Formal Charges
Introduction
A formal charge on an atom indicates that it has the ‘wrong’ number of valence electrons or, in other words, it has an ‘abnormal’ number of bonds (non-standard compared to our skeletal representations). Formal charges are an essential part of molecular diagram. You will lose marks if they are missing or are incorrect.
The ‘Wrong’ Number of Valence Electrons
How can an atom have the ‘wrong’ number of valence electrons? In most organic molecules, all the atoms are obeying the octet rule and have a full valence shell. When we are considering the ‘wrong’ number of electrons, we are looking at a single atom and not the molecule. We are looking at how each atom shares electrons.
Consider the hydronium ion (H3O+), the oxygen atom has the ‘wrong’ number of electrons and has a formal positive charge. To see what we mean, first draw the Lewis structure. The oxygen has eight valence electrons as we would expect. Next look at the covalent bonds. Each bond is made by atoms sharing one electron each. In effect, the oxygen has five valence electrons, one less than it should (oxygen is in Group 16 and an atom of oxygen should have six valence electrons). Thus it has a formal positive charge.
The diagram above shows how you can look at the bonding to determine formal charge
You don’t have to draw out the Lewis structure every time you want to determine the formal charge on an atom. There is a formula that allows you to determine the formal charge easily. It is:
Formula to determine the formal charge from line diagram
In the diagram below there is an example of this formula being used to determine the formal charges in nitric acid:
Determining the formal charges on the atoms of nitric acid
An ‘Abnormal’ Number of Bonds
Most chemists do not use this formula to determine the formal charges, they do it intuitively, simply looking for atoms that do not have the normal number of bonds. Carbon is Group 14 so has four valence electrons. It will form four bonds to achieve a full valence shell (the octet). If a carbon atom has fewer bonds, it will have a formal charge. The table below gives you the normal number of bonds for each of the common elements:
Standard number of bonds for common elements in organic molecules
Generally, if an atom has less bonds than expected it will have a negative formal charge (the alkoxide below), while if it has more bonds than expected it will have a formal positive charge (the oxonium ion). This is shown for oxygen but is true of other elements.
Bonds to oxygen - normally it has 2 bonds; more or less and it will have a formal charge
Carbon is an exception to this. It never has more than four bonds. A carbon with three bonds can either be negatively charged or positively charged depending on whether it has a lone pair of electrons or not.
A carbon with three bonds can either have a formal positive or negative charge
Other Exceptions
Elements in the third row of the periodic table can have more than one ‘normal’. These elements often obey the octet rule and have eight valence electrons but they can exceed it and still have a neutral atom (elements of the third row can start to fill the 3d orbital).
Phosphorus can have three or five bonds and no formal charge. Sulfur can have two, four or six bonds and still have no formal charge.
Elements of the third row can have different numbers of bonds and still have no formal charge
The other element that tricks the unwary is boron. A neutral boron atom only has three bonds and six valence electrons.
Drawing Conventions
A common question from students is, “how do I know if carbon has a lone pair of electrons or not?” This can be found from our drawings. By convention, we always show the formal charge on an atom but not the lone pair of electrons. This leads to cleaner diagrams. We can use the formal charge to determine the number of electrons in the valence shell.
For example, if we look at one of the resonance structures of dimethyl sulfoxide (DMSO, a common solvent). It has two formal charges. By using the formal charge equation, it is possible to show that the oxygen must have three lone pairs of electrons. The oxygen atom has a formal negative -1 charge. An atom of oxygen has six valence electrons (it is group 16) and it has one bond. As 6 - 1 - number of unshared electrons = -1, the number of unshared electrons is 6 or three pairs.
We can do the same for the sulfur atom, and we find it has one lone pair of electrons (2 unshared electrons).
Determining the number of lone pairs of electrons from the formal charge
And, yes, this molecule is the same as the sulfoxide above, which we showed without any formal charges. These are two resonance structures and we shall discuss such things later.
Conclusion
Formal charges are a useful way of keeping track of electrons within a molecule. They tell us whether atoms have gained or lost valence electrons. They tell us about the bonding within a molecule but they shouldn't be confused with bond polarisation. A formal negative charge does not tell us that an atom is more electronegative than another. Funnily enough, only electronegativity tells us about electronegativity! This will become important when we look at the reaction of reagents such as the borohydride anion (either look up the reactions of the carbonyl group, reductions or wait a few months for me to make that summary!).
Practice with the Worksheet found HERE.