## Formal Charge

### Introduction

A hydrogen atom is made up of one proton and one electron. The formal charge of the atom, the sum of the charge of the proton and the charge of the electron, is zero. The formal charge on any atom is zero when the number of protons (the atomic number) and the number of electrons that "belong" to that atom are equal. We have seen that it requires 13.6 kcal/mol to separate an electron from a hydrogen atom. The resulting hydrogen nucleus, the proton, has a formal charge of +1.

Assigning formal charges to isolated atoms and ions is easy. So is assigning formal charges to atoms that are covalently bonded within molecules.

#### Rule 2: Calculating Formal Charges

To determine the formal charge of an atom within a molecule, separate the atom from its bonding partner(s), dividing all bonding electrons equally between the bonded atoms. Then compare the number of electrons that "belong" to each atom to the atomic number of that atom. Figure 1uses color coding to illustrate the procedure for methane, CH4.

### Figure 1

#### Assigning Electrons I

Each hydrogen is assigned one of the two electrons it shares with the central carbon atom; the formal charge on each hydrogen atom in methane is zero. The central carbon is assigned one of the two electrons it shares with each of the four hydrogens. These are its four valence electrons. But the carbon atom also has two inner shell electrons to consider. The total number of electrons assigned to the carbon is six; this is the same as the atomic number of carbon, and the formal charge on the carbon atom is zero.

Exercise 1 Calculate the formal charge on each of the atoms in ethane, CH3CH3.

a. The formal charge on carbon is

b. The formal charge on hydrogen is

Exercise 2 Calculate the formal charge on each of the atoms in propane, CH3CH2CH3.

a. The formal charge on C1 or C3 is

b. The formal charge on C2 is

c. The formal charge on hydrogen is

Figure 2 extends the procedure demonstrated in Figure 1 to methanol, CH3OH, where the oxygen atom has two lone pairs of electrons.

### Figure 2

#### Assigning Electrons II

Since the two lone pairs on the oxygen are not shared with any other atoms, they are assigned to the oxygen atom. The formal charge on the oxygen atom is zero. Its atomic number, 8, is equal to the sum of the number of its valence and inner shell electrons. Like before, the formal charge on the cabon and the hydrogen atoms are all zero.

Exercise 3 Calculate the formal charge on each of the atoms in ethanol, CH3CH2OH.

a. The formal charge on C1 is

b. The formal charge on C2 is

c. The formal charge on O is

d. The formal charge on hydrogen is

Exercise 4 Calculate the formal charge on each of the atoms in fluoromethane, CH3F.

a. The formal charge on C is

b. The formal charge on F is

c. The formal charge on H is

An equivalent method of calculating formal charges ignores the inner shell electrons; when the number of valence shell electrons assigned to an atom is the same as its group number, the formal charge on that atom is zero. In Figure 2, the group numbers of hydrogen, carbon, and oxygen are 1, 4, and 6, respectively, the same as the number of valence electrons assigned to each of these atoms. The formal charge on all three atoms is zero.
Up to this point, we have considered atoms for which the formal charge is zero. Now let's examine some situations where it is not. We'll start with nitromethane, CH3NO2. A Lewis structre of nitromethane is shown at the left of Figure 3 with the partitioning of the valence electrons to the right. No color coding is included.

### Figure 3

#### Formal Charges in Nitromethane

As before, the formal charges on hydrogen and carbon are zero. So is the formal charge on the oxygen atom that is doubly bonded to the nitrogen. But the formal charge on the oxygen atom that is singly bonded to the nitrogen is -1; it has 7 valence electrons to go with its 2 inner shell electrons, giving it 9 units of negative charge versus the 8 units of positive charge in the nucleus of the atom. The four valence shell electrons and the two inner shell electrons of the nitrogen atom are one less than its atomic number. Thus the formal charge on the nitrogen atom is +1. Overall nitromethane is neutral. A more complete representation of the structure of nitromethane than that shown in Figure 3 would include the formal charges on the oxygen and the nitrogen atoms:

Exercise 5 Calculate the formal charge on each of the atoms in the following structures:

1. The formal charge on C is

2. The formal charge on the doubly bonded O is

3. The formal charge on the singly bonded O is

4. The formal charge on hydrogen is

1. The formal charge on C is

2. The formal charge on N is

3. The formal charge on H is

1. The formal charge on O is

2. The formal charge on H is

1. The formal charge on O is

2. The formal charge on H is

6. Amino acids exist as zwitterions, electrically neutral compounds containing positive and negative charges. Calculate the formal charge on each of the atoms in the amino acid glycine:

a. The formal charge on N is

b. The formal charge on the singly bonded C is

c. The formal charge on the doubly bonded C is

d. The formal charge on the doubly bonded O is

e. The formal charge on the singly bonded O is

f. The formal charge on hydrogen is