Formal Charges and Resonance Lecture Review

Formal charge serves as a critical diagnostic tool used to identify the most reasonable or likely Lewis structure for a given molecule or polyatomic ion when multiple valid structures appear possible.
It helps predict how atoms are ordered and how electrons are distributed within a molecular framework.

The formal charge is defined as the hypothetical charge an atom would possess in a molecule if the electrons in all chemical bonds were redistributed evenly among the participating atoms.
Calculation Formula:
- $FC = \text{Valence Shell Electrons of a Free Atom} - \text{Lone Pair Electrons} - \frac{1}{2}(\text{Bonding Electrons})$
Rules for Summation:
- In a neutral molecule, the sum of all formal charges for every atom must equal $0$ .
- In a polyatomic ion, the sum of all formal charges must equal the overall charge of the ion.

Step 1: Determine total valence electrons.
- Iodine (I): $7$ valence electrons.
- Chlorine (Cl): $7 \times 4 = 28$ valence electrons.
- Ionic Charge: $-1$ (adds one electron).
- Total: $7 + 28 + 1 = 36$ electrons.
Step 2: Construct the Lewis structure.
- Iodine is the central atom because it is the least electronegative.
- Connect four chlorines via single bonds ( $8$ electrons used, $28$ remaining).
- Complete octets for chlorine by adding three lone pairs to each ( $24$ electrons used, $4$ remaining).
- Place the remaining $4$ electrons as two lone pairs on the central iodine atom.
- Enclose the structure in brackets with a $-1$ charge outside.
Step 3: Calculate formal charges.
- For Chlorine ( $Cl$ ):
  - Each chlorine has three lone pairs and one bonded pair.
  - $FC = 7 - 6 - \frac{1}{2}(2) = 0$
- For Iodine ( $I$ ):
  - Iodine has two lone pairs and four bonded pairs.
  - $FC = 7 - 4 - \frac{1}{2}(8) = -1$
Verification:
- Sum: $(4 \times 0) + (-1) = -1$ . This matches the charge of the ion.

Molecular structure refers to the specific arrangement of atoms within a molecule or ion. Formal charges help determine the best order based on these preferences:
- 1. Preference for Zero: It is highly preferable for all atoms to have a formal charge of $0$ .
- 2. Minimizing Charge: If zero is impossible, formal charges should be as close to zero as possible.
- 3. Adjacent Atom Charges: Formal charges on adjacent atoms should ideally be $0$ or carry opposite signs.
- 4. Electronegativity Alignment: Negative formal charges should ideally reside on the more electronegative atoms.

Example Structures:
- Structure A: Carbon in center, double bonds to both Oxygens ( $O=C=O$ ).
  - Formal charges: All atoms ( $O$ , $C$ , and $O$ ) are $0$ .
- Structure B: Triple bond between one Oxygen and Carbon, single bond to the other ( $O\equiv C-O$ ).
  - Formal charges: Right oxygen is $-1$ , left oxygen is $+1$ , and carbon is $0$ .
- Structure C: Oxygen in the center ( $O-O-C$ ).
  - Formal charges: Left Oxygen is $0$ , middle Oxygen is $+2$ , Carbon is $-2$ .
Conclusion: Structure A is the most likely and correct structure because it keeps all formal charges at the preferred value of $0$ .

Structure 1 ( $N-C-S$ ):
- $N = -1$ , $C = 0$ , $S = 0$ .
Structure 2 ( $C-N-S$ ):
- $C = -2$ , $N = +1$ , $S = 0$ .
Structure 3 ( $C-S-N$ ):
- $C = -2$ , $S = +2$ , $N = -1$ .
Conclusion: The first structure is the most likely because its formal charges are closest to zero.

Valence electron count: Sulfur ( $6$ ) + Oxygen ( $6$ ) + $2 \times$ Chlorine ( $14$ ) = $26$ electrons.
Initial Structure (Single Bonds):
- Sulfur centrally bonded to Oxygen and two Chlorines.
- Chlorines and Oxygen obtain octets; remaining electrons on Sulfur.
- Formal charges in this version:
  - $O = -1$
  - $S = +1$
  - $Cl = 0$
Optimized Structure (Double Bond):
- Converting a lone pair from Oxygen into a bonding pair (forming a double bond with Sulfur) changes the charges.
- Formal charges in the optimized version:
  - $O = 6 - 4 - \frac{1}{2}(4) = 0$
  - $S = 6 - 2 - \frac{1}{2}(8) = 0$
  - $Cl = 7 - 6 - \frac{1}{2}(2) = 0$
Conclusion: The double-bonded structure is better because all formal charges are reduced to zero.

Known as laughing gas; used as an anesthetic in surgeries (e.g., wisdom tooth extraction).
Structure 1 ( $N \equiv N-O$ ):
- Terminal Nitrogen: $FC = 5 - 2 - \frac{1}{2}(6) = 0$
- Central Nitrogen: $FC = 5 - 0 - \frac{1}{2}(8) = +1$
- Oxygen: $FC = 6 - 6 - \frac{1}{2}(2) = -1$
Structure 2 ( $N-O-N$ ):
- Terminal Nitrogen: $FC = 5 - 4 - \frac{1}{2}(4) = -1$
- Central Oxygen: $FC = 6 - 0 - \frac{1}{2}(8) = +2$
- Second Nitrogen: $FC = -1$
Selection: Structure 1 is the more likely structure because the formal charges are closer to zero and the negative charge resides on the more electronegative atom (Oxygen).

Resonance occurs when a single Lewis structure is insufficient to accurately describe the bonding in a molecule or ion.
Definition: A situation where two or more Lewis structures have the exact same arrangement of atoms but different arrangements of electrons. These individual structures are called resonance forms.
Resonance Hybrid: The actual electronic structure of the molecule, which is an average of the multiple resonance forms. It is not that the molecule flips between forms; rather, it exists as a single "hybrid" state.
Nitrite Ion ( $NO_2^-$ ) example:
- Two equivalent structures can be drawn by shifting the double bond between the central Nitrogen and the two different Oxygens.
- Neither structure is better; they are both possible and are separated by a double-sided arrow.
Carbonate Ion ( $CO_3^{2-}$ ) example:
- Carbon is in the center with three Oxygens.
- A double bond can be placed on any one of the three Oxygen atoms, resulting in three resonance forms.
- In reality, all three $C-O$ bonds are identical. The true structure is the average of the three possible placements of the double bond.