollo; through the next few baragrabhs and you can become convinced. My attempts to convey to my classes the consequences of Compact Comments having extremely small particles comprising our material world has resulted in my search for an example to illustrate Gale Rhodes this factor. After a numher of false starts, the following cala n d David Goodmanson culation has evolved. Not only does it illustrate the smallness Whitman College of molecules, but also it is a good exercise in dimensional Walla Walla, WA 99362 analvsis. he first part of the example describes the amount of water In most introductory chemistry texts, equations for interon the earth's surface. Seventv-one percent of the earth's conversion between temperature scales (e.g., Fahrenheit1 surface is covered by water; 97% of the water on the earth's Celsius) are simply given or they are plucked from the air after surface is in the oceans; 2% is tied up as ice and snow; 1% is discussion of the fact that the conversion process must take fresh water; and 0.001% is in the atmosphere. There are apinto account (1)the difference between themagnitudes of the proximately 3.17 X lo8 cubic miles (1.3 X 109km3) of water in degree units on each scale and (2) the fact that the scales are the oceans,' so the calculation of the number of moles of water offset; that is, they do not have' common zero. in the world is A clear derivation of a temperature scale interconversion equation can he carried out by plotting temperatures of one m3 (1000)3cm3 1g 1mole 100 (10W3 1.3XlOSkm3X-X 97 1km3 1m3 mXii%T scale against correspondina temperatures of the other. For indtnnre, on a graph of Fahrenheit versus Celsius trmpera= 7.4 X loz2moles tures, two known points ( W F , O°C) and (212°F. 100°C~deLet us assume some time in the distant past a John Doe termine a line whose slooe S is 180°F/10UoC or 0°F/5"C , ~-~ - ,.a n d dies. He is interred, his body dessicates, and the water that was whose interception t h > ~axis is 3 2 T . Therefore the equaincorporated in his hody is evenly distrihuted all over the tion of the line is world. Now let us calculate the numher of moles of water in John Doe's hody. About two-thirds of the human hody is water. Let us assume John Doe weighed 150 pounds (68.0 kg) when he died. 68,0 kg 2 kg of water 1000 g 1mole 3 kg of body weight 1 Another method of FahrenheitICelsius interconversion is = 2.5 X lo3 moles of water hased upon the fact that -40QC = -40°F. A plot of OF 40 versus OC 40 has a slope of 915 and passes through the origin. Now, let us calculate the numher of moles of water in a 12-02. The equation of the line is (0.35 liter) drinking glass. 1g 1mole 0.35 1X 1OOOml X X -= 19 moles of water 1rnl 18.0g If the water from our John Doe is distrihuted evenlv all over the world. how many moleculesofwater from his body are in the water in the 12-02. drinking glass? One molecule? Two? " From these equations, 2.5 X 103moles 6.02 X loz3 19 moles of of water from molecules water in the X JohnDo; X ofwater = 3.9 x lo5 drinking 7.4 X lo2 moles 1mole of water molecules of and glass of water in water the world C = (F + 40)] - 40 (6) 390.000 molecules of water! In other words, the interconversions are carried out by adding ?;his number of molecules seems very large, hut it could only 40, multiplying by 9/5 (for " C to OF) or 519 (for OF to "C), and he a laree numher if molecules are verv small. The nivotal subtracting 40. These conversions are easier to remember than point ofthe calculation is of course the l"arge value of kvogadro's Number. the less symmetrical ones hased on eqn. 2.
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506 / Journal of Chemical Education
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