ARITHMETIC IN FIRST-YEAR CHEMISTRY* H. P. WARD,THECATHOLIC UNIVERSITY OF AMERICA, WASHINGTON, D. C. Much thought and many words have been spent in the discussion of objectives in teaching high-schoo! chemistry. The general tendency is to emphasize the facts of applied chemistry because these are of most practical value to the vast majority of pupils who study chemistry only one year and who never go to college. A writer in a recent issue of the JOURNAL oa CHEMICALEDUCATION is SO in favor of this practical objective that he would have nothing in the high-school course which did not hear some direct relation to everyday life. He would, among other things, eliminate all mathematics in first-year chemistry on the ground that i t means nothing in the life of an intelligent citizen. I have no doubt that this writer would not care to go on record as minimizing the importance of mathematics in the progress and appreciation of science. I am sure he would agree that the scientific mind is trained to the search for truth and this search is essentially mathematical and quantitative. It may be, however, that the ability level of high-school students can never be raised to the fullness of this appreciation. There is undoubtedly a big jump mentally in the capacity of pupils of high-school age and the mature students we get in college. Many of the latter fail to show an interest in mathematics anywhere near commensurate with its importance to science. It is generally agreed that an appreciation of chemistry is a legitimate objective in teaching high-school chemistry. This cannot be done without mathematics. Nevertheless, if I were asked "Why teach chemical arithmetic in the high schools?" I should answer "Why, indeed?" The arithmetic required for first-year chemistry is just plain, simple, grammargrade arithmetic. There seems to be no reason a t all why the high-school teacher should have to spend his time showing pupils how to calculate. It is being done, however, not only in the high school but in college. It is astonishing a t times to note the success and the ingenuity of certain students in complicating the simplest kind of arithmetical calculation. They are sure to get any problem involving numbers 100% wrong. 1 would say i t was just a natural gift if it were not for the good money that somebody has spent for them to acquire it. So far as I can see, nothing can be done about such gifted minds. They simply cannot be made to calculate, no matter how much money is spent on their education. It is also my opinion that mathematically inclined minds-like poetic ones-are born, not made. Their owners calculate for the mere love of calculating. Most of us belong to the middle class, both socially and mathematically. We like to do what is interesting to us. It is so with the average high* Read before the Washington Association of Chemistry Teachers on November 20, 1925.
VOL. 3, NO. 5
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school student who may like chemistry but not mathematics. His distaste for chemical arithmetic may be due to the fact that the solution of the problems involved in the ordinary course in general chemistry is made unnecessarily dull, if not unnecessarily difficult, by the use of too many mathematical schemes and formulas. For example, a writer in the JOURNAL OR CHEMICAL EDUCATION recently pointed out that there are a t least six (6) different formulas proposed in high-school chemistry texts for the Laws of Boyle and of Charles. Perhaps the good pupil derives one of these formulas once and so justifies his use of it, but how many pupils simply memorize the formula of their text and solve gas-law problems in a mechanical fashion? Why not teach the solution of the gas-law problems by a method which insures a t least some expenditure of mental energy in thinking as well as in memorizing? The gas laws should be associated in the pupil's mind with the Molecular Hypothesis. Gases should be thought of as freely moving molecules separated by space. Pressure brought to bear on gases will push the molecules closer together and thus decrease their volume, provided the temperature be constant. Again, speeding up the motion of the molecules by heat will cause the gas to expand provided the pressure be not changed. Thus any gas-law problem can be solved by multiplying the observed volume by two correction fractions as pointed out by a previous writer in THISJOURNAL.^ If this method of solving such problems is used constantly, the quantitative relations known as Boyle's Law and Charles' Law become firmly fixed in the pupil's mind which need not be burdened by trying to remember a formula that it may forget. Practically all the problems involved in first-year chemistry calculations can be attacked in this common-sense fashion. I t is not the purpose of this paper to point out the easiest methods of solving problems in general chemistry, but rather to emphasize the need of making pupils masters of chemical arithmetic. This requires constant drilling. A practice in use a t this university is to devote part of our freshman laboratory time once a month to problem work. In addition, problems involving the usual types in general chemistry are printed on cards and are occasionally distributed to freshmen, in the laboratory, who may be waiting for a turn a t the quantitative balances. The problems, as a rule, are all of a practical nature. If they are all of a kind, say on gas laws, we have the pupil work out the detailed answer of one or two problems and, for the others, indicate merely the method. This covers a lot of work in a short time and is primarily designed to emphasize the chemistry rather than the arithmetic of the problem. It seems a good idea to reverse this practice once in a while and emphasize the arithmetic rather than the chemistry. The chemical significance of Stuart R. Brinkley, "Problem Work in General Chemistry," THISJOURNAL, 2, 136-11 (1925).
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570
MAY,1926
a problem is slow to be realized by beginners and, in our zeal to drive this significance home, we are tempted to pass over too lightly the arithmetical operations involved. Mournful numbers often come from careless calculating as well as from ignorance of the principles involved. The following type of problem can be solved with profit in first-year chemistry by even the most practical-minded, intelligent citizen-to-be, for he can apply it to everyday life. Calculation of a Formula Years ago, alchemists spent their lives searching for the philosopher's stone that could "preserve health, make the old young, turn the coward into a hero, strengthen the mind and sober the drnnkard." ("History of Chemistry" by Emst von Meyer.) Their search was vain. Here is a good substitute for the philosopher's stone. There is enough for everyone, so calculate its formula and use your share. I t has the following composition: Boron Radium
Iodine Nitrogen
Sulfur
percentage composition
Atomic weights
Atomic
2.66 55.14 30.98 3.42 7.80
10.9 226.0 126.9 14.0 32.0
0.244 0.244 0.244 0.244 0.244
ratios
Simplest whole
numbers
1 1 1 1 1
Pormu1a
