;Q+
4tkc New England Association of Chem
M a d e l i n e P. G o o d s t e i n Central Connecticut State College New Britain, Connecticut 06050
Interpretation of Oxidation-Reduction
The oxidation-reduction (or redox) concept is currently in widespread use in chemistry (1) as an organizing structure for chemical knowledge; (2) as a guide to the prediction of reactions, and (3) as a mathematical device to enable the balancing of certain complex reactions. Despite characterization of the concept as arbitrary and arithmetical, the oxidationreduction concept has been found too useful to abandon. Since World War 11,new theoretical ideas and usages have developed in reaction mechanisms, complex ion formation, and electronegativity which are of significance to the redox concept. I n the light of these developments, it has become feasible to reexamine redox usage for governing principles. According to a study made by Yalman which appeared in 19.59 ( I ) , electronegativity was employed in the definition of oxidation state in half of the introductory college texts examined. Electronegativity is a construct calculated from experimentally-determined parameters; the recent emergence of its use in the calculation of oxidation states suggests a physical principle as a basis for the redox classification. The following discussion is devoted to the development of this idea. The Oxidation N u m b e r The Oxidation Number ond Eledronegotivity
The key elements to current utilization of the redox concept lie within the definition of the oxidation number. (The terms oxidation number and oxidation state am nsed interchaneeablv.) A set of rules has been 1 It can be seen that current practice in bhe calculation of oxidation states of stable free radical molecules such ss NO and NO2 treats two electrons as bonded by the less electronegative atom to the more electronegative atom giving the latter a complete electron octet. Several different conventions are currently in use for designating oxidation numbers. I n t h i ~paper, positive oxidation states are indicated by a Roman numeral in parentheses following the atom (Stock convention), When the sign is negative, a minos sign follows t,he numeral within the parentheses; when the sign is positive, it has been chosen to make its inclusion optional. The same convention is adopted for oxidation numbers not in formulas. There may appear t o be a. discont,inuity in the calculation of oxidation numbers in that electrons shared by atoms of equal electronegativity count 8s zero in the calculation of oxidation numbers, but as soon as the sharing is the least unequal the oxidation number of each atom changes. However, it is noted that finite changes to, from, or through the condition of equal electron-sharing ordinarily take place only by redox mechanisms (see litter) and only with abrupt changes in orbital electron densities.
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developed for the calculation of oxidation states; these rules are generally consistent among the various introductory texts. Application of the rules enables rapid identification of the more electronegative atom in a bonded pair of atoms. When this relative order of electronegativities is established, the oxidation number of an atom may readily be calculated. The zero reference state is assigned to any atom which is bonded only to atoms of equal electronegativity or is non-bonded. Accordingly, an atom in the elemental state or in the atomic ground state configuration has a zero oxidation number. The oxidation number of a given atom increases by one unit for each electron entered by the given atom into a bond with a more electronegative atom, and decreases by one unit for each electron bonded to thegiven atom by an atom of lesser electronegativity.' For example, a hydrogen atom in the elemental state or the monatomic ground state configuration has an oxidation number of zero. The oxidation number of hydrogen when bonded to a more electronegative atom is (I+).? When bonded to an atom of lesser electronegativity such as lithium, hydrogen is assigned the oxidation state of (I-). When the atoms linked to a given atom are all more electronegative than the given atom, the oxidation number is positive; it is negative when all of the linked atoms are less electronegative. When a given atom in a molecule, such as the carbon atom in an alcohol or aldehyde group, is bound to a more electronegative atom in one bond but to a less electronegative atom in another, the oxidation number may be less meaningful in that it gives only a net count of electrons linked to atoms of differing electronegativities. For example, the terminal carbon H
I
atom in -C-C=O is more electronegative than the linked H atom, equal in electronegativity to the linked C atom, and less electronegative than the linked oxygen in two bonds. The sum of the count at each bond may (I-) (0) = (I+),3 the oxidabe shown as 2(I+) tion state of the carbon atom. The oxidation number of a given atom equals the sum of the electrons linked by the given atom to atoms of higher electronegativity, less the sum of the electrons linked to the given atom by atoms of lesser electronegativity.
+
+
Change in Oxidation Number
Consistent with the electronegativity criterion, the oxidation number of an atom changes as a result of any
changes in the relative order of electronegativity with linked atoms. Since every increase in oxidation number during an oxidation-reduction reaction is accompanied by a decrease in oxidation number eleswhere among the reactants, it follows that every alteration in order of electronegativity affecting the bonding of one atom in a reaction is accompanied by a change in order of electronegativity in the opposite direction a t a bond of another atom. Three variations in order of electronegativity are possible, i.e., those in which an atom is bonded to an atom of (1) greater electronegativity; (2) equal electronegativity, and (3) lesser electronegativity. A shift in either direction between any of these categories alters the oxidation state of the atom. I n order to include in tile above definition the redox changes which affect non-bonding electrons, such as in the oxidation of R3P: to Ral': 0, the following consideration is convenient. An atom which possesses a lone pair of electrons, such as the P atom in RJ':, may be regarded as linking the lone pair of electrons to an atom of zero eleetronegativity. Thus, the phosphorous atom in R3P: is the "more electronegative" atom linking the lone pair of electrons to an atom of lesser (zero) electronegativity. This approach permits the above definition to be extended to cover all changes in oxidation st,ate and makes it easier to recognize the physical changes underlying the treatment being developed. The approach by which an atom is regarded as at,taching its non-bondi~igelect,rons to an at,om of zero electronegativity is not novel; Gillespie (2) applied this treatment to a non-bonding pair. Electron Density Models of Oxidation State Changes
C represent atoms whose electronegativities increase from A to B to C. Figure 2b illustrates a case in which redox does not take place even though a shift in electron density occurs. If the molecule AB, for example, were to represent hydrogen chloride, the molecule could dissociate to form H + and C1-. Since the relative order of electronegativities would remain unchanged, this would not be a redox reaction. For the same reason, displacement of B, as pictured, by the more electronegative atom C is not considered to be an oxidation-reduction reaction. For atom A to have undergone a change in oxidation state, the bond between atoms A and B would have had to rupture and, in the new bond formed by atom A, the electron density would have had to shift so that it was either equally shared or was greater near atom A. Comparison of Lewis Acid-Bose ond Oxidation-Reduction Reocfions
I t is expedient to compare the redox concept as presented wit,h the Lewis acid-base concept. The redox concept distinguishes between those Lewis acid-base reactions which are redox reactions and those which are not. I n non-redox Lewis acid-base reactions, an atom, A, may be initially bound by a paired-electron link to an atom of lesser elect,ronegativity. When this bond is broken, atom A bonds to another atom whose electronegativity is also less than t,hat of A. In redox chemist,ry, however, A would bond t,o an atom of greater elect,roriegativit,y t h i ~ nthat of A. Some Relevant Aspacts of the Electronegativity Concept
The changes in the order of electronegativities which take place in an oxidat,ion or reduction may conveniently be pictured by the use of molecular orbital representations. Figures l a and l b illustrate, respectively, equal and unequal sharing of an electron pair. In Figure 2a, changes in relative orders of electronegativities are pictured in which the letters A, B, and
Although the electronegativity concept has been freely used in t,he foregoing, mention must be made of considerations pertinent to its use. The definition of and the establishment of values for electronegativity have beeo much debated in the literature. Current, aspect,s of t,he matter have been reviewed by l'ritchard and Slcinner (3) and by Ferreira (4). The most widely accepted definitions are those of Mulliken ( 5 ) , and Pauling (6). New ideas on electronegativity have
Figure I. Boundary surfocc. of m.lecu1.r 0rbitdr: 0, homonucleo. diotomic molecules; b, diatomic molecules, B mwe eledronegotive than A.
Figure 2. Boundary rvrfocer of molecular orbitals, relative order of B >A: o, redox changes of atom 8: magnitudes of electronegativitier, C b, redor chmger do not occur in these rhifh of electmn density.
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been proposed recently by Iczkowski and Margrave (7), Hinze, Whitehead, and Jaff6 (8),and by Klopman (9), among others. A number of methods for the determination of electronegativity values have been developed among which may be mentioned those of Pauling (lo), of Rfulliken (5), of Sanderson (11), and of Allred and Rochow (12). Discussion of the above is beyond the scope of this paper. With respect to the topic as applied herein, the following comments are made. Ferreira has noted that the meaning of electronegativity seems to be intuitively understood by chemists (4) Still, the construction of a precise definition has been fraught with problems. Theoretically, an atom develops an electron-attracting power as a result of the effective nuclear charge outside of the atomic kernel acting upon the outermost shell of electrons. This effect is complicated by the partial screening effects of valence electrons upon each other. Electronegativity was defined by Pauling as the power of a neutral atom in a molecule to attract electrons to itself (6). Ferreira has pointed out that, because molecules are not just simple additive combinations of atoms, electronegativity cannot, in principle, be called an atomic parameter. However, the valencebond theory and the LCAO-molecular orbital theory "preserve" the atoms in the molecules. By accepting this idea of a "preserved" atom, it becomes possible to use knowledge of atomic electronegativity for the understanding of chemical phenomena (4). As of now, the Rlulliken definition appears to be the most widely accepted theoretical definition of atomic electronegativity. Mulliken defined electronegativity as one-half the sum of the ionization potential and electron affinity of an atom (5). As a result of new experimental procedures, it is now possible to reliably determine ionization potentials and many electron affinities (IS). Numerical values of electronegativity obtained by the Pauling thermochemical methods are roughly proportional to the Mnllikenvalues although the validity of the Pauling procedure has been questioned (4). Because thermochemical data are relatively easy to obtuin and because agreement exists with other methods of establishing elect,ronegativity values, the Pauling electronegativity scales are much used. Iczkowski and Margrave (7) have recently proposed that electronegativity may be treated as the property of an orbital in an atom, and may be defined as
dipole moment (14). The bond moment may be present due solely to differences in atomic size so that the centers of positive and negative charge do not coincide. I n the case of the hydrogen fluoride molecule, a bond moment exists not only because of the difference in electronegativities but also because the small hydrogen atom is almost embedded in the larger electron cloud of the fluorine atom. I t can be postulated that there are bondings where the direction of the bond dipole is opposite to that of the order of electronegativities, as was proposed by Coulson for the tetravalent carbon-to-hydrogen bond (15). Oxidofion State Change and Complex Formation
The recent development of theories of complex formation apparently is in accord with the above interpretation. Complex formations are, by themselves, not regarded as oxidation-reduction reactions by chemists; they do not involve changes in oxidation state (i.e., the electrons in the complex linkage are initially non-bonding electrons within the orbitals of the more electronegative atom). This corresponds to the view of complex formation as essentially involving overlapping of orbitals without transfers in electron density between ligand and central atom. Pauling has claimed that the electronegativities of atoms and the non-cornplexed ions which they form are practically equal. This suggests that the change in energy per change of charge in the orbital of an atom is fairly constant., a t least until the electron shell is filled or stripped. The modification of t,he electronic structure of the cent,ral ion which occurs in complex formation may alter the electron screening within the valence shell of the ccntral ion which, in turn, may alter the central ion's electron-attracting power. Since this change in electron attracting power is not the result of an increase or decrease in electron density from an outside source but is due instead to the distribution of the atom's own electron density, it must be considered a change in its atomic electronegativity. The change in electronegativity with change in oxidation state may then alter the relative stability of the different oxidation states of the element. As in all other redox reactions, electronegativity difference is not the only factor involved in the reaction energetics. While it might be desirable to determine the electronegativity of the central atoms of complexes, in practice the oxidation potential is an even more useful parameter. Clarriflcotion of Reactions Involving Oxidation State Changes
where x is electronegativity, E is the energy of an orbital and n the number of electrons in the orbital. The Mulliken definition becomes a special case of the Iczkowski-Wlargrave definition, where the change - i n n is one electron-(8). It might seem that bond polarity would be a more convenient term to use in the redox treatment than electronegativity. This urould be the case if bond polarities could be directly equated with bond dipole moments. However, asymmetric distribution of electron density within a molecular orbital as a result of differences in electronegativity is not the only determinant of a bond dipole moment. Mulliken has pointed out that even a purely covalent bond may have a large 454 / Journal of Chemical Educofion
The rules given in introductory chemistry texts enable relatively unequivocal determinations of oxidation numbers, whether the rules are considered to be arbitrary or whether they are interpreted in terms of the physical meaning of the electronegativity principle as developed above (within the limitations imposed by electronegativity values precise to, a t best, two significant figures). However, the situation is much less clear when it comes to the classification of reactions in which changes of oxidation state occur. I t might seem that any reaction where oxidation state changes occur would be classed as a redox reaction, but this is not so. An oxidation-reduction reaction is defined by most introductory texts as any reaction in which a change of oxidation state occurs. However, advanced texts and
journals may differ from this by the grouping of certain reactions which embody changes of oxidation state together with non-redox reactions; any mention of change in oxidation state is omitted. Although the nonredox treatment accorded such reactions is fairly uniform, deviations from the prevalent practices may be found. More puzzling is the fact that some reactions in which oxidation state changes occur have been specifically identified as non-oxidative (18). No explanations of the above deviations from redox treatment were found in the literature, nor was any statement given on governing criteria. Apparently, textbook and journal writ,ers have intuitively understood the basis for the classification of these reactions without regard t o their changes in oxidation state. The next section of this paper will present a classification scheme based on the rather complicated practice prevailing in the literature for reactions in which changes in oxidation state occur. Offered with this will be a rationale hypothesized as underlying the present redox classification treatment. I t is noted that, in the same sense that any classification system in necessarily of an arbitrary nature, SO also is any system which classifies redox reactions. The scheme to be prescntcd is based on the idea that a reaction in which given atoms undergo oxidation stat,c changes is not considered to be an oxidat,ion-reduction reaction unless the difference in relative electronegativities is a factor in causing the reaction t o occur. Furthermore, the degree to which the reaction tends to be treated as a redox reaction in advanced texts and in journals depends t o a considerable extent, on the degree t o which the electronegativity difference between the atoms undergoing oxidation state change is a factor in causing the change in oxidation number. The greater the electronegativit,y difference and, correspondingly, the more significant its effect on the reaction, the more likely it is t,hat the reaction dl be treated as a redox reaction. Accordingly, three categories of reactions embodying oxidation state changes were set up; they were named, for convenience herein, (I) the stronger oxidations, (2) the very weak oxidations, and (3) the pseudoredox react,ions. The stronger oxidations are those in which the electronegativity difference between atoms undergoing oxidation state changes is a significant factor in causing them to undergo the changes in oxidation state. The very weak oxidations are those correspondingly in which the electronegativity difference between atoms undergoing a change in oxidation state is a very minor factor in causing the reactions t o take place. The pseudo-redox reactions comprise the reactions in which the electronegativity difference between atoms undergoing a change in oxidation state is not a factor in causing the reaction to occur. The line of demarcation between the stronger and the very weak oxidations is not sharply delineated. The three categories will be discussed next in greater detail. The Pseudo-Redox Reaction
The criterion for this category is as stated above. Typical of the reactions in this category are organic elimination reactions, photoexcitations, radiolyses, and the solution of halogens in water.
I n both the organic elimination and the halogen solutions, the atoms undergoing change in oxidation state are atoms of the same element initially bonded to each other. One atom is then reduced, the other oxidized. For example, in the elimination of carbon dioxide from a p k e t o acid n n
C' is reduced while C v is oxidized. Likewise, when chlorine dissolves in water, the bond between the chlorine atoms undergoes scission; one chlorine atom forms C1- with an oxidation state of (I-) while the other combines to form OCI- where it has a n oxidation state of (I+). I t is evident that the difference in relative electronegativities of the atoms undergoing oxida t'~ o n and reduction is not a causative factor of reaction. I n the p k e t o acid elimination, bond scission is the result of a n inductive effect transmitted from the strongly electronegative carbonyl carbon. The bond scission which occurs when the halogens dissolve in water is the result of the strong polarizing effect of the medium. The practice of excluding radiolyses and photoexcitations from the redox category is a170 in accord with the idea that the relative atomic electronegativity differencebet.ween the atoms undergoing oxidation state change is not a factor in causing the oxidations and reductions t o occur. Radiolyses result from the penetration of particles initially external to the medium while photoexcitations in which changes of oxidation state occur require strong steric or electron-delocalizing effects. An example of a photo-excitation in ~vhich changes of oxidation state occur is
Here, the clectron is pulled out of the bond away from the more electronegative atom. I n the pseudo-redox reaction, the changes in oxidation state are due to factors other than the atomic electronegativity differences of the "preserved" atoms in molecules. Definition of an Oxidation-Reduction Readion
I t is proposed that an oxidation-reduction reaction be defined as a reaction in which a change i n the relative order of atomic electronegatiuities takes place between a given atom and the atoms lo zohich it i s bonded prior and subsequent to reaction; concurrently, an opposite chanqe i n order of electronegatiuities takes place elsewhere among the ~eactants. The difference i n relative electronegativities of the atoms undergoing oxidation state change is a factor i n causing the changes to occur. Stronger and Very Weak Oxidofions
Many kinds of reactions in which changes of oxidation state take place are treated as redox reactions in texts and periodicals. Among these are (1) inorganic reactions in which net transfer of electrons occur; (2) electrochemical reactions; (3) free radical autoxidations; (4) free radical reactions in which transfers of electrons take place (as with metallic complexes or semi-quinones); (5) many organic reactions of which a partial listing would include all of those reactions in which carbon progresses through the oxidation stages Volume 47, Number 6, June 1970
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