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Formal Charge

Formal Charge and Lewis Formulas

A concept know as formal charge can help us choose the most plausible Lewis structure where there are a number of structures which would all be satisfactory according to the rules used thus far.  For example if we look at the cyanate ion, NCO-, we see that it is possible to write for the skeletal structure, NCO-, CNO-, or CON-.  Using formal charge we can choose the most plausible of these three Lewis structures.

To determine the formal charge of an atom we first assign valence electrons to atoms in a Lewis structure as follows.

• All unshared (lone pair) electrons are assigned to the atom on which they are found.
• Half of the electrons in a bond between two atoms are assigned to one atom and half to the other.

After assigning all the valence electrons, we determine the formal charges as follows.  The formal charge on an atom is the number of valence electrons on the free (nonbonded) atom minus the number of electrons assigned to that atom in the Lewis structure.  We can state this mathematically as follows.

FC = V - (L + 1/2 S)

Where V is the number of valence electrons on the free atom, L is the number of electrons present as lone pairs and S is the number of shared electrons.  Note that the sum of the formal charges on all the atoms in a molecule will be zero while for an ion it will be equal to the charge on the ion.  In using the concept of formal charge we should keep the following rules in mind.

• Usually the most plausible Lewis structure is one with no formal charges (formal charges of zero on all atoms).
• Where formal charges are required, they should be as small as possible, and negative formal charges should appear on the most electronegative atoms.
• Adjacent atoms in a structure should not carry formal charges of the same sign.
• Formal charges on the atoms in a Lewis structure must total to zero for a molecule and to the net charge for a polyatomic ion.

Getting back to the example of the cyanate ion, the three Lewis structures with the formal charges indicated are shown below.  Structure (a) would be the most plausible Lewis structure.

(a)              (b)               (c)

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