Two chlorine atoms cannot settle their differences the way sodium and chlorine do: each wants one more electron, and neither will give one away. They share instead. A pair of electrons between two nuclei, attracted by both, is the covalent bond, and it holds together almost every molecule in a living thing, in fuel, in plastic and in air. This chapter shows why sharing lowers the energy, how to draw who shares what (Lewis structures), how to choose between drawings, and what happens when two atoms do not share equally.
By the end you can
- Explain a covalent bond with the energy curve of H₂, and define bond length and bond energy.
- Draw the Lewis structure of a small molecule or ion, with multiple bonds where needed.
- Use formal charges to pick the best structure, and recognise resonance.
- Name the three kinds of exception to the octet rule.
- Predict whether a bond is nonpolar, polar or ionic from electronegativities.
Bring two hydrogen atoms together. Far apart they ignore each other. As their electron clouds begin to overlap, each electron can spend time between the two nuclei, where it is attracted by both protons at once, and the energy drops. Bring them too close and the two protons repel each other strongly. Somewhere in between is a minimum: there the two atoms stay, as a molecule. The two electrons now belong to the pair of atoms together. That shared pair is a covalent bond.
Slide the atoms together. Far apart, nothing happens: zero energy. As the clouds overlap, the two electrons spend more time between the nuclei, where both protons pull on them, and the energy drops. Push closer than 74 pm and the protons' repulsion wins: the curve shoots up. The molecule sits at the bottom, at the bond length; the depth is the energy needed to pull it apart. (A real molecule keeps vibrating even at the bottom, so it takes slightly less, 4.48 eV or 432 kJ/mol.) H₂⁺, with a single shared electron, still bonds, at half the depth. Two helium atoms bring four electrons, and the extra pair undoes the bond: helium stays a gas of single atoms.
Two numbers describe every bond. The bond length is the distance between the nuclei at the bottom of the curve (74 pm for H₂). The bond energy, or bond dissociation energy, is the energy needed to break one mole of the bonds into separate atoms in the gas (436 kJ/mol for H₂ at room temperature). A deep, narrow well means a short, strong bond.
A Lewis structure shows every valence electron of a molecule. A shared pair is drawn as a line between two atoms; a pair that belongs to one atom only, a lone pair (or nonbonding pair), is drawn as two dots beside it. In water, oxygen shares one pair with each hydrogen and keeps two lone pairs: counting both, oxygen has eight electrons around it and each hydrogen has two. Building such structures for any molecule follows a recipe.
| Step | What to do |
|---|---|
| 1 | Add up the valence electrons of all atoms; add one per negative charge, remove one per positive charge. |
| 2 | Write the skeleton: usually the least electronegative atom (never hydrogen) in the centre, the others around it. Join each to the centre with a single bond (2 electrons each). |
| 3 | Give the outer atoms lone pairs until each has an octet (hydrogen: just its bond). |
| 4 | Put any electrons still left on the central atom, as lone pairs. |
| 5 | If the central atom has fewer than eight, turn lone pairs of outer atoms into extra bonds (double or triple) until it has eight. |
Double and triple bonds
Two atoms can share two pairs (a double bond, as in CO₂ and in ethene, C₂H₄) or three (a triple bond, as in nitrogen, N≡N, and in ethyne, C₂H₂). The number of shared pairs is the bond order. More shared electrons between the same two nuclei pull them closer and hold them tighter, so as the bond order goes up, the bond gets shorter and stronger. It does not get three times stronger, though: the second and third pairs sit off the line between the nuclei and bind less (the next section shows why).
| Bond | Order | Length (pm) | Energy (kJ/mol) |
|---|---|---|---|
| C–C | 1 | 154 | 347 |
| C=C | 2 | 134 | 614 |
| C≡C | 3 | 120 | 839 |
| N–N | 1 | 145 | 163 |
| N=N | 2 | 125 | 418 |
| N≡N | 3 | 110 | 945 |
| C–O | 1 | 143 | 358 |
| C=O | 2 | 123 | 745 |
| C≡O | 3 | 113 | 1072 |
These are average values. The same kind of bond differs a little from molecule to molecule (C=O is 799 kJ/mol in CO₂, 745 on average), which is good enough for estimates. The Thermochemistry section uses them to estimate the heat of reactions.
Often more than one structure obeys the octet rule. For carbon dioxide, O≡C–O (a triple and a single bond) also gives every atom eight electrons. To choose, chemists compute a formal charge for each atom: the charge it would have if every bond were shared perfectly evenly, one electron to each partner.
The formal charges always add up to the charge of the molecule or ion. The best structure is usually the one whose formal charges are as close to zero as possible, and, if a negative formal charge is needed, the one that puts it on the most electronegative atom. In O=C=O every formal charge is zero. In O≡C–O the triple-bonded oxygen has 6 − 2 − 3 = +1 and the single-bonded one 6 − 6 − 1 = −1, so O=C=O wins, and indeed both C–O distances in CO₂ are equal (116 pm).
Practise with the builder. Each molecule's skeleton is fixed; you choose the bonds and the lone pairs, and the panel checks the count, the octets and the formal charges for you.
The recipe: (1) count the valence electrons, adding one per negative charge; (2) connect the atoms with single bonds; (3) give the outer atoms lone pairs until each has its octet (hydrogen: 2); (4) put any electrons left on the central atom; (5) if the central atom is still short, turn a lone pair of a neighbour into a second bond. The count on the right must match exactly, every ring must turn green, and among the structures that do, the best has the smallest formal charges. Try CO: the only way to give both atoms an octet is a triple bond, with a formal −1 on carbon and +1 on oxygen. Try BF₃: boron is happier with six electrons than with a double bond to fluorine. And O₃ or NO₃⁻: there is more than one best answer.
Ozone, O₃, has two equally good Lewis structures: O=O–O and O–O=O. Neither is right on its own. If either were, ozone would have one short double bond (121 pm, like O₂) and one long single bond (148 pm, like hydrogen peroxide). Measured, both bonds are 128 pm: the real molecule is a single, fixed structure in between, with one and a half bonds on each side. Lewis structures cannot draw that, so chemists draw all the equivalent structures with double-headed arrows between them and call them resonance structures. The real molecule is their average, the resonance hybrid.
| Species | Resonance structures | Bond order of each bond | Measured |
|---|---|---|---|
| O₃ | 2 | 1½ | both O–O 128 pm |
| NO₃⁻ | 3 | 1⅓ | all three N–O 125 pm |
| CO₃²⁻ | 3 | 1⅓ | all three C–O 129 pm |
| benzene, C₆H₆ | 2 | 1½ | all six C–C 140 pm, between 154 and 134 |
| Case | Examples | What happens |
|---|---|---|
| odd number of electrons | NO, NO₂, ClO₂ | with an odd total, some atom must have an unpaired electron; such molecules (radicals) are usually very reactive |
| fewer than eight | BF₃, BeCl₂ (gas) | boron and beryllium have too few valence electrons; BF₃ keeps 6 around boron, which makes it eager to accept a lone pair from another molecule |
| more than eight | PCl₅, SF₆, XeF₄ | atoms of period 3 and below are large enough to fit five or six neighbours around them; their Lewis structures show 10 or 12 electrons |
The third case is often explained by saying the central atom uses its empty d orbitals. Modern calculations show the d orbitals play almost no part: what matters is that a big atom has room for more neighbours, with the bonding electrons spread over several atoms. The 10- and 12-electron Lewis structures remain a useful way to count, as long as they are not taken literally. The other famous failure is oxygen: its Lewis structure O=O has every electron paired, but liquid oxygen sticks to a magnet, which takes unpaired electrons. Molecular orbitals, in the next section, get it right.
Two identical atoms share their pair exactly evenly. Two different atoms do not: the more electronegative one (the Periodic Trends chapter) pulls the pair toward itself. In H–Cl the pair spends more time near chlorine, which gets a small negative charge, written δ− (delta minus, a fraction of an electron's charge), while hydrogen gets δ+. Such a bond is polar covalent, and it has a bond dipole: two opposite charges a small distance apart. The bigger the electronegativity difference Δχ, the more polar the bond, until at a large difference the pair practically belongs to one atom and the bond is ionic.
Pick any two atoms. The blue cloud is the bonding pair. With equal electronegativities (H–H, Cl–Cl) it sits in the middle. As the difference Δχ grows, the more electronegative atom pulls the pair closer: it gets a partial negative charge δ−, its partner δ+, and the bond has a dipole, drawn as an arrow with a crossed tail pointing to the negative end. Pauling estimated the ionic character as 1 − e^(−Δχ²/4): 3% for C–H, 21% for H–Cl, 55% for H–F, 71% for NaCl. There is no sharp border: the 0.4 and 1.8 marks are conventions, and every bond is somewhere on one continuous scale.
So ionic and covalent bonds are two ends of one scale, not two separate worlds. A common rule of thumb calls a bond nonpolar below Δχ = 0.4, polar between 0.4 and about 1.8, and ionic above. Even sodium chloride, at 2.23, is not 100% ionic, and the polar bonds in water (Δχ = 1.24) are what make water such a good solvent. Whether a whole molecule ends up polar depends also on its shape: the subject of the next chapter.
1. Ammonia, NH₃: 5 + 3 × 1 = 8 electrons. Three N–H bonds use 6; the last 2 form a lone pair on nitrogen. Nitrogen: 6 + 2 = 8 electrons; every formal charge is zero.
2. Hydrogen cyanide, HCN: 1 + 4 + 5 = 10 electrons. H–C–N uses 4; nitrogen takes three lone pairs (6), leaving carbon with only 4. Moving two of nitrogen's pairs into bonds gives H–C≡N with one lone pair on nitrogen: all formal charges zero.
3. Formal charges in the ammonium ion, NH₄⁺: nitrogen has 4 bonds and no lone pair, FC = 5 − 0 − 4 = +1; each hydrogen 1 − 0 − 1 = 0. The total is +1, the charge of the ion.
4. The cyanate ion OCN⁻ has two structures with a total formal charge of size 1: [O=C=N]⁻ with −1 on nitrogen and [O–C≡N]⁻ with −1 on oxygen. Oxygen is more electronegative, so the second is the better description.
5. Rank by polarity: C–H (Δχ 0.35), N–H (0.84), O–H (1.24), F–H (1.78). The order is the order of the electronegativity of the partner of hydrogen.
| Wrong | Right | Why |
|---|---|---|
| forgetting the ion's charge in the count | add one electron per negative charge | NO₃⁻ has 24 electrons, not 23 |
| hydrogen in the middle | hydrogen is always on the outside | it can only make one bond |
| a double bond is twice as strong as a single | it is stronger, but less than twice | C–C 347, C=C 614 kJ/mol |
| resonance structures interconvert quickly | the molecule is one hybrid, always | all bonds in O₃ measure the same, 128 pm |
| formal charge is the real charge | it is a bookkeeping device | real charges depend on electronegativity, as in CO |
Key ideas
- A covalent bond is a shared electron pair attracted by both nuclei; the energy minimum gives the bond length and the bond energy.
- Lewis structures: count valence electrons (adjusting for charge), single bonds first, complete outer octets, leftovers to the centre, then multiple bonds.
- Higher bond order means a shorter, stronger bond, but not proportionally stronger.
- Formal charge FC = V − L − B/2; the best structure has formal charges closest to zero, negative ones on electronegative atoms.
- Resonance: when several structures are equally good, the real molecule is a fixed hybrid with averaged bonds.
- Odd-electron molecules, boron and beryllium, and large atoms of period 3 and below break the octet rule.
- The electronegativity difference sets bond polarity: nonpolar, polar covalent or ionic, one continuous scale.