In the Classroom
Valence, Covalence, Hypervalence, Oxidation State, and Coordination Number Derek W. Smith Department of Chemistry, University of Waikato, Hamilton, New Zealand;
[email protected] The terms valence (or valency), oxidation state (or oxidation number), and coordination number have all been in use for decades and are adequately defined in any freshman text. However, a cursory perusal of the recent literature reveals inconsistencies of usage that are likely to confuse students, instructors, and researchers. Before discussing these in detail, I present a brief historical sketch. Valence as a measure of the combining power of an atom was in common use by the 1870s, when chemists were becoming accustomed to writing “graphic” or “constitutional” formulas. These portrayed substances as molecules; the valence of an atom was equal to the number of bonds it formed in such a molecular formulation (1). Atoms could be classified as mono-, di-, tri-, tetravalent, and so forth.1 Clear relationships between valences of elements and the groups of the periodic table enabled the rationalization of the stoichiometries of many organic and inorganic compounds. A student or instructor today who browses through a chemistry book written in the 1880s will be impressed by the number of structures, especially among organic compounds, that would be perfectly acceptable in a modern text. However, the modern reader would recognize three serious problems: A. Many compounds that were well known at the time could not be rendered as molecules in which the constituent atoms exhibited their usual valences. B. Some old molecular formulations offend modern principles of bonding theory. C. Many compounds that could be described graphically as molecules were later found to be of nonmolecular constitution.
An example of problem A was the mineral cryolite, then written as AlF3⭈3NaF, which came to prominence in 1886 with the discovery of the Hall process for the extraction of aluminum metal. There are no residual valences in AlF3 or NaF to hold this “molecule” together. There was also the problem of compounds such as CoCl3⭈nNH3 (n = 3–6). For a time these were depicted as, for example, Co(NH3⫺NH3⫺Cl)3, with pentavalent nitrogen (which was also invoked in HNO3, NH4Cl, etc.). These chain structures were soon superseded by Werner’s coordination theory; the central atom in such complex compounds was assigned a primary valence and a secondary valence. These terms—whose definition has been the source of much confusion since they were introduced—were superceded by oxidation number (or oxidation state) and coordination number. The oxidation number (or electrovalence in the older literature) is derived from the ionic (or electrovalent) approach to bonding; charges are assigned to atoms according to the most satisfactory ionic formulation. Except in complexes with “non-innocent” ligands whose formal charges are doubtful, it is generally possible to assign an unambiguous oxidation number—identical to Werner’s primary valence, af1202
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ter allowing that oxidation number has a sign—to the central atom(s) in coordination compounds. The coordination number is not quite the same as Werner’s secondary valence (2); it is simply the number of atoms in the primary coordination sphere directly bonded to the central atom. Werner’s terminology should by now be regarded as of purely historic interest; but it is by no means extinct. In the latest edition of a standard inorganic text it is stated that, for manganese, “[the] divalent state is the most common and most stable oxidation state”, and that “[there] are numerous zerovalent complexes of palladium and platinum” (3). In almost any issue of a contemporary inorganic or organometallic journal reference can be found to, for example, “low-valent ruthenium complexes”. Here, the terms “valence” (with its associated terminology such as “divalent”) and “oxidation number” are being treated as synonymous and interchangeable. This should cause no confusion if it is understood that Werner’s primary valence is being referred to. However, since many contemporary general and inorganic texts do not mention Werner’s terminology, students are likely to infer from “trivalent iron” molecular structures in which iron atoms form three bonds. Students are also likely to be puzzled by the labelling of, for example, the nickel atom in [Ni(CO)4] as “zerovalent”, from which it might be inferred that the Ni atom has no combining power. The representation [Ni(←CO)4] is not considered to be an adequate description of the bonding; there is ample evidence for Ni→CO π backbonding. In an obvious alternative formulation [Ni(⫽C⫽O)4], nickel would appear to have a valence of eight. Problem B became apparent as the Lewis–Langmuir– Sidgwick electronic theory of bonding was translated into quantum mechanical language in the 1930s. Lewis’s concept of the electron-pair covalent bond and Kossel’s contemporary electrovalent approach (both of which appeared in 1916) emphasized the importance of the noble gas configuration. The number of bonds formed by an atom in a Lewis structure can be described as its covalence and is often—but not always—identical to its classical valence. The electrovalence of an atom is in most cases identical to its oxidation number in modern parlance. In the 1930s Pauling’s valence bond theory invested Lewis structures with quantum mechanical integrity. Molecules of the type NO2X (X = OH, F, CH3, etc.) were often rendered until well into the 1930s with two N⫽O double bonds and pentavalent nitrogen as in classical pre-electronic graphic formulas, although Lewis structures with tetracovalent nitrogen—obeying the octet rule—could be devised. With the development of orbital-based theories of bonding, it became clear that nitrogen is restricted to a covalence of four; having only four valence orbitals at its disposal, it cannot form more than four bonds. Here we have a fruitful source of confusion. In a recent discussion of Pauling’s electronegativity scale (4), it is stated
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In the Classroom
that “seven main group atoms have oxidation state maxima that are less than the number of valence electrons: N, O, F, He, Ne, Ar, and Kr”, and must therefore have the highest electronegativities. On this basis it is argued that nitrogen must have a higher electronegativity than chlorine, which exhibits the VII state in perchlorates. This reasoning is incorrect; nitrogen exhibits the V state in many familiar compounds such as HNO3. The error presumably arises from confusion among the terms oxidation state, covalence, and valence, which are often used interchangeably; it would have been correct to assert that nitrogen never exerts its maximum group covalence of five, or that it does not exhibit hypervalence (to be discussed below). I have already noted that in the coordination chemistry of the transition elements oxidation number can be equated to valence, in the sense of Werner’s outdated primary valence. In main group molecules oxidation number and valence are often but by no means always the same. Thus nitrogen is trivalent in N2 but its oxidation state is zero. Some of the difficulties and confusion can be resolved if we define the valence of an atom as being equal to the number of electrons it commits to bonding; this is often but by no means always the same as its oxidation number. Thus we can have pentavalent nitrogen in NO2X (X = F, Cl, OH, CH3, etc.) while obeying the octet rule, and without invoking a structure with two N⫽O bonds as in classical pre-electronic descriptions. The case of POX3 (X = F, Cl, OH, etc.) is instructive. Most texts (5) describe the bonding in terms of resonance among the three structures: ⴙ
X3P
ⴚ
O (or X3P
I
O)
X3P
ⴚ
O
X3P
II
ⴙ
O
III
It has been argued that structure II—commonly used to depict phosphates and so forth—is inappropriate (6). In C3v symmetry, the O atom has two equivalent 2p orbitals available for π bonding. Thus—if the phosphorus 3d orbitals are used—we can have two π bonds, as in III, or—if the phosphorus 3d orbitals are deemed to be unavailable—no π bond, as in I; but we cannot have just one π bond. What is the valence of the P atom in POX3? Its covalence is four, five, or six in I, II, and III, respectively. But if we define valence in terms of the number of electrons committed by the P atom in a Lewis structure, all contain pentavalent phosphorus; tetracovalent P + and hexacovalent P − are equivalent to pentacovalent (or simply pentavalent) P. What is the valence or covalence of oxygen in POX3? In the structure X3P→O the O atom is contributing no electrons to the bonding, and might therefore be described as zerovalent, like the Ni atom in [Ni(←CO)4]. On the other hand, the polar formulation X3P+—O− can be regarded as being derived from divalent oxygen, as in alkoxides and so forth. Thus the covalence of an atom can vary from one Lewis or resonance structure to another, but the valence—modernizing classical valence in terms of the number of electrons involved in a plausible molecular formulation—is open to less ambiguity. The third problem, C, arises from the fact that many of the “molecules” depicted in the classical literature do not exist as such, except at high temperatures in the gas phase. A high school student can rationalize the stoichiometry of CaF2 in terms of the valences of the atoms, consistent with their www.JCE.DivCHED.org
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positions in the periodic table. But the same student may be surprised to learn that calcium fluoride does not consist of F⫺Ca⫺F molecules under ordinary conditions. Most teachers will be familiar with incorrect molecular formulations by students of substances having nonmolecular structures; the molecular basis for the classical concept of valence can only encourage such misconceptions. However, as discussed by Nelson (7), it is possible to assign “bond numbers” in crystals like CaF2 that can be simply related to classical valences. Nelson (7) argues that three kinds of valence numbers—primary or classical, coordinate, and nonclassical—can rationalize the compositions of molecular, nonmolecular, and coordination compounds and suggests that these refinements to valence terminology have advantages over oxidation numbers for the purpose of classification. His approach—which contradicts the spirit of my proposals—should be carefully studied and compared with the present article. In 1969 Musher (8) introduced the term hypervalent to describe molecules in which atoms of groups V, VI, VII, and VIII (nowadays more often referred to as groups 15, 16, 17, and 18) exhibit valences that entail violation of the octet rule when represented by Lewis or valence bond structures with two-center electron pair bonds. Musher was concerned with such molecules as PF5, SF6, and the noble gas compounds; however, complex ions such as [SiF5]− were later classed as “hypervalent” (9). There is nothing “hyper” (defined as “more than normal” in dictionaries) about the valence of Si in [SiF5]−. The Wernerian primary valence is four, as in simple law-abiding molecules like SiF4. We could regard this complex ion as [F4Si←F−], where Si is pentacovalent but contributes only four electrons to the bonding, or alternatively as [Si−F5]. The latter formulation could be described as hypervalent (isoelectronic with PF5), but pentacovalent Si− is equivalent to tetravalent Si (cf. the discussion of POX3 above). Although Lewis structures for SiF5− in terms of two-center electron-pair bonds violate the octet rule, this is—arguably perhaps—an insufficient criterion for admission to Musher’s category. In any case, Musher’s discussion was focused on molecules, rather than on complex ions, and it may be argued that it is inappropriate to assign classical valence numbers—based on molecular descriptions of chemical constitution—to atoms in ions. Quantum mechanical calculations have cast doubt on the value of the hypervalence concept and the notion of valence shell expansion in the heavier main group elements has been played down in recent years (6, 9, 10). However, five- and six-coordinate Si(IV) compounds continue to be classified as “hypervalent” (11). More seriously, six-coordinate Si(IV) compounds have been incorrectly described (12, 13) as containing “hexavalent silicon”, which would imply the preposterous Si(VI). Conclusions Most of the difficulties, ambiguities, and sources of confusion arise where coordinate or dative bonds are invoked. The classical concept of valence—as a numerical measure of an atom’s combining power, expressed by the number of bonds it forms in a molecular formulation of the compound in question—was unable to cope with coordination compounds and has been difficult to translate into modern terms. The covalence of an atom is the nearest modern equivalent,
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but is subject to ambiguity since it often depends on which bonding model is being invoked. We have the confusing situation in which some authors—especially in transition metal chemistry—equate valence with oxidation number, while others in main group chemistry seem to use valence, covalence, and coordination number—or sometimes valence, covalence, and oxidation number—as interchangeable terms. This a thoroughly unsatisfactory state of affairs; evidently some writers would describe [SiF6]2− as containing hexavalent silicon, while others classify [PtF6]2− among complexes of tetravalent platinum. What is to be done? In our teaching and writing, we should remember that valence is a classical concept, formulated prior to electronic theories of bonding and based on a molecular view of chemistry, which cannot readily accommodate coordinate or dative bonds unless the outdated Wernerian terminology is retained. If applied to compounds having extended structures, it can lead students into writing inappropriate molecular formulations. Valence and its associated terminology (divalent, etc.) should be avoided in these situations except where no confusion or ambiguity is possible. In coordination compounds of both main group and transition elements, the oxidation number and coordination number terminology is to be preferred, especially in dealing with nonclassical complexes such as carbonyls. However, valence numbers are still useful in molecular substances—including most organic compounds—whose modern graphic formulations differ little if at all from those being drawn a century ago. It is far more useful to ascribe to carbon a (nearly) constant valence of four than to try to assign oxidation numbers that may take any value from ᎑4 to +4. Valence terminology should be retained in other areas of main group chemistry. It is still useful to depict phosphates and so forth as containing pentavalent phosphorus with P⫽O bonds for the purpose of rationalizing their stoichiometries and structures; likewise the structures of sulfates and derivatives can be usefully rendered for pedagogic purposes in terms of hexavalent sulfur with S⫽O bonds, notwithstanding objections to such formulations (9). However, educators should be careful to avoid sources of ambiguity and confusion in valence terminology.
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Acknowledgment I thank the reviewers for their critical but helpful dissection of the original version of this article. Note 1. Linguistic purists prefer the Latin prefices uni-, bi-, ter-, quadri-, quinque-, sexa- and so forth to the Greek mono-, di-, tri-, tetra-, penta-, hexa- and so forth because valence is derived from Latin and not Greek; however, although the Latin forms are common in the older literature the Greek forms have taken root in an age in which fewer practising chemists have studied classical languages.
Literature Cited 1. Palmer, W. G. A History of the Concept of Valency to 1930; Cambridge University Press: Cambridge, 1965. 2. Kauffman, G. B. Inorganic Coordination Compounds; Heyden: Philadelphia, 1981. 3. Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry, 6th ed.; Wiley-Interscience: New York, 1999; pp 758, 1065. 4. Murphy, L. R.; Meek, T. L.; Allred, A. L.; Allen, L. C. J. Phys. Chem. A 2000, 104, 5867–5871. 5. See, for example, Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry, 6th ed.; Wiley-Interscience: New York, 1999; p 382. 6. Kutzelnigg, W. Angew. Chem., Int. Ed. Engl. 1984, 23, 272– 295. 7. Nelson, P. G. J. Chem. Educ. 1997, 74, 465–470. 8. Musher, J. I. Angew. Chem., Int. Ed. Engl. 1969, 8, 54–68. 9. Gillespie, R. J.; Robinson, E. A. Inorg. Chem. 1995, 34, 978– 979. 10. Noury, S.; Silvi, B.; Gillespie, R. J. Inorg. Chem. 2002, 41, 2164–2172. 11. Kinrade, S. D.; Hamilton, R. J.; Schach, A. S.; Knight, C. T. G. J. Chem. Soc., Dalton Trans. 2001, 961–963. 12. Kinrade, S. D.; Gillson, A.-M. E; Knight, C. T. G. J. Chem. Soc., Dalton Trans. 2002, 307–309. 13. Gossage, R. A. J. Chem. Soc., Dalton Trans. 2002, 2256–2257.
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