Formal Charge

The Meaning of Formal Charge

A Lewis dot structure shows how atoms are connected and where electrons sit, but it does not tell you the actual shape of the molecule. More importantly, when you look at a polyatomic ion — say, the nitrate ion ($\text{NO}_3^-$) or the ammonium ion ($\text{NH}_4^+$) — the net charge belongs to the whole ion, not to any single atom. You cannot point to one oxygen in nitrate and say "that oxygen carries the negative charge."

Yet it is useful to assign a formal charge to each individual atom. This is a bookkeeping tool, not a measurement of real charge. It helps you decide which Lewis structure is the most plausible when more than one can be drawn.

The Definition and Formula

The formal charge (F.C.) on an atom in a Lewis structure is defined as:

Formal charge = (number of valence electrons in the free atom) − (number of non‑bonding electrons on the atom in the Lewis structure) − $\frac{1}{2}$ (number of bonding electrons shared by that atom)

In symbols:

where:

• $V$ = total number of valence electrons of the atom in its isolated (free) state
• $L$ = total number of electrons present as lone pairs (non‑bonding) on that atom in the Lewis structure
• $B$ = total number of electrons shared in bonds involving that atom (each bond contributes 2 electrons, so $B$ is always an even number)

How to Apply the Formula — Step by Step

Consider a simple example: the oxygen atom in a water molecule ($\text{H}_2\text{O}$). In the Lewis structure, oxygen has two lone pairs (4 electrons) and forms two single bonds (each bond contributes 2 shared electrons, so $B = 4$). Free oxygen has $V = 6$ valence electrons.

The formal charge on oxygen in water is zero. That makes sense — water is a neutral molecule.

Now take the hydronium ion ($\text{H}_3\text{O}^+$). Oxygen has $V = 6$. In the Lewis structure, oxygen has one lone pair ($L = 2$) and forms three single bonds ($B = 6$).

The formal charge on oxygen is $+1$, which matches the overall charge on the ion. The hydrogen atoms each have $V = 1$, $L = 0$, and $B = 2$ (one bond), so:

The $+1$ charge is assigned to oxygen, not to any hydrogen.

Why Formal Charge Matters

Formal charge is not just an arithmetic exercise. It is the key to choosing the most stable Lewis structure when multiple valid structures exist for the same molecule or ion. The guiding rule is:

The most stable Lewis structure is the one in which the formal charges on all atoms are as close to zero as possible. If charges cannot be avoided, the structure with the smallest magnitude of formal charges is preferred.

Additionally, negative formal charges should ideally reside on the more electronegative atoms, and positive formal charges on the less electronegative ones.

The Classic Worked Example — Ozone ($\text{O}_3$)

Number the atoms of the bent O$_3$ molecule 1 (central), 2 and 3 (terminal). In its Lewis structure the central oxygen carries one lone pair, a double bond to atom 2 and a single bond to atom 3; atom 2 has two lone pairs; atom 3 has three lone pairs. Each oxygen brings $V = 6$.

Central O (atom 1): $L = 2$, $B = 6$ (double + single bond) →

Double-bonded end O (atom 2): $L = 4$, $B = 4$ →

Single-bonded end O (atom 3): $L = 6$, $B = 2$ →

The structure is therefore written with $+1$ on the central oxygen, $0$ and $-1$ on the two ends — and the sum $(+1) + 0 + (-1) = 0$ matches ozone's zero net charge.

A Second Worked Example — The Carbonate Ion ($\text{CO}_3^{2-}$)

Let us apply the formula to each atom in one possible Lewis structure of carbonate. The structure has a central carbon atom bonded to three oxygen atoms. One of the C–O bonds is a double bond, and the other two are single bonds. Each oxygen with a single bond carries three lone pairs; the doubly‑bonded oxygen carries two lone pairs.

For carbon ($V = 4$): …