Formal charge is a useful concept in chemistry for determining how electrons are distributed among the atoms in a Lewis structure.
It helps us evaluate whether a Lewis structure is reasonable and identify the most stable resonance structure.
What Is Formal Charge?
Formal charge is the hypothetical charge assigned to an atom in a molecule or polyatomic ion when bonding electrons are assumed to be shared equally between the bonded atoms.
The formal charge of an atom can be calculated using:
Formal Charge = Valence electrons − Nonbonding electrons − ½(Bonding electrons)
A commonly used version is:
FC = V − N − B
where:
- FC = formal charge
- V = number of valence electrons in the free atom
- N = number of nonbonding electrons (lone-pair electrons)
- B = number of bonds around the atom
In the second form, B represents the total number of bonds, with a single bond counting as 1, a double bond as 2, and a triple bond as 3.
Quick Reference
| Atom | Valence electrons |
|---|---|
| H | 1 |
| C | 4 |
| N | 5 |
| O | 6 |
| F | 7 |
| Cl | 7 |
| Br | 7 |
| I | 7 |
For most main-group elements, the group number can help you determine the number of valence electrons.
How to Calculate Formal Charge
Follow these steps:
Step 1: Draw the Lewis structure
First, determine how the atoms are connected and place the bonding electrons and lone pairs.
Step 2: Choose the atom
Calculate the formal charge one atom at a time.
Step 3: Count valence electrons
Determine how many valence electrons the neutral atom normally has.
Step 4: Count nonbonding electrons
Count all electrons present in lone pairs around the atom.
Step 5: Count bonds
Count the number of bonds connected to the atom.
Remember:
- Single bond = 1
- Double bond = 2
- Triple bond = 3
Step 6: Apply the formula
Use:
Formal charge = Valence electrons − Nonbonding electrons − Number of bonds
Finally, the sum of all formal charges must equal the overall charge of the molecule or ion.
Example 1: Formal Charge of Oxygen in H₂O
The Lewis structure of water is:
..
H — O — H
..
Oxygen has:
- 6 valence electrons
- 4 nonbonding electrons
- 2 bonds
Therefore:
FC = 6 − 4 − 2
FC = 0
So, the formal charge on oxygen in H₂O is 0.
Each hydrogen has one bond and no lone pairs:
FC = 1 − 0 − 1 = 0
Therefore, all atoms in H₂O have a formal charge of 0.
Example 2: Formal Charge of Oxygen in OH⁻
Consider the hydroxide ion:
..
H — O :
..
Oxygen has:
- 6 valence electrons
- 6 nonbonding electrons
- 1 bond
Therefore:
FC = 6 − 6 − 1
FC = −1
Hydrogen has:
FC = 1 − 0 − 1 = 0
The total charge is therefore:
0 + (−1) = −1
This agrees with the charge of OH⁻.
Example 3: Formal Charge in NH₃
The Lewis structure of ammonia is:
..
H — N — H
|
H
Nitrogen has:
- 5 valence electrons
- 2 nonbonding electrons
- 3 bonds
Therefore:
FC = 5 − 2 − 3
FC = 0
Each hydrogen has:
FC = 1 − 0 − 1 = 0
Therefore, all atoms in NH₃ have a formal charge of 0.
Example 4: Formal Charge in NH₄⁺
The ammonium ion has four N–H bonds:
H
|
H — N — H
|
H
Nitrogen has:
- 5 valence electrons
- 0 nonbonding electrons
- 4 bonds
Therefore:
FC = 5 − 0 − 4
FC = +1
Each hydrogen has a formal charge of 0.
So the overall formal charge is:
+1
which agrees with the charge of NH₄⁺.
Example 5: Formal Charge in CO₂
One valid Lewis structure for carbon dioxide is:
O = C = O
Carbon
Carbon has:
- 4 valence electrons
- 0 nonbonding electrons
- 4 bonds
Therefore:
FC = 4 − 0 − 4 = 0
Each oxygen
Each oxygen has:
- 6 valence electrons
- 4 nonbonding electrons
- 2 bonds
Therefore:
FC = 6 − 4 − 2 = 0
Thus:
- Carbon = 0
- Oxygen = 0
- Oxygen = 0
The total is 0, which matches the neutral charge of CO₂.
Example 6: Formal Charge in O₃
Ozone is an excellent example because it demonstrates why formal charge is useful for comparing Lewis structures.
One resonance structure can be represented as:
O — O = O
The singly bonded terminal oxygen has three lone pairs.
Single-bonded oxygen
- Valence electrons = 6
- Nonbonding electrons = 6
- Bonds = 1
FC = 6 − 6 − 1 = −1
Central oxygen
The central oxygen has one single bond and one double bond, as well as one lone pair.
- Valence electrons = 6
- Nonbonding electrons = 2
- Bonds = 3
FC = 6 − 2 − 3 = +1
Double-bonded oxygen
- Valence electrons = 6
- Nonbonding electrons = 4
- Bonds = 2
FC = 6 − 4 − 2 = 0
Therefore, the formal charges are:
−1, +1, 0
The total is:
−1 + 1 + 0 = 0
which agrees with the neutral charge of ozone.
The other resonance structure simply places the charges on the opposite oxygen atom.
Formal Charge and Bond Type
A useful shortcut is to recognize common patterns.
Oxygen
A neutral oxygen usually has two bonds and two lone pairs.
| Oxygen arrangement | Formal charge |
|---|---|
| 1 bond, 3 lone pairs | −1 |
| 2 bonds, 2 lone pairs | 0 |
| 3 bonds, 1 lone pair | +1 |
Nitrogen
A neutral nitrogen commonly has three bonds and one lone pair.
| Nitrogen arrangement | Formal charge |
|---|---|
| 2 bonds, 2 lone pairs | −1 |
| 3 bonds, 1 lone pair | 0 |
| 4 bonds, 0 lone pairs | +1 |
These patterns are useful for quickly checking Lewis structures.
Formal Charge vs. Oxidation State
Formal charge and oxidation state are not the same thing.
Formal charge assumes that bonding electrons are shared equally between bonded atoms.
Oxidation state assigns bonding electrons to the more electronegative atom.
For example, in H₂O, oxygen has a formal charge of 0, but its oxidation state is −2.
Therefore, do not use oxidation-state rules when calculating formal charge.
How Formal Charge Helps Choose a Lewis Structure
When several possible Lewis structures can be drawn, formal charge helps determine which structures are more reasonable.
Generally, a preferred Lewis structure tends to:
- Minimize the magnitude of formal charges.
- Minimize the number of atoms carrying formal charges.
- Avoid unnecessary charge separation.
- Place negative formal charge preferentially on more electronegative atoms when possible.
- Have formal charges whose sum equals the overall charge of the species.
These are useful guidelines rather than absolute rules.
A Faster Method
Once you become comfortable with formal charge, you can often calculate it without counting every individual electron.
Use:
FC = Valence electrons − Lone-pair electrons − Number of bonds
For example, suppose an oxygen atom has:
- 3 lone pairs
- 1 single bond
Oxygen has 6 valence electrons.
Therefore:
FC = 6 − 6 − 1 = −1
If oxygen has:
- 2 lone pairs
- 2 bonds
then:
FC = 6 − 4 − 2 = 0
And if oxygen has:
- 1 lone pair
- 3 bonds
then:
FC = 6 − 2 − 3 = +1
Common Mistakes
1. Forgetting lone-pair electrons
A lone pair contains two electrons, not one.
If an atom has three lone pairs, it has:
3 × 2 = 6 nonbonding electrons
2. Counting electrons instead of bonds
When using:
FC = V − N − B
you count the number of bonds, not the total number of bonding electrons.
For example, a double bond contains four electrons but counts as 2 bonds in this formula.
3. Forgetting the charge of the ion
For a polyatomic ion, the sum of the formal charges must equal the ion’s overall charge.
For example, for NO₃⁻:
Sum of formal charges = −1
not zero.
4. Confusing formal charge with oxidation state
Formal charge and oxidation state use different assumptions about bonding electrons.
Always use the formal-charge formula when the question specifically asks for formal charge.
Practice Questions
Try these questions yourself before looking at the answers.
Question 1
What is the formal charge on oxygen in H₂O?
A. −1
B. 0
C. +1
D. +2
Question 2
An oxygen atom has one single bond and three lone pairs. What is its formal charge?
A. −2
B. −1
C. 0
D. +1
Question 3
What is the formal charge on nitrogen in NH₄⁺?
A. −1
B. 0
C. +1
D. +2
Question 4
In the Lewis structure O=C=O, what is the formal charge on carbon?
A. −2
B. −1
C. 0
D. +1
Question 5
An oxygen atom has three bonds and one lone pair. What is its formal charge?
A. −1
B. 0
C. +1
D. +2
Question 6
In one resonance structure of O₃, the formal charges are assigned as −1 on a terminal oxygen, +1 on the central oxygen, and 0 on the other terminal oxygen. What is the total charge?
A. −2
B. −1
C. 0
D. +1
Question 7
A nitrogen atom has two bonds and two lone pairs. What is its formal charge?
A. −1
B. 0
C. +1
D. +2
Question 8
What is the formal charge on each hydrogen atom in NH₃?
A. −1
B. 0
C. +1
D. +2
Practice Answers
1. B — 0
Oxygen in H₂O has two bonds and two lone pairs:
FC = 6 − 4 − 2 = 0
2. B — −1
One bond and three lone pairs:
FC = 6 − 6 − 1 = −1
3. C — +1
Nitrogen in NH₄⁺ has four bonds and no lone pairs:
FC = 5 − 0 − 4 = +1
4. C — 0
Carbon has four bonds and no lone pairs:
FC = 4 − 0 − 4 = 0
5. C — +1
Oxygen with three bonds and one lone pair:
FC = 6 − 2 − 3 = +1
6. C — 0
The formal charges add up to:
−1 + 1 + 0 = 0
7. A — −1
Nitrogen has 5 valence electrons, 4 nonbonding electrons and 2 bonds:
FC = 5 − 4 − 2 = −1
8. B — 0
Each hydrogen has one valence electron, no lone-pair electrons and one bond:
FC = 1 − 0 − 1 = 0
Key Takeaway
The most important formula to remember is:
Formal Charge = Valence electrons − Nonbonding electrons − Number of bonds
For every atom:
- Find its valence electrons.
- Count its lone-pair electrons.
- Count its bonds.
- Apply the formula.
- Check that all formal charges add up to the overall charge of the molecule or ion.
Once you can draw Lewis structures accurately, formal charge becomes a straightforward calculation and an important tool for evaluating possible structures and resonance forms.