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# Formal Charge

When molecules are formed, they don't just combine in any way they can. Structures are optimized to be as stable as possible. One way molecules do this is by keeping the electrons within the molecule as symmetrical as possible, i.e. we want as neutral of a molecule as possible.

So how do we know whether an atom is neutral inside a molecule? We use a concept called formal charge. In this article, we will be learning all about formal charge: what it is, how to calculate it, and why it's important.

• First, we will define what formal charge is
• Next, we will learn how to calculate the formal charge and work through some practice problems
• Then, we will learn about resonance forms and how they are related to the formal charge
• Lastly, we will reiterate why formal charge is so important

## Formal Charge Explanation and its Properties

Let's start by defining formal charge.

Formal charge (FC) is the charge assigned to an atom in a molecule when we assume that electrons in all bonds are shared equally between atoms.

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.

Valence electrons are the electrons that exist in the highest energy level/shell. They are the electrons that participate in bonding. Atoms want 8 total valence electrons (except H and He, which want 2), because then they would have a filled shell and neutral/low energy.

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.

Lone pairs are a set of valence electrons that do not participate in bonding. Because of this, they are also called non-bonding electrons.

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:

Given the diagram below, what are the formal charges for each possible Lewis structure?

Fig.3-We use the Lewis structures to calculate formal charge

Counting from left to right, carbon is in the 4th column in the periodic table. This means it has 4 valence electrons. Carbon is double-bonded to each oxygen, so it has 4 bonds in total. This means:

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

$$FC=(4)-(0)-(4)=0$$

Now for oxygen. Oxygen is in the 6th column, so it has 6 valence electrons. It is double-bonded to carbon, so it has two total bonds. It also has 2 lone pairs (4 electrons in total).

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

$$FC=(6)-(4)-(2)=0$$

Now for the second structure:

$$FC=(4)-(0)-(4)=0$$

For single-bond oxygen:

$$FC=(6)-(6)-(1)=-1$$

For triple-bond oxygen:

$$FC=(6)-(2)-(3)=+1$$

Let's try another problem:

Given the structures below, which is the most likely structure?

Fig.4 Knowing that a compound has 2 oxygen and 1 nitrogen, we drew two possible structures

The first thing you'll probably notice is that this molecule has a charge (-1). This means that the formal charge should add up to -1.

For nitrogen: Nitrogen is in the 5th column, so it has 5 valence electrons.

$$FC=5-4-2=-1$$

For center oxygen:

$$FC=6-2-3=1$$

For right oxygen:

$$FC=6-6-1=-1$$

Now for the second structure:

For nitrogen:

$$FC=5-2-3=0$$

For left oxygen:

$$FC=6-4-2=0$$

For right oxygen:

$$6-6-1=-1$$

The correct structure is the second option, since it minimizes the formal charge while keeping the net charge on the molecule, -1.

## Adding Formal Charges to Resonance Forms

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

When two or more Lewis structures with the same arrangement of atoms and number of electrons can be written, these are called resonance structures/forms. In reality, the actual structure is an average of the different possible Lewis structures.

Molecules with the same atoms can have different orientations with different charges, but they are not resonance structures. For example: CO2 and CO2- are similar, but because they have a different number of electrons, they aren't resonance structures of each other

There are two types of resonance structures: those with the same formal charge, and those with different formal charges.

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 CO32-

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.

We often write the formal charge of an atom underneath it, so we can see how it will react!

## Formal Charge - Key takeaways

• Formal charge (FC) is the charge assigned to an atom is a molecule when we assume that electrons in all bonds are shared equally between atoms.
• Structures that have a FC of 0 for all atoms have the lowest energy
• Valence electrons are the electrons that exist in the highest energy level. They are the electrons that participate in bonding. For non-transition metals (excluding H which has 2), the number of valence electrons is equal to the number of spaces across on the periodic table when you skip the transition metals.
• Lone pairs are a set of valence electrons that do not participate in bonding. Because of this, they are also called non-bonding electrons.
• The formula for formal charge is: $$FC=(\text{number of valence electrons})-(\text{number of lone pair electrons})-(\text{number of bonds})$$
• Formal charge is used to determine the best Lewis structure for a molecule. It is also important for predicting/understanding a molecule's reactivity.

#### Flashcards in Formal Charge 8

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how to calculate formal charge?

The formula for formal charge is:

FC=number of valence electrons-number of lone pair electrons-number of bonds

What is formal charge?

Formal charge (FC) is the charge assigned to an atom is a molecule when we assume that electrons in all bonds are shared equally between atoms.

How to find formal charge from Lewis structure?

Using the Lewis structure, we can determine the number of bonds and lone pair electrons. Subtracting that from the number of valence electrons, we get the formal charge.

How to assign formal charges?

We use the formula for formal charge to calculate the formal charge for each individual atom. We then write that charge beneath each atom. The net charge is written on the top right of the molecule.

How to draw Lewis structures with formal charges ?

Formal charges tell us which Lewis structure is the ideal structure. Whichever Lewis structure has its formal charges closest  to zero is the correct structure.

## Test your knowledge with multiple choice flashcards

If a chlorine atom has 4 bonds and 2 lone pairs, what is its formal charge?

How many resonance forms does CO2 have?

If a carbon atom has 2 bonds and 2 electrons in a molecule, what is its formal charge?

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