CALCULATION of SIMPLEST FORMULA from PERCENTAGE COMPOSITION CARROLL W. GRIFFIN Vassar College, Poughkeepsie, New York
u
SUALLY in classes in general chemistry there are many students who, while they may memorize the steps for calculating the simplest formula of a compound from its percentage composition, have difficultyin understanding just why the manipulations which they carry out are a logical method for obtaining the formula. The writer, in common with instructors in chemistry generally, believes i t of utmost importance that the student appreciate the logic of a given attack on a problem and toward this end presents the analogy below as a means of clarifying the method of procedure in solving problems of the type mentioned. Suppose we are told that a certain compound has a composition by weight as follows: sodium 32.43%, sulfur 22.55%, oxygen 45.02%. In the various texts we are instructed to proceed as follows in order to obtain the simplest formula.
Suppose we get an "analyst" to break up the bunches and gather together all the red marbles in one pile, all the white marbles in another pile, and all the blue ones in a third. He then turns in, say, this report:
Obviously, if all the red marbles weigh 160 grams and each one weighs 8 grams there must be a total of 20 red marbles. In a like manner we see that there must be a total of 10 white marbles and 40 blue marbles. If all the clusters were alike and of the simplest constitution possible then each must have been made up of two red, one white, and four hlne marbles, this being the same ratio as 20: 10:40. We could "formulate" a cluster then by such an abbreviation as R2WBI. % At. Atontic I"4cgrol Furthermore, if the analyst had reported the percentEIcnzenl Corno. WI. Rolior Rollor age of the total weight contributed by each color as being 32% red, 20% white, and 48% hlne, instead of the absolute weights of 160, 100, and 240 grams, respecThe figurer of the third column are obtained by dividing the eorcespondtively, our calculations would have been just as simple. ing figures of the first column by those of the second,while the figuresof eolNeither should we have been troubled had he told us u m n four are obtained by dividing fhone of column three by the smallest number in t h a t group. that the relative individual weights of the, three kinds of marbles (based, say, on the weight of the white The reason why such a procedure yields the correct marble as unity) were 0.8, 1.0, and 0.6 instead of giving simplest formula of the compound having the stated their actual weights of 8, 10, and 6 grams. The result composition should be clear from the analow would have been the same as seen below. -. now described. Suppose we have a box containing 540 grams of marbles. Su~nosefurther that the marbles are arRed 32 0.8 "Formula" ranged in clusters, and that each cluster is likr every white 20 1.0 FUWBa Blue 48 0.6 80 other cluster and contains red, white, and hlne marbles. Imagine each cluster to be a "molecule" and the variously colored marbles to represent different kinds of The above kmd of computation is exactly that which atoms constituting the molecule. Now we cannot in we made in the case of sodium sulfate. That is, we the case of real molecules mechanically take apart a divide the percentage by weight of each element by its single molecule and count the atoms, thus obtaining atomic weight, just as we divided the percentage by its formula. If we likewise deny ourselves this pro- weight of each kind of marble by the relative weight of cedure in the case of our clusters of marbles we may that marble, and then reduce the ratio to the simplest nevertheless ascertain the numbers of diierently colored whole numbers. The two cases are thus analogous marbles in each bunch (that is, determine the "for- because atomic weights are relative weights, all being mula") as follows. based on that of oxygen taken as 16. .A
'
1
