CORRESPONDENCE "BALANCING OXIDATION-REDUCTION EQUATIONS" To the Editor DEARSIR: In reply to Mr. Barthauer's communication in the February number of the JOURNAL, relative to the application of simple mathematical concepts, to the balancing of chemical equations, I beg to submit the following. There is nothing new in the use of this idea. It has been used by two of us a t the Central High School, Philadelphia, for the last ten or fifteen years a t least. It is applicable, not only to oxidation and reduction changes, but to most, if not to all, other cases. Dr. Henwood and I have tried it upon some of the most difficult reactions, and i t has never failed us. But we feel, in the last analysis, that the chemical method teaches more chemistry. The mathematician cannot make a start until the chemical facts are known. He is usually not trained to ascertain these facts. We claim no originality for the method. It was explained and commented upon, .in one of the earlier editions of Walker's "Physical ChemiSry," some thirty odd years ago. Many of our more mathematically inclined students "lap it up" as a kitten does milk. PHILIPMAAS
To the Editor DEARSIR: I wish to call your attention to an article which appears in the JOURNAL OF CHEMICAL EDUCATION, 17, 91-2 (1940), entitled, "Balancing Oxidation-Reduction Equations." The author seems to believe that this method has not been used in the past. I believe, however, that he will find it identical with one which appeared in THIS JOURNAL, 8, 2453 (1931), entitled, "Balancing Chemical Equations." MODDIETAYLOR
To the Editor DEAR SIR: In the February, 1940, issue there was published, under "Correspondence," a letter from Gerald Barthauer reaardina the "Balancinc of Oxidation-Reductiou ~ ~ u & o n s . " May I state that I had a student, Walter Rothschild, in my inorganic chemistry class of 1930, who either discovered or independently rediscovered this algebraic method of balancing equations? We have used this method each year since that time, presenting it to interested students only, in our classes. Walter Rothschid's method is the same in principle as that of Henry Green. There is one difference which can best he illustrated by a comparison. Using the method of Henry Green, from the February issue, he obtained the following algebraic equations from the reaction of, .. a Cu b HNOI +c Cu(NO& d NO e HzO
-
-
+
.
Cu a = c N b=2c+d H b=2e 0 3b=6c+d+e
~~
+
,
~~~~~
+
..
Resolving these in terms of a, he obtains
So far, Green's and Rothschild's methods are similar. However, Green lets a = unity, obtains fractional coefficients, and then clears of fractions. Rothschild's method involves the selection of the smallest possible value of a that will permit b, c, d, and e to be whole numbers. For the illustration cited, this value is, by a quick inspection, the number 3. This, when substituted, yields the coefficients
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-
