7.4 Formal Charges and Resonance

Formal Charges and Resonance

Formal charges and resonance help you figure out which Lewis structure for a molecule is the best one, and how electrons are actually distributed. These two tools work together: formal charges let you evaluate competing Lewis structures, while resonance explains why some molecules can't be captured by a single structure.

Formal Charges in Lewis Structures

A formal charge is the charge an atom would have if all bonding electrons were shared equally. It tells you whether an atom in a Lewis structure "owns" more or fewer electrons than it normally has.

To calculate it, you compare three things: the atom's valence electrons (what it starts with), its lone pair electrons (fully owned), and half of its bonding electrons (shared equally).

$\text{Formal charge} = \text{Valence electrons} - \left(\text{Lone pair electrons} + \frac{1}{2} \text{Bonding electrons}\right)$

• Valence electrons: the number from the atom's group on the periodic table (Group 1A = 1, Group 4A = 4, Group 6A = 6, etc.)
• Lone pair electrons: non-bonding electrons sitting entirely on that atom
• Bonding electrons: all electrons in bonds connected to that atom (count every bond as 2 electrons, a double bond as 4, a triple bond as 6)

Carbon monoxide (CO) example with a triple bond, $:C \equiv O:$

1. Carbon: 4 valence electrons, 2 lone pair electrons, 6 bonding electrons (triple bond)

   • $\text{FC}(C) = 4 - (2 + \frac{1}{2}(6)) = -1$

2. Oxygen: 6 valence electrons, 2 lone pair electrons, 6 bonding electrons (triple bond)

   • $\text{FC}(O) = 6 - (2 + \frac{1}{2}(6)) = +1$

Notice that the formal charges across the whole molecule add up to zero, which they always should for a neutral molecule. (For an ion, they should add up to the ion's charge.)

Evaluating Structures with Formal Charges

When you can draw more than one valid Lewis structure for a molecule, formal charges help you pick the best one. Follow these rules in order:

1. Minimize formal charges. The structure where formal charges are closest to zero on every atom is generally most stable.
2. Put negative charges on electronegative atoms. If two structures have the same total formal charge, the better one places negative formal charges on more electronegative atoms (like O, N, F) and positive charges on less electronegative atoms (like C or S).
3. Avoid same-sign charges on adjacent atoms. Having two positive or two negative formal charges next to each other is unfavorable.

Comparing two Lewis structures for $CO_2$:

• Structure 1: $O=C=O$ (two double bonds)
  • $\text{FC}(C) = 4 - (0 + \frac{1}{2}(8)) = 0$
  • Each $\text{FC}(O) = 6 - (4 + \frac{1}{2}(4)) = 0$
  • Sum of absolute formal charges = 0
• Structure 2: $O-C \equiv O$ (one single bond, one triple bond)
  • $\text{FC}(C) = 4 - (0 + \frac{1}{2}(8)) = 0$
  • Single-bonded $\text{FC}(O) = 6 - (6 + \frac{1}{2}(2)) = -1$
  • Triple-bonded $\text{FC}(O) = 6 - (2 + \frac{1}{2}(6)) = +1$
  • Sum of absolute formal charges = 2

Structure 1 wins because all formal charges are zero. Structure 2 also has the problem of placing a positive charge on oxygen, which is the more electronegative atom.

Resonance Forms of Molecules

Sometimes no single Lewis structure accurately represents a molecule. Resonance is what happens when you can draw two or more valid Lewis structures that differ only in where the electrons are, not where the atoms are. The real molecule is a blend (a resonance hybrid) of all the forms.

To draw resonance forms:

1. Start with one valid Lewis structure (all atoms have correct octets/duets, correct total electron count).
2. Move lone pairs or pi-bonding electrons to adjacent positions to create a new valid structure.
3. Do not move any atoms. Only electrons shift.
4. Make sure every new structure still satisfies the octet rule (or duet for hydrogen).

Ozone ($O_3$) example:

• Form 1: $O=O-O$ (double bond on the left, single bond on the right)
  • Central O has formal charge +1, right terminal O has formal charge -1
• Form 2: $O-O=O$ (single bond on the left, double bond on the right)
  • Central O has formal charge +1, left terminal O has formal charge -1

Neither form alone is correct. The real ozone molecule is a hybrid where each O-O bond has a bond order of 1.5, and the negative charge is spread equally across both terminal oxygens. This spreading of electrons across multiple atoms is called electron delocalization, and it stabilizes the molecule.

A quick way to recognize when resonance is likely: look for molecules with a double bond next to a lone pair, or with alternating single and double bonds.

Advanced Concepts in Resonance

These ideas go slightly beyond the basics but are worth knowing at the intro level:

• Conjugation occurs when alternating single and double bonds create a pathway for electrons to delocalize over several atoms. Molecules like butadiene ($C_4H_6$) have conjugated systems where the pi electrons are spread across the whole chain.
• Aromaticity is a special, extra-stable type of resonance found in cyclic, planar molecules with a continuous ring of delocalized pi electrons. Benzene ($C_6H_6$) is the classic example: its six carbon-carbon bonds are all identical, with a bond order of 1.5, rather than alternating single and double bonds.
• These delocalized pi electrons are more accurately described by molecular orbital theory, which you'll encounter in later courses. For now, just know that resonance structures are a useful shorthand, but the real electron distribution is a smooth blend, not a flip between forms.