Correspondence
I
FURTHER REMARKS ON THE DETERMINATION OF FORMULAS DEAREDITOR: The note by Dodds [J. CHEM.EDUC.,8,2244-6 (Nov., 1932)] is believed t o be open t o criticism on two scores: first, it is incorrect in stating that present methods of instruction in the calculation of formulas are based upon percentage composition and, secondly, it uses, in its arithmetic, symbols which would unnecessarily confuse the average student. The writer's experience has shown that calculation of formulas is seldom handled satisfactorily by the majority of the class unless a considerable amount of drill is given t o it. This raises the question as to whether it might not be well t o omit it altogether from an elementary course in chemistry. Is it not, perhaps, one of those phases of the work dear to the teacher whose broad experimental background enables him to see clearly what is involved, but meaningful t o the average student only after further courses have built up his background and interest in the subject? It may serve t o distinguish the superior students. Also, it may serve to emphasize that formulas are derived from experimental results. The author believes it better to say that proved formulas tell the valence of the constituent elements, than t o emphasize valence as a means of writing formulas. If one is to teach calculation of formulas, however, he naturally wishes to place the instruction upon as reasonable a basis as possible. The following scheme has been grasped and applied more readily by students than any of several others that the writer has tried. To know the formula for a compound we must know what elements are present in the compound. Suppose we find by experiment that a compound contains calcium, carbon, and oxygen. Its formula must coutain the symbols for these three elements but since we do not yet know the subscripts, let us indicate them as x , y, and z, respectively. We have then Ca,C,O.. Our experiment then must give us not only what elements the compound contains, but the weight of each in a given weight of the compound. Also we must have the atomic weights of the elements involved. Suppose that we lind by analysis that calcium = 0.2581 g., carbon = 0.1548 g., and oxygen = 0.4129 g., in a sample whose weight is the sum of these, 0.8258 g. Since the table of atomic weights gives 40, 12, and 16, respectively, for calcium, carbon, and oxygen, we can make a trial at the formula asfollows: 557
JOURNAL OF CHEMICAL EDUCATION
558
MARCH.1932
The symbol stands for the atomic weight, the subscript for how many times this weight is taken. Accordingly, in the case of calcium, actual weight in grams of calcium given by experiment = the number of gram-atom of calcium times the gram-atom of calcium is taken = x. Similarly, y and z represent the number of times the gram-atoms, respectively, of carbon and oxygen are taken. That is, our experimental 0.1548 0.2581 results lead to x,or --, gram-atoms of calcium united with y, or 4l 12 ' 0.4129 gram-atoms of carbon, and z, or ------ , gram-atoms of oxygen to form 16 0.8258 gram of the compound. The conception of atoms as particles indivisible in ordinary chemical reactions requires, however, that the subscripts be whole numbers, but they must be whole numbers in the same ratio as the trial subscripts which we have already found. All of the other chemical principles involved have been considered when we write: or C ~ ~ L S C ~(The ~ ~ average O ~ ~ ~ O . c a0 . 2 c0.1~8 ~~ ~ 00.4121 - = Ca0.~616C~.012900.0258, A"
7"
.7,
." 7c
student does so poorly with calculations involving decimals that experience has shown it worth while to drop them. Usually be will readily grant that had we used 100,000 times as much of the compound each subscript would have been 100,000 times as large.) We now have whole-number subscripts, but in the simplest formula we use the simplest ratio of the subscripts, therefore we abandon the above formula and substitute CaC204,since 045 : 1290 : 2580 = 1 : 2 : 4. It may be pointed out that the simplest formula is not necessarily the correct formula and that to know the correct formula we must know also the molecular weight of the compound. As to the problems where the experimental data are given in percentage the writer simply treats these as special cases in which the number of grams of the respective elements per 100 grams of the compound is considered. In actual practice this method is far shorter than the explanation of it. The student goes directly from the analytical data and atomic weights to the trial formula with its fractional subscripts, and be seems to get a much clearer idea of the meaning and relationship of atomic weights, molecular weights, symbols, and formulas. F. J. ALLEN PWRDUEUNIVERSITY LAEAYETTE, INDIANA
