S2.2.14 Formal Charge and Lewis Formulas (Higher Level Only)

Formal Charge and Determining Preferred Lewis Structures

Imagine you’re assembling a puzzle, and some pieces seem to fit in several ways. How do you decide which arrangement is correct?

In chemistry, when constructing Lewis structures for molecules or ions, we often face similar dilemmas—multiple valid arrangements of bonds and lone pairs can exist.

Formal charge acts as a guiding tool, helping us identify the most plausible structure by determining which arrangement is the most stable and consistent with experimental evidence.

What Is Formal Charge?

Definition

Formal charge

Formal charge is a theoretical concept that assigns a charge to each atom in a molecule or ion. It assumes that bonding electrons are shared equally between the bonded atoms.

The formula for calculating formal charge is:

$Formal Charge (FC) = VE - (NBE + \frac{1}{2} BE)$

Where:

VE = Number of valence electrons the atom has in its free (unbonded) state.
NBE = Number of non-bonding (lone pair) electrons assigned to the atom.
BE = Number of bonding electrons assigned to the atom (count all electrons in bonds directly attached to the atom).

Tip

Formal charge is a useful tool to evaluate which Lewis structure is most likely to represent a molecule's actual bonding arrangement.

Steps to Calculate Formal Charge

Draw the Lewis Structure: Ensure all valence electrons are accounted for, and aim to satisfy the octet rule wherever possible.
- Assign Electrons to Atoms:
  - Lone pair electrons belong entirely to the atom they are on.
  - Bonding electrons are split equally between the two atoms in the bond.
Apply the Formula: Use the formal charge formula for each atom in the structure.
Sum the Formal Charges: The total formal charge of the molecule or ion must equal its overall charge.

Example question

Deduce the formal charge in water.

Solution

Step 1: Draw the Lewis Structure

Water consists of two single bonds between oxygen and hydrogen, with two lone pairs on the oxygen atom.

Step 2: Assign Electrons

Oxygen: It has 4 lone pair electrons and 4 bonding electrons (2 from each bond).
Hydrogen: Each has 0 lone pair electrons and 2 bonding electrons (1 from the bond with oxygen).

Step 3: Calculate Formal Charges

Oxygen: $FC = 6 - (4 + \frac{1}{2} \times 4) = 6 - 6 = 0$
Each Hydrogen: $FC = 1 - (0 + \frac{1}{2} \times 2) = 1 - 1 = 0$

Step 4: Verify the Total

The total formal charge is $0 + 0 + 0 = 0$ , which matches the neutral charge of the water molecule.

Note

The sum of all formal charges in a molecule must equal its overall charge. If it doesn't, recheck your Lewis structure and calculations.

Example question

Choose the preferred structure of sulfate ion ( ${SO}_{4}^{2 -}$ ) based on the formal charges.

Solution

Step 1: Draw Possible Lewis Structures

Two common Lewis structures for ${SO}_{4}^{2 -}$ are:

All single bonds between sulfur and oxygen, with three lone pairs on each oxygen.
Two double bonds between sulfur and oxygen, and two single bonds with oxygen atoms carrying lone pairs.

Step 2: Calculate Formal Charges

Structure 1 (All Single Bonds):
Sulfur: $FC = 6 - (0 + \frac{1}{2} \times 8) = 6 - 4 = + 2$
Each Oxygen: $FC = 6 - (6 + \frac{1}{2} \times 2) = 6 - 7 = - 1$

The total formal charge is $+ 2 + (- 1 \times 4) = - 2$ , consistent with the ion's charge.

Structure 2 (Two Double Bonds):
Sulfur: $FC = 6 - (0 + \frac{1}{2} \times 12) = 6 - 6 = 0$
Oxygen (doubly bonded): $FC = 6 - (4 + \frac{1}{2} \times 4) = 6 - 6 = 0$
Oxygen (singly bonded): $FC = 6 - (6 + \frac{1}{2} \times 2) = 6 - 7 = - 1$

The total formal charge is $0 + (0 \times 2) + (- 1 \times 2) = - 2$ .

Step 3: Choose the Preferred Structure

Structure 2 is preferred because:

It minimizes the formal charges (closer to zero).
Negative charges are placed on the more electronegative oxygen atoms.
The range of formal charges is smaller ( $0$ to $- 1$ ) compared to Structure 1 ( $+ 2$ to $- 1$ ).

Common Mistake

One common mistake is assuming that a structure with all single bonds is always preferred. Minimizing formal charges is a better indicator of stability.

Assumptions in Formal Charge vs. Oxidation States

While formal charge assumes equal sharing of bonding electrons, oxidation states assume that the more electronegative atom "owns" all the bonding electrons. This leads to different conclusions:

Formal Charge: Predicts the most stable Lewis structure and reflects electron distribution in covalent bonding.
Oxidation State: Reflects hypothetical charges if all bonds were ionic, useful for redox reactions.

Example

In ${SO}_{4}^{2 -}$ :

Formal Charge: Assigns $0$ to sulfur and $- 1$ to oxygen (in the preferred structure).
Oxidation State: Assigns $+ 6$ to sulfur and $- 2$ to oxygen

Note

Formal charge focuses on individual atoms within a structure, while oxidation state applies to the entire molecule or ion.

Reflection and TOK Connection

Self review

Draw the Lewis structures for ${CO}_{2}$ and ${NO}_{3}^{-}$ . Calculate the formal charges for each atom and identify the preferred structure.
Compare the formal charge and oxidation state of nitrogen in ${NH}_{4}^{+}$ and ${NO}_{2}^{-}$ .
Consider the molecule ${ClO}_{3}^{-}$ . Draw two possible Lewis structures and use formal charge to determine which is preferred.

Theory of Knowledge

How do the assumptions behind formal charge and oxidation state reflect the limitations of models in science? To what extent can these models provide insight into real-world molecular behavior?