Using Formal Charges in Teaching Descriptive Inorganic Chemistry David G. DeWit Augustana College, Rock Island, IL 61201 Courses in descriptive inorganic chemistry are often regarded a s unusually challenging by students, who often express resentment a t having to memorize seemingly unrelated factual information. In response, most of us who teach such courses carefully attempt to link factual information with principles encountered by students in prerequisite general chemistry courses, including, periodic properties, expected oxidation states i n various families, simple inorganic reaction types, and valence bond (VB) theory principles of bonding and structure. Invoking appropriate ordering principles a t critical points in the course does indeed enhance students' abilities to understand, recall, and even predict chemical phenomena. The first course in inorganic chemistry a t Augustana College is a one-semester course required for chemistry majors and taken primarily by freshmen and sophomores. One of the principles I have used quite successfully to help students rationalize and remember a wide variety of chemical information is the principle of formal charges. This principle is generally given sparse treatment in most general chemistry textbooks and is, I believe, under-used in teaching descriptive inorganic chemistry. I t is a simple extension of the process of drawing Lewis structures, and most students, even the weaker ones, seem quite able to compute the formal charge of a n atom in a molecule or ion once they manage to produce the correct Lewis structure. In this article, I have chosen examples ( I ) that demonstrate how widely the concept can be applied. Many other good examples could have been cited. The Principle of Formal Charges The formal charge on a n atom in a molecule or ion is computed by comparing the number of valence electrons (u) for the neutral uncombined atom with the number of electrons (n)that can be assigned exclusively to the atom in the Lewis structure of the molecule or ion. formal charge = u - n The value of n is determined by counting one for each unshared electron on the atom (two for a lone pair) and one for each bond to the atom. (One electron of the shared pair is assumed to belong to each of the atoms bonded.) An important consequence of this definition, especially for students checking their work, is that the sum of the formal charges on all atoms equals the actual charge on the species. Consider the Lewis structures of the isoelectronic molecules Nz and CO.
Each nitrogen atom has a formal charge of zero because u = 5 for atoms in Group V, and n = 2 (lone pair) + 3 (three bands) = 5
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However, the carbon atom in CO has a formal charge of -1 because u = 4 (Group N)and n = 5; the oxygen atom has formal charge 6 - 5 = +l. Maximum stability is achieved by minimizing formal charges, and when nonzero formal charges must occur, negative formal charges are more stable on more electronegative atoms. With this in mind. it is easv to convince a student that Nz, with its triple bind and zero formal charges, ought to he verv stable and relatively inert, whereas CO should be more reactive. Because thenegative formal charge is on carbon instead of the more electronegative oxygen atom, a student might even expect CO to display some uniquely interesting properties. I n fact, CO is a ligand that is unusual in a way that is predictable from its formal charge distribution (see Clues to Reactivity below). Some of the physical properties of carbon monoxide illustrate how influential the formal charge principle can be.
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(a,) In spite of the large difference in eleetranegativity hetween oxygen and carbon,the formal charge distribution works in direct opposition to the expected polarity so that esu) CO is almost a nonpolar molecule (p = 0.12 x with the positive end of the dipole an the oxygen. (h.1 The C-0 stretching frequency in CO is 2143 cm-', which is much lower than the N-N stretching frequency in N2 (2331 cml). (c.) The C-0 hand di+ance (1.1282 A)is longer than the N-N distance (1.0975 A). F a d s b and c hoth indicate that the CO bond order is a hit less than 3, suggesting that resonance structures such a s 3 and 4 make nonnegligible contributions to the overall bonding picture. :c=o C+Lo:-'
..
. ..
Students recognize that these structures are illegal according to the octet rule but readily understand that they might be valid contributors: 3 has zero formal charge for hoth atoms, and 4 has formal charges that are a t least in line with expected electronegativities. (Students usually can also see that 3 and 4 are not major contributors.) Pauling estimates that 2 contributes 50%, 3 contributes 40%, and 4 contributes 10% to the true nature of CO (2). In a recent paper in this Journal (31, Perry and Vogel correctly point out that formal charges must be carefully distinguished from "real" charges (i.e., ionic charges and ~ a r t i acharges l due to bond uolarities) and oxidation numbers. 1ndee; we must emphasize with students that formal charees merelv indicate a votential for charge builduu on atoms in a molecule or ion. However, the effect of formal charge is often real. The polarity of a bond may be enhanced beyond what is expected from eledronegativity differences, or a n expected bond polarity may be counteracted (weakened or even reversed) a s in the case of CO. Students must always be made aware that theories often are imperfect models that can lead to incorrect predictions. ~ h notion k of formal charges as well as simple VB theory upon which it is based
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are certainly simplistic models and give unrealistic and occasionally erroneous pictures of the electronic nature of molecules. However, as the following examples (1)show, the general success of the formal charge principle should give it a valid place in an intermediate-level undergraduate inorganic course. Predicting Bond Properties ~ 0 4 and ~ - 5704~-
When asked to sketch Lewis structures of the two isoelectronic ions (P043-and Si04"), most students produce structures 5 and 6 and, on the basis of VSEPR, correctly predict that these ions are tetrahedral.
.. :p:
..0.
-1
5
6
7
However, although 6 is an appropriate representation of orthosilicate SiOaG, phosphate ions are normally regarded, most notably by biochemists, as having a P=O double bond as in structure 7. The preference for structure 7 is clear, based on the principle of formal charges. Structure 5 has a n unnecessary +1formal charge on phosphorus, whereas 7 simply localizes the three negative charges of orthophosphate ion on three of the four electronegative oxygen atoms. (Students must be prepared to expect expanded valence shells for central atoms in the third and higher rows of the periodic table.) A structure analogous to 7 for Si04&would place a negative charge on silicon rather than on the considerably more electronegative oxygen atom. The Ligand Behavior of Dimethylsulfoxide
Structural Insights N k 0 and CH&
When students can predict for themselves the correct structure for an important molecule, they gain a special sense of the validity of that structure, and this increases their chances of remembering it. In the case of hydroxylamine, NHBO,students quickly see that, on the basis of formal charges, 10 is clearly preferable to other permutations like 11 and 12, even though all three obey the octet rule.
.. ..
H
I I
H-N-0-H
H-N+%:
H
H
I
...I
..
..+ L H
..
H-N-~
.. ?H
10 11 12 Similarly, students can discover the functional group for a n organic acid by evaluating proposed structures for CHzOz (formic acid) like 13, 14, and 15. Only 14 has the correct number of valence electrons and zero formal charge on all atoms, even though all three structures obey the octet rule.
13
14
15
HCOr- versus HNOr
Although isoelectronic species are often isostructural, such is certainly not the-case for formate ion (16) and the nitrous acid molecule (17).
DMSO can be thought of as a resonance hybrid of Lewis structures 8 and 9.
It is evident from these structures that DMSO can function as an ambidentate ligand because both oxygen and sulfur have lone electron pairs to donate to a Lewis acid. A particularly convenient way to determine whether DMSO is oxygen-bonded or sulfur-bonded in a given complex is to compare its S O infrared stretching frequency to that of free DMSO (vso = 1050 em-')). A lower stretching frequency suggests the oxygen-bonded form, and a higher frequency the sulfur-bonded form. This criterion is based on the expectation that 8, with a -1 formal charge on oxygen and a +1formal charge on sulfur, ought to be a much better oxygen donor than sulfur donor whereas 9, with zero formal charge on both oxygen and sulfur, should be a better sulfur donor than oxygen donor (sulfur is less electronegative). Because 8 has a S O single bond, its vo should be lower than 9, which has a S = 0 double bond. For example, we correctly predict that [CUCIZ(DMSO)ZI with vso = 923 cm-' (lower than in free DMSO) has oxygen-bonded DMSO (81, whereas [PtC12(DMS0)21 with vso = 1111cm-' (higher than in free DMSO) has sulfur-bonded DMSO ligands (9).
17 16 If H C O l were to adopt a structure like 17, the more electropositive carbon atom would bear the -1 formal charge rather than oxygen. On the other hand, if HNOz were to adopt a structure like 16, an unnecessary separation of formal charge would result, with +1 on nitrogen and -1 on oxygen. H N a versus k P O 4
Students who have come to expect similarity in behavior within a family are discouraged when seemingly arbitrary exceptions arise. Why, for example, do the formulas for the +5 oxyacids of nitrogen and phosphorus differ? Clearly, the best possible Lewis structure for HN08 (18)has an unresolvable separation of formal charges.
I
18
I
H
H
19
20
The phosphorus analogue of nitric acid, HP03, can easily remedy this charge separation in aqueous solution by adding one H20 molecule (H+-OH-). The Hi part of the water molecule is attracted to the oxygen atom bearing the -1 formal charge, whereas the OH- part of water attacks the phosphorus (with a +1formal charge), giving H3P04(19) Volume 71 Number 9 September 1994
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for which all formal charges are zero. This solution to the formal charge problem is possible for phosphorus but not nitrogen because phosphorus can expand its valence shell beyond a n octet and, being physically larger, can easily accommodate an extra group around it. One might a t first expect that adding H 2 0 to HN03 would give H3N04 (20). However, because a n N=O double bond would violate the octet rule. the formal charge .. ~. r o b l e mof HNOs would Dersist in H3SOl r + l on nitrogt:n and -1 on oxygen. along with the ndditionnl p r d ~ l c mof increased sterir crowding. Clues To Reactivity Bronsted Acid Strength of H N Q vs. HNOr The remarkable difference i n acid stren&h for these two acids rnn he riltioni~lizcdin a number of \I& hut the principle of f i ~ n n dcharges provides an easy onr. 'Tho -1 fi,~mal c h a r ~ eon the nitroxrn of the itrongacid HNO" t181would act a s a repelling influmce on the proton, whereas the nitlwpn of I I N O t 17. has a zero firmal chargt: and no such influcncc. The same argument works in other wries of rclated acids, for example, HC104> HCIO, > HCIO, > HCIO where the formal charges on chlorine (in the resonance structures with Cl-0 single bonds only) are +3, +2, +1, and
:- N + ~ i j T l
23 The Allotropes of Oxygen Students soon discover that elements often have different allotropic forms which, for a variety of reasons, have different stabilities. Oxygen is an element with allotropes, O3 (24) and 0, (25), whose relative stabilities are easy to predict.
..+I :ofio\" -1 0:
24
