8.3: Formal Charge

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Introduction

The concept of formal charge is actually very simple, and relates the number of electrons around an atom in a molecule's Lewis dot structure to the number of electrons the atom donates to the Lewis dot structure In the next section we will cover drawing Lewis dot structures, and the first step is to calculate the number of electrons each atom donates to the molecule, and then to essentially draw a structure based on those electrons. A negative formal charge means there are more electrons around an atom then it donated, a positive means there are fewer electrons around an atom then it donated, and a neutral formal charge means the number it donated is the same as in the structure.

In a molecule there are two types of orbitals, lone pair and bonding. In a lone pair, both of the electrons are considered to belong to the atom they are attached to, in a bonding pair, the electrons are split between the two atoms bonding, so one belongs to the first atom, and the second to the second atom.

Some Important Things to Note about Formal Charges

1. Formal charges are not real charges, they are a way of looking at electron distributions in a Lewis dot structure. In section 8.7 we will cover electronegativty and molecular polarity, and then we will look at the actual charge distribution in real molecules, which does not always reflect the formal charge distribution.
2. The sum of the formal charges of all the atoms in a molecule equals zero
3. The sum of the formal charges of all the atoms in an ion equals the charge of the ion.

Uses of Formal Charges

1. Formal charges can help identify the more important resonance structures, that is, hitherto we have treated all resonance structures as equal, but ones this is not always the case
   • The Resonance Structure with the most atoms having Formal charges closest to zero is usually the preferred resonance structure
   • Negative formal charges are preferred on more electronegative atoms (see section 8.7: Bond Polarity and Electronegatvity)
     
2. Formal charges can help identify the more likely of two isomers, that is, two different structures made from the same set of atoms, like HCN and HNC.
   • RULE of THUMB: The best Lewis dot structure has the most atoms with zero formal charge, or the closest to zero.

Calculating Formal Charge:

The following equation determines the formal charge for each atom in a molecule or polyatomic ion. The first part is the number of valence electrons the atom donates to the Lewis dot Structure. From this is subtracted the lone electrons around that atom, and then half the bonding electrons, as they are split between both nuclei of the bond. If this is zero, then the electrons the atom donated to the structure are around the atom. If it is positive, that means the atom contriubted more electrons than are around it, and some of "its" electrons are around other atoms. If it is negative, that means there are more electrons around it than it contributed to the Lewis dot structure.

\[\textrm{formal charge = # valence shell electrons (free atom) − # lone pair electrons − }\dfrac{1}{2}\textrm{ # bonding electrons}\]

Lets look at the formal charge of HCN and HNC. Note, these are not resonance structures but two different molecules, hydrocyanic acid and hydrogen isocyanide, with the respective Lewis dot structures of:

H-C\(\equiv \)N: and H-N\(\equiv \)C:

For hydrocyanic acid(H-C\(\equiv \)N:) we get the formal charges of:
H=1-0-1/2(2)=0
C=4-0-1/2(8)=0
N=5-2-1/2(6)=0

For hydrogen isocyanide (H-N\(\equiv \)C:), we get the formal charges of
H=1-0-1/2(2)=0
N=5-0-1/2(8)=+1
C=4-2-1/2(6)=-1

Intuitive Visualization:

Lets use different symbols to represent the electrons and show the bonds as electron pairs (next to each other) instead of lines. In figure 8.4.1 we see that hydrogen donates one electron (the star), diamond donates 4 (the diamonds) and nitrogen donates 5 (the circles)

Fig. 8.4.1 Using stars (hydrogen), diamonds (carbon) and circles (nitrogen) to represent the electrons each atom donates to the molecule's Lewis dot structure.

When combined to form hydrocyanic acid and hydrogen isocyanide, and using the above symbols instead of lines, we get the following two Lewis dot structures.

Fig.8.4.2: Lewis dot structures using stars, diamonds and circles to represent the electrons donated from Hydrogen (1 star), Carbon (4 diamonds) and Nitrogen (5 circles) respectively.

What we see on the Lewis dot structure on the left ((H-C\(\equiv \)N:) is that the star is around hydrogen, the diamonds are around carbon and the circles are around Nitrogen, and so as in the above equation, the formal charge of all species is zero. But in the second structure, ((H-N\(\equiv \)C:) we see that hydrogen's star is still around hydrogen and so it formal charge is still zero, but one of Nitrogen's circles is now around carbon. So this means one of the electrons nitrogen contributed to the structure is on a different atom (the carbon), and so nitrogen has a positive formal charge, while carbon, gaining that electron, has a negative formal charge. It needs to be emphasized that these are not real charge distributions, and we will cover that later in this chapter when we introduce the concept of molecular polarity.

Which isomer would you predict to be the more stable, hydrocyanic acid or hydrogen cyanide?

From the "Rule of Thumb", we would predict HCN to be more stable, as all the atoms have a zero formal charge.

Formal Charge and Free Radicals

A free radical is a molecule that has one electron. Free radicals are very reactive and there are very few stable free radicals. For example, atomic chlorine is a free radical, \(\underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\textrm{:Cl}\cdot}}\) , and two of them will combine to form a bond, which is why chlorine is a diatomic

\( \underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\textrm{:Cl}\cdot}} +\underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\cdot\textrm{Cl:}}}\) \( \rightarrow\) \(\underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\textrm{:Cl}}} -\underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\textrm{Cl:}}}\)

Lets look at two resonance structures of NO₂.

\(\underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\textrm{O}}}={\overset{\Large{\cdot\cdot}}
{\textrm{N}}}- \underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\textrm{O}\cdot}}\) \(\longleftrightarrow\)\(\underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\textrm{O}}}={\overset{\Large{\cdot}}
{\textrm{N}}}- \underset{\Large{\cdot\cdot}}
{\overset{\Large{\cdot\cdot}}
{\textrm{O:}}}\)

In the left resonance structure, all the atoms have zero formal charge, while on the right structure, the nitrogen has a +1 formal charge, and the oxygen with the single bond has a -1 formal charge.

Can you draw two additional resonance structures for the above molecules?

Yes, just switch the single and double bonds for the above two structures (with the oxygens and their lone electrons).