ANALYTICAL EDITION
438
111). The highest ash content among all the samples was 14.34 per cent, and the lowest 4.84 per cent. The average for the entire series was 9.27 per cent. The maximum error for an average low-purity product amounts thus to 3 parts in 93, which is much better than the permissible error in the chemical method. It is undoubtedly possible to attain higher precision in the conductometric ash determinations than in those which form the basis of the comparison-namely, the less accurate and more difficultly reproducible values obtained by incineration. The real meaning of this apparent paradox is that the reproducibility and reliability of the conductance measurements introduce greater consistency among themselves than is to be found among the chemical ash determinations. A striking example is the following application of the above idea: Suppose a sugar of 0.01 per cent ash content were treated with a purified carbon to see whether or not the ash would be reduced by this treatment, and that the carbon actually removed 10 per cent of the total ash. It is at once apparent that in such a case the incineration method would have to furnish data much beyond its order of accuracy, or else excessive quantities of sugar would have to be ashed. On the other hand, a pre-
Vol. 4,No. 4
vious knowledge of the changes in the various conductance values as they are related to changes in ash content would a t once furnish an insight into the changes produced by the carbon treatment, even though these changes are exceedingly slight. Moreover, only a small quantity of sample would be required.
ACKNOWLEDGMENT The writers wish to thank John E. Mull of this laboratory for his kind assistance in making the conductance determinations in the presence of phosphoric acid.
LITERATURE CITED (1) Sattler and Zerban, Facts About Sugar, 23, 686, 713 (1928). (2) Sattler and Zerban, IND. ENQ.CHEM,,Anal. Ed., 3, 38 (1931). (3) Zerban and Sattler, Facts About Sugar, 21, 1158 (1926). (4) Zerban and Sattler, Ibid., 22, 990 (1927). ( 5 ) Zerban and Sattler, IND.ENQ.CHEM.,Anal. Ed., 2, 32 (1930). (6) Zerban and Sattier, Ibid., 2, 322 (1930). (7) Zerban and Sattler, Ibid., 3, 41 (1931). RBCBIVBD July 19, 1932. Presented before the Division of Sugar Chemistry a t the 84th Meeting of the American Chemical Society, Denver, Colo., August 22 to 26, 1932.
Graphical Method for Converting Atomic Per Cent into Weight Per Cent ARKEOLANDER,University of Stockholm, Stockholm, Sweden
T
HE following method for converting atomic per cent into weight per cent, and vice versa, seems not to be generally known, and as the numerical calculation is relatively tedious, it seems to be worth communicating. The theorem of Menelaos states: If OF intercepts the sides of a triangle ABC, the product of the three quotients of the intercepts of each side is OA .-BE .-C D -
OB CE DA
11 AC, when two pairs
1
If we have two substances with the atomic (molecular) weights A and B, mixed in the proportions of atomic per cent a and b (a b = loo), which is weight per cent p and 4 (P P = 1001,
+
+
Aa
+ Bb
p --lo0
This formula will be used for the numerical calculation. It can be transformed into
=’
This is easily proved by making BF of similar triangles give
A
- -A a
Now, it is clearly seen how Menelaos’ theorem is to be used. On a coordinate paper the atomic weights of the two components are set off on the line OAB. The point C is chosen arbitrarily, but 100 or 200 mm. from OB. If the triangle ABC is completed, the two new sides are divided in per cent by the coordinate net. Let AD signify p ; i. e., weight per cent of the component A. Then the extension of OD to E gives BE = a; i. e,, atomic per cent of A. CD and CE are the corresponding quantities for the component B. But the formula can also be written
and then BE may signify q and AD, b. The corresponding quantities p and a for A are in this case CE and CD. One has only to remember that the intercept nearest to the plotted atomic weight is weight per cent of this component, and that the projection on the other side of the triangle is the correPponding atomic per cent. The line OE will of course not, be drawn, but a rule or the edge of a paper will be put through 0 and the known percentage. RECEIVED May 4, 1932.
