student actually receives this sum. Similarly, although the average atomic mass of a copper atom is 63.55 u, no copper atom actually has this mass. More Complex Problems Other monetary analogies illustrate more complex atomic mass problems. For example, a common type of problem requires students to determine the atomic mass of one isotope, given the atomic mass(es) of the other isotope(~),the percent abundance of each isotope, and the average atomic mass. Students might be asked to determine the atomic mass of boron-10, given that the percent abundance and atomic mass of the only other naturally occurring isotope of this element are 80.2% and 11.009 305 u, respectively, and that the average atomic mass of boron is 10.81u. Apossible analogy again involves students in parttime jobs. Ten students have summer jobs that pay an average of $10.81h. If there are two different rates of pay and eight students each earn $11.01/h, how much do the other two earn? (Answer: $lO.Ol/h.) Of course, some elements have more than two naturally occurring isotopes and some students become flustered when the quantity of data increases. In a typical problem of this type, the student is asked to calculate the average atomic mass of magnesium, given that the percent abundances and atomic masses of its three isotopes, magnesium-24, magnesium-25, and magnesium-26, are 78.99% and 23.985 042 u, 10.00% and 24.985 837 u, and 11.01% and 25.982 593 u, respectively. Again, the instructor could turn to a n analogy that involves students in part-time jobs. In a group of 100 students, 79 obtained part-time summer employment with an employer who paid $23.99lday. Ten members of the group found jobs that paid $24.99lday, while the 11 remaining students were more fortunate in finding an employer who paid $25.98/day. What were the average daily earnings of t h e students? (Answer: $24.31lday.) To this point, we have only wnsidered examples in which the student is required to calculate either the average atomic mass of an element or the atomic mass of a particular isotope. Another variation requires the student to determine the percent abundance, given the atomic mass of each isotope and the average atomic mass of the element. One such problem is to determine the percent abundances of each of the naturally occurring isotopes of lithium, given that their atomic masses are 6.015 121 u and 7.016 003 u, and that the average atomic mass of lithium is 6.94 u. Our monetary analogy is slightly different from the preceding examples in that it is concerned with spending money rather than earning it. While on a field trip to a local chemical company, a group of chemistry students eats lunch in the company's cafeteria. The students find that there are two lunch specials available: liver, broccoli, boiled turnip and herbal tea for $6.02; or cheeseburger, fries, coleslaw and a cola drink for $7.02. If the average cost of lunch for the group is $6.94, what percentage of students chose the more expensive meal? (Answer: 92%.) Finally, to give students an opportunity to demonstrate their higher-level thinking skills, an instructor could provide the atomic masslpercent abundance data for a n element and ask students to make up their own analogies. This task can be given as a take-home assignment. Students providing the most original analogies can be askedto share them with the rest of the class. Literature Cited 1. Wsaat, R. C., Ed.The Hondbmk ofchemisfm odPhyaics, 66th ed.; CRC P
Raton, FL 1985.
r e ~h: a
2. Greenwood, N. N.; Peiser, H.S. hf.Newletfar Chem Edue. 1990,33, 22-24. For mnuenience, the value for lithim was mvnded to three sigmificant figures. 3. D e l o m z o , R A P m b h m Sduingin &nerd ChmiSfoi Heath Lexmgton,MA, 1981; i pp421-422.
Pictorial Analogies IV: Relative Atomic Weights John J. Fortman Wright State University Dayton. OH 45435
The idea of a relative scale of masses for the different elements and their compounds is pivotal to the understanding of moles-to-mass and mass-to-moles conversions for elements and compounds. Good analogies have been reported using fruit salads ( I ) and coins (2). For these pictures dogs and chickens were chosen because they could be illustrated easily and could be assigned a reasonable set of comparative masses, even though it requires the student to accept standard constant weights for all dogs and chickens in the comparison. Pan of a presentation at the 195th National ACS Meeting and 3rd Chemical Congress of North America, Toronto, Canada, June 9, 1988.
Atomic Weights are Relative Weights
1 dog weighs 5 times weight of 1 chicken Figure 1. Analogy to a relative weight scale.
If Numbers are the Same Weights are in Same 5 1 Ratio
12 dogs weigh 5 times the weight of 12 chickens Figure 2. Analogy to a constant relative weight ratio if numbers are kept the same. Volume 70 Number 3 March 1993
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If 10 Tons of Dogs and 2 Tons of Chickens (5:l mass ratio)
There will be the same number of chickens and dogs Figure 3. Analogy to identical numbersof items if the same mass ratio is maintained.
If weights of groups are the Same, the Numbers are Not 10 lbs of dogs & 10 lbs of chickens
1 dog
5 chickens
Figure 4. Analogy to the ratio of the number of items obtainable if the weights are the same. Figure 1 shows a 5:l weight or mass relationship between our "standard" dogs and "standard" chickens. In Figure 2 the same 5:l weight ratio is depicted for a com-
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Journal of Chemical Education
If 8 Tons of Dogs and 8 Tons of Chickens
There will be 5 chickens for every 1 dog Figure 5. Analogy to the generalization of the number relationshipfor equal weight samples. parison of 12 "standard" dogs to 12 "standard" chickens. Figure 3 points out that if there is the same 5:l mass ratio of dogs to chickens there will be equal numbers of each, no matter what the actual masses. Figure 4 illustrates the reverse comparison and shows the one to five number relationship between the dogs and chickens if one has the same weight of each, and Figure 5 infers the same number ratio no matter what equal weights are chosen. Mass and weight have been used interchangeably in these comparisons and if this difference has been stressed this should be pointed out to the students. Although this relationship has a number of misconceptions possible if extended too far, it has been successful inshowing the correspondence of mass (or weight) to count which is so important in applying a relative set of atomic or molecular weights to stoichiometric problems. Photocopies of these illustrations will be sent on request to those wishing to make a set of overhead transparencies. Acknowledgment Bruce Stiver of the Media Services Department of Wright State deserves credit for the artwork and the chemistry department for paying for his services. Literature Cited 1. Feltr W. L. J. C k m . E d u c 1886.62, 61. 2. Myers R.T.J. C k m . E d v r 1889,66,249.
