LearnChem · Part II — Why do atoms stick together?
Nothing ties atoms together. They fall together — into a valley — and the valley's depth is the price of getting them back out.
“Do atoms actually touch? What's between them?”
Last time, the staircase of ionisation energies turned the periodic table from a wall chart into a floor plan: every atom got a price list for its own electrons, and a pulling strength, χ, for other atoms'. But a price list is not a reason. Nothing in it says why two priced atoms, brought near, should stay stuck — why there is any such thing as a molecule. Module 05 promised a tug-of-war over a shared pair. First, though, the ground the tug is fought on.
Press your palm on the table and it stops — firmly, at a definite place. So the atoms of your hand and the atoms of the table must be meeting somewhere. Yet module 01's zoom ladder showed each atom as almost entirely empty space, and module 04 blurred even the electrons into a cloud of probability. What exactly is doing the stopping? When two atoms come at each other, is there anything there to touch?
Take the simplest possible case: two hydrogen atoms, alone, drifting towards each other in a vacuum. Each is one proton wearing one electron.
Two hydrogen atoms drift towards each other. Commit: what happens as the gap closes?
Commit before you look. First answers are counted anonymously, never named.
Both things happen — in that order. From far away, each atom is neutral and bland. Nearer, each nucleus starts to feel the other atom's electron as well as its own, and each electron is pulled by two nuclei instead of one. Module 01's one borrowed rule of physics — opposite charges pull, and separating them costs energy — starts paying out on the new arrangement: the pair slides downhill in energy as the gap closes. Push closer still and the two electron clouds crowd each other, the nuclei see each other's bare charge, and the energy soars. Downhill, then a wall.
Downhill, then a wall, makes a valley. Watch it get traced out:
Drag the gap closed slowly and read the energy as you go: flat, then falling, then — past the floor — soaring. Then set the atoms a little apart and release them: they fall in, overshoot, swing back, and — shedding energy as they swing, the way real pairs shed it to collisions and light — settle into the valley. (The cartoon lets them come fully to rest; a real pair keeps a small vibration forever.) The floor is not a wall they land on. It is the gap at which the pull inward and the push outward exactly cancel — move either way and the energy climbs.
Switch pairs and the valley changes: deeper here, shallower there. The standoffish “noble” pair barely dips at all — but it does dip, and that shallow dip is why helium, made cold enough, turns liquid.
That settling gap is what a chemist means by the bond length. And this is the honest answer to the question at the door. Atoms never touch the way marbles touch — there are no surfaces in there to meet. They approach until push balances pull, and hold that spacing. Your palm stops at the table because a hundred thousand trillion electron clouds on each side cannot overlap without the energy soaring — a truce line, held everywhere, all the time. Nor is there emptiness between two bonded atoms: their shared cloud is thickest right between the nuclei. What holds the spacing, both ways, is the valley.
Quick check — so do atoms actually touch?
Now put a number on the valley, because the number is the whole subject. Two hydrogen atoms that fall into their shared valley end up lower in energy than they were apart. That pair, sitting in its valley, is the molecule H2 — and the drop is not a metaphor. Fall in, and the difference is paid out to the surroundings, as motion and light. (Loose lone atoms are rare guests in everyday life, but where two do meet — at the tip of a welder's atomic-hydrogen torch, where an arc splits H2 and the atoms fall back together on the metal — this payout is the heat.) Climb out — split the molecule back into two loose atoms — and the same difference must be paid back in, to the last bit.
The prices come in the two currencies you already hold. Per single event, the atom-sized unit from module 01: snapping one H–H bond costs about 4.5 eV — a few eV, the usual size of a chemical price. Per mole of events, module 03's counting bridge turns that into human-sized numbers: one eV per event, counted out over a mole, is 96.5 kJ. So the H–H valley prices at 436 kJ per mole of bonds, at room temperature — enough heat, from two grams of hydrogen, to bring a litre of water from cold to boiling. Chemists call the mole-sized price the bond enthalpy (your textbook's full name: bond dissociation enthalpy).
Every kind of bond has its own valley and its own price. Oxygen's O=O — a double bond: two shared pairs — runs 498 kJ/mol; chlorine's Cl–Cl is a cheapish 243; H–Cl is a steep 432; the C–H bonds that module 01 priced a candle by average about 413. Keep the sign straight: breaking a bond always costs; forming a bond always pays. There are no exceptions: falling in and climbing out are the same valley, walked in opposite directions. When a fire gives out heat, it is not because breaking bonds released something — it is because the new valleys the atoms fell into (in CO2 and H2O) are deeper than the ones they climbed out of. The flame's heat is the difference between two ledgers, exactly as module 02's candle kept insisting.
Nobody has tweezers for a single bond, but molecules confess their valley two ways. The sharp way is light: a molecule's rungs of vibration crowd together towards a top — the energy at which the two atoms fly apart for good — and that top, read off a spectrum, prices the climb out just as module 05's series limits priced ionisation. The blunt way is heat: burn or split a known amount in a sealed, weighed apparatus and account for every joule (module 12 builds that instrument). Put on the same footing, the two ledgers agree — which is most of why chemists trust either. The H–H, O=O, Cl–Cl and H–Cl prices above are worked from the CODATA reference tables, the internationally agreed audit of exactly such measurements; the C–H figure is a textbook average over many molecules.
Quick check — breaking one mole of H–H bonds swallows 436 kJ. Making one mole of H–H bonds…
So far the two atoms in the valley were twins, and the electron pair between them sat exactly in the middle — it had no reason to sit anywhere else. But module 05 left a loaded question waiting. Its league table of pulling strength — electronegativity, written χ (chi) — says a chlorine atom (χ 3.16) pulls a shared pair far harder than a hydrogen atom does (χ 2.20). Put those two in one valley, sharing one pair, and the tug-of-war is no longer between equals.
Hydrogen and chlorine share a pair, and chlorine pulls harder — χ 3.16 against 2.20. Where does the pair end up?
The pair is charge, not a parcel, and charge can thicken at one end. In H–Cl it thickens at the chlorine end: that end of the molecule runs slightly negative, the hydrogen end slightly positive, and the bond is called polar — one bond, leaning. How far a bond leans is measured by the gap between the two χ values, written Δχ (delta-chi). And here is the fact that tidies a whole chapter of chemistry into one line: Δχ is a dial, not a switch. Turn it up and the pair slides further towards the harder puller. Far enough along, the pair has effectively moved house: one atom is now a positive ion, the other a negative one, and the bond is called ionic. “Covalent” and “ionic” are not two kinds of glue. They are the two ends of one dial.
Walk the dial's landmarks. Cl–Cl: Δχ = 0, a dead-even tug, the pair centred. H–Cl: Δχ = 0.96, the pair well over towards chlorine — polar, leaning, but shared. Na–Cl: Δχ = 2.23, the pair so thoroughly at chlorine's end that honesty gives up on “sharing” and calls it a handover. Chemists keep rough boundary marks on the dial — below about 0.4 call it plain covalent, above about 1.7 or 1.8 call it ionic (books disagree on the number, which tells you it is a convention) — and the dial under the marks is continuous. Real bonds sit everywhere along it, and asking “is it covalent or ionic?” is like asking whether 40 °C water is hot or cold: the useful answer is a position, not a box.
Textbooks often put this whole section in desire words: an atom is said to want a full outer eight, to grab and hoard electrons until it gets one. You now hold the better sentence. An atom has no wants — there is only energy, running downhill. Chlorine's pull on a shared pair is strong because its felt charge is high and its outer floor is close (module 05's two dials); arrangements that thicken charge near such an atom sit lower in energy, so matter ends up in them — and the bookkeeping happens to come out at eight for the table's top rows. Further down it often doesn't: module 05 showed the d-rooms carrying the count past eight. “Wanting” is a memory aid that answers no questions. The valley answers them all.
Quick check — three bonds: H–H, H–Cl, Na–Cl. Reading only Δχ (0, 0.96, 2.23), which order runs from equal sharing to near-total transfer?
Follow the dial towards its far end and you arrive at the most familiar crystal in your house. Sodium — a metal soft enough to cut with a knife, and so violent with air and water that it is stored under oil — and chlorine, a green-yellow gas. Bring them together and they burn into table salt: 2 Na(s) + Cl2(g) → 2 NaCl(s), with a flare of yellow light and a great deal of heat. Somewhere in there, each sodium atom's outer electron moved house to a chlorine atom. Δχ = 2.23; the far end of the dial; a handover.
Now price the handover. Module 05 measured the eviction: 5.14 eV, which the mole bridge turns into 496 kJ per mole. The other half has been measured too, by laser, to six figures — the electron affinity module 05 named in passing: parking an electron on a lone chlorine atom pays out 349 kJ per mole.
Take one sodium atom's electron and hand it to one chlorine atom, both alone in a vacuum. Price the trade: the eviction costs 496 kJ per mole, and the acceptance pays back 349. Profit or loss?
That wrecks the story most books tell. Even chlorine — the hardest electron-puller in row 3 — pays back less for an electron than it costs to take one from sodium, the cheapest seller in the row. The bare handover, atom to atom, loses about 147 kJ per mole. If gas-phase atoms trading electrons were the whole story, salt would fall apart into atoms and hand you the difference. Salt exists anyway. So the account must have an income line the two-atom picture cannot see.
It does, and you have met this move before: the answer lives in the crowd. A sodium ion does not pair off with one chloride ion. In the crystal, every Na+ is boxed in by six Cl−, every Cl− by six Na+, and the pattern repeats, wall to wall, through every grain of salt — module 01's lesson again: the property that matters belongs to the many, not the pair. Assembling that crowd from loose ions pays out enormously, because opposite charges always end up nearest, so the pulls outweigh the pushes — and because the pull between two charges grows with the size of each: double both, and every pair pulls roughly four times harder. Chemists audit the whole affair as one round trip: start from ordinary sodium metal and chlorine gas, price every step, and demand the books balance against the measured overall payout. Walk it:
Read the bottom line off the bench. Every step but one runs at a loss, and even after chlorine's payment the books stand 375.9 in the red — yet the crystal's own entry, the one the ledger is forced to solve for, lands near −787 kJ per mole: about twice that whole deficit, wiped out in one line. That is what pays for salt. Not chlorine's appetite; the lattice's arithmetic — a billion billion ions, opposite charges always nearest, the pulls outweighing the pushes, summed into an abyss. The heat of the flare when sodium meets chlorine is this ledger's bottom line paid out at once (the flare's yellow is sodium's own signature colour — module 04 taught you to read it). And the ledger trick itself — pricing an unmeasurable step by making a round trip's books balance — is one of chemistry's most reused tools; module 12 will hand it to you as an instrument.
On 22 April 1915, at Ypres, chlorine gas rolled across trenches as the first massed chemical weapon. At high doses it burns the lungs; even low doses sting eyes and airways. It still injures people at home: bleach mixed with an acidic toilet cleaner releases chlorine gas into a closed bathroom — never mix the two. And yet the chlorine in your salt is the same element, same nucleus, and it sits in food. The whole difference is one electron's worth of dress. Cl2 is two chlorine atoms sharing evenly, each still able to sit lower by taking an electron; Cl− in salt has taken it and settled at the bottom of its valley, chemically spent. Danger belongs to the species — the element plus its electron arrangement — never to the element alone, which is why “contains chlorine” on a label tells you nothing until you know which chlorine.
Quick check — the chlorine that gassed soldiers in 1915 and the chlorine in your salt cellar are…
These check themselves, and “New numbers” deals a fresh set — there is nothing to memorise. Within a few per cent counts as right unless the check says otherwise.
1. The counting bridge from module 03, revisited: a bond's valley is deep. One eV per event, counted over a mole, is 96.5 kJ. Price a mole of these bonds.
2. Module 04's ladder of light, revisited: light arrives in fixed parcels. A flash whose parcels carry lands on a bond costing to snap. Each parcel can break one bond — with how many eV left over?
3. Reading the strip: . How far apart are the two pulls — what is Δχ, to two decimals?
4. A practice ledger, for an invented salt (round practice numbers, not measurements): . What must the crystal's payout be, for the books to close? (Type its size, as a positive number, to the nearest kJ.)
The real entries, in kJ/mol: loosening a mole of sodium atoms from the metal costs 107.5; evicting their electrons costs 495.8; freeing a mole of chlorine atoms from Cl2 costs 121.3; parking the electrons on the chlorines pays 348.7; and the measured overall drop, metal-and-gas to crystal, is 411.1. Find the crystal's payout, and type its size as a positive number. Then say to yourself, in one sentence, why “chlorine pays for the electron” cannot be the reason salt exists.
Worked through. Costs: 107.5 + 495.8 + 121.3 = 724.6 out. Income before the crystal: 348.7 back. Running total: 375.9 in the red. The books end 411.1 in the black, so the crystal's entry must pay 375.9 + 411.1 = 787.0 kJ/mol. And the sentence: chlorine's payment (348.7) does not even cover sodium's eviction (495.8) — the electron trade alone loses money, so what makes salt is not the taker's appetite but the crowd's embrace: the lattice.
Magnesium oxide lines furnace walls; the same furnace would treat table salt as a puddle in waiting. Play the ledger in your head for MgO: magnesium must give up two electrons (the second, taken from an already-positive ion, costs about double the first — read it off module 05's staircase), and oxygen, offered a second electron, charges for it instead of paying. So MgO's electron trade runs far deeper in the red than NaCl's — yet MgO out-toughs salt by a mile. For MgO to exist at all, what must its crystal's entry look like next to NaCl's −787? And a crystal that survives a furnace sits in a deep valley: what about Mg2+ and O2−, compared with Na+ and Cl−, digs it that deep? There is no marking here; write your reasoning down before looking.
The discussion. Every cost in MgO's ledger is steeper: two evictions (the second from an already-positive ion), and an oxygen that must be paid to hold its second extra electron — alone in a vacuum it will not hold it at all; only the crystal's field keeps it there, and its price is inferred from cycles like this one. For the books to close on a crystal that survives furnaces, the lattice entry must be an abyss well past NaCl's −787 — and it is the double charges that dig it. §4's rule again: the pull between two charges grows with the size of each, so doubling both makes every pull (and every push) roughly four times stronger — and since opposites sit nearest, the net payout multiplies with them. The doubly charged ions are smaller and sit closer, too. That is why the red-ink trade still ends in the black — and why firebrick is firebrick. (The same idea returns priced as hardness and melting in module 09; module 12 hands you the ledger as a general instrument.)
A bond is not glue. It is two atoms sitting lower than they stood apart.