The shared pair
Why methane is CH₄ and never CH₅ — a rule that worked for forty years before anyone could say why it was true. Lewis extracted the octet from the formulae that exist and the formulae that do not, drew it as a cube, and was right about the pairing and wrong about the picture.
- State what valence saturation is, and why it is a negative fact rather than a positive one
- Explain how the octet rule was extracted from evidence without any theory behind it
- Distinguish what Lewis got right — the shared pair — from what he got wrong, the cube
- Name the real exceptions to the octet, and say why they are not quibbles
Start with a fact so ordinary that it is easy to walk straight past. Every element combines with a fixed number of other atoms, and not more. Hydrogen takes one partner. Oxygen takes two. Nitrogen takes three. Carbon takes four. Edward Frankland set this out in 1852 and called it combining power; the word valence came later. It is the oldest quantitative fact about chemical structure that we still use, and it is what makes a structural formula possible at all. Kekulé built organic chemistry on carbon being four-handed in 1857. Every ball-and-stick model in every school in the world is a statement about combining power. And for sixty years nobody had the faintest idea why it should be true. Why four? Why not three, or five, or a different number on Tuesdays?
Here is the sharper version of the question, and it is the one that matters. Methane is CH₄. There is no such thing as CH₅. Not rare. Not unstable. Not difficult to make. Absent. Chemists spent the entire nineteenth century making carbon compounds — hundreds of thousands of them, by every method anyone could devise — and never once made that one. This is worth being precise about, because it changes what a theory has to do. Explaining why methane exists is easy; almost any theory can arrange for a thing that exists to exist. The hard job is explaining an absence. Something has to actively forbid CH₅, and forbid NH₄, and forbid H₂O with a third hydrogen on it, while permitting the four hundred thousand compounds that sit right next door. A rule that only ever says yes is not a rule.
The elements that would not react
- The question
- Nitrogen prepared from air is very slightly heavier than nitrogen prepared from ammonia. Is that an error, or is there something else in the air?
- The apparatus
- Rayleigh’s globes, weighed to a fraction of a milligram, and Ramsay’s method of passing atmospheric nitrogen over hot magnesium until everything that would react had reacted. Whatever survived that treatment was collected and its spectrum photographed. Moissan then took the survivor and exposed it to fluorine, the most aggressive element known, in an electric discharge.
On the chemistry of the day every element has a combining power, so a newly isolated element should combine with something — and certainly with fluorine, which had been made to react with almost everything by that point, including xenon’s neighbours in the table and the noble metals.
Argon reacted with nothing. Not with fluorine, not with hot magnesium, not with anything Moissan or Ramsay could offer it. Helium, neon, krypton and xenon behaved the same way. An entire family of elements with a combining power of zero.
How sure could they be? The whole discovery hangs on Rayleigh refusing to round off a discrepancy. Atmospheric nitrogen came out at 1.2572 g/L against 1.2505 g/L for nitrogen from ammonia — a difference of about one part in two hundred, repeated over years, which he published as an unexplained anomaly rather than a mistake.
This is the anchor for everything that follows. Argon has eight electrons in its outer shell and no chemistry whatsoever; neon has eight and no chemistry; krypton and xenon have eight and very nearly none. Eight is the number an atom stops at. That is not a theory — it is an observation about a column of the periodic table, and it is where the octet came from.
Richard Abegg saw the pattern before anyone could use it. In 1904 he pointed out that for a great many elements, the largest positive valence and the largest negative valence add up to eight. Sulphur is +6 in sulphates and −2 in sulphides. Nitrogen is +5 and −3. Chlorine is +7 and −1. That is a genuine regularity, drawn straight out of the formulae in the tables, and it puts the number eight in front of you without offering the slightest hint as to why it should be eight. So by 1910 chemistry had three things and no way to join them: fixed combining powers, an inert family with eight outer electrons, and Abegg’s sum of eight. What was missing was a picture of what happens between two atoms.
And Lewis drew it, which is where the trouble starts. In his picture the outer electrons of an atom sit at the corners of a cube. Neon fills all eight corners and is therefore inert. Carbon has four occupied corners. Two atoms bond by sharing an edge of their cubes — an edge has two corners, so a shared edge is a shared pair. It is a beautiful device. It makes the number eight geometric rather than arbitrary, it makes a shared pair a visible thing, and it explains the inert gases in a single stroke. Lewis had sketched it out as far back as 1902, while preparing a class at Harvard, and reproduced that memorandum in the 1916 paper. It is also wrong, and Lewis was the first to say so. We will come back to that, because the way he handled being wrong is more instructive than the rule itself.
Drag the separation — on the plot or with the slider — until the force reads zero. That distance is the bond length. Then stretch it a little and press “Let go”, and watch what the molecule does with the well. Let go exactly at the minimum and nothing moves, because there is no force there.
The rule is a procedure, and it is a very good one. Four steps: Count every outer electron in the molecule, adding one for each negative charge and subtracting one for each positive. Join the atoms with one shared pair each. Distribute what is left as lone pairs, filling the outer atoms first. Check that every atom other than hydrogen has eight around it. Where one falls short, pull a lone pair in from a neighbour to make a second or third bond until it does not. That gets you carbon dioxide as O=C=O, nitrogen as N≡N, water bent around two bonds and two lone pairs, and the structure of essentially any small molecule you care to name, in about a minute, with no calculation whatsoever. It is still the first thing taught in every chemistry course on earth, one hundred and ten years later, and it is still taught first because it still works.
Three molecules on one axis: one shared pair, two, and three. Compare the depths before you read the numbers underneath — and then read them, because they do not say what the picture suggests.
Are three pairs worth three times one?
If a shared pair were a self-contained unit of bonding, then a triple bond ought to be worth three of them. The well depth of H₂, with one shared pair, is 4.747 eV. The well depth of N₂, with three, is 9.902 eV. By what factor is the nitrogen bond deeper? Compare your answer with 3.
- H₂, one shared pair
- Dₑ = 4.747 eV at 0.741 Å
- N₂, three shared pairs
- Dₑ = 9.902 eV at 1.098 Å
- O₂, two shared pairs
- Dₑ = 5.213 eV at 1.208 Å
Liquid oxygen sticks to a magnet
- The question
- Is oxygen magnetic? And if it is, what does that say about the electrons inside the molecule?
- The apparatus
- A strong electromagnet with a gap between its poles, and liquid oxygen poured through the gap. Nitrogen poured the same way falls straight through. The demonstration is done in lecture theatres to this day, with a neodymium magnet and a few millilitres of pale blue liquid.
Under the octet rule, the oxygen molecule is O=O: two shared pairs between the atoms and two lone pairs on each. Every electron in the molecule is in a pair. A substance with all its electrons paired is diamagnetic — feebly repelled by a magnetic field. It should fall straight through.
It does not fall through. Liquid oxygen bridges the gap and hangs there. Oxygen is strongly paramagnetic, and quantitatively so: its magnetic susceptibility corresponds to two unpaired electrons per molecule.
Two unpaired electrons is exactly what the Lewis structure forbids, in the second most common gas in the atmosphere, and Faraday had shown it sixty-eight years before Lewis wrote. It is not a marginal exception. The eventual explanation came from a different theory altogether — Hund and Mulliken’s molecular orbitals, from about 1928 — in which the last two electrons of O₂ go into two orbitals of equal energy and stay unpaired because that is cheaper. The pair is not sacred. It is usually favourable.
Atoms obey the octet rule.
Atoms do no such thing, and the exceptions are ordinary rather than exotic. Boron trifluoride sits perfectly happily with six electrons around the boron, which is why it is such a useful catalyst — it is actively looking for a pair. Phosphorus pentachloride has ten around the phosphorus and sulphur hexafluoride has twelve; SF₆ is a bench chemical, an industrial insulating gas, and about as inert as a molecule gets. Nitric oxide has an odd number of valence electrons, eleven, so no arrangement whatsoever pairs them all — and it is the signalling molecule that dilates your blood vessels. Oxygen itself is paramagnetic, as above. Lewis knew about the odd-electron molecules and discussed them in the 1916 paper; he did not pretend they were not there. The honest statement is that the octet is an excellent description of the second row of the periodic table — carbon, nitrogen, oxygen, fluorine — a good one either side of it, and something you should stop trusting the moment you go past the third row.
So what kind of thing was this? It was a rule with no explanation. Lewis did not derive the octet; he read it off the formulae that exist and the formulae that do not, and off a column of elements that refuse to react. The cube was an illustration of the rule, not a reason for it, and it was wrong. Nothing in the physics of 1916 said that electrons should pair, or that eight of them should close a shell, or why a shared pair should hold two nuclei together rather than letting them fly apart. The first genuine piece of the reason arrived in 1925, when Wolfgang Pauli stated the exclusion principle: two electrons and no more may occupy the same state. That is why a pair is a pair. And it explains the eight — two in one s orbital and six in three p orbitals, which is the whole of a second-row outer shell. The rest took much longer. Why a shared pair lowers the energy at all was not answered until 1927. Why sulphur can carry twelve was not answered until 1951, and the answer most textbooks still give — that sulphur uses its d orbitals — is not the accepted one. Forty years of a rule that worked, taught and used and relied upon, with the explanation arriving in instalments and some of it arriving wrong.
Two atoms may conform to the rule of eight, or the octet rule, not only by the transfer of electrons from one atom to another, but also by sharing one or more pairs of electrons.
- 1852Frankland: every element has a fixed combining power. Nobody knows why.
- 1857Kekulé makes carbon four-handed, and organic structural chemistry becomes possible.
- 1894Rayleigh refuses to round off a half-per-cent discrepancy in the density of nitrogen; argon follows.
- 1902Lewis sketches the cubical atom in a teaching memorandum at Harvard, and does nothing with it for fourteen years.
- 1904Abegg: for many elements the largest positive and negative valences sum to eight.
- 1916Lewis: the bond is a shared pair. Kossel, the same year, argues that it is a transferred electron.
- 1919Langmuir names the octet and coins "covalence", and the idea becomes universal.
- 1925Pauli’s exclusion principle finally explains why a pair holds two electrons and not three.
- 1951Pimentel and Rundle explain SF₆ without d orbitals — thirty-five years after the exception was noticed.