Formal charge is bookkeeping. It tells you which atom in a structure carries a charge. It checks that the charges you wrote add up to the charge on the whole molecule. And when a molecule can be drawn more than one way, it helps you pick the better drawing. You will use it in almost every chapter, often under time pressure, so it pays to get fast at it.
Formal charge is worked out on a Lewis structure: a drawing that shows every atom, every bond as a line, and every lone pair as two dots. A lone pair is a pair of electrons that stays on one atom and is not shared. Lewis structures teaches how to draw one from a formula. On this page the structures are given, and the job is to count.
Start with two examples
Take water, H₂O. A lone oxygen atom has 6 valence electrons, the outer-shell electrons from Atomic structure. In water, the oxygen has two lone pairs and two bonds, one to each H.
Now decide which of those electrons the oxygen owns. The convention is simple. An atom owns both electrons of each of its lone pairs. It owns one of the two electrons in each bond, and the partner atom owns the other. So the oxygen owns 4 lone-pair electrons plus 2 bond electrons, 6 in all. That is the same 6 it brought, so its formal charge is 0.
Now take the ammonium ion, NH₄⁺. A lone nitrogen atom brings 5 valence electrons. In NH₄⁺, the nitrogen has four bonds and no lone pair. It owns one electron from each bond, 4 in all. It brought 5 and owns 4, so it is one electron short. Its formal charge is +1.
An atom's formal charge is that difference: the electrons it brought minus the electrons it owns in the structure. The owned electrons are its lone-pair electrons plus one per bond, which gives the formula:
The valence electrons come from the last digit of the group number. Carbon is in group 14, so it has 4; see Atomic structure. The ones you need most: C = 4, N = 5, O = 6, the halogens = 7, H = 1.
The last term counts bonds, the lines in the drawing, not the connections to other atoms. Acetone, (CH₃)₂C=O, shows why that matters. Its oxygen has two lone pairs and a double bond to carbon. A double bond is two lines, so it counts 2: FC = 6 − 4 − 2 = 0. A triple bond counts 3. Count the double bond as 1 and the oxygen comes out +1, a charge acetone does not have.
Some books write the last two terms as "lone-pair electrons plus half the bonding electrons". A double bond holds 4 electrons, and half of 4 is 2, so both forms give the same answer. Use whichever one you can do faster without a slip.
Worked examples
NH₄⁺. Nitrogen has 4 bonds and 0 lone pairs. FC = 5 − 0 − 4 = +1. Each hydrogen is 1 − 0 − 1 = 0. The sum is +1, the ion's charge. ✓
OH⁻. Oxygen has 1 bond and 3 lone pairs, which is 6 lone-pair electrons. FC = 6 − 6 − 1 = −1. The hydrogen is 0. The sum is −1. ✓
H₃O⁺. Oxygen has 3 bonds and 1 lone pair, which is 2 electrons. FC = 6 − 2 − 3 = +1. Each hydrogen is 0. The sum is +1. ✓
Methoxide, CH₃O⁻. A CH₃ group (a carbon carrying three hydrogens) is bonded to an oxygen. The oxygen has 1 bond and 3 lone pairs, so FC = 6 − 6 − 1 = −1. The carbon has 4 bonds and no lone pairs: 4 − 0 − 4 = 0. The hydrogens are 0. The sum is −1, the ion's charge. ✓
Methoxide is hydroxide with a CH₃ group in place of the H. The oxygen's count does not change. The formula sees only bonds and lone pairs, not what sits at the other end of a bond.
Methylammonium, CH₃NH₃⁺. The nitrogen has 4 bonds and 0 lone pairs: 5 − 0 − 4 = +1, exactly as in NH₄⁺.
Nitromethane, CH₃NO₂, has a CH₃ group bonded to a nitrogen, and the nitrogen bonded to two oxygens. The molecule has no overall charge.
The tempting structure. Most people first give the nitrogen a double bond to each oxygen. Nothing is charged, and it looks tidy. Now count the nitrogen's bonds: one to carbon plus two double bonds makes five. Five bonds put ten electrons around the nitrogen. A period-2 atom (one from the second row of the periodic table, such as C, N or O) has only four outer orbitals, room for eight electrons. This structure cannot exist.
The structure that works. Give the nitrogen four bonds: one to carbon, a double bond to one oxygen and a single bond to the other. The double-bonded oxygen keeps two lone pairs, and the single-bonded oxygen keeps three.
The counts. Nitrogen: 5 − 0 − 4 = +1. The double-bonded oxygen: 6 − 4 − 2 = 0. The single-bonded oxygen: 6 − 6 − 1 = −1. The carbon and the hydrogens: 0. The sum is +1 − 1 = 0, which matches the neutral molecule.
What it teaches. A neutral molecule can still contain charged atoms, and nitromethane has to. A nitro group is an N bonded to two O's, as here. Nitro groups turn up in many molecules besides this one, including the explosive TNT, and every one is drawn this way. Any nitro group drawn without a +1 on the nitrogen and a −1 on one oxygen is wrong.
Structures are often drawn with the charges shown and the lone pairs left off, and you are expected to supply the lone pairs. Rearrange the formula: lone-pair electrons = valence electrons − bonds − FC.
An oxygen with one bond and a −1, as in methoxide: 6 − 1 − (−1) = 6 electrons, so 3 lone pairs.
A nitrogen with three bonds and no charge, as in methylamine, CH₃NH₂: 5 − 3 − 0 = 2 electrons, so 1 lone pair.
A carbon with three bonds and a +1, as in the methyl cation, CH₃⁺: 4 − 3 − 1 = 0, so no lone pair. That carbon has an empty orbital instead. A carbon like this is a carbocation.
Flip that charge to −1 and the same three-bonded carbon becomes the methyl anion, CH₃⁻. Now 4 − 3 − (−1) = 2 electrons, so it keeps 1 lone pair. A carbon like this is a carbanion.
Nine patterns worth memorizing
The same few counts come up again and again. Once you know them, you can read charges off a structure at a glance instead of doing the arithmetic. That is what you will be doing while you draw reaction mechanisms, the step-by-step pictures of how bonds break and form.
The patterns hold for an atom with a full octet, eight electrons in its bonds and lone pairs. The one exception in the list is the carbocation, which has only six.
- Oxygen: 3 bonds is +1, 2 bonds is 0, 1 bond is −1.
- Nitrogen: 4 bonds is +1, 3 bonds is 0, 2 bonds is −1.
- Carbon: 4 bonds is 0. With 3 bonds and a lone pair (still a full octet), it is −1: a carbanion. With 3 bonds and no lone pair (only six electrons), it is +1: a carbocation.
The built-in check: charges add up
Every worked example above ended with a sum. NH₄⁺ summed to +1, methoxide to −1 and nitromethane to 0. Each time, the sum matched the charge on the whole molecule or ion.
That always holds. The formal charges of all the atoms add up to the overall charge, and for a neutral molecule they add up to exactly 0. This is arithmetic, not a guideline, so it cannot fail for a correctly drawn structure. If your total does not match, you have miscounted a lone pair or drawn the wrong number of bonds somewhere.
The check also works across a reaction step. When ammonia, NH₃, picks up a hydrogen ion, H⁺, the nitrogen's lone pair becomes a new N–H bond. The curved arrow in the figure shows that pair moving: it starts at the pair and ends on the H⁺ that the pair bonds to. Drawing Molecules & Moving Electrons teaches curved arrows in full. Before the step, the charges sum to 0 + 1 = +1. After it, NH₄⁺ also sums to +1. Every reaction step conserves charge like this, so if the total changes across a step you drew, an arrow or a count is wrong.
Why it matters: picking the right structure
Diazomethane has a CH₂ group bonded to a nitrogen, and that nitrogen bonded to a second nitrogen. Two structures give every atom an octet.
Structure A, H₂C=N⁺=N⁻. The carbon has 4 bonds: 0. The middle nitrogen has 4 bonds and no lone pair: +1. The end nitrogen has 2 bonds and 2 lone pairs: 5 − 4 − 2 = −1.
Structure B, H₂C⁻–N⁺≡N. Two pairs sit in different places. The C=N double bond is now single, and its spare pair is a lone pair on the carbon. One of the end nitrogen's lone pairs is now a third N–N bond. The carbon has 3 bonds and 1 lone pair: 4 − 2 − 3 = −1. The middle nitrogen still has 4 bonds: +1. The end nitrogen has 3 bonds and 1 lone pair: 5 − 2 − 3 = 0.
Compare. Both structures sum to 0, and both carry one + and one −. They differ only in where the − sits: on nitrogen in A, on carbon in B. Nitrogen is more electronegative than carbon (it pulls harder on electrons; see Electronegativity), so it holds a negative charge better. A is the better structure, and it is the one chemists usually draw.
B still matters. Real diazomethane is a blend of both drawings, and B's lone pair on carbon explains why the carbon is the atom that picks up an H⁺ when diazomethane reacts with an acid.
Diazomethane is a real reagent, but you will not find it in a bottle. It is a toxic, explosive gas, so chemists make it fresh, in solution, just before they use it. What is sold in bottles is a relative, trimethylsilyldiazomethane, which does not explode but is still highly toxic if inhaled.
Diazomethane was settled by the second of three ranking rules. When several structures give every atom an octet, the best one:
- Has the fewest formal charges. A structure with no charges beats one with a + and a −.
- Puts a negative charge on the most electronegative atom, and a positive charge on the least electronegative one. This is the rule that picked A.
- Avoids like charges on neighboring atoms. Two + charges side by side repel each other, which costs energy.
The same rules come back for resonance structures: two or more drawings of one molecule with the atoms in the same places and only the electrons moved, like A and B. Drawing Molecules & Moving Electrons ranks them with these three rules, plus one that comes first: a structure that gives every atom a full octet beats one that leaves an atom short.
Reading charges to find reactive sites
Take the methyl cation, CH₃⁺, from the backwards example. Its carbon is +1 and has only six electrons around it, in three bonds, which is two short of an octet. It is charged and short of electrons at once, so it reacts with almost anything that has a pair of electrons to offer. Carbocations are among the most reactive species in the course.
A formal + on its own does not make an atom short of electrons. The nitrogen of NH₄⁺, the oxygen of H₃O⁺ and the nitrogen of nitromethane all carry a + and all have full octets, so none of them can take more electrons. What makes an atom electron-poor is a + together with fewer than eight electrons, as on the carbocation carbon. An atom with a formal − usually has a lone pair to spare, so it seeks out an atom that is short of electrons. How Reactions Happen gives those two roles their names.
So when you meet a new molecule, assigning formal charges is a good first move. It takes a few seconds, and it often shows you where the molecule will react.
What carries forward
You will compute formal charges constantly. You will use them to check Lewis structures in Lewis structures, to rank resonance structures in Drawing Molecules & Moving Electrons, and to check that each step of a mechanism conserves charge. You will also use them to spot the charged species, such as carbocations and carbanions, that form partway through the reactions in Substitution & Elimination and every chapter after it.