Non-stoichiometric Equations O m 0 F . STEINBACH
City College of New York, New York City
w .
HILE chemical equations may balance algebra~cally,they are not necessarily stoichiometrically exact. The following equations, many of which are given to students for practice balancing and which are found in textbooks, illustrate the above statement. The most flagrant instance of the above statement are reactions involving hydrogen peroxide. The reaction between hydrogen peroxide and potassium permanganate is a good example of variable coefficients. Thus the possible coefficients are KMnO,
+ H*O, + H&04
-
IZHSO,
substance acts as a reducing agent, it is possible to obtain variable coefficients. When hydrogen peroxide acts as an oxidizing agent, no such situation is found. Variability of coefficients is not limited to equations wherein hydrogen peroxide is a reactant. The following equations will illustrate this: KOCl 1' 4
+ Kc101
+ KC108
1 1
+ KC1
1 2
1 8
+ MnSO, + HIO f Or
The correct coefficients are indicated by an asterisk. An interesting fact is that the same stoichiometric coefficients result if either chlorite or hypochlorite The row preceded by the asterisk is recognized as the ion is assumed to be the oxidizing agent when the correct stoichiometric equation. Obviously there is equation is balanced by ion-electron or valence-change an infinite number of solutions for the coefficients. methods. Tables of oxidation-reduction potentials indicate that the chlorite ion is a slightly stronger Only a few of the total possible solutions are given. The reaction between potassium dichromate and oxidizing agent than the hypochlorite ion. With a hydrogen peroxide is another example. Thus the reaction such as this, changes in concentration of the reactants would permit either to be the oxidizing coefficients for the equation are agent, due to change in oxidation potentials. The equation HClOs + HCIO, Clr Or HsO
+ + +
1 3 1 2 6
'3
5 7
lo 10
$1
-
+ H2Oz 1
NaBr 1
+ HpO + 01 1
8KC108
1
+ 24HC14
+ ;
$4
5
Again the correct stoichiometric coefficients are indicated by the asterisk. The author has tried other eauatious involvine hydrogen peroxide and found th'at whenever this
2 1 7
4 2
'9
1 1 3 4 2
2
also shows a variability in coefficients. The variability is probably due to the fact that in this particular equation, two or more chemical reactions are taking place and such an equation has no particular significance. An equation frequently given to express the reaction between potassium chlorate and hydrochloric acid for the production of chlorine dioxide is
The row marked with the asterisk is recognized as the correct stoichiometric equation. Apparently there is an infinite number of solutions for this equation also. Another equation which shows a similar variability in coefficients is NaOBr
1 1 3
lo 16
22
8KCl 2 3 4 5
+ 9Clp + 12HzO + 6C102 1 4
7 10
2 5 8
11
2 2 2 2
The numbers underneath the equation represent some other possible solutions for the coefficients. The coefficients preceded by the asterisk are obtained on balancing the equation by either valence-change or (Continued on page 69)
66
NON-STOICHIOMETRIC EQUATIONS (Continuedfrom page 66) ion-electron method on the assumption that chloride ion is oxidized to chlorine while "chlorine" in chlorate is reduced to chloride and chlorine dioxide. The coefficients preceded by the dagger result when the equation is balanced on the assumption that chloride ion is oxidized to chlorine while the chlorate "chlorine" is reduced to chlorine dioxide. When equations are balanced by either the valancechange or the ion-electron methods, the coefficients obtained are the comect stoichiometric ones. The above reaction is not an exception to the rule. The variability is due to the fact that the equation probably represents several distinct chemical reactions. When such a condition exists, it is reasonable to expect
that the stoichiometric coefficients obtained will depend upon the selection of the oxidation and reduction products. Equations such as these have no stoichiometric meaning, and it is doubtful whether they have any real significance other than that they contain the shorthand suggestion of the reactants used and the products obtained. They do, however, have a definite suggestion that further investigation would he most desirable. It is by examples such as these that the wide divergence between the stoichiometric equation and the actual mechanism of a chemical reaction is so poignantly revealed. The author wishes to thank Professor Ross A. Baker for his many helpful suggestions.
