Formal Charge

Formal charges are a way for us to keep track of electrons.  In organic chemistry, you will not only need to calculate formal charges but also understand what they mean and how to use them.  You will use formal charges to understand structures, intermediates, and reaction mechanisms.

Calculating formal charge

Let us go over the textbook definition 1st!  The formal charge is usually defined as follows;

You simply subtract the number of lone pair electrons and 1/2 the bonding electrons (or simply the number of bonds) from the number of valence electrons.  Let us try it for ourselves.

What is the formal charge on the carbon atom in the following structure?

How many valence electrons does carbon have?  Well, you need to have a periodic table and count from the left until you hit the atom of interest.  So for C, it would be, Li (1), Berylium (2), boron (3), and finally carbon (4).  Thus carbon has 4 valence electrons.  That's how many electrons a neutral carbon would have for it to be neutral.  

How many lone pairs does the C in the above structure have?  zero (0)

What is half the number of bonding electrons? There are 3 bonds which means there are 6 bonding electrons.  So, 6/2=3.

Therefore the Formal Charge for the Carbon atom =  4 - 0 - 3 = +1

We would write the + next to the carbon as follows;

What does it really mean?

First of all, there is no reason to memorize the above equation if you just consider that formal charge is simply the number of electrons an atom has in its neutral state (i.e. # of electrons it wants to have to be stable) minus the number of electrons it has (or owns).  You'll notice that we only subtract half the bonding electrons.  Since these are covalent bonds the electrons are shared and the carbon (C) atom formally "owns" only one of the two electrons in each bond, while the H atom owns the other electron.

Limitations of Formal Charge

Calculate the formal charge on the nitrogen atom in the following structure.

From the periodic table, you see that nitrogen has 5 valence electrons (i.e. it wants to have 5 electrons around it).  The nitrogen in the structure above has only 4 electrons it owns, so the formal charge is 5 - 4 = +1 and we would write the structure as follows.  This is called an ammonium ion.

Let us compare the methyl carbocation and ammonium ion to gain an appreciation of what's going on.

Think about why each structure has a positive formal charge.  In the case of the ammonium ion, it is because the nitrogen atom is sharing its lone pair electrons with a hydrogen (proton).  On the other hand the methyl cation just does not have enough electrons.  Because of this, they behave differently.  For example, molecules that like a positive charge (i.e. a nucleophile) will attack the carbon atom of the methyl cation.  However, a nucleophile will never attack the positive nitrogen atom.  We will learn more about this soon!