Lewis Structures, Formal Charge, and Oxidation Numbers A More User-Friendly Approach John E. Packer and Sheila D. Woodgate University of Auckland, Private Bag, Auckland, New Zealand Two articles emphasizing difficulties experienced by students in writine Lewis structures have recentlv aooeared in this journal (1,-2). Pardo (1) correctly pointedoit'that one reason for these difficulties is that few elementary textbooks give a simple set of rules for doing so. He identified the main oroblems encountered. T h e second article (2) based on an k n a ~ ~ sof i sstudent errors on drawing Lewis structures on a comouter confirmed that Pardo's identification of problem areas was essentially correct. The substance of ~ a r d o ' sarticle had been to give a set of rules designed to overcome these difficulties. ~ n c o r t u n a t e lhe ~ , appeared not to have seen the excellent article by Snadden (3) or read the appropriate section on Gillesoie's well-known North American text ( 4 ) . These authors present essentially the same rules more simolv. A small New Zealand txmk (5) whose authors had inde. p&dently followed the snadden and Gillespie approach adopts a still more "user-friendly" manner. In this article this "user-friendly" approach is outlined with three examples and compared with the Snadden, Gillespie, and Pardo methods hopefully demonstrating that if students follow a set of rules faithfully, the difficulties classified by Brady e t al. (2)should not arise. Rules for Drawing Lewls Structures (a) Determine the total number of valence electrons in the species by adding together the numbers of valence electrons of each atom and, if an anion, by adding the overall charge of the ion and, if a cation, by subtracting the overall charge of the ion. (b) Place the atoms in their relative positions. (c) Draw a line representing a single bond containing two eleetrona between joined atoms. (d) Distribute the remaining electrons evenly in pairs on the outer atoms so these have up to eight electrons (except for hydrogen). Any still not used after this should be placed on the central atom. (e) If the central atom is now surrounded by fewer tban eight electrons, move sufficient nonbonding pairs from outer atoms other tban halogens to between joined atoms, thusmaking them bonding, t o bring the number on the central atom up to a maximum of eight. ( f ) Count the number of electrons "owned" by each atom pretending bonding electrons are evenly shared. To evaluate the formal charge at that atom, compare the result with the number of valence electrons of the neutral atom. Show only nonzero charges. (g) For central atoms from the second or later rows of the periodic table, move further nonbonding pairs to bonding positions to lower the positive formal charge on the central atom to one or zero. Three examples for C0s2-, N01, and SOz, are given in Figure 1.
Discussion of Rules These rules require no chemical knowledge other than the number of valence electrons of atoms (i.e., elementary atomic structure) and which atoms are joined together. The latter information must he given as fact a t the time Lewis structures are first introduced if i t is not obvious from the formu456
Journal of Chemical Education
Figure 1. Examplesoftheapplicationoftherulesfor drawing Lewis structures.
la. Rule (e) leads to multiple bonds, and rule (g) allows for the fact that elements of the second and later rows of the periodic table can have more than eight valence electrons (d electrons), but there is no mention of either of these more also advanced conceots in the actual rules. This aooroach .. requires minimal arithmetic and provided students f o l l ~ w t h m faithfully . thev. will nlwavs oroducea valid Lewis strutture. Furthermore, rule (g) allows students toobtain the best representative Lewis structure. In the case of SO2 this rule leads to the structure 2 rather than the commonly given structure 1. Very recently in this Journal Purser has argued cogently the case for the superiority of structure 2 (5). Snadden's first step is the same as rules (b) and (c). His second step, "Count up the number of bonding electrons and subtract from the total number of valency electrone provided by the individual atoms or ions. The difference gives the number of electrons which must be accommodated in the
structure either as non-bonding lone nairs or additional bonding pairs," could he too much for some students. His third sten is in essence the same as (c) and (d) but reauires more arithmetic. His fourth and fifth steps &e essenkally the same as (e). Our rule (f) for determiningformal charge by electron counting is much less formidable than the equation given by Snaddenand many textbooks: "Formal charge of an atom in a molecule = number of valency electrons in the unhonded atom - (half the numher of shared electrons number of non-bonding electrons)". Gillespie's rules are perhaps closer to those given here than are Snadden's. However, his rule corresponding to our (d) puts the electrons on the more electronegatiue atoms rather than the outer ones, requiringa concept not necessary a t this stage. He assigns formal charge hefore moving electron oairs to comolete an octet around the central atom. effeciively reversing the order of our (e) and (f) but does not includeinstructionsun how todo this within his Lewisstructure rules. He determines formal charge in the same way as Snadden hut uies core charge, a further concept, or group number, no longer ronsistent with the 1I:PAC periodic tahlc format, instead of "number of valencs electrons in the unbonded atom." Inspection of Pardo's steps ( I ) show that they are more complex still. He requires calculation of the number of bonding electrons by determining the numher of valence electrons individual atoms would have and subtracting the numher of valence electrons actually available. Then the numher of a electrons are determined from the structure. and the numher of T electrons calculated from the difference between the totalnumber of bonding electrons and the number of a electrons. All this is unnecessary to ohtain a correct structure, and in most courses simple Lewis structures would be met before the more sophisticated concept of a and a honds is introduced. If the skill of writing Lewis structures has been mastered a t an early age by practice using a set of simple rules, the rationale of the rules and the inadequacies of a single Lewis structure can he introduced later a t the appropriate time. Thus the moving of electrons to minimize formal charge illustrates the well-known fact that it requires energy to separate unlike charge, and species spontaneously tend toward adopting a state of minimum energy. A single Lewis structure of COa2- implies that one C-0 bond is different from the other two, whereas physical measurements show all the honds are the same. Thus the "real" structure may be represented by all three possihle Lewis structures each making an equal contribution, i.e., the simple representation of resonance. Early in most courses students meet the equilibrium 2N02 + N204 with the implication the hond in the dimer must be weak. The Lewis structure of NzO4,3, shows two positive charges close together implying that formal charge is a physically meaningful concept.
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The rules for writing Lewis structures suggested in this paper and by Snadden and Gillespie start with the assumption the students know which atoms are ioined toeether in the species. By applying the rules and arriving a t a Lewis structure showing the distribution of valence electrons, it is a simple further step to predict the actual shape by assuming that honds (sinale or multiole), nonhondine electron pairs. and single unpaired electrons represent electron clouds that adopt a geometry to keep as far away from each other as possihle to minimize the energy of the species, i.e., the valence-shell electron pair repulsion (VSEPR) theory of Nyholm and Gillespie.
In their article "Lewis structure skills: taxonomy and difficulty levels" Brady et al. (2) identified 12 individual skills that they perceive students require to do all the 51 examples given to them and determined the difficulty of each skill (on a four-point scale) from the success or failure rate of the students. The students had had one lecture on drawing Lewis structures and had done some homework but bad not practiced long enough to become adept. Three of these skills were under the beading "central atom skills" and had to do with student difficulty in identifying the central atom from the given formulas, such as FN02, SCN-, POC13, S Z O ~ ~ - . This is hardly a Lewis structure skill hut something more sophisticated, and i t would he unreasonable to expect students to predict the arrangement of atoms in such species a t the time they should first meet Lewis structure writing. In fact, one can write perfectly valid structures for different possihle isomers of all the ahove species, e.g., 4 and 5 for POC13. In a recent national examination in New Zealand students were asked to draw a Lewis structure of ozone. 09. being told only that i t was a nonlinear molecule. About 30% eave structure 6. a nerfectlv valid answer that received full marks in view of tKe fact that they were not told the hond angle was greater than 60'.
Six other of the perceived skills were classified as "adjustment skills" and were called: odd (i.e., odd numher of electrons.. e.e.. - . NO. Clog): nromote he.. multinle honds. ex.. NO3-, C02); tr&l
