using formal charges in teaching descriptive inorganic chemistry

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 as unusually challenging by students, who often express resentment a t having to memorize seemingly un- related factual information. In response, most of us who teach such courses carefully attempt to link factual information with principles encountered by students in prereq- uisite 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 an 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 an 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

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 electro- - - negative atoms.

With this in mind. i t 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. In fact, CO is a ligand that is un- usual in a way that is predictable from its formal charge distribution (see Clues to Reactivity below).

Some of the physical properties of carbon monoxide illus- trate how influential the formal charge principle can be.

(a,) In spite of the large difference in eleetranegativity he- tween oxygen and carbon, the formal charge distribution works in direct opposition to the expected polarity so that CO is almost a nonpolar molecule (p = 0.12 x esu) 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).

Fads b and c hoth indicate that the CO bond order is a hit less than 3, suggesting that resonance structures such as 3 and 4 make nonnegligible contributions to the overall bonding picture. ..

: c=o . C+Lo:-' .. Students recognize that these structures are illegal ac-

cording 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.) Paul- ing 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 a l charges due to bond uolarities) and oxidation num- bers. 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 an expected bond polarity may be counteracted (weakened or even re- versed) as in the case of CO. Students must always be made aware that theories often are imperfect models that can lead to incorrect predictions. ~ h k notion of formal charges as well as simple VB theory upon which it is based

750 Journal of Chemical Education

are certainly simplistic models and give unrealistic and oc- casionally 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 undergradu- ate 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.

.. -1 :p: .. .. 0

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 an unnecessary +1 formal 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 ex- panded 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

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 com- plex 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 +1 formal 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 = 1111 cm-' (higher than in free DMSO) has sulfur-bonded DMSO ligands (9).

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 hydroxyl- amine, NHBO, students quickly see that, on the basis of formal charges, 10 is clearly preferable to other permuta- tions like 11 and 12, even though all three obey the octet rule.

H .. .. I ...I .. .. H-N-0-H H-N+%: H - N - ~ + L H

I H

I .. H

.. ? H

10 11 12 Similarly, students can discover the functional group for

an 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).

16 17 If HCOl were to adopt a structure like 17, the more elec-

tropositive 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 kPO4

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 unre- solvable separation of formal charges.

I I H H

18 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 +1 formal charge), giving H3P04 (19)

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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 ac- commodate an extra group around it. One might a t first expect that adding H20 to HN03 would give H3N04 (20). However, because a n N=O double bond would violate the octet rule. the formal charge ~rob lem of HNOs would Der- .. . sist in H3SOl r + l on nitrogt:n and -1 on oxygen. along with the ndditionnl prd~lcm of increased sterir crowding.

Clues To Reactivity Bronsted Acid Strength of H N Q vs. HNOr

The remarkable difference in acid stren&h for these two acids rnn he riltioni~lizcd in a number of \I& hut the principle of f i ~ n n d charges provides an easy onr. 'Tho -1 fi,~mal c h a r ~ e on the nitroxrn of the itrongacid HNO" t181 would act a s a repelling influmce on the proton, whereas the ni- tlwpn of I I N O t 17. has a zero firmal chargt: and no such influcncc. The same argument works in other wries of rc- lated 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

Lewis Acid Strength of S@ vs. SOr

Both SO3 and SOz (21 and 22) can function a s Lewis acids, forming complexes with Lewis bases such a s F-, trimethyl amine, and OH-.

C ..

21 22 However, SO, is a much stronger Lewis acid, consistent

with the more positive formal charge on sulfur that helps make SO3 more electrophilic. For example, the preference of the base 02- for SO3 is evident from H values for reaction of NazO with SO3 (g) and SO2 (g) to give Na2S04 and Na2S03, that is, -568 k J and 3 8 0 kJ. The tendency of SO3 to self-associate also indicates its highly acidic nature (see below).

Oxidizing/Reducing Power

HNO* i s one of the commonest laboratorv oxidizing agents Lsed by students. Its oxidizing strength is evide2 from high reduction potentials for HNO3.

HNO, + 2e- + 2Hi + HNO, + H20 En = +0.94 V

From the Lewis structure of HN03 (18) one can easily visualize why and how the above reduction occurs. The central nitrogen, bearing a +1 formal charge, should readily attract extra electrons from a reducing agent, whereas the oxygen atom with the -1 formal charge would attract Hi ions. Two H+ ions are able to cleave this oxveen atom along with its pair of bonding electrons to give HZ&, which allows the two electrons from the reducing acent to add to the nitrogen as a lone pair, producing ~ N 0 ; ( 1 7 ) . All formal charges are zero in both products.

A similar rationale works in other cases. For example, NgO is reduced very readily to Nz.

NzO + 2 e + 2Ht 3 Nz + H20 Eo = +1.77 V

Considering the most stable resonance structure for NzO (231, a similar scenario can be imagined where the electrons attack the central nitrogen and the hydrogen ions attack the oxygen to give the very stable Nz molecule (1) and HzO.

: - 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: <e-0

24 25 We would expect the formal charge separation in 0, to

make i t the less stable allotrope. In fact, conversion of O3 to Oz is very favorable.

20, + 30, AGO = -327 kJ

Students are not surprised to learn that O3 is a n explosive substance and a much stronger oxidizing agent than Oz.

The facility of this reduction is enhanced by the formal charge separation, a s i t is for HNO, and NzO (above).

Ligand Behavior of CO and C N

These isoelectronic species (2) and (26) are two of the strongest monodentate ligands encountered in coordina- tion chemistry.

They are typical soft ligands (preferring to bond to large transition metal centers with low charges and many d electrons), nearly always bonding through the carbon atom. They prefer to bond through carbon because the -1 formal charge is on the carbon atoms rather than on the more electronegative oxygen or nitrogen atoms, making the carbon lone pairs more available for bonding. Structures 27 and 28 show that coordinating to a metal is a way of reducing the formal charge on each carbon atom to zero.

In spite of their similarities, however, these two ligands differ in a n important way. CO is a very weak o donor (do- nating the electron pair on the carbon to make a o bond with the metal) but is regarded a s one of the strongest x- acceptor ligands, readily accepting electron density from the metal to make a second (x) bond between the metal and carbon atoms. This reduces the bond order between carbon and oxygen.

&ceo:+' L M+k~=o' : This also reduces the +1 formal charge on oxygen to zero.

In fact, this + l formal charge could be viewed a s attracting the electron density from the metal in the first place. Of course, the extent to which this x back-bonding takes place


depends on the availability of electron density on the metal, and one exnects CO to bond most strondv to metals with several d ;k t rons in their valence shelii

The C N ligand is a much weaker n accentor than is CO because the nitrogen atom in 28 already has a zero formal charge. However, CN- is a much stronger a donor than CO because the lone pair on carbon in C N is not being con- strained by a positive formal charge on the neighboring atom. Thus, the strength of CW as a ligand derives mainly from forming exceptionally strong a bonds with Lewis acids.

Carbon and Silicon Halides

I often ask students to predict reasonable products for simple reactions based on relative metallic or nonmetallic character and oxidation states expected in main group families. For example, reaction of phosphorus and chlorine is expected to give either PC15 or PC13 because +5 and +3 are the most important positive oxidation states in Group V After learning that +4 and +2 are the important positive oxidation states in Groun N. students are chaerined to discover that CClz and ~ i & are not r eas~nab l~~roduc t s for the reaction of carbon and silicon with chlorine under nor- mal conditions. I t is easy to demonstrate that a really good Lewis structure cannot be drawn for these molecules: 29 does not obey the octet rule (important for nonmetals like carbon and silicon), and 30 has a particularly unstable formal charge separation with the positive charge on the more electronegative atom.

29 30 Tendency To Polymerize

Polvmerization and oligomerization are widespread phenomena in inorganic chekstry and ought to bepresented to students at an early stace of their study. Aggregation of . - monomer units occurs for a number of reasons,-but the formal charge principle is a driving force that can be invoked in a surprising number of cases.

Sulfur trioxide is usually one of the first molecules con- sidered when Lewis structures and resonance are first in- troduced in chemistry courses. It is usually presented as a hybrid of three equivalent resonance structures like 21, where each oxygen atom has an equal chance of being double-bonded. A contribution from resonance structures with more than one S=0 double bond would reduce somewhat the +2 formal charge on sulfur predicted by 21, but overall, sulfur will retain significant positive formal charge, ac- counting for the high Lewis acidity of S03.

The negative formal charge localized on oxygen makes it entirely reasonable for SO3 molecules to associate with each other, with an oxygen atom (bearing a negative formal charge) attracting and attacking the sulfur atom (bearing a positive formal charge) of a neighboring molecule. The resulting structure (31) provides an easy way to minimize formal charge separation and is found, in one form or other, in the several different phases of solid and ..d' ..o.. .'d'

W .. I .. II .. II -s-0-s-o-s-0-~-~ I1 I I I I I

liquid SO3. For example, P-S03 consists of infinite helical chains, and ?SO3 consists of cyclic trimers.

Polyphosphates

Polyphosphate chains (32) of various lengths are com- mon in inorganic chemistry (e.g., phosphate detergent ad- ditives) and are absolutely vital in biochemical systems (e.g., ATP and ADP).

32 It is enlightening to view polyphosphates as polymers of

P O 3 (331, whose behavior can be compared with the analogous nitrate ion.

T' P+' _ ../ \ ....

':o 0:

33 As in the case of SO3 (above), it is natural for the phos-

phorus (with +I formal charge) to undergo nucleophilic a& tack by an oxygen (with -1 formal charge) of a neighboring ion to produce 32, where formal charges are minimized. Nitrate ion with a Lewis structure analogous to 33 does not polymerize because nitrogen cannot expand its valence shell beyond an octet as phosphorus does in 32. All termi- nal N-0 bonds would thus have to be single, resulting in the same formal charge separation that simple NO3 has (+1 on each nitrogen and -1 on unshared oxygens), thereby gaining nothing but increased crowding around the nitrogen atoms.

Polyphosphazenes

This class of inorganic polymers (34) has found a re- markably wide range of commercial and biological uses.

X X X .. I .. I .. I -wp-N=p-N=p-

I X

I X

I X

34' The precursor polymer (where Xis chlorine) is made by

reacting PC15 with NH3.

polymer Very likely, nucleophilic attack of NH3 on PC15 occurs

first to give an intermediate like 35. Such an intermediate is especially prone to HCl elimination because the -1 formal charge on phosphorus repels C1-, and the +1 formal charge on nitrogen repels H'.

35 The possible Lewis structures of the monomer unit

ClzPN (36 and 37) give clues to its tendency to polymerize.

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:a' .. 36 37

In 36, a nitrogen (-1 formal charge) can attack the phosphorus (+1 formal charge) of a neighboring molecule. Structure 37 requires phosphorus to participate in a triple bond, not a stable configuration for third-row and larger atoms due to poor overlap of rr atomic orbitals. In either case, aggregation of ClzPN units to produce 34, with all zero formal charges, is expected. The cyclic trimer (C12PNk is a major product under most conditions, but high molecular weight linear polymers are formed at high tempera- tures.

Polythiazyl, (SN),

This fascinating material has the appearance (gold lus- ter) and electrical conductance properties of a metal. I t is a one-dimensional conductor along the S-N chains and be- comes a superconductor at 0.26 K. It is interesting to compare SN with its analogue NO (38). NO shows almost no desire for aggregation in spite of its unpaired electron, a fact often attributed to repulsion of the lone pairs on the small nitrogen atoms.

38 The remarkable effect obtained from replacing oxygen

with sulfur has two major causes: sulfur's ability to expand its valence shell beyond an octet and sulfur's much lower electronegativity. Because sulfur is less electronegative than nitrogen, the unpaired electron in SN would reside primarily on the sulfur rather than on the nitrogen. In other words, the highest occupied molecular orbital (HOMO), where the unpaired electron would reside, is more sulfur-like than nitrogen-like because sulfur's valence orbitals are higher in energy than the corresponding orbitals of nitrogen. Thus, 39 and 40 are valid Lewis structures for SN, and both predict the likelihood of polymeriza- tion.

+e,.j" - ''SEN: .s - .. 39 40

In 39 nucleophilic attack of a nitrogen (-1 formal charge) on the sulfur (+I formal charge) of another molecule can occur. In 40 sulfur is participating in a triple bond, normally an unstable situation for third-row and larger atoms. In either case, we would predict a polymer with structure 41, which has zero formal charge on all sulfur and nitrogen atoms. .. .. .. . . .. ..

-$=N-S=N-S=N-

41 The single unpaired electron appearing on each sulfur

along the chain in 41 is VB theory's attempt to portray what band theory predicts more elegantly: A delocalized partially filled valence band occurs in this material and should lead to metallic conductivity.

Silicates and Silicones

The silicates belong to a diverse family of natural materials that contain anions comprised of Si04 tetrahedra with each silicon in the +4 oxidation state. These anions vary in how many oxygen corners of each tetrahedron are shared with other Si04 tetrahedra. When none of the oxygens are shared the anions are discrete Si04" (orthosili-

cate) ions (6). Sharing one oxygen comer per tetrahedron produces the discrete pyrosilicate ion, SipOT6 (42). Note that the formal charee of the shared oxvcen is zero. In .. . ., other words, sharing has reduced the number of negatwe formal charges per S104 unit from four (as in 61 to three.

42 Sharing two oxygen comers per tetrahedron gives the

polymeric metasilicate family comprised of linear (py- roxene) chains (431, written most simply as (SiOs").. Each Si04 unit in 43 now bears only two negative formal charges corresponding to the two unshared oxygens.

43 Sharing three oxygen comers per tetrahedron produces

the disilicate family, (Si2052-),, consisting of two-dimensional planar polymeric sheets with only one negative formal charge per Si04. Finally, all four oxygen comers per Si04 can be shared giving the very stable three-dimensional auartz lattice. (Si0.J.. with zero formal charees . . ". - throughbut.

Aluminosilicates have aluminum atoms substituted for some of the silicon atoins in a silicate structure (44).

44 45 Each aluminum, with -1 formal charge, requires one com- pensatory positive charge from an added cation (e.g., Na', K+, 1/2Ca2+, Hi). In zeolites, the cations are trapped along with H20 molecules inside open cages. When the added cation is Hi, oxygen atoms near the A1 atoms are pro- tonated (45). Due to the resulting +1 formal charge on oxygen, these zeolites are very strong Bronsted acids. Some (e.g., ZSM-5) have commercial uses.

Silicones are synthetic polymeric materials with stable Si-0 backbones analogous to those found in the different families of silicates, except that organic groups (e.g., CH3) replace the unshared oxygens. The physical properties of these materials are determined by the nature of the R groups and the number of shared oxygens per silicon. In general, the silicones are unreactive and have high ther- mal stabilities, attributable to the Si-O-Si-O- linkages. As with the silicates, shared oxygen atoms have zero formal charges. Minimization of formal charge through sharing may be seen as one driving force for linking simple units to make these polymeric materials.

Conclusion

I t must be strongly emphasized to students that the principle of formal charges is one explanatory tool but certainly not the only one. In fact, sometimes the principle


can simply be wrong in its predictions and must yield to better models. For example, one might expect NO2 (46) to be more stable if the unpaired electron were on one of the oxygens (47) because then the formal charges of all atoms would be zero.

46 47 Nevertheless, 46 is a better depiction of NOz because the

unpaired electron resides in the highest occupied molecular orbital, which resembles the valence atomic orbitals of nitrogen (the less electronegative atom) more than the lower-energy atomic orbitals of oxygen.

However, in spite of its artificial view of bonding and oc- casional failings the widespread validity of its predictions makes the principle of formal charges a useful way to help relatively inexperienced students make sense of many of the chemical phenomena they encounter in descriptive chemistry courses.

Literature Cited 1. Data and fadual mformation vsed in them exsmples were taken from the following

sources. Bmm, T. L.; LeMsy, H. E.: Bursten. B. E. Chemistry: The CanlmlS&ncp. 5th ed.; Rentice-Hall: Englewood Cliffs, NJ, 1991. Cotton, F. A,: Wilkinson, G. A d n u a d Inorganic Ckmisfy : A Compnhansiu~ %xi, 4th ed.; Wileley: New York. 1980. Shtiver, D. F.: Atkins, P W.; Langford, C. H. Inorganic Chambry: Freeman: New Y d , 1990. Nakamoto, K Iafmmd and Ramon Spectra ofInorgonic and Co- ordination Compound6 4th ed.: Wiley: New York. 1986.

2. Pau1ing.L. J C k m . Educ 189a,69,519521. 3. P e q W. D.; Vogel, G. C. J. Chem. Educ. 1992.69.222-224,

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using formal charges in teaching descriptive inorganic chemistry

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