CHEMICAL CALCULATIONS For Eleventh Students
and
Twelfth
Grade
MYRTLE C. BACHELDER Institute for the Study of Metals, University of Chicago, Chicago, Illinois
Tm
PURPOSE of this diagnostic test is to determine the degree to which the student has failed to master the fundamentd calculations of first-year chemistry and to make that degree apparent to the instructor so that he may correct the deficiencies by working either individually or with the class as a whole. Much of the thinking in first-year chemistry is based upon certain fundamental chemical cahlations. For example, equations are used as a sort of chemical shorthand to express in a summary manner what would take a paragraph to describe in longhand, and these in turn are the basis for the calculation of the straight-weight problem. Comprehension, mastery, and correlation of these fundamentals eliminate the possibility of an endurance contest in which the student who does not possess a prodigious memory is bound to lose. Once the fundamentals have been presented to a class, it is imperative that the teacher make himself aware of any lack of understanding. It is a t this point that the diagnostic test hecomes significant. The examination and use of numerous standard and diagnostic tests failed to accomplish for instructor and student the two objectives which the writer felt should be met. They did not force the student to think about a single problem from several points of view, nor did they emphasize.the negative results of the student's effort by stressing a teacher-analysis of errors. The strength of the present test lies in: (1) the necessity for the student integration of the information which has been presented in the form of basic types of problems, and (2) the teacher-participation which occurs in the analysis of the test results by checking on the record sheet of errors a complete summary of each individual's errors, thus pointing out the areas upon which remedial teaching must be concentrated both for the individual and the group. A careful review of the entrance examinations given a t the University of Massachusetts1in chemistry over a period of ten years and the College Entrance Board Examinations2 over a period of fifteen years was made to find the essentials which should be included. These
were comhined with a basic text, "Chemical Calculations," by Bernard Jaffe,3used in the classroom to produce approximately fifteen types of fundamental prohlems. The test was organized and given to a class of twenty-five boys and girls in grades eleven and twelve. Results of the first attempt indicated many weak spots and these were improved in a second form, also given to the class for further criticism. It came quickly, and the comhined efforts of the instructor and students were incorporated in the h a 1 forms which were revised from time to time. Form A of the test was administered after class instruction in the mathematical calculations had been completed. An analysis of the record sheet of errors was made the basis for review and corrective work which varied, both in time and areas, with the classes. Form B was then administered and served as a check on student improvement as well as the effectiveness of instruction. The total possible score for either form of the test is fifty-two points, and the single score indicated after each question represents the number of basic steps necessary to the solution of the question. The total scores which students made on a given test were used to determine the class median and to set up a class distribution curve, both of which were kept for comparative purposes. The test is intended to be used as a measure of power, or lack of it, but should it be diverted to the use of obtaining a record-hook grade the total score may he readily converted to a per cent evaluation. The record sheet of errors is a significant part cif the test from the point of view of instruction. Student failures on all parts of the test are readily checked on the sheet, and reading the results will give a picture of good or poor instruction, as the case may be, as well as the pattern of failure in the class and among individuals. Poor results on the first major question, I, 1-12, should make one suspect that the student has tried to memorize the rules of valence as applied to formula writing without grasping the concept of the structure of the atom and the significance of the ulanetary electrons in the formation ofthe molecule which is bask to an underof unpublished testsgiven each spring as qudfying examinations st the University of ~aasachusetts. ~mherst,. standmg of the calculation of the molecular weight of a
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Mmachusetts. "College Entrance Board Examinations," pany, Boston, published annually.
Ginn and Com-
a JAFFE,BERNARD, "Chemical Calcuhtions," World Book Company, Chicago, 1931. 217
JOURNAL OF CHEMICAL EDUCATION
substance. I n the second major question,^^, elements 11. 150 grams of an oxide of nitrogen gave by analysis 104.36 g r a m of oxygen and 45.64 g r a m of nitrogen. 2.054 a and b bring out a t once whether or not the idea of per g r a m of the material vaporized a t 750.1 mm. and 30°C. cent, the relationship of the part to the whole, is underto produce 652.33 cc. stood. If it is not, the calculation of the simplest a. What is the per cent of each element present in the formula from percentage composition cannot be made oxide?. ............................ .a. -(1) b. -(1) in element c. Element d, calculation of the molecular c. Find the simplest formula.. .............c. -(4) weight, assumes the use of the Periodic Chart and d. Give the molecular weight for the simplest simple arithmetical evaluation, hut leads to element e formulrt.. ............................d. -(1) and Avogadro's law. As in e, Avogadro's law and the e. If this is also the true formula, what would he the weight of one liter?. ............e. -(1) significance of 22.4 liters is inherent in elements g, h, i,j, f. What volume would this gas occupy under and k. Element j introduces Charles' and Boyle's laws standard conditions?. .................j. -(8) which are important to the solution of elements g, weight g. What would be the weight of one liter of of one liter of gas, and h, the determination of the true the gas under standard conditions?. ... .g. -(2) h. Whet is the true formula?. .............. h. -(3) formula, for the reference t o standard conditions. Faili. If the weight of one liter for the simplest ure to find thespecific gravity of agas in element I should formula is not the same as the weight of lead to a reexamination of the student's comprehension one liter from which the true formula is of the relationship between the weight of one liter of a calculated, what does this tell you about gas, its vapor density, specific gravity, and the calcuthe two formulae?. ...................i. -(1) lation of the molecular weight of a substance from any j. Are the weights of ertchliter the same?. ....j. -(1) k. Using the weight of one liter for the simone of these factors. The major questions, 111,IV, and plest formula, and the weight of one liter V, are straightforward checks on the understanding of for the true formula, show how yon would the weight-volume problem, straight-volume problem find the subscrint firmre hv which the simdest formula must be &ultinlied to ~~-~~~~ (Gay-Lussac's and Avogadro's laws), and the straightgive the true formula.. ...............k. -(1) weight problem. What is the specific gravity of the gas?. ....1. -(1) Theimprovement in comprehension and ease in han- 111. If1.5 liters of CO*are produced by the reaction dlmg chemical problems achieved through theuse of the tesrsovcr R of thrre years, more than justiGrd the wrirrr's faith in rhem, as well ns the belief tl~ntchemical what weight of carbon &sulfide must be used?. ................................ ,111.-(5) calculations need not become a mental hazard to the IV. 25 liters of oxygen reacted with hydrogen sulhigh-school student. ~
FORM A Diagnostic Test on the Mathematical Calculations of Chemistry I. Given the following valences, complete the c h t with the proper formulas (one point each):
~
~~
A~
~~
~
~~
~
~
fide gas. Find the volume of sulfur dioxide resulting. 2&S
+ 30,
-
2&0
+ 2503.. ...IV. -(5)
V. Calculate the weight of chlorine prepared when 500 gram8 of salt, containing 3 per cent impurities, are used for electrolysis. 2NaCI Total Score..
2Na
+ Ch.. .......V. -(5)
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Acknowledgment is made to those former students in the High School, South Hadley Falls, Massachusetts, whose interested efforts are incorporated in the test.
