Lesson 3 · 35 min

Lewis structures and formal charge

Count the valence electrons and draw Lewis structures step by step; use formal charge to pick the most reasonable one, and meet resonance, electron deficiency and the expanded octet.

In this lesson

Count the valence electrons of a molecule or ion and draw its Lewis structure step by step
Compute formal charges and use them to choose the most reasonable of several structures
Recognise resonance and explain how the real species relates to its resonance forms
Recognise the three kinds of octet exceptions: electron-deficient, odd-electron and expanded octets

In 1916 the American chemist G. N. Lewis sketched a simple notation: dots for valence electrons, and a pair of dots shared between two atoms for a covalent bond. More than a century later these dots-and-lines drawings are still chemistry’s favourite scratch paper. They answer many questions — for example, how many double bonds belong between nitrogen and the three oxygens of the nitrate ion, $\ce{NO3-}$ ? Experiment finds all three N–O bonds equally long (about 125 pm), yet any single Lewis drawing shows one N=O and two N–O. How is that contradiction resolved?

Predict first

How many valence electrons must a Lewis structure of $\ce{NO3-}$ contain?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

22 23 24 32

Four steps to a Lewis structure

Count valence electrons: add up the atoms’ valence electrons; add one per negative charge, subtract one per positive charge.
Build the skeleton: usually the least electronegative atom (never H) goes in the middle; join the others with single bonds, 2 electrons each.
Complete the outer atoms first: give them lone pairs until they have an octet (H needs only 2), then put any electrons left over on the central atom.
Complete the centre: if the central atom still has fewer than 8 electrons, turn a lone pair on a neighbour into a shared pair, making a double or triple bond.

Following these steps can give more than one plausible structure. To choose between them, use the formal charge: pretend every shared pair is split evenly between its two atoms, and count whether each atom ends up with more or fewer electrons than when neutral.

\mathrm{FC} = V - N - \tfrac{1}{2}B

The formal charges always add up to the overall charge of the molecule or ion.

$V$: valence electrons of the free atom
$N$: electrons in the atom’s lone pairs
$B$: electrons in the bonds to the atom

A good Lewis structure follows three guidelines: formal charges as small as possible (ideally zero); where they cannot be avoided, negative formal charge sits on the more electronegative atom; and adjacent atoms do not carry charges of the same sign.

Count · octets · formal charge · resonance

Lewis structure workbench

\ce{CO}

Carbon monoxide

Valence electrons available 10 · drawn 2 · left 8

8 valence electrons are still missing.

Bonds (click to cycle single/double/triple)

Lone pairs

Atom	Lone pairs	Electrons around	Formal charge
C	0	2 short	+3
O	0	2 short	+5

Formal charges sum to +8; the ion’s charge is 0

Formal charge

\mathrm{FC} = V - N - \tfrac{1}{2}B

V: valence electrons of the free atom; N: non-bonding electrons; B: bonding electrons.

Click a bond to cycle single, double and triple; adjust lone pairs with + and −; formal charges and octet checks update live. Try CO: what does it cost to give both atoms an octet? Then look at the “exceptions” BF₃, PCl₅ and SF₆.

Resonance: molecules one drawing cannot capture

Back to nitrate. The double bond can be drawn to any of the three oxygens, giving three structures of identical energy called resonance forms, linked by a double-headed arrow ↔. The real ion does not flip between them; it is their average: each N–O bond has order $4/3$ and each oxygen carries about $-1/3$ of a charge. That is why all three bonds measure the same. Ozone, $\ce{O3}$ , is similar: both O–O bonds are 127.8 pm — between a single bond (148 pm) and a double bond (121 pm) — bond order 1.5.

Worked example

The Lewis structure of carbonate, CO₃²⁻

Draw the Lewis structure of $\ce{CO3^2-}$ and find each atom’s formal charge and the average bond order.

Three kinds of octet exceptions

Electron-deficient: boron in $\ce{BF3}$ has only 6 electrons. A B=F bond would complete the octet but put a positive formal charge on fluorine, so it is usually not drawn; boron’s empty orbital makes $\ce{BF3}$ an eager acceptor of an electron pair.
Odd-electron: $\ce{NO}$ and $\ce{NO2}$ have odd numbers of valence electrons (11 and 17), so one electron is always unpaired. Such molecules are radicals and tend to be reactive.
Expanded octet: atoms from period 3 onwards can be drawn with 10 or 12 electrons, as in $\ce{PCl5}$ and $\ce{SF6}$ . Second-period atoms cannot — their valence shell has only four orbitals, 2s and 2p.

Concept check

In the best Lewis structure of ozone, $\ce{O3}$ , what is the formal charge on the central oxygen?

−1 0 +1 +2

Try the calculation

How many valence electrons does the sulfate ion, $\ce{SO4^2-}$ , have?

Key takeaways

Lewis structures show valence electrons as dots and lines: count them, build the skeleton, complete the outer atoms, then the centre.
Formal charge FC = V − N − B/2; the best structure has the smallest formal charges, with negative charge on the more electronegative atoms.
Resonance forms describe one and the same molecule, whose real structure is their average (bond order 4/3 in NO₃⁻ and CO₃²⁻, 1.5 in O₃).
The octet rule has exceptions: electron-deficient (BF₃), odd-electron (NO) and, beyond period 2, expanded octets (PCl₅, SF₆).

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Data and references

G. N. Lewis, “The atom and the molecule”, J. Am. Chem. Soc. 38, 762 (1916).
IUPAC Compendium of Chemical Terminology (Gold Book): formal charge, resonance.
N. N. Greenwood, A. Earnshaw, Chemistry of the Elements, 2nd ed. (nitrate and ozone bond lengths).
A. E. Reed, F. Weinhold, J. Am. Chem. Soc. 108, 3586 (1986); and later work on hypervalent bonding without d-orbital participation.