Lewis Dot Structures – Advanced Concepts

Formal Charge

To determine the formal charge of an atom from a Lewis dot structure we need to assign each electron to an atom in the structure. To do this use the following rules:

• All nonbonding electrons (unshared electrons) are assigned to the atom on which they are found.
• Each atom in a bond is assigned ½ of the total number of electrons in the bond (i.e. for a single bond each atom is assigned 1 electron, for a double bond each atom is assigned 2 electrons, etc.)
• For each atom the number of electrons assigned in the above steps is subtracted from the number of valence electrons in the atom.

Example

Assign formal charges to each atom in HCN.

First draw the Lewis dot structure:

The two non-bonding electrons are assigned to nitrogen, as are three electrons from the triple bond. The other three electrons in the triple bond (remember there are a total of 6 electrons in a triple bond) are assigned to carbon. Both carbon and hydrogen receive one electron from the single bond. If I total these up and subtract from the number of valence electrons associated with each atom (5 for N, 4 for C and 1 for H), I obtain the formal charges:

N = 5 – 5 = 0

C = 4 – 4 = 0

H = 1 – 1 = 0

Before going any further I want to make it clear that formal charges do not correspond to the real charge on an atom in a molecule. After all in covalent molecules we know that many of the electrons are shared, so that the atoms do not exist as cations and anions as they do in ionic compounds.

This might make you wonder why we would even bother with calculating formal charges. To understand the usefulness of formal charges consider the fact that in many cases you can draw more than one Lewis dot structure that will satisfy the octet rule. How then do we know what the correct Lewis dot structure is? We can use formal charges and the following rules to make such decisions.

If two or more Lewis dot structures can be drawn which satisfy the octet rule, the most stable one will be the structure where:

• The formal charges are as small as possible.
• Any negative charges are located on the more electronegative atoms.

Example

Use the concept of formal charges to determine the most stable Lewis dot structure for CO2.

It may not have occurred to you, but we can draw five different Lewis dot structures for CO2 that satisfy the octet rule.

If I now calculate formal charges for each atom in each structure.

I see that the formal charges are minimized when the carbon atom is in the middle and forms double bonds to each oxygen, structure (a).

Example

Use formal charges to determine the most stable Lewis dot structure for N2O.

The Lewis dot structures which obey the octet rule, complete with the formal charges, are shown below:

From this we see that both (a) and (d) do an equally good job of minimizing the formal charges. However, structure (d) is more stable because the negative formal charge is on oxygen rather than nitrogen (recall that oxygen is more electronegative than nitrogen).

Note that in the above examples the formal charges add up to zero in every case. This is not an accident. If assigned correctly the formal charges must add up to equal the charge on the molecule (zero for neutral molecules).

Resonance Structures

Sometimes we encounter a situation where two or more Lewis dot structures describe a molecule equally well.

Example

Draw two equivalent Lewis dot structures for ozone, O3?

There is no way to distinguish between these two structures, they are equivalent in every aspect including formal charges. They are called resonance structures, and we draw resonance structures by placing brackets around each structure and writing a double headed arrow between the each resonance structure.

What does it mean for a molecule to have resonance structures? Perhaps it is easier to point out the things that a resonance structure does not mean.

• If we were to look at individual molecules in a sample of ozone, we would not find some molecules with the Lewis dot structure (a) and some molecules with Lewis dot structure (b).
• If we were to freeze an individual molecule at a moment in time, we would not see one oxygen-oxygen single bond and one oxygen-oxygen double bond.

Instead the two electrons which are needed to make a single bond into a double bond (we will see in chapter 9 that this "extra" bond is called a pi bond) are shared equally between both oxygen pairs. This means both oxygen-oxygen bonds are equivalent. They are shorter and stronger than an oxygen-oxygen single bond, but longer and weaker than an oxygen-oxygen double bond (see next section). To quantify this we use the terminology of bond order:

• single bond ® bond order of 1
• double bond ® bond order of 2
• triple bond ® bond order of 3

Both oxygen-oxygen bonds in ozone have a bond order of 1.5. We can calculate the bond order of a molecule with resonance structures by averaging over all of the resonance structures.

You can also draw resonance structures for a molecule like SO3. In this molecule you get three resonance structures, each one with 2 single S-O bonds and 1 double S=O bond. Thus we see that the bond order of the sulfur-oxygen bonds in SO3 is 1.33

Exceptions to the Octet Rule

There are three situations where the octet rule.

1. Molecules with an odd number of electrons (i.e. NO2).

If you have an odd number of electrons there is no way to satisfy the octet rule. Try it if you don’t believe me.

2. Molecules where an atom has less than an octet (i.e. BF3, BeH2, AlCl3).

This only happens to atoms near the boundary between metals and non-metals, such as Be, B, Al and Ga. The electronegativity of these atoms is not high enough to force more electronegative non-metals into forming double and triple bonds. When working with such atoms never draw multiple bonds and you will be able to get the correct Lewis dot structures.

3. Molecules where an atom has more than an octet of electrons (i.e. ClF3, PCl5, XeF2).

This is fairly common for elements in the 3rd period (row) and below. However, elements in the first two periods, H – Ne, cannot violate the octet rule in this way.