Formal Charge

Formal Charge Explanation and its Properties

Let's start by defining formal charge.

Formal charge ignores the concept of electronegativity. Which is the tendency for an atom/molecule to attract and share electrons unequally. For example, fluorine is very electronegative, while hydrogen is less so, so the electrons in the H-F bond will tend towards fluorine.

Here are some things to remember about formal charge:

1) Every atom can be assigned a formal charge

2) If there are multiples of the same element, they can have different formal charges

3) The formal charge is dependent on:

-The number of bonds

-The number of paired and unpaired electrons

4) Formal charges are assigned based on Lewis structures (2D structure)

When we draw a Lewis structure, we want every element to have 8 total valence electrons.

We can move around bonds and lone pairs, as long as we make sure every element has their valence shell filled. So here's the problem, how do we know how many bonds/lone pairs we should have? That's where formal charge comes in.

Formal charge helps us determine the ideal Lewis structure of a molecule. Ideally, we want every atom to have a FC of 0. This is because having a neutral charge is lower in energy, so it is the most stable state. Here's an example. Let's say you want to draw the Lewis structure for carbon dioxide, so you draw the two possible structures as shown below:

Fig.1-Possible Lewis structures for CO₂

Before we discuss the formal charge, let's do a brief refresher on Lewis structures.

The lines drawn between elements represent a bond, which contains two electrons each. In example 1, you'll see the C=O bond is a double bond, meaning it contains 4 electrons.

The "dots" near our atoms represent lone pairs.

Like I mentioned earlier, we can change the number of bonds and lone pairs so that each element has a full octet. The way we determine this number is first by finding the formal charge.

Now back to our example. Let's look at the formal charge: 1) Carbon: 0 Oxygen: 0 2) Carbon: 0 Oxygen (single): -1 Oxygen (triple): +1

Even though both have a net FC of 0, the first structure is the best option since it minimizes FC for each atom.In the "Calculating Formal Charge" section, we will go over how I got these formal charges together.

Formal Charge Formula and Equation

Now that we know what a formal charge is, let's learn how to calculate it. Here is the general formula:

$$FC=(\text{number of valence electrons})-(\text{number of lone pair electrons})-(\text{number of bonds})$$

We can look at the Lewis structure to determine the number of bonds/lone pair electrons, however, to calculate the number of valence electrons, we need to look at the periodic table.

Fig.2-The periodic table

For non-transition metals, you count from left to right, skipping over the transition metals. For example, fluorine is 7 across, so it has 7 valence electrons. The main exception to this is helium (He), which has 2 valence electrons.For transition metals, you also count from left to right. For example, vanadium (V), is 5 across, so it has 5 valence electrons

Calculating Formal Charge

Let's use our example from before to learn how we got those formal charges:

Let's try another problem:

Adding Formal Charges to Resonance Forms

Sometimes when we draw Lewis structures, we may encounter resonance structures.

When resonance structures have different formal charges, we can use said FC to determine the "best" structure. When we looked at CO₂ (Figure 3), we were looking at its different resonance forms, which had different formal charges. The "correct" structure is an average of the three possible forms (the third form is just the triple bond being on the opposite oxygen, so it is essentially the same as the second).

When we look at resonance structures with the same formal charge, none of the options are the "best". As an example, here are the three resonance forms of CO₃^2-

Fig.5-Resonance forms for the carbonate ion

Since the bonding is basically the same, so is the formal charge. The "true" form of carbonate is an average of the three forms, where there is a 1 1/3 bond between each oxygen and carbon.

Importance of Formal Charge

Formal charge is important for several reasons. As we discussed earlier, it is helpful for determining the best Lewis structure for both resonance and non-resonance forms.

Another reason why it is important is reactivity. By calculating the formal charge, we can determine where (if any) charges are within the molecule. This helps us understand/predict the kind of reactivity the molecule will have. For example, the right oxygen in the (correct) NO₂ structure (see Figure 4) has a -1 charge, so it can either attract positively charged atoms/molecules and/or donate electrons. Without knowing where the charge is, we can't fully understand a molecule's reactivity.