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-
mentary Chemistry" (1891). B. Menschutkin of Leningrad claims it was invented by V. A. Kistiakovski; in 1919. An English chemist, John H. Melville, has a copy of a Dutch text of 1897 and a German text of 1894 both of which contain the method. The German text refers to Debus (1882) who first used the method. It is therefore very'old and may go back still further. Dr. H. G. Derning presented in 1934 a very worth-while criticism of the method in which he does away with all but the independent variables and so cuts down on the number of eqnations. Dietz (J. CAEM.EDUC.,9, 361 (1932)) points out that only eqnations where the number of linear algebraic equations is equal to one less than the number of variables can be balanced. He proposes:
a KMn04
+ b HzS04+ c Hz02 + fHz0
-+d KHSOI +go2
+ e MnSOl
as an example where only six equations can be made from eight variables. The method is, of course, only an interesting curiosity and is far inferior for speed to the tried and tested valence-change method or for teaching value to the up-to-date ion-electron method (Ibid., 4, 1021-30, 1158-67 (1927)). I have, however, presented the algebraic method as a diversion in my second year classes. Two different students have volunteered this interesting short cut. For the equation a CU
+ b HNOv
-+
c Cu(NO&
+ d NO f
this method yields fractional coefficientsa t first but such exceptions are rare.
SHORT CUTS 1N.BALANCING OXIDATION-REDUCTION EQUATIONS To the Editor DEARSIR: Dr. Gerald Barthauer, in the JOURNAL OF CHEMICAL EDUCATION, Febmaxy, 1940, presented a method of balancing these equations. On trying this method with students in chemistry classes a t West High School in Cleveland, Ohio, the following suggestions were made by students. In the equation Mn02
+ NaCl + HISO&
-+ C12
+ N&O4 + MnSO4-F
He0 let coefficient of Mn02 = 1, C12 = A, H2S04 = B. MnSOl = 1, NaCl = 2A, N&04 = A, HIO = B. The 0 equation becomes 2 or A = 1 B = 2
+ 4B
=
4A
+4 +B
(Collecting and Solving)
The equation then is
e H20 Mn02
+
2NaCl
+
one of the possible final equations is
2H2S0, + C1, MnSOl 2Hz0
+
+
N&Or
+
We can cut down on the nymber of letters needed to express coefficients whenever an element occurs in only Now all the authors in the extensive correspondence one of the compounds (or as an element) on each side of let c = 1 whence a = 1, e = &//a, b = 8/8, and d = %/a. the equation. We can avoid fractions by care in the Then to clear of fractions multiply by three. Now the choice of coefficient that equals 1. new suggestion is that we let c = 3. Then all the co- Thus, efficients come out as whole ?umbers and the correct Coefficient 2 6 24. 6 A 1 ones a t that. The rule would be to give the variable Equation Caa(P04)2 SOz C --t CaSiOJ CO P4 on the right side of the equation t h e same value as that The equation for oxygen becomes 16 12 = 18 A. of the denominator of the fraction which is its coefA = 10 ficient. Pa is given a coefficient of 1 because there are more atoms here than in Caa(P04)* 3e = 46, then e = 4 / J ~ 3e = 4c whence e = V3c.
+
and the denominator is 3 so let The coefficientof c is c = 3. Then e = 4, and so forth. so let c = 1. If e = 4cit is really e = 4/~c, We have come across a t least one equation where even
2Ca3(P0&
+
+
+ + +
+ 6Si02 + lo€ + 6CaSi0, + lOC0 + P4
W. G. LAWRENCE WEST H r o S ~CHOOL
CLEVELAND. OHIO
