edited by DONNABOGNER Wichita State University Wichita. KS 67208
Teaching Stoichiometry: A Two Cycle Approach Richard L. Poole Athens High Schwl The Plains, OH 45780 Recently we were not only reminded of the difficulty of teaching stoichiometry to beginning chemistry students, but also informed of five possible reasons for this difficulty.' These reasons included the notions of (1)the horrendous word stoichiometry, (2) the use of unfamiliar chemical equations, (3) the use of mole, (4) the use of unfamiliar mass units-grams, and (5) the use of "simplifying" algorithms. The impact and credibility of these notions for impeding student learning are no doubt a function of many variables not the least of which are the curriculum and the textbook used in the classroom. For my students the sequential presentation and unfolding of the topics of atoms and mass units (amu's and grams), atoms and moles, compounds and moles, formulaand equation writing, and the laws of definite composition and multiple seem to be adeauate - proportion - . andkffective. However, for my students the "horrendous nature" of stoichiometry seems to be due to the omission of both a conceptual algorithm for the prigcess itself and one for the mathematical aspects-the dimensional analysis or factor labelling technique. Accordingly, i t is the intent of this article to describe and illustrate a tandem a ~ n r o a c hfor the teachine of stoichiod have been usiig for at least metry that I have d e ~ % ~ eand eiaht vears. This aooroach was . promoted . bv the fact that the text i w a s using2 &d more recent editions:,' presented stoichiometrv de nova and without reaard to the material that the students have previously learned. Before describing this tandem process it appears worthwhile in view of thepreceding to point out the &,ymology of stoichiometry. As with any large or unknown word or concept, students should be taught to examine it from the part to the whole and from the known to the unknown. Most students are able to see that stoichiometrv is com~osedof two parts "stoichio" and "metry." These students &stantly recognize "metry" from their study of the metric system as being related to the act or process of measuring. And a t least one student of Greek ancestry5 may recognize "stoichio" as coming from the Greek word stoicheion meaning element or first element. Hence, the horrendous word is auicklv decoded and neutralized. Flrst Cycle: Conceptual Model Given the fact that stoichiometry deals with quantitative relationships between elements and com~ounds.or between reactants a i d products, or between k n o k quantities of reactants producing unknown quantities of products, i t fol-
' Steiner. R. P. J. Chem. Educ. 1986, 63.1048.
Metcaife,H. C.; Williams, J. E.: Castka, J. F. Modern Chemistry; Holt. Rinehart &Winston:New York. 1978. Metcalfe. H. C.; Williams, J. E.; Castka. J. F. Modern Chemistry; Holt. Rinehart & Winston: New York. 1982. * Metcalfe. H. C.; Williams, J. E.; Castka, J. F. Modern Chernisfry: Holt, Rinehart & Winston: New York. 1986. Prokos, N.. Athens High School. personal communication. 1981.
Factors and Calculating lnlormatlon Factor Numbfn 2
1
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Factor Statement grams K Date within Me Source problem
4
3
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moles K moles UK grams UK gram formula balanced formula gram formula equation weight weight +
lows that the fundamental stoichiometry statement is "The known (K) defines, delimits, or determines the unknown (UK)." Moreover, if the word "defines", "delimits", or "determines" is represented by an arrow, then the basic and general stoichiometric statement can he expressed as K-UK
(1)
For astoichiometric problem of the mass-massvariety the specific paradigm becomes mass K grams K
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moles K
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moles UK
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mass UK
moles K -moles UK -grams UK
(2)
(3)
The nature of and sources of information for each of these factors follow. Factor 1: Grams of Known Contained within the statement of the problem itself is the specification of the quantity of the "known", or known substance, and it is to be communicated to students that this substance may be either a reactant or product. Teachers should then oresent not onlv both tvDes of examoles in their presentation'but also explain thati'he directionality of the stoirhiometric model is indeoendent of the directionalitv of equation writing. Factor 2: Moles of Known The quantity of the known substance is, of course, converted to moles by dividing by its gram formula weight, or by multiplying by the appropriate conversion factor, and the source of dataor info&na$ou necessary to perform this calculation is the gram formula weight of the known substance. The calculation of this factor and factor 4 should not oresent a major problem for students since they have had drevious instruction in converting grams to moles and vice versa. Factor 3: Moles of Unknown The number of moles of the unknown substance is determined from the mole ratio of the unknown substance to the known substance as given by the coefficients in the balanced formula equation. The prerequisite for this factor is the ability to "read" balanced formula equations, so during equation writing activities i t is necessary for the teacher to dwell on having the students translate equations into quantitative mole statements. Once this skill is mastered, i t becomes the most recently acquired information to be applied to the emerging concept of stoichiometry. Volume 66
Number 1 January 1989
57
Factor 4: Grams of Unknown The quantity of the unknown substance is converted from moles (factor 3) by multiplying by its gram formula weight, or by the appropriate conversion factor. As with factor 2, the students have had previous instruction with moles to mass conversions and vice versa and are aware that the necessary information or source of data for this is the gram formula weight of the substance. Accordingly, the basic stochiometric statement as well as the data sources for each factor can be formulated and linked as given in the table. In a similar manner the models for the other types of stoichiometric problems-mass-volume, volume-mass, and volume-volume-are, respectively, grams K
-
moles K
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moles UK -liters UK
(5)
liters K -moles K -moles UK
(6)
liters UK
grams K
--
2KC1+ 302 moles K
75.0 g KCIOs
gfwt of KC103
I5'Og
is 122.6 g 1mol KC10, 122.6 g KC10,
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How many grams of oxygen can be produced from the decomposition of 75.0 g of potassium chlorate?
moles UK 3 mol O2 mol
=
0.612malKC10~X
moles K moles K -moles UK moles UK -grams UK
where K = known suhstance, UK = unknown suhstance, efwt = eram formula weieht. - . and V.. W., Y..and Z are numerical quantities. T o clarifv the a~nlicationof this bicvcle anoroach to a classical stiichiom%ic problem conside; the fiilowing:
Another way of visualizing the basic stoichiometric statement is t o consider i t as a series of conversion factors. In this
2KC103 grams K
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With the expected substitutions these dyads become
(4)
liters K -moles K -moles UK -grams UK
-
surement as well as when they are asked to translate the mass of a substance to moles, or vice versa. Thus eq. 3 becomes
-
grams UK gfwt of 0% is 32.0 g
0.612 mol KC103 3 mol 0, 2 mol KC10,
= 0.918 mol02
32.0 g 0, 0.918mol O2x -= 29.4 g 0% 1mol 0, context factors 2,3, and 4 become conversion factors in the typical "from-to" mode, and this is seen in the next section. Second Cycle: Factor Labelllng The second cycle translates the four factors of the conceptual model into three dyads with each dyad having a recurring phrase. Each dyad is formulated utilizing the "from-to" notion of any mathematical conversion sequence where the units of measurement found in the numerator of one factor are also found in the denominator of the next factor of the dyad. Such conversions are encountered by students when they are introduced to the metric system and are taught to make conversions between it and the English system of mea-
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58
Journal of Chemical Education
Prior to my development of this approach, my students would complete the material on equation writing and then be hit with stoichiometry. Now, they have a conceptual linear model on which they can hitch not only their recently learned equation writing skills, but also their more distantly learned chemical-mathematical conversion skills. In addition, the approach appears to be well received by both average and above average students with some of them phonetimol K mol UK g cally writing out the model (g K UK) at a subvocal level as they solve problems. Hopefully, with the aid of this bicycle your students will be able to ride through stoichiometry rather than to stumble through it.
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