In the Classroom
Common versus Uncommon Oxidation Numbers of Nonmetals Wayne P. Anderson Department of Chemistry, Bloomsburg University, Bloomsburg, PA 17815 Despite the difficulties that sometimes arise in assigning values of oxidation numbers (oxidation states) to atoms (1), the concept continues to play an important role in chemistry. Additional insight on chemical species can be obtained if an element contains an unusual oxidation number. Predicting Common Oxidation Numbers Box diagrams for the valence electrons of elements can be used to predict common oxidation numbers (2). 1. To obtain the negative oxidation number of a nonmetal, add enough electrons to complete the partially filled valence sublevel in the box diagram. 2. To obtain common positive oxidation numbers, first remove all unpaired electrons as a set to give the lowest positive oxidation number. Then remove remaining electrons in pairs to obtain higher positive oxidation numbers. 3. To obtain the oxidation number of zero, add or remove no electrons.
Consider chlorine as an example. The box diagram for the valence electrons contains one unpaired electron: 3s
3p
Therefore, one expects oxidation numbers of {I, 0, +I, +III, +V, and +VII for chlorine. This is consistent with the observed oxidation numbers of chlorine in Cl{, Cl2 , ClO{, ClO2{, ClO3 {, and ClO4{. Based on the box diagram of phosphorus 3s
3p
one expects oxidation numbers of {III, 0, +III, and +V consistent with the formulas of P3{, P4 , PF3 , and PF5 . Using this approach, the predicted common oxidation numbers of the representative elements are shown in Table 1. Uncommon Oxidation Numbers Having established the predicted common oxidation numbers of the elements (Table 1), it is now possible to conTable 1. Predicted Oxidation Numbers of the Representative Elements Group Predicted Oxidation Number Numbers 1
+I, 0, ({ I)
2
+II, 0
sider the origins of unusual values based on Lewis structures. Common oxidation numbers occur for an atom X of an element whenever (i) all atoms attached to X have a higher electronegativity than X or (ii) all atoms attached to X have a lower electronegativity than X. Whenever an atom is attached to another atom having the same electronegativity, as occurs in a homonuclear bond, an oxidation number of 0 or an unusual oxidation number is expected. Also, if some of the attached atoms have a higher electronegativity than X and others have a lower electronegativity than X, an unusual oxidation number is obtained for X. If the atom X contains nl bonds to atoms having lower electronegativity than X and nh bonds to atoms having higher electronegativity than X, then the oxidation number of X is simply n h – nl (3). Normally oxidation numbers are obtained directly from formulas rather than from Lewis structures. Rules for assignment of oxidation numbers can be found in nearly all general chemistry textbooks. These rules, which are generalizations based on oxidation number assignments from Lewis structures, give average oxidation numbers for all atoms of the same element in a given formula. Such average oxidation numbers avoid the complication that arises when different resonance structures give different oxidation number assignments based on Lewis structures. Nitrogen is a classic example of an element that exhibits several oxidation numbers not listed in Table 1. To restrict our discussion, we will consider only species listed in the book The Elements, by Emsley (4). Examples of these are shown in Table 2. The unusual oxidation numbers can be attributed to three factors: 1. The compound contains an odd number of electrons. NO and NO2 contain an odd number of electrons. Presence of an odd number of electrons in a molecule automatically precludes noble gas configurations for all atoms. Therefore, it is not surprising that an odd number of electrons in a molecule leads to an unusual oxidation number for one of the elements. 2. The compound contains a N–N bond. N2H4 , N2O 2 , H2 N2O2 , and N2O4 contain N–N bonds. If an atom is bonded to another atom by means of a homonuclear covalent bond,
Table 2. Uncommon Oxidation Numbers of Nitrogen Average Oxidation Formula Number of N N2H4
{ II
NH2OH
{I
N 2O
+I
13
+III, +I, 0
14
+IV, +II, 0, ({ IV)
15
+V, +III, 0, { III
H2N2O2
+I
16
+VI, +IV, +II, 0, { II
NO
+II
17
+VII, +V, +III, +I, 0, { I
NO2
+IV
+VIII, +VI, +IV, +II, 0
N2O4
+IV
18
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In the Classroom Table 3. Electronegativities of Hydrogen and Phosphorus Electronegativity Scale Pauling
Hydrogen
Phosphorus
Reference
2.20
2.19
5
Allred–Rochow
2.20
2.06
5
Allen
2.30
2.25
5
Sanderson
2.59
2.52
5
Mulliken
2.25
sp3: 2.41 20% s: 2.30 p: 1.84 5.62 eV
5
Pearson absolute
7.18 eV
6
the electrons in the bond are divided equally between the bonded atoms. Thus, neither atom gets both electrons in the bond as is required to achieve “normal” oxidation numbers for all elements. 3. The attached atoms have electronegativities that bracket those of nitrogen. In NH2 OH the nitrogen is bonded to two hydrogen atoms (lower electronegativity than N) and one oxygen atom (higher electronegativity than N) by single bonds. Therefore, the oxidation number of N must be 1 – 2 or {I (see previous section). The presence of hydrogen atoms often leads to unusual oxidation numbers because hydrogen is less electronegative than most other nonmetals, whereas fluorine, oxygen, and chlorine are usually more electronegative than other nonmetals. Hydrogen–Phosphorus Bonds An ambiguity is encountered when H–P bonds are present in a chemical species. Depending upon the electronegativity scale (5, 6) used (Table 3), hydrogen can be assigned an electronegativity equal to that of phosphorus (Pauling), higher than that of phosphorus (Allen, Sanderson, Pearson absolute, Allred–Rochow), or lower than that of phosphorus (Mulliken sp3 ). Thus, the phosphorus atom in PH3 could be assigned an oxidation number of {III (Mulliken sp3 ), 0 (Pauling), or + III (Allen, Sanderson, Pearson absolute, and Allred–Rochow). Hydrogen is traditionally assigned a value of +I in species containing H–P bonds (7–9), giving phosphorus an oxidation number of {III in PH 3 , + III in H 3PO 3 {HPO(OH) 2 }, and + I in H 3PO 2 {H2PO(OH)}. Only the Mulliken electronegativity scale is consistent with this assignment. Therefore, the Mulliken scale would seem to be the most appropriate one to use if one wishes to obtain traditional oxidation numbers using Lewis structures. The Mulliken electronegativity, however, depends on the hybridization of each atom involved in a bond. Often the choice of hybridization is unclear. Jørgensen, in his excellent book Oxidation Numbers and Oxidation States (10), assigns hydrogen a negative oxidation number when it is attached to phosphorus. This assignment is consistent with the majority of the electronegativity scales, but it leads to a nonconventional description of some redox reactions. Using the Jørgensen approach, H3PO4 {(HO)3PO}, H3PO3 {HPO(OH)2}, and H3PO2 {H2PO(OH)} would all contain phosphorus in a +V oxidation state. Reduction of H3PO4 to H3PO3 and reduction of H3PO 3 to H3 PO2 would be viewed as: 2 H+ + (HI O)3PVO + 2e{ → H {IPVO (OHI) 2 + H 2O (1) and 2H+ + H {IPVO (OHI)2 + 2e{ → H{I2PVO(OH I) + H2O (2)
188
Based on Pauling electronegativities, the most reasonable assignment of oxidation numbers involving a hydrogen– phosphorus bond would be H(0) and P(0). This would lead to oxidation numbers of + IV and +III for P in H3 PO3 and H 3PO 2 . Reduction of H3PO 4 to H3 PO3 and reduction of H3 PO3 to H3PO2 would be viewed as: 2H + + (HIO)3 PVO + 2e{ → H 0PIVO (OH I) 2 + H 2 O (3) and 2 H+ + H0P IVO (OH I)2 + 2e { → H02PIIIO (OH I) + H2O (4) Since the reduction half-reactions that occur are unchanged by the choice of oxidation numbers, the assignment is somewhat arbitrary. Also the Louis–Langmuir partial charge (11) on the hydrogen atom of the H–P bond is close to zero irrespective of the electronegativity scale used. However, the traditional volt equivalents versus oxidation number (oxidation state) diagram of phosphorus is based upon the assignment of +I to the oxidation number of all hydrogen atoms (7, 8). The presence of an H–P bond is one of several situations leading to oxidation number assignments that depend on the electronegativity scale used. Similar problems arise when N–Cl, As–H, or C–S bonds are present. Other Examples A list of compounds and ions having uncommon oxidation numbers (4), based on the use of Mulliken electronegativities, is given in Table 4. The rationale for each exception is specified. In most cases the unusual oxidation number arises from homonuclear bonds between atoms of the element whose oxidation number is being determined. This accounts for the common exception that oxygen has an oxidation number of {I in peroxides. Although species containing homonuclear bonds are usually not discussed in general chemistry courses, such species are certainly not rare. Most of the remaining exceptions contain attached hydrogen atoms.
Table 4. Uncommon Oxidation Numbers of Nonmetals of the Second and Third Periods Group 14
15
16
17
18
CH3OH {II
P2H4 {II
H2O2 {I
Cl O2 +IV
Kr F +I
HCHO 0
H3PO2 +I
O2F2 +I
Cl2O6 +VI
P 2I 4 +II
S2F2; S2Cl2 +I
H4P2O6 +IV
S2O42{ +III S2O62{ +V S2F10 +V HS2O4{ +III H2S2 {I
Note: Underlined: contains homonuclear bonds. Bold: contains attached H. Italic : contains an odd number of electrons. Oxidation numbers are average oxidation numbers based on Mulliken electronegativities.
Journal of Chemical Education • Vol. 75 No. 2 February 1998 • JChemEd.chem.wisc.edu
In the Classroom Conclusions
Literature Cited
Common oxidation numbers of representative elements can be predicted from valence electron box diagrams. Exceptions to these predicted oxidation numbers generally result from the presence of an odd number of electrons, homonuclear bonds, or attached atoms having electronegativity values that bracket that of the atom in question. Assignment of oxidation numbers is ambiguous when the identity of the more electronegative element in a bond differs from one electronegativity scale to another. Acknowledgment I wish to thank Arlen Viste of Augustana College (South Dakota) for helpful ideas and suggestions concerning this manuscript.
1. Woolf, A. A. J. Chem. Educ. 1988, 65, 45–46. 2. Day, M. C.; Selbin, J. Theoretical Inorganic Chemistry; Reinhold: New York, 1962; pp 115–119. 3. Nelson, P. G. J. Chem. Educ. 1997, 74, 465–470. 4. Emsley, J. The Elements, 2nd ed.; Oxford: New York, 1991. 5. Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry: Principles of Structure and Reactivity, 4th ed.; Harper: New York, 1993; p 187. 6. Pearson, R. G. Inorg. Chem. 1988, 27, 734–740. 7. Phillips, C. S. G.; Williams, R. J. P. Inorganic Chemistry, Vol. 1; Oxford: New York, 1965; p 632. 8. Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements; Pergamon: New York, 1984; pp 587, 590. 9. Lee, J. D. Concise Inorganic Chemistry, 5th ed.; Chapman and Hall: New York, 1996; pp 519–520. 10. Jørgensen, C. K. Oxidation Numbers and Oxidation States; Springer: New York, 1969; pp 12, 206. 11. Allen, L. J. Am. Chem. Soc. 1989, 111, 9115–9116.
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