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MORE ON OXIDATION NUMBERS D. F. SWINEHART University of Oregon, Eugene, Oregon T H E interminable argument goeson as to whether

or not the coventional assignments of oxidation numbers to individual atoms in molecules or ions are L'real."l Generally a conclusion is reached that puzzling and/or nonintegral oxidation humbers may usually be explained as being averages of reasonable assignments of oxidation numbers to individual atoms and that, after all, the chief value of oxidation numbers lies in their utility, particularly when writing redox equations. I t is true, of course, that oxidation numbers play an important and logical role in many simple cases such as those involving chloride, bromide, or even sulfate and permanganate ions. Trouble arises when covalent bonds enter the picture where it is certainly not true that electrons are transferred completely. This is especially true when covalent bonds occur between like atoms. It has been pointed out by VanderWerf2 that actual transfers of electrons cannot reasonably he considered to occur during many reactions in a one-to-one correspondence with the usual assignment of oxidation numbers to particular atoms. This paper is written to point out that the utility argument for oxidation numbers is not really convincing, since the conventional system of oxidation numbers is highly arbitrary and it is perfectly possible to get along without them. It is a favorite question of the author's during arguments on this subject to ask students (or professors for that matter) to balance an equation for the oxidation of ammonium thiocyanate by acid permanganate with the following products specified:

being careful to point out that it is up to experiment to decide finally whether these are really the products or not. I t needs to he pointed out periodically, especially to undergraduate students and even to graduate students, that the mere ability to write an equation is not necessarily an indication that the reaction will occur or that the products are right even if a reaction does occur. Many students, including some graduate students, who are in the habit of using the oxidation-numherchange method of balancing redox equations, will hem and haw, get weak knees, and finally give up trying to balance the above equation. The stronger ones will persist andusually arrive a t the following assignment of oxidation numbers: -8,

1

H,f,

+ I , -s.

-2

S--

o N2

+

+4,

-2

O3

+

+I. - 2

+6.-2

O+

04--

EBLIN, L. P., J. CHEM.EDUC., 28,221(1951). 2

VANDERWERF, C. A,, J. CHEM.EDUC., 25, 547 (1948).

The oxidation number change is then computed as follows: for nitrogen 0hydrogen +4 carbon +4 sulfur +6 total

(-6) = +6 (+4) = 0 (+4) = 0 (-2) = +8 +14

sucessfully leading to a final balanced equation. This computat,ion works without the half-reaction being atomically balanced because, by convention, hydrogen and oxygen have oxidation numbers of +1 and -2 respectively in most of their compounds, as is true here, and so iuvolve no change of oxidation number. Consider, however, the following highly arbitrary assignment of oxidation numbers:

The oxidation number change is computed as follows: 0 - (-3)

for nitrogen

=

hydrogen +28 - (+Xi) = oxygen - 6 - (-48) = carbon 6 - (-11) = sulfur -14 6) total

+

(+

+3

-28 +42 +17

=2 +14

with a total change as before. A few examples of this type quickly convinces one that any arbitrary assignment of oxidation numbers, subject to the single requirement that for each molecule or ion the sum of the oxidation numbers must add up to the net charge on that molecule or ion, will serve as well for the writing of equations as the conventional assignment. For a halfreaction it is thus only the over-all net change of oxidation numbers that is unique and not the oxidation numbers themselves. Thus the usual convention that oxygen shall (almost) always have an oxidation number of -2 in its compounds is seen to he convenient and reasonable hut also arbitrary and not necessarily the only possible one. If, however, one uses the ion-electron method of Jette and LaMer,3 the following detailed procedure balances the above oxidation half-reaction: (1) Observing that there are two gram atoms of nitrogen and four of hydrogen in a formula weight of ammonium thiocyanate, one writes two water molecules and one each of the other products on the right side. (2) Observing that there are now eight oxygen atoms on the right side and that the solution is acid, one a JET~E, E. R., m~ V. K. LAMER,J. CHEM.EDUC.,4. 1021, 1158 (1927).

may add eight water molecules on the left side and write the extra 16 hydrogen atoms as hydrogen ions on the right side, obtaining NH4+,CNS-

+ 8HaO = NS + CO1 + 2H10 + SO4- + 16 H t

There are now the same number of each kind of atoms on both sides but not the same net charge. (3) By merely counting the net charges on each ion, one sees that there are no charges on the left and a net of +14 charges on the right. Thus the addition of 14 electrons on the right balances the charges. Two watermolecules may, of course, be subtracted from both sides. An exactly similar argument balances the reduction half-reaction and the addition of the two half-reactions, each multiplied by an appropriate constant such that .the electrons cancel out, results in the complete ionic equation. Now the point of this detailed description is that at no mint i n the wrocedure is the auestion asked. "What is the bxidation number of that element in that molecule?" It is simply not necessary ever to ask this question.

Thus, whenever a question or ambiguity arises with respect to an oxidation number, it is really not worth worrying about. One dosen't need it. For the reason that the ion-electron method avoids asking this ques.tion and so avoids any dependence on highly arbitrary assignments of oxidation numbers, the author believes that this method is more intellectually honest and fundamental than the oxidation-number-change method and for that reason is to be preferred, especially for academic purposes. At the same time, likewise in the interest of honesty, it must be recognized that any equation may be written using oxidation-number change if one has the boldness . to assign arbitrary oxidation numbers in case of necessity. Setting all of them equal to zero in a neutral molecule is frequently useful. In the limit where all the oxidation numbers in neutral molecules are set equal t o zero, the two methods become essentially identical. It is also true that the time required to balance the usual classical equations by the oxidation-numberchange method frequently is less than that by the halfreaction method.