CORRESPONDENCE BALANCING OXIDATION-REDUCTION EQUATIONS To the Editor DEARSIR: I am submitting what I believe is a clever method of balancing oxidation-reduction equations. It may be that this method has been applied or even published before. However, as far as I have been able to determine i t has never been used in the past. If such is not the case, my apologies go to the originator. Whatever credit there should be should go to a freshman chemistry student, Henry Green, of Cleveland, Ohio, who, evidently having some difficulty with the electron-interchange method, resorted to the method
explained below. Happening to-be an assistant in the courseat that time, I was fortunate enough to observe his work and believe that i t is of sufficient merit to deserve passing on. So with some further experimentation and application, here are the results and methods. Let me say in passing that I have met with no situation in which the method is not applicable. No doubt, however, such problems do exist. However, I believe you will agree that there are many quantitative equations which are difficult to balance even by electron interchange. It is my belief that in many of these cases the method suggested helow may be profitably employed. Let us start with a simple example. Suppose that we wished to balance the equation
Cu
+ H(NOJ +Cu(N0t)r + NO + Hz0
+
Now let the unknown coefficientsbe a, b, c, and d as we go from left to right. Looking a t the elements and their subscripts we get Equation 1 from capper.. ........... .a Equation 2 from nitrogen.. b Equation 3 from hydrogen.. ......... .b Equation 4 from oxygen ........... .3b -
...........
~
=c = 2c
= 2e = tic
MnO,
d
+d +c
be the It is apparent that it simplest to resolve all values in terms of "a." Thus we have directly that c = a. But b = 2e (Equation 6c - d (Equation 4) and d = 3). Since e = 3b b 2c (Equation 2), we have by substituting e = 3b - 6c - b 2c. But e = 1l2b and c = a. Thus l/zb = 3b - 6a - b 2a or b = 8/aa. Then from Equation 2 we have a/3a= 2a d or d = '/&. Then e = 1/2b (Equation 3) or, since b has been found to have a value of a, then e = %a. So we now have b=8/sa, c =a, d= 2/sa,and e=4/8a. Letting "a" equalunity, we have Cu + a/1HN08 +Cu(NOs)a '/rNO 4- '/tH*O
-
-
+
+
+
+
and clearing fractions: 3Cu 8HNOn --+ ~ C U ( N O ~ )2NO ~
+
+
+
+ + 3d +
2c Equation 1 from hydrogen.. ..........3a = b Equation 2 from phosphorus.. ........a = b 4- d Equation 3 from oxygen.. ...........3a = 36 c
Here i t seems more logical to resolve in terms of d. We "c." It is known that (Equation 2) a = b can then substitute in Equation 3 so that 3b 3d = 3b c. Canceling 3b on each side we have 3d = c or d = '/&. Subtracting Equation 2 from Equation 1 we have. canceling "b" in each equation &at 2a = 2c 2d. But d = c so 2a = 2c or a = J/G NOWsolving for b in Equation 2 we have 'lac = b I/JC orb = C. Now we have a = '/%c, b = c and d = '/ac. Letting "c" equal unity we have
+ +
+
+
+
'/rHPOs
-+HPO
+
+ Hz0 +
or clearing fractions we have 4HnPOa --+ 3HPOa
'18
PHI.
+ 3H10 + PHa
And finally one involving seven different compounds-MnO,
+ ZNaCl+ 2HdO.--t
Ch
+ Na2S0, + &SO,
f 2H20
And there i t is. Althou~hin some cases the method may appear cumbersome, one is surprised to see how quickly one can develop the knack of securing different combinations, and quickly bring order out of the different equations, It is apparent that the more elements which are involved in the reaction, the more easily the problem lends itself to solution. The value . 1s especially apparent in cases where many molecules are involved in the reaction. Anyhow, i t is lots of fun solving them in this manner, and a t times the fun can be put to practical use. GERALD BARTHAUER~ H
w COLLEGE
HI^, OH~O -
Present address: Purdue University, Lafayette, Indiana.
+ 4H80.
A slightly more difficult example might be the treatment of phosphorous acid to produce metaphosphoric acid and phosphine. We have as reactants HsPOi --+ HPOI HnO PHs
+
from Equation 4 we have 2a = e a or e = a. But b = 2e (Equation 3) so b = 2a. Since b = 2a, then d = a (Equation 2). Now we have b = 2a, c = 2a, d = a, e = a, f = a, and g = 2a. Now let "a" equal unity and we have directly
+ NaCl + H&04 --+ C11 + Na&01+
............ .............. ..... .............
MnSO,
+ HrO
Equation 1 from manganese. .a = f b = 2d Equation 2 from chlorine. Enuation 3 from sodium.. ................ b = 2e ~ o u a t i o n4 from the sulfate radical.. c =c f Equation 5 from hydrogen.. .c = g Equation 6 from oxygen.. .............. .2a = g
+
Smce it appears simplest to resolve in terms of "a" we have directly that (Equations 1 and 6) f = a and g = 2a. From Equation 5 we have c = 2a. Then
ANDREW WITTMAN-DISCOVERER OF ZINC To the Edit09 DEARSIR: R. D. Billinger in a recent paper (1)in THISJOURNAL has ably described the early discpvery and subsequent history of z i n in ~ the Lehigh Valley. In this article i t was declared that the true character of the ore was not definitely known until Mr. W. T. Roepper examined it and identified it as calamine. The present writer in a short paper (2) on the same subject made a similar statement.. Richmond E. Myers in a lengtgy article (3) states that Andrew Wittman conducted several experiments in 1845 and managed to obtain a few globules of metal which he could not identify. This seems unlikely. It is diicult to believe that one sufficientlyskilful to obtain a sample of metal from an ore would b e a t a loss as to how to identify the metarif i t was not immediately recognized from its physical properties. In order to settle the matter one way or another the writer has, during the past several years, examined a large portion of the printed material extant on the subject and has come to the conclusion that Andrew Wittman was not only the first person to identify the ore as a zinc ore but was also the first one to obtain some of the metal. A very interesting paragraph which accurately describes the true sequence of events and which sums up the present writer's views in the matter is to be found in the "History of Lehigh Co., Pa.," by Charles R. Roberts, et al. (4). As this information is hidden in what really amounts to a genealogical record one feels
