## Introducing Formal Charges and Resonance

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In the previous topic, we discussed how to write Lewis structures for molecules and polyatomic ions. As we have seen, however, in some cases, there is seemingly more than one valid structure for a molecule. We can use the concept of formal charges to help us predict the most appropriate Lewis structure when more than one is reasonable.

## Calculating Formal Charge

The **formal charge** of an atom in a molecule is the *hypothetical* charge the atom would have if we could redistribute the electrons in the bonds evenly between the atoms. Another way of saying this is that formal charge results when we take the number of valence electrons of a neutral atom, subtract the nonbonding electrons, and then subtract the number of bonds connected to that atom in the Lewis structure.

Thus, we calculate formal charge as follows:

\(\text{formal charge}=\text{# valence shell electrons (free atom)}-\text{# lone pair electrons}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\text{# bonding electrons}\)

We can double-check formal charge calculations by determining the sum of the formal charges for the whole structure. The sum of the formal charges of all atoms in a molecule must be zero; the sum of the formal charges in an ion should equal the charge of the ion.

We must remember that the formal charge calculated for an atom is not the *actual* charge of the atom in the molecule. Formal charge is only a useful bookkeeping procedure; it does not indicate the presence of actual charges.

## Example: Calculating Formal Charge from Lewis Structures

Assign formal charges to each atom in the interhalogen ion \({\text{ICl}}_{4}{}^{\text{−}}.\)

### Solution

*We divide the bonding electron pairs equally for all I–Cl bonds:**We assign lone pairs of electrons to their atoms*. Each Cl atom now has seven electrons assigned to it, and the I atom has eight.*Subtract this number from the number of valence electrons for the neutral atom:*I: 7 – 8 = –1Cl: 7 – 7 = 0The sum of the formal charges of all the atoms equals –1, which is identical to the charge of the ion (–1).

## Example: Calculating Formal Charge from Lewis Structures

Assign formal charges to each atom in the interhalogen molecule BrCl_{3}.

### Solution

*Assign one of the electrons in each Br–Cl bond to the Br atom and one to the Cl atom in that bond:**Assign the lone pairs to their atom.*Now each Cl atom has seven electrons and the Br atom has seven electrons.*Subtract this number from the number of valence electrons for the neutral atom.*This gives the formal charge:Br: 7 – 7 = 0Cl: 7 – 7 = 0All atoms in BrCl_{3}have a formal charge of zero, and the sum of the formal charges totals zero, as it must in a neutral molecule.