In the Classroom edited by
Applications and Analogies
Ron DeLorenzo Middle Georgia College Cochran, GA 31014
A Known-to-Unknown Approach to Teach About Empirical and Molecular Formulas P. K. Thamburaj Department of Chemistry, Ohio University Center, Zanesville, OH 43701;
[email protected] Professor Clarence Stephens of SUNY at Potsdam once said, “We teach students we have, not the ones we wish we had.” It is a challenge to teach chemistry in places where a significant percentage of students arrive under-prepared for an introductory course in chemistry. Chemistry teachers have to be creative in communicating the concepts in chemistry. It is interesting that many students who appear to be less than competent in solving chemistry problems rarely miss the correct answer when the problem is about money. Most students have no difficulty in calculating the money they expect to earn by baby-sitting X number of kids for Y hours, but many struggle with the determination of empirical and molecular formulas from experimental data.1 The following approach has been shown to be effective. Before presenting problems requiring the determination of empirical and molecular formulas, the following scenarios are presented. If possible, the instructor may use Monopoly game money and some volunteers from the class. The first scenario may be presented as follows. Tom has only $5 and $10 bills in his wallet. Fifty percent of the money in the wallet is made of $10 bills and the other 50% is made of $5 bills. What is the ratio between the numbers of the two bills in Tom’s wallet? Students feel comfortable when the data and steps are presented in a table format as shown in Table 1. Since the information is in percentages, one may assume that Tom has 100 dollars. For every $10 bill, Tom must have two $5 bills. This is a wonderful analogy to problems involving empirical formulas of the type AX2 (e.g., SO2 and CH2). The steps necessary to the determination of the empirical formula of an oxide of sulfur that is 50.0% in sulfur are outlined in Table 2. Students begin to “see” the connection between the two problems. The teacher at this point may introduce a more challenging situation to show that determining the whole-number ratio of the number of bills is not always simple. The following scenario illustrates that point. Seventy-five percent of the money Teresa has is made of $10 bills and the rest is made of $5 bills. What is the ratio of the numbers of the two bills? Students may assume that the total money Teresa has is one hundred dollars. The steps used are outlined in Table 3. We have a problem here! We cannot have 7.5 or 1.5 bills. This is an opportunity to warn students about dangers in rounding off prematurely. They may be tempted to round 7.5 off to eight or 1.5 to two. It is necessary to tell them that rounding off here would contradict the information given in the problem. Multiplying each number in the 1.5:1 ratio by 2 will give a 3:2 ratio, which agrees with the information given. Students must be reminded that mole ratios found in
chemical formulas, like the number of bills, are always whole numbers, and never fractions. The teacher now may ask, “How much money do you suppose Teresa had?” Some may answer 100 dollars because that was the assumed total in the beginning. A more relevant question may be, “What is the minimum amount of money Teresa must have to keep the ratio?” Most students see that the answer is $40 (three tens and two fives). The teacher then may suggest that Teresa has more than forty dollars. Most students realize that the next possible answer is $80. It doesn’t take too long for them to see that the total acceptable to retain the 3:2 ratio must be an integral multiple of $40. The teacher may call upon a volunteer who has the two bills in this ratio
Table1. Format for Simple Money Problem Type of Bill
Tot. Value from Each Type of Bill
No. of Each Bill = Tot./Value of Each Bill
$10
$50
$50/$10 = 5
$5
$50
$50/$5 = 10
Simple Whole Number Ratio of the Bills 5:10 = 1:2
Table 2. Format for Determining Formula of SO2 (AX2) % by Element Mass or Grams
Atomic Mass/ (g/mol)
No. of Moles = Mass/Atomic Mass
Whole Number Mole Ratio 1.56:3.12 = 1:2 empirical formula is SO2
S
50.0
32.1
50.0/32.1 = 1.56
O
50.0
16
50.0/16.0 = 3.12
Table 3. Format for More Complex Money Problem Type of Bill
Tot. Value from Each Type of Bill
No. of Each Bill = Tot./Value of Each Bill
Simple Whole Number Ratio of the Bills
$10
$75
$75/$10 = 7.5
$5
$25
$25/$5 = 5.0
7.5:5.0 = 1.5:1.0 3:2
Table 4. Format for More Complex Chemical Problem % by Element Mass or Grams
Atomic Mass/ (g/mol)
No. of Moles = Mass/Atomic Mass 40.0/12.0 = 3.33
C
40.0
12
H
6.7
1
O
53.3
16
6.7/1.0 = 6.7 53.3/16.0 = 3.33
Whole Number Mole Ratio 3.33:6.7:3.33 = 1:2:1 empirical formula is CH2O
JChemEd.chem.wisc.edu • Vol. 78 No. 7 July 2001 • Journal of Chemical Education
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In the Classroom
and ask this person to tell the class the total money he or she has. From the information, the class will determine the exact number of each bill that volunteer has. For example, the total may be 120 dollars. Most students get the right answer, nine tens and six fives. The teacher may call on a few students to explain the methods they used. Some may have determined 75% of $120 ($90) and then the number of tens. The remainder ($30) must have been made of six fives. Some students realize the relationship between the total given and the total associated with the simple ratio. In this problem, since the given amount ($120) is three times as large as the total associated with the simplest whole number ratio ($40), the number of each type of bill must be three times the number found in the simplest ratio. The person had nine tens and six fives. The relationship between a total given amount and the empirical amount (the total corresponding to the simplest ratio) is total given amount = n × empirical amount where n is always an integer. At this point one may present a problem similar to the one in Table 4. Questions that may be of help here are: 1. What does the formula, CH2O, tell us? 2. The molar mass (the mass of one mole) of a substance with empirical formula CH2O was found to be 180 g/ mol. What is the molecular formula of this substance?
Remind the students of the steps they took to solve the money problem. Find the empirical formula. Relate the empirical
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formula mass to the molar mass. The relationship is molar mass = n × empirical formula mass where n is always an integer and
n=
molar mass empirical formula mass
In our case, n is six (180/30). The molecular formula is C6H12O6, six times the empirical formula. Problems involving three or more different bills could make the approach more interesting. This approach can easily be adapted to other teaching strategies such as cooperative learning and peer-led team teaching. Professor Stephens also said, “We ask students to do what they know how to do before we ask them to do what they don’t know how to do.” Our approach does just that and has brought very good results. Note 1. An interesting idea related to this topic may be found in the following citation. As the first step, the mass of the substance that contains one mole of atoms of each element (minimum molar mass based on the element) is calculated by dividing one mole of atoms of the element by its percentage. The empirical formula is then derived by comparing minimum molar masses obtained from mass percentages of all the elements present. (Gilbert, G. L. J. Chem. Educ. 1998, 75, 851.)
Journal of Chemical Education • Vol. 78 No. 7 July 2001 • JChemEd.chem.wisc.edu
