. OXIDATION NUMBERS AND VALENCE SAMUEL GLASSTONE Boston College, Chestnut Hill, Massachusetts
INTHE course of a discussion of various aspects of valence, a question was raised concerning the significance of the so-called "valence numbers" which are frequently employed in the balancing of oxidation-reduction equations. The "valence number" often coincides with the recognized valence of the element in the given compound, e . g., 7 for Mn in KMn04, 6 for S i n HzSOr, 3 for N in NHa, etc., but there are many instances in which this is not the case. The N atom in NzOs and in HN03,,for example, has a "valence number" of '+5, but accordmg to the usually accepted electronic theory of valence it can form only four covalent bonds. In the NH4+ion, on the other hand, in which the N atom also has four covalent bonds, the "valence number" is -3. Carbon is another element for which there is no correlation between the "valence number" and the number of bonds. The "valence numbers" of C in oxalic acid, formic acid, and formaldehyde are +3, +2, and 0, respectively, yet there is no question concerning the quadrivalence of carbon in these compounds. Other instances of the same kind could be quoted, but the foregoing are sufficient to illustrate the general nature of the problem. The difficulty might be resolved, as is indicated in some texts, by stating that the "valente number" is equivalent to the valence the element under consideration would have if all the bonds in the'given compound were purely ionic (electrovalent) in character. The fact remains, however, that many of the bonds present in substances taking part in oxidation-reduction reactions are definitely not ionic. It cannot be denied that "valence numbers" are useful in many respects and that they lead to correct results when properly employed to balance equations, but in the mind of the inquiring student the question of their physical or chemical significance must inevitably arise. Some authors have appreciated the situation and have referred to "apparent valence numbers," but even this qualified expression has its dangers. In view of the possible misleading association, it is suggested that the use of the word "valence" in this connection he avoided, and that the term "oxidation number," which is employed in some texts, be universally adopted. This name has the advantage of bemg in agreement with the fundamental principle underlying the evaluation of these numbers, as will be seen shortly, as well as with their application in oxidation-reduction equations. The oxidation number of a particular element in a given compound, as usually determined, actually represents the number of electrons (or negative charges) that would be necessary to restore an atom of that element to
its neutral state after converting all the other elements into their respective ions. The number is positive when electrons would have to be supplied, e. g., +7 for Mn in KMnO,, and negative when they would have to be removed, e. g., -3 for N in NH,, to leave the specified atom without charge. It can be readily shown that this interpretation of the oxidation number agrees with the usual assignments, and also with such apparently unusual cases as that of oxygen, to which the values of -2, -1, and 0 are ascribed in HzO, HzOz,and Oz, respectively. In HzO, for example, the formation of two (positive) hydrogen ions would leave the 0 atom with an excess of two electrons, and hence -2 electrons would be "required" to restore it to the neutral state. In HzOz,the -2 electrons are shared between two 0 atoms, so that each atom requires -1. The Oz molecule, on the other hand, is made up of two neutral atoms, and no electrons need to be added or removed; the oxidation number of the 0 atom is consequently zero. It will thus be apparent that the oxidation number provides an indication of the "electron demand" of a given element, in a particular molecule or ion, in terms of a consistent basis of reference. Since oxidation capacity may be regarded as the ability to accept electrons, the name "oxidation number" would appear to be justified. It may be pointed out that the basis of reference conventionally employed is not the only one possible, hut it has the advantage of yielding oxidation numbers that are frequently, although not always, in agreement with the valence of the element as rommonly defined by the ratio of the atomic weight to the equivalent weight. As used here and subsequently the equivalent weight refers to the weight of the element which combines with or replaces a gram atom of hydrogen, onehalf gram atom of oxygen, etc. Another aspect of the matter under consideration is the relationship of the valence of the element, as just defined, and the number of valence bonds it exercises in a given compound. It is often tacitly accepted, in accordance with historical precedent, that these numbers are the same, but this is by no means always the case. Reference may be made, once again, to N205and HN03. The valence, i. e., the atomic weight divided by the equivalent weight, of N in the former, and presumably in the latter, is 5, but it seems that the N atom forms no more than four valence bonds in these, or any other, compounds. In the related phosphorus compounds, however, i. e., P205and HP03, the P atom probably forms five bonds. Nevertheless, with other derivatives of this element complications arise, for X-ray diffraction studies indicate that in the solid state PCls has the
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structure [PCla]+[PCl&, so that one P atom is bonded to four and the other to six CI atoms. Solid PBr6, on the other hand, appears to have the structure [PBr4]+Br-, making it similar to a phosphonium compound in which the central atom is quadricovalent. Incidentally, in the vapor state the P atoms in both of these pentahalides are probably attached to five halogen atoms. In HaOzthe equivalent weight of oxygen, as defined above, is equal to its atomic weight, so that the valence, like the oxidation number, is unity, yet each 0 atom possesses two valence bonds. Similar considerations apply to Hg in mercurous chloride (Hg,CL). The structures of the silicates are based on a unit consisting of an Si atom attached by single linkages to four 0 atoms, in agreement with the value of 4 for the valence of silicon. It is of interest to note, however, that aluminum, in spite of its valence of 3, often replaces silicon in minerals, each A1 atom being connected to four 0 atoms. By including coordination compounds, further discrepancies between the valence and the number of bonds become apparent. It may be mentioned that some writers have suggested-it must be admitted not without good reasonthat the concept of definite bonds or linkages joining
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particular atoms is a convenient fiction, for all the atoms in the molecule as a whole are held together by elect~ical forces. Even if this view is ultimately adopted, as it may well be, and the idea of specific atom linkages is discarded, the number of immediate neighbors of a given atom, which is equivalent to the number of bonds, will still have significance. This number, no matter what it is called, will consequently still differ from the valence in certain instances. The conclusion to be drawn from the arguments presented here is that there are three dist,inct properties of a particular element in a specified compound: (1) the oxidation number, often misnamed the "valence number"; (2) the valence, i. e., the ratio of the atomic weight to the conventional equivalent weight in terms of combination with or replacement of hydrogen or oxygen; and (3) the number of bonds. In general, although not always, the oxidation number is the same as the valence; the number of bonds is sometimes the same but frequently different. These points should be made clear to the student at the outset if he is to be saved from the inevitable confusion which will arise when he delves more deeply into the problems of valence and molecular structure.
