The octet rule and Lewis structures

Why do atoms join?

The noble gases hardly react at all. Their outer shells hold eight electrons, or two in helium. In 1916 Kossel and Lewis took this as the key to bonding. Atoms join so that each one reaches the same stable outer arrangement as a noble gas.

There are two ways to get there.

• Transfer. One atom gives electrons to another. The two ions attract each other. Kossel described this ionic or electrovalent bond.
• Sharing. Two atoms share pairs of electrons. Lewis described this covalent bond.

Lewis symbols

A Lewis symbol is the element's symbol with one dot for each valence electron. Only the outer electrons take part in bonding, so only they are drawn.

• Lithium has 1 dot, carbon 4, nitrogen 5, oxygen 6, fluorine 7 and neon 8.
• The number of dots gives the usual valence. It is the dots themselves, or 8 minus the dots.

The octet rule

Atoms lose, gain or share electrons so that each has eight electrons in its valence shell.

In a chlorine molecule each atom has 7 valence electrons. They share one pair, and now each chlorine counts 8. A shared pair is a single bond, drawn as a line. A pair that belongs to one atom alone is a lone pair.

Two atoms can share more than one pair. Carbon dioxide has two double bonds, $\text{O=C=O}$. Nitrogen has a triple bond, $\text{N}\equiv\text{N}$.

Drawing a Lewis structure, step by step

1. Count the valence electrons of all the atoms. For an anion add one electron per negative charge. For a cation take one away per positive charge.
2. Pick the central atom. It is usually the least electronegative atom. Hydrogen is never central.
3. Join each outer atom to the centre with a single bond. Each bond uses 2 electrons.
4. Complete the octets of the outer atoms with lone pairs. Hydrogen needs only 2.
5. Put any electrons left over on the central atom.
6. If the central atom still has fewer than 8, turn lone pairs of an outer atom into double or triple bonds.

Take hydrogen cyanide, HCN, as a worked example.

1. Valence electrons: $1 + 4 + 5 = 10$.
2. Carbon goes in the middle: $\text{H-C-N}$.
3. Two single bonds use 4 electrons. Six are left.
4. The six go on nitrogen as three lone pairs. Nitrogen now has 8.
5. Nothing is left for carbon, which has only 4.
6. Move two lone pairs of nitrogen into bonds with carbon. The result is $\text{H-C}\equiv\text{N}$ with one lone pair on nitrogen. Carbon and nitrogen both have 8.

Start with phosphorus and five chlorines, as set. Then try boron with 3, sulfur with 6, and xenon with 4. Which ones keep the octet?

Formal charge

Sometimes more than one Lewis structure fits the count. The formal charge of each atom helps you choose:

Here $V$ is the atom's valence electrons, $L$ its lone pair electrons, and $B$ the electrons in its bonds.

Ozone, $\text{O}_3$, has 18 valence electrons. Its Lewis structure is $\text{O=O-O}$.

• The left oxygen, with a double bond and 2 lone pairs: $6 - 4 - 2 = 0$.
• The middle oxygen, with 3 bonds and 1 lone pair: $6 - 2 - 3 = +1$.
• The right oxygen, with a single bond and 3 lone pairs: $6 - 6 - 1 = -1$.

The formal charges always add up to the charge of the species, here 0. Two rules pick the best structure. Formal charges should be as small as possible. A negative charge should sit on the more electronegative atom.

Formal charge is bookkeeping. It does not mean the atom really carries that charge.

When the octet rule fails

The rule is a good guide, but three kinds of molecule break it.

• Incomplete octet. The central atom has fewer than 8 electrons. Lithium in LiCl has 2, beryllium in $\text{BeH}_2$ has 4, and boron in $\text{BCl}_3$ has 6.
• Odd number of electrons. Nitric oxide, NO, has 11 valence electrons, and nitrogen dioxide, $\text{NO}_2$, has 17. With an odd total, one atom must have an unpaired electron.
• Expanded octet. From the third period on, atoms can use their d orbitals and hold more than 8. Phosphorus in $\text{PF}_5$ has 10, and sulfur in $\text{SF}_6$ has 12. Sulfur in $\text{H}_2\text{SO}_4$ has 12 too.

The rule has other limits. Xenon and krypton form compounds such as $\text{XeF}_2$, $\text{XeF}_4$ and $\text{KrF}_2$, although they already have an octet. The rule also says nothing about the shape of a molecule or the energy of its bonds.

Practise with new numbers

Try it in Python

The program counts the valence electrons for four species. Then it works out the formal charges in ozone.

Common mistakes

• Forgetting the charge. $\text{NH}_4^+$ has $5 + 4 - 1 = 8$ electrons, not 9.
• Putting hydrogen in the middle. It can form only one bond.
• Counting a lone pair as one electron in a formal charge. $L$ counts electrons, two for each pair.
• Thinking every molecule obeys the octet rule. $\text{BF}_3$, NO and $\text{SF}_6$ do not.

Remember these

• Atoms bond to reach a noble gas arrangement: by transfer (ionic) or by sharing (covalent).
• Lewis structures: count the electrons, join, fill the outer atoms, then the centre, then make multiple bonds.
• $\text{FC} = V - L - \tfrac{1}{2}B$. The best structure has the smallest formal charges.
• Exceptions: incomplete octet, odd electrons, expanded octet.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. How many valence electrons does the Lewis structure of methanal, $\text{H}_2\text{CO}$, use?

2. Draw the Lewis structure of methanal. Which bond is a double bond?

3. What is the formal charge of nitrogen in the ammonium ion?

4. Why can nitrogen dioxide never give every atom an octet?

5. Phosphorus forms $\text{PCl}_5$, but nitrogen does not form $\text{NCl}_5$. Why?