My personal opinion is that Rothschild's method is chemically clearer and mathematically easier than Green's method. However, both these students deserve commendation for original work. CARLETON S. SPEAR
Substitute the values for h, e, j, and c 2d -d
+ 8 = 2g + 7 = g solve these two simultaneously. g
=
"/B
and d = a/E. thus a = a/=
Multiply all by 2 and the balanced equation is:
The oxidation of sodium oxalate t o carbon dioxide by acid permanganate, and of secondary propyl alcohol t o To the Editor acetone by acid dichromate can also be easily worked DEARSIR: out. Although Barthauer states, "Let 'me say in passing Mr. Gerald Barthauer's article on "Balancing-Oxidation Reduction Equations" which appeared in THIS that I have met with no situation in which the JOURNAL (February, 1940)brings to light avery interest- method is not applicable," he does admit the possibility ing coincidence. The identical method was presented of a limitation to the method. "No doubt, however, to me by a freshman student, Mr. F. Posey, while I was such problems do exist." Since this method of unan assistant in freshman chemistry a t the University determined coefficients is in reality solving simultaneous equations with one equation less than the number of of California a t IAX Angeles. I believe that this method of balancing equations unknowns, and this equation supplied arbitrarily by has its best application in the field of quantitative letting one unknown equal unity, a discrepancy will oxidation-reduction in organic chemistry. Since, arise if the equations prove to be inconsistant. The a t best, most methods for balancing these organic method also fails if we can only set up n-2 equations reactions are, after all, schematic, the objections that where n is the number of unknowns. An example is one may have to the fact that electron changes are not (a) NHIOH (6) NHP (4Cb +(d) Ha0 (4 NHCI pictured, do not apply. (fl N2 (N) a+b=c+2f As a typical method, the one given' by Robertson' 36 = 2d + 4e (HI 5a will be contrasted with this method of "undetermined (0) a =d coefficients" in the oxidation of ethyl alcohol to acetic (Cl) 2c = e acid by means of acid dichromate. Here a case arises where there are four equations in
+
+
+
+
+
H
$+
H
Consider the C-C bond with valence of 0, and the CH, or CHp parts are neglected, then the net valence of the partially oxidized carbon atom in the alcohol is -1, while in the acid 3+, a loss of fo& electrons. Thus four equivalents of an oxidizing agent are needed. The method of "undetermined coefficients" would be
Now we can simplify Barthauer's method. Instead of resolving all equations in terms of a, b, or c we can let one letter equal unity a t once. In this case we can let b=1. Thene=l,f=l,c=1+30r4,lettinga=d and solving the equation from hydrogen and oxygen.
ROBERTSON, "Laboratory practice of organic chemistry," The Maemillan Co., New York City, 1937.
six unknowns or if we let one unknown equal t o unity, then we have five equations jp six unknowns. Our algebraic laws sap that this cannot be solved. The limitations of this method then can be summed up as follows: Whenever a case appears where there are two more compounds than elements in a chemical reaction, the method of undetermined coefficientscannot apply. ARTHURFURST
To the Editor DEARSIR: In the February, 1940, issue of the JOURNAL OF CHEMICAL EDUCATION on pages 91-3 Gerald Barthauer writes of a new algebraic method of balancing oxidationreduction equations. This method was fully discussed in the correspondence columns of THISJOURNAL during the years 1931-1934. (J. CHEM.EDUC.,8,2453 (1931); 9, 358-63, 560, 7514, 944-5, 1124-6, 1299-301 (1932); lo, 250, 707 (1933); 11, 125 (1934).) A review of this correspondence shows that the origin of the method is in doubt, hut it is found on page 218 of Fr. RiidoB's German high-school textbook, "Grundniss der Chemie" (1919), Sir James Walker's "Introduction to Physical Chemistry" (1899), and Barker's "Textbook of Ele-
