OCTOBER, 1948
A CONSISTENT TREATMENT OF OXIDATIONREDUCTION CALVIN A. VANDERWERF University of Kansas, Lawrence, Kansas
A
TRAINED CEEMIST can almost invariably inspect a chemical equation and ascertain a t a glance whether or not the reaction represented belongs to the type called oxidation-reduction. Obviously, the concept of oxidation-reduction is clearly established and generally accepted. The usual definitions of oxidation and reduction have gained equally wide acceptance. Oxidation is defined as a chemical change involvim a loss of electrons, reduction as a chemical change involving a gain of electrons.. Thus, oxidation-reduction reactions are held to be fundamentally diierent from all other types of chemical transformations. From these definitions the inference is usually drawn that all systematic methods for balancing oxidation-reduction equations depend ultimately upon the axiom that, in any complete electron transfer, the total number of electrons gained by one atom or group of atoms must be equal to the number of electrons lost by a second atom or group of atoms. General acceptance of these definitions came largely during the five-year period from 19251930, as a result of the forceful arguments presented by leading chemistry teachers of the day, who described the advantages of the ion-electron method, as opposed to some of the antiquated.and cumbersome methods then in vogue for balancing oxidation-reduction equations. The fact that the introduction of the ion-electron method clearly
marked a significant advance in chemical thinking on the subject may perhaps have red t o a somewhat uncritical acceptince of the definitions which classified all oxidation-reduction as chemical changes involving complete electron transfer. G. N. Lewis had already demonstrated that in nonionized linkages, electrons are not completely transferred. But, the full significance of Lewis' ideas did not a t first strike home. I n the meantime, the complete electron-transfer definitions of oxidation-reduction became established in the chemical literature equally as firmly as they did in the minds of teachers of chemistry. DEFINITION VS. CONCEPT
We have now reached the stage in our understanding of chemical structure where the fsct that not all reactions which by universal agreement are classified as oxidation-reductions do involve complete electron transfer has become so obvious as to be somewhat disturbing. I n fact, it is undoubtedly true that all of us, in judging whether or not given reactions are oxidationreductions, in a majority of cases apply some criterion other than that of electron transfer; in many clear-cut cases of oxidation-reduction, we should find it impossible to show, in terms of our accepted definitions, why the reactions were so classified. I n other words, it appears that our accepted definitions of oxidation-reduction do not coincide with our accepted concept of oxidation-
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JOURNAL OF CHEMICAL EDUCATION
reduction. This divergence between definition and concept has no doubt troubled many teachers of chemistry. In so far as i t does exist, we should, in the interests of logic and fairness to our students, reconsider either the definitions, or the concept, or both. But the concept has proved eminently utilitarian. And the definitions have served so neatly to catalog oxidationreduction as a mode of chemical reaction fundamentally different from all other types that any challenging of them would be quite discomforting. The electron-transfer definitions have, in fact,,become so closely identified with all that is revered as "modern" in chemistry that only a hopeless chemical reactionary would question them. Consequently, we usually dismiss the problem by stating that the exceptions to our definitions are too infrequent and too unimportant towarrant consideration. Obviously, however, even if there were but a single exception, logic should compel us to be concerned. It becomes even more apparent that the gap between definition and concept cannot be so cavalierly dismissed when we realize that many oxidation-reduction reactions which occur in nature probably do not involve complete electron transfer, or that over half of the energy used by society in its present state of civilization is supplied directly by oxidation-reduction reactions u~hich almost certainly are not complete electron transfers. In addit,ion,the definitions are seen to apply somewhat fuzzily to a large number of familiar laboratory redox reactions when the naturaof these reactians is examined critically. DEFINITIONS NOT DIRECTLY APPLICABLE
As a first requirement, a definition of oxidationreduction which is taught to beginning students should certainly be directly applicable on the basis of the initial and final states of a reaction, without regard to its mechanism, real or assumed. That our electron transfer definitions do not satisfy this requirement is immediately apparent upon inspection of a few typical examples. In reactions involving elements and simple ions or ionic compounds, identification of oxidation with complete loss of electrons and of reduction with complete gain of electrons is entirely valid. This relationship may be illustrat,ed by means of such simple reactions as the following: Zn + 2Ag+ Zn+++ 2Ag 2K + C12+ 2K+ + 2 c12Br- + A Br, 2F-
-
+
which is of primary importance in our civilization-the complete combustion of carbon to carbon dioxide:
-
+ 0, co* .. .. .C. + :o:o: -0::C::O C
..
..
By universal agreement, the carbon is oxidized by four units. Ignoring the various resonance structures of carbon dioxide, consideration of which mould not alter the basic argument, we see that the carbon has not lost four electrons. Had it done so, it would exist in the carbon dioxide molecule as a quadrivalent carbon ion Cf4, an assumption which is entirely inadmissible. It is often argued that, although the carbon atom does not actually lose four electrons outright to the oxygen atoms, nevertheless these electrons are somewhat "shifted" away from the carbon toward the oxygens. In discussing this argument we shall adopt the language of organic chemistry and, for the sake of simplicity in expression, speak of electron shifts, realizing that we are taking broad license with the findings of wave and quantum mechanicists. We may say, then, that virtually all chemical reactions involve electron shifts toward certain atoms and away from others; where then does oxidation-reduction stop and where do other types of reaction begin? In the reaction H H FI--&ii: +I +
.. CHS-c ..
..-
For 4 oxygens 7eFor 8 hydrogen ions Oe-
--
6e-
le-
Total loss, 4eT o t d gain, 8e-
In the present state of our knowledge it is quite im- The manganese appears to have gained one electron, possible to assign a certain fraction of the valence each of the four oxygen atoms to have lost one, and the electrons in the permanganate ion to the manganese eight hydrogen ions to have gained a total of eight atom and a certain fraction to the oxygen atoms. electrons. It is apparent, then, that attempts to assign a specific Hence, me cannot tell on the basis of the complete electron gain or loss to each atom or ion in a partial equation alone whether the permanganate ion has equation of tbis type are rather futile; we do not as yet gained or lost electrons, unless we make the totally unknow enough about the nature of covalent bonds to do tenable assumption that the manganese is stripped of so, and different conventions lead to different results. seven valence electrons and exists in the permanganate In any case, however, two interesting facts emerge: on as a heptavalent ion, &In+'. (1) the electrons gained are certainly not taken on exThere is no valid process of reasoning by Nhich one clusively by the accepted oxidizing agent, the permancan, on the sole basis of initial and final states of the total. reaction, arrive at the conclusion that per- ganate ion; and (2) the hydrogen ions play an immanganate ion has gained five electrons in its reduction portant role in absorbing the electrons gained by the to manganous ion. This conclusion rests entirely system. The latter statement gains support from the upon an assumed mechanism, i. e., the half-cell reaction. fact that in all half-cell reactions in which either hydroIt follows, therefore, that the accepted definition of gen ion, water, or hydroxide ion is involved, the pH of oxidation-reduction cannot be applied simply on the the solution is increased during reduction and decreased basis of the initial and &a1 states of a total reaction. during oxidation. Thus, in the half-cell oxidation of For further explanation of its valic'rity, we are forced sulfite ion t o sulfate ion, two electrons are lost by the to turn to speculations regarding the qpechanism of system, though apparently not by the sulfite ion, and the pH of the solution is decreased. redox reactions. In considering these relationshius. we are skirtinz the solution to a ~ e k i n e n question t that may urofitabi; be ARGUMENT BASED ON MECHANISM raised here. -we have found i t easy to believe t h i t in Most oxidation-reduction reactions which Occur half-cell reactions the ion conventionally regarded as spontaneously in aqueous solution can be carried out the oxidizing agent is compl&ely responsible for as cell reactions, with the oxidation taking place at the absorbing the electrons taken up a t the cathode, beanode (the electrode to which electrons are supplied from the solution) and the reduction a t the cathode cause of the fact that the number of electrons gained by the system is equal to the observed decrease in (the electrode from which electrons are removed by the solution). For the oxidation of sulfite ion by per- .oxidation number for the oxidizing agent. If a decrease rnanganate ion, the over-all equation for the complete in oxidation number cannot be completely identified with a gain of electrons why is this equivalence noted? reaction may be arrived a t as the sum of the actual Consideration of a rather simple case will show that electrode reactions : this relationship is a consequence of the conventions 2 X (Mn04- + 8H+ + 5e- e M n t + 4H~0) adopted for calculating oxidation numbers.
+ + HIO - 2e- S SO4- + 2H+) + 5S01- + 6H+- 2Mn++ + 580,- + 3H20
5 X (SOa2Mn0,-
Let us look somewhat more critically a t the half-cell reaction for the reduction of permanganate ion. The
SeOl-
+ 2H+ + 2e-
r 0 1 -
SeOaq+HpO
r
1-
JOURNAL OF CHEMICAL EDUCATION
550
Let us. consider the equation for the half-cell reaction in which selenate ion is reduced to selenite ion. There is no change in the number of valence electrons about selenium in the reduction from selenate to selenite ion. But because combined oxygen is assigned an oxidation number of -2, the loss of a single oxygen reduces the oxidation number of selenium by two units. Obviously, it is precisely this oxygen which requires the two hydrogen ions to form a molecule of water, and the charge on these ions must be balanced by the addition of two electrons. Here the element reduced exists in an ion whose sign does not change in the reaction; hence the electron gain is exactly twice the number of oxygen atoms lost by the oxidizing agent. It should be noted that we are making no assumptions concerning the form which the oxygen takes as it leaves the selenate ion; the discussion is based entirely upon initial and final states, and the fact that selenium neither gains nor loses valence electrons in its change from selenate t o selenite ion canhot be denied. In the more complex lialf-cell reaction, MnOl8H+ 5e- % Mn++ 4Hz0, the change from permanganate to manganous ion supplies four oxygen atoms, which require eight protons to form four molecules of water. Now if the charge on the permanganate and manganous ions were the same, the decrease in oxidation number for manganese would be eight and eight electrons would be required to balance the charges on the hydrogen ions. But the charge on the mangauous ion is three units higher, algehraically, than that on the permanganate ion. This means that the decrease in the oxidation number of manganese is not eight, but eight minus three, or five. At the same time, the increase in charge from -1 in permanganate ion to +2 in manganous ion brings about the release of three of the eight electrons required for the eight hydrogen ions; hence only five need be supplied at the electrode. By similar arguments, it may be shown that the equivalence of gain in oxidation pumher and loss of electrons in an oxidation which takes place in a half-cell is merely a logical consequence of the pules for determining oxidation numbers. Whatever may be the exact fate of the transferred electrons in half-cell reactions, we are not certain that the mechanism of the reaction which takes place when the oxidant and reductant are brought into actual contact is a combination of the two half-cell mechanisms. One may well question, for example, whether the actual mechanism of the oxidation of su1fit.e by permanganate ion, 2Mn045S056H+ + 2Mn++ 5SOr 3Hz0, is not simpler than that indicated by the half-reactions. Even stronger suspicions are aroused where the complete equation shows no electron gain or loss whatsoever. If the groups which appear to participate in the electron transfer in the half-cell' reactions cancel each
+
+
+
+
+
+
other in the over-all reaction, it seems unnecessary to assume that electron gain and loss must occur when the reaction takes place in asingle vessel. In the oxidation of sulfite by selenate ion in acid solution, for example, SeO$SO8Se0.-
+ 2 H + + 2e- E SeOa- + HzO + HzO - 2e- S SO+- + 2H+ + SOI-
-
Se08-
+ SO,-
the electron transfer seems to have centered about the water molecules and hydrogen ions, which do not appear in the complete equation. ARBITRARY NATURE OF CONCEPT
If, as appears certain, our present definitions for oxidation-reduction cannot serve as the criterion by which we classify reactions, so long as we retain our present concept of oxidation-reduction, we may of course alter the concept. In advanced study, either a more limited concept comprising only reactions involving a complete electron transfer, or a broader concept based on increase and decrease in electron density, would have advantages. But in the general course our present concept is of tremendous value in that it provides the framework within which a high degree of systematization is possible. But we err in attempting t o maintain that, according to our present concept, oxidation-reduction is a fundamental type of reaction, different from all other types. The following pairs of equations will serve further to illustrate this fld.
R R-A:
I
R R-N:
1 I
R
+ .. + ti: .. F
B:F
..
0
R
1 - .. I .. I
R-N:o:
R R F I .. R-N:B:
-
I
R 0
+
I t is significant, also, that many complete equations which are the sums of two half-cell equations, represent reactions which are not of the redox type.
The first transformation of each pair is generally 1.egarded as oxidation-reduction, the second is not. Similarly, reactions as the additions of hydrogen bromide and of bromine, respectively, to ethylene, revenl the arbitrary nature of the oxidation-reduction concept:
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Br-Br
H H
+ -:C-C+
H H
-
H H B r C C + f BrH H
-
H H BrC-CBr
H H
Despite the essential similarity of the mechanisms in the two cases, the carbon atom which adds the proton is considered to be reduced, whereas the carbon atom which adds the positive bromine ion is oxidized.
In any balanced equation which we may represent in general as A + B + . . . . . . d C + D + ......
it follows that, whether A, B, C, and D represent molecules or ions, the algebraic sum of the oxidation numbers on the left side must be the same as the sum of the oxidation numbers on the right'side of the equation. I n other words, any atoms or ions can A CONSISTENT DEFINITION increase in oxidation number in the change represented Perhaps then, we might in our teaching to admit by the equation only if other atoms or ions undergo an that our concept of oxidation-reduction, although equivalent decrease in oxidation number. highly useful, is, nevertheless, arbitrary, and define it, I n all clear-cut cases of complete electron transfer therefore, in admittedly arbitrary terms. We may between ions, and in half-reactions, the fact that electhen, not too reluctantly, fall back upon the simple tron loss is oxidation and electron gain is reduction definition of oxidation which gives it, more nearly than should certainly be stressed. Above all, we wish to any other definition, its generally accepted meaningemphasize that use of the new definitions by no means namely, an increase in oxidation state. Reduction is implies the rejection of the ion-electron method for a decrease in oxidation state. Calculation of oxidation balancing equations, where it is applicable, or of halfnumber is based on the few simple oxidation state cell reactions. On the contrary, the importance of halfrules. For most students, use of the oxidation number cell reactions in electrochemistry may be stressed withidea is a time- and labor-saving device for many out contradiction even when it is found that the compurposes, such as the writing of formulas, in balancing plete equation for the cell reaction does not represent equations, in calculating equivalent weights, and as an a redox change. aid to the memory. Complex equations, both ionic The fundamental advantage of the proposed definiand molecular, are readily balanced by application of tion of oxidation-reduction is simply that it is conthe oxidation number rules. The mathematical basis sistent with our accepted concept. Thus, through for the oxidation state method of balancing equations its use, we shall enable students to deal with oxidationis inherent in the oxidation number rules and does reduction reactions on the basis of the definitions which not depend upon an equivalence of electron gain w'ith we teach them. For logical and consistent teaching electron loss. we should do no less.
