LETTERS T h e Dimensional Method of Problem Solving
To the Editor: In his paper on "The Solution of Elementary Chemical Problems" in the August, 1940, number of the JOURNAL OP CHEMICAL EDUCATION, Spicer makes two suggestions: (1) that the student justify in writing each step of the solution, and (2) that "proportions" be discarded. These suggestions should meet with universal approval. They can be put into effect most simply and expeditiously by labeling with its proper dimensions each number involved in the solution. In problems based on equations, such as Spicer suggests, the use of the proportionality constant, which is only one step away from the anathematized proportion, is unnecessary and can very profitably be replaced by a single dimensional setup:
+ H 8 0 , = ZnSO, + HI
Zn wt. Hz = 10 g. Zn X
mol HI g. H, mol Zn X 2 m~ =
XI-
Zn 65.4 mol Zn g.
Of course both this method and Spicer's are only proportions in disguise, but the dimensional method is two steps away from the straightforward proportion. By the dimensional method the cited gas-laws problem becomes: volume = 6 1. X
pressure pressure
and, since the pressure is decreasing from 700 mm. to 500 mm., we must get for the answer a volume greater than 6 liters. Hence the larger pressure must be in the numerator and volume = 6 1. X
-
700 mm. ---- = 8.4 I. 500 mm.
The concentration in mol/l. g.
NaOH
g. NaOH X- 300 cc. X 1000 cc./l. 40 mol NaOH
Finally, to find the freezing-point lowering of a solution containing three grams of methyl alcohol in 100 grams of water, we use the dimensional method: 3 g. CH,OH
lowering =
g. CHpO& mol CHSOH
32 -
100 g. HIO 1.860
X loo0 g./kg. X deg.
mol CHSOH kg. HIO
Atomic Weight Unit
To the Editor: In the November, 1940, JOURNAL,Mr. Fred Fordemwalt asks, "Why hasn't this unit ever been given a name?" He is referring to an atomic weight unit. It has, the microcrith. This is defined in the Unabridged Standard Dictionary as "the weight of the hydrogen atom." It is also defined in Williams' "Introduction to Chemical Science" (1888). my first chemistry textbook. Both Williams and Newth (1907) use the term crith for the weight of one liter of hydrogen. I have not seen these terms in recent texts. At that time hydrogen was the standard, with the atomic weight of oxygen 15.96. I also noted with interest at the number of molecules in a liter was given as lo2' in 1888. Crith is from the Greek word for barleycorn and was used to indicate a very small weight. I believe with Ostwald that the atomic weight is "a definite number which either by itself, or when multiplied by a whole number, determines the quantity that enters into compounds." Atomic weights are ratio numbers. There must be a standard, (as O equals 16) but do ratios have units? S. FRANCIS HOWARD NORWICH UNIVERSITY
To find the molar concentration of a solution containing four grams of NaOH in 300 cc. of solution, we proceed as follows:
=
These solutions are just as logical and expressive of the student's grasp of the problem, and are far shorter than the solutions given by Spicer. They have also the advantage that the complete numerical solution is set up before any calculations are performed so that any short cuts by cancellation are quite obvious.
= 1.74'
NonTmIem, VERMONT
To the Editor: Fred Fordemwalt brings out a very difficult point jn the teaching of general chemistry: what is the unit for our atomic weights?. . It seems to me that the use of such a word as "pel" would lead immediately to the difficulty of defining it. If the students did not ask for a definition of the word they would surely in. quire concerning its origin. WILLLAMC. FRISHE
.
..
Editor's nu&: Mark us down among the inquisitive, too. And we wonder whether the "pel" is a small enough unit, for its diminutive would seem to he "pellet," which we recollect as a rather large chunk of stuff.
