VOL.9, No. 2
CORRESPONDENCE
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solution) makes it almost impossible for practical use. It surely would be a very good hobby for any one interested in chemistry to keep in mind. Very respectfully yours, ARTHURR. CLARK FRANKLIN AND MARSAALL COLLEGE LANCASTER, PENNA. DEAREDITOR: The algebraic method of balancing chemical equations set forth in the recent communication of A. W. S. Endslow U. CHEM.EDUC.,8,2453 (Dec., 1931)l requires the solution of as many simultaneous linear equations as there are substances symbolized in a given chemical equation. It follows that there must be a t least (n- 1) different elements involved in a chemical equation of n substances, since one algebraic equation is formulated for each element, and in addition, a is set equal to one. This requirement is met by many, but not by all, chemical equations. For example, cannot be balanced by this method, since i t is possible to formulate only six independent linear equations, whereas seven are necessary. Very truly yours, NICHOLAS DIETZ,JR. TnE UNIVERSITY OF PITTSBURGH P I T T ~ B ~PENNS~VANIA GH, T DEAREDITOR: From time to time I see in the JOURNAL OF CHEMICAL EDUCATION and other magazines articles on methods of balancing equations. The one occurring in the correspondence section of the December, 1931, issue of THIS JOURNAL (p. 2453) caused me to submit the method I have used in my general chemistry classes for a number of years. This method seems simple to me, though my description may appear involved. My students have had very little trouble using it on even the most difficult equations. It might be helpful to others. I classify reactions in three groups as follows: Case No. 1. Reactions that are non-oxidation-reduction or simple oxidation-reduction. Case No. 2. Oxidation-reduction rextions in which one element is oxidized and one reduced. Case No. 3. Oxidation-reduction reactions in which two different elements are oxidized or reduced and, in rmjunction, one or two reduced or oxidized.
362
JOURNAL OF CHEMICAL EDUCATION
FEBRUARY, 1932
Before attempting to present equations in a comprehensive way, I have the students, during the first six weeks, memorize a number of formulas of compounds, one representative of each element in each of its states of oxidation. Also they have been drilled in deriving valences of all elements and radicals with which they are familiar by referring to the hydrogen atom as a basis. To balance any equation the students are instructed to first make sure that in the skeleton equation each element is accounted for at least once on both sides of the arrow, and that all formulas are correct. When reactions are of solutions HpO may be added to either side of the equation as occasion demands. Case No. I : A l l non-oxidation-reduction reactions and simple oxidation-reduction reactions. (This case is introduced as soon as formulas are presented.) For the first few times enclose each formula in a circle and never alter the numbers inside the circles during the rest of the operation of balancing the equation. Applying this principle to the skeleton of the equation for the reaction of A1 on HCl we have: A1
+ HC! +AICI. + H9
If a poly-atomic elemental gas is involved, hold a finger over the number indicating the atoms to a molecule of the gas. (Here the "2" of the "Hz.") Balance the equation taking the least common element first (usually a metal), then the acid radical, then HzO, if involved, and finally any free element appearing in the prodyt. If the finger was held over a number during the balancing, take away the finger and immediately multiply coefficients of all other molecules by the number uncovered. The result of the above example will be 2.41
+ 6HCl --+ lAICIa + 3H2
Case No. 2 . A l l oxidation-reduction reactions involving one element oxidized and one reduced. Using positive and negative charges mark the valence on each indizidual atom and radical. (Precaution: All free elements have a valence of zero. For each radical make the mark over the entire radical.) Below the equation write separately those elements changing in valence and the extent of their change. Holding the left hand a t an assumed zero level decide how many units each atom goes up or down. (Positive is up and negative is down.) Record these. Then place a large X opposite both lines. (See the example below.) At the other extremes of the lines of the X write the same figures. These give the ratio in which the oxidation-reduction takes place. These numbers in themselves or when multiplied by 2 usually give the numbers to he used. Rarely do they have to be multiplied by a higher number. If either element appears in more than one substance on either side of the arrow, insert
VOL. 9, No. 2
CORRESPONDENCE
863
the numbers in the skeleton equation, but only on the side where the element appears more than once and as the coefficients of the atoms of the elements which changed in valence. Join by arcs across the arrow the element which appears more than once on one side. Then on each arc write the necessary number of atoms of the arc-ed element. Add together and place the sum as the coefficient of the element on the other side. Balance the other molecules by sight as in Case No. 1. Taking the same example that Mr. Endslow used in his letter appearing in the December, 1931, JOURNAL OF CHEMICAL EDUCATION and applying the method outlined above we have: 0
3Cu
-
-a-2 +215-2 +2-2 +-2 + 8HNOa + 3Cu(NO& + 2NO + 1H,O +
\--
C"
/
2
from 0 to +2 = up 2 = dawn 3 x
N from +5 to +2
32
If neither of the elements changing in valence appears more than once on either side, then the numbers on the right of the large X can be inserted on both sides of the equation and the rest of the equation balanced by sight. For example, HN03 on H2S:
+
+
+
2HN03 HnS+2N02 2H,O S S from -2 to 0 = up 2 1 N from * 5 to +4 = down 1 2
Case No. 3: Oxidation-reduction reactions i n which two different elements are oxidized or reduced and, in conjunction, one or two reduced or oxidized. Rarely is there a case of two oxidized and two reduced. All the elements oxidized and reduced must occur in not over two of the reacting substances. If they occur in more than two, separate equations must be written in order to meet this requirement. The method of balancing is essentially the same as for Case No. 2, but is a little more involved. An example of Case No. 3 would be the action of hot concentrated HN03 on arsenious sulfide. In the light of Case No. 2 the figures below explain themselves. 24 X 4
\ AaSa 38HN01 +2As(NOa)s 16Hn0 3H2SO' 28NO2 1 Since 3s. 3 S from -2 to +6 = up 8 N from +S to +4 = down 1 8 numbers are 24 As from +3 to +S = up 2 1 Since 2As in mal., 2 4 N from +S to +4 = down 1 2 numbers must be
+
-/ol-
+
+
+
1
1
Sincerely yours, EARLOTTO C o m n COLLEGE LINCOLN. NBBRASKA
