A Key Skill: How to Calculate Formal Charge

in Functional Groups, Nomenclature, Organic Chemistry 1, Where Electrons Are

Need to figure out if an atom is negative, positive, or neutral? Here’s the formula for figuring out the “formal charge” of an atom:

Formal charge = [# of valence electrons] – [electrons in lone pairs + 1/2 the number of bonding electrons]

This formula explicitly spells out the relationship between the number of bonding electrons and their relationship to how many are formally “owned” by the atom. However, since the “number of bonding electrons divided by 2″ term is also equal to the number of bonds surrounding the atom, here’s the shortcut formula:

Formal Charge = [# of valence electrons on atom] – [non-bonded electrons + number of bonds].

Let’s apply it to some examples. for example BH4 (top left corner).

The number of valence electrons for boron is 3.
The number of non-bonded electrons is zero.
The number of bonds around boron is 4.

So formal charge = 3 – (0 + 4) = 3 – 4 = –1

The formal charge of B in BH4 is negative 1.

Let’s apply it to :CH3 (one to the right from BH4)

The number of valence electrons for carbon is 4
The number of non-bonded electrons is two (it has a lone pair)
The number of bonds around carbon is 3.

So formal charge = 4 – (2 +3) = 4 – 5 = –1

The formal charge of C in :CH3 is negative 1.

Same formal charge as BH4!

Let’s do one last example. Let’s do CH3 (with no lone pairs on carbon). It’s the orange one on the bottom row.

The number of valence electrons for carbon is 4
The number of non-bonded electrons is zero
The number of bonds around carbon is 3.

So formal charge = 4 – (0 +3) = 4 – 3 = +1

You can apply this formula to any atom you care to name.

Here is a chart for some simple molecules along the series B C N O . I hope beryllium and fluorine aren’t too offended that I skipped them, but they’re really not that interesting for the purposes of this table.

Note the interesting pattern in the geometries (highlighted in colour): BH4(–), CH4, and NH4(+) all have the same geometries, as do CH3(–), NH3, and OH3(+). Carbocation CH3(+) has the same electronic configuration (and geometry) as neutral borane, BH3. The familiar bent structure of water, H2O, is shared by the amide anion, NH2(–). These shared geometries are one of the interesting consequences of valence shell electron pair repulsion theory (VSEPR – pronounced “vesper“, just like “Favre” is pronounced “Farve”.)

The formal charge formula also works for double and triple bonds:

Here’s a question. Alkanes, alkenes, and alkynes are neutral, since there are four bonds and no unbonded electrons: 4 – [4+0] = 0. For what other values of [bonds + nonbonded electrons] will you also get a value of zero, and what might these structures look like? (You’ll meet some of these structures later in the course).

One final question – why do you think this is called “formal charge”?

Think about what the formal charge of BF4 would be. Negative charge on the boron. What’s the most electronegative element here? Fluoride, of course, with an electronegativity of 4.0, with boron clocking in at 2.0. Where do you think that negative charge really resides?

Well, it ain’t on boron. It’s actually spread out through the more electronegative fluoride ions, which become more electron-rich. So although the “formal” address of the negative charge is on boron, the electron density is actually spread out over the fluorides. In other words, in this case the formal charge bears no resemblance to reality.