What do Formal Charges tell you?

Formal charges have an important role in organic chemistry since this concept helps us to know whether an atom in a molecule is neutral/bears a positive or negative charge. Even if some molecules are neutral, the atoms within that molecule need not be neutral atoms.

Formal Charge Formula

By finding the charges associated with the molecule, we would be able to predict the reactivity of the molecule. This has a major important role in organic chemistry. When two atoms are bonded, the atoms should possess bond pair electrons or bonding electrons and also lone pair electrons which are also referred to as the non-bonding electrons. In a Lewis structure, we can denote these electrons.

The formal charge of an atom can be determined by a mathematical equation. The formal charge formula can be expressed as follows:

The number of bonds will be equal to half of the number of bonding electrons.

Another way of expressing formal charge formula is given below, where F.C is the formal charge.

The formal charge can be verified by determining the sum of the formal charges for all the atoms within the molecule. 

Note: Formal charge is a hypothetical charge and not the actual charge.

Calculation of Formal Charges

Consider a molecule, ammonia, ${\text{NH}}_3$. The bond between nitrogen and carbon is a single bond.

First step is to draw the molecule, then put the lone pair electrons to each atom.

Formal charge of the atoms,

a) Nitrogen $\left(\text{N}\right)$

Nitrogen atom’s electronic configuration is$1{\text{s}}^{2}2{\text{s}}^{2}2{\text{p}}^3$. Thus, the valence electrons of the N atom are 5 electrons.

We see one set of lone pair of electrons. Thus, the number of non-bonding electrons is 2 electrons.

N forms three bonds with hydrogens and number of bonding electrons will be six.

Therefore, $\text{Formal charge on N }=\left[5\right]–\left[2+3\right]=5–5=0$

The nitrogen in this molecule is neutral with zero formal charge.

b) Hydrogen $\left(\text{H}\right)$

The electronic configuration of H-atom is$1{\text{s}}^1$. Thus, the valence electron of H-atom is 1.

All the three hydrogens present in the molecule have no non-bonding electrons.

The hydrogens form only one bond in the molecule. Thus, the number of bonding electrons is two.

Therefore, $\text{The formal charge on H}=\left[1\right]–\left[0+1\right]=0.$

The hydrogen in this molecule is neutral.                  

 Therefore, the molecule is neutral since all the four atoms of the molecule are neutral.

Use of Formal Charges in Predicting the Structures of Molecules

Formal charges can predict the structures of several molecules.

For instance, ${\text{CH}}_3{}^{-}$

Formal charge on carbon atom, $\text{C}=\left[4\right]–\left[2+3\right]=-1$

Carbon bearing a negative formal charge is of pyramidal geometry.

Another example is methane, ${\text{CH}}_4$

Formal charge on carbon, $\text{C}=\left[4\right]–\left[0+4\right]=0$

Carbon being neutral is of tetrahedral geometry.

Another example is,${\text{CH}}_4{}^{+}$

Formal charge on carbon, $\text{C}=\left[4\right]–\left[0+3\right]=+1$

Carbon bearing a positive charge is of trigonal planar geometry.

Rule to predict the structure using formal charges

To predict the structure with formal charges the following rule has to be considered.

 A molecular structure having zero (0) formal charge is the preferred structure for a molecule.

For example, consider a molecule${\text{CH}}_2\text{Br}$. In this molecule, the bond between carbon and bromine is a double bond. Formal charges on;

a) Bromine $\left(\text{Br}\right)$

Bromine is of the halide series and it is an electronegative atom. The general electronic configuration having electrons of halogens is ${\text{ns}}^2{\text{np}}^5$. Thus, the valence electrons of Br atom are 7 electrons.

We see two sets of lone pair electrons. Thus, the number of non-bonding electrons is 4 electrons.

Br forms two bonds with carbon.

Therefore, formal charge on $\text{Br}=\left[7\right]–\left[4+2\right]=7–6=+1$

Thus, the bromine in this molecule bears a $+1$ formal charge.

b) Carbon $\left(\text{C}\right)$

The electronic configuration of carbon with atomic number $6$ is $1{\text{s}}^2 2{\text{s}}^2 2{\text{p}}^2$. Thus, the valence electrons of C atom are four.

There are no nonbonding electrons over the C-atom.

Carbon forms four bonds in the above-mentioned molecule.

Therefore, formal charge on the carbon atom is $\text{C}=\left[4\right]–\left[0+4\right]=0$. The carbon in this molecule is neutral.

c) Hydrogen $\left(\text{H}\right)$

The electronic configuration of H-atom is$1{\text{s}}^1$. Thus, the valence electron of H-atom is 1.

Both the hydrogens present in the molecule have no nonbonding electrons.

Both the hydrogens form only one bond in the molecule.

Therefore, the formal charge on $\text{H}=\left[1\right]–\left[0+1\right]=0$

But bromine is a more electronegative atom than carbon and so bromine cannot bear a positive charge.

Now, the bromine will have three lone pairs of electrons forming one bond with carbon.

So the formal charge of bromine, $\text{Br}=\left[7\right]–\left[6+1\right]=7-7=0$

The carbon will have one nonbonding electron with three bonds in the molecule.

So the formal charge of carbon will be $\text{C}=\left[4\right]–\left[1+3\right]=0$

Preferred Lewis structure

The Lewis structure having formal charges with the least non-zero charges is the preferred structure.

Consider a thiocyanate ion, ${\text{NCS}}^{-}$.

We can have three possible Lewis structures of thiocyanate

i) Formal charge of $\text{N}=\left[5\right]–\left[4+2\right]=5–6=-1$

Formal charge of $\text{C }=\left[4\right]–\left[0+4\right]=4–4=0$

Formal charge of $\text{S }=\left[6\right]–\left[4+2\right]=6-6=0$

ii) Formal charge of $\text{C }=\left[4\right]–\left[4+2\right]=4-6=-2$

Formal charge of $\text{N }=\left[5\right]–\left[0+4\right]=5-4=1$

Formal charge of $\text{S }=\left[6\right]–\left[4+2\right]=6-6=0$

iii) Formal charge of $\text{C }=\left[4\right]–\left[4+2\right]=4-6=-2$

Formal charge of $\text{S }=\left[6\right]–\left[4+2\right]=6-6=0$

Formal charge of $\text{N}=\left[5\right]–\left[4+2\right]=5–6=-1$

Among the three structures, the structure with the least non-zero formal charge is the first one.

 Common Mistakes

The formal charge is not the actual charge of the atom. It’s just a theoretical charge of an atom within a molecule. We can get the molecule’s charge by adding the formal charge of individual atoms present within the molecule.

Practice problem

1) The shape of the carbocation is

a) Pyramidal

b) Bent

c) Linear

d) Trigonal planar

Answer: d) Trigonal planar

2) What is the formal charge on the carbon in $\text{S = C = S}$

$\begin{array}{l}\text{a) 0}\hfill \\ \text{b) +1}\hfill \\ \text{c) -1}\hfill \\ \text{d) +2}\hfill \end{array}$

Answer: $\text{a) 0}$

$\begin{array}{c}\text{Formal charge on Carbon }=\left[4\right]–\left[0+4\right]\\ =0 \end{array}$

Context and Application

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for Bachelors and Masters in Chemistry.