1The idea in one paragraph

When two non-metal atoms meet, neither can take an electron from the other, so they share. A covalent bond is a pair of electrons held between two nuclei and attracted to both. Count the pairs round each atom and you have a Lewis formula. Let those pairs push each other as far apart as they can and you have the molecule's shape. Combine the shape with the unequal pull of different atoms on the pairs and you know whether the molecule is polar. That decides which intermolecular forces act between molecules, and those weak forces, not the strong bonds inside, decide how easily a molecular substance melts, boils and dissolves. A few substances, such as diamond, never form separate molecules at all: they are covalent networks, and they behave nothing like molecular substances.

2The covalent bond and the octet rule

A covalent bond is the electrostatic attraction between a shared pair of electrons and the positively charged nuclei of the two bonded atoms.

Figure 1 shows why that holds two atoms together. The pair sits between the nuclei and each nucleus is attracted to it, so the atoms cannot separate without pulling a nucleus away from a pair it is attracted to.

Each chlorine atom in Figure 1(b) has seven outer electrons; by sharing one each, both reach eight. The octet rule describes that tendency: atoms tend to gain, lose or share electrons until they have eight in their valence shell, a noble gas configuration. Hydrogen's shell holds two.

Covalent bonding, unlike ionic bonding, can join atoms of the same element, because it needs no giver and taker. It is typical between non-metals. Noble gases rarely form covalent bonds because their valence shells are already full.

3Lewis formulas

A Lewis formula shows every valence electron: bonding pairs, usually as lines, and non-bonding pairs (lone pairs), as dots, crosses or lines. Five steps work every time.

1. Count the valence electrons. For a negative ion add one per charge; for a positive ion take one away.
2. Draw the skeleton. The atom forming most bonds goes in the middle (never hydrogen). Join each outer atom to it with a single bond.
3. Complete the outer atoms' octets with lone pairs.
4. Put leftover electrons on the central atom as lone pairs.
5. If the central atom is still short of eight, turn a lone pair on an outer atom into another shared pair.

Carbon dioxide: 4 + 6 + 6 = 16 electrons, 8 pairs. O–C–O uses 2 pairs; completing both oxygens uses 6, so carbon is left with only 4 electrons. Move one lone pair from each oxygen into the bonds: O=C=O, and every atom has 8. Figure 2 shows this and seven more.

Always check the total. Hydroxide has 6 + 1 + 1 = 8 valence electrons: one bond and three lone pairs, in square brackets with the charge outside.

Not every molecule obeys the octet rule. Boron in BF₃ has three valence electrons, forms three bonds and stops at six; beryllium in BeCl₂ stops at four. These incomplete octets are real, stable molecules and you must be able to draw them. Molecules with an odd number of electrons, such as NO, cannot give every atom eight, and atoms from period 3 down can hold more than eight (section 15, HL). The octet rule is a useful model for period 2 and a poor law.

4Single, double and triple bonds

A single bond is one shared pair, a double bond two, a triple bond three. More pairs between the same two nuclei means more negative charge between them, so the nuclei are attracted more strongly and pulled closer. Bond strength is measured by bond enthalpy, the energy to break one mole of the bond in the gas state (data booklet). Figure 3 shows the pattern.

More shared pairs: a shorter bond, and a stronger bond.

A double bond is not twice as strong as a single one: a clue that its two pairs are different, which HL section 17 explains.

5Coordination bonds

In a coordination bond both electrons of the shared pair come from the same atom. It needs a lone pair on one atom and room on the other. Figure 4 shows the standard cases.

H⁺ has no electrons, and ammonia's nitrogen has a lone pair, which becomes the shared pair of a new N–H bond: the ammonium ion, NH₄⁺. Water accepting H⁺ to make H₃O⁺ is the same. In carbon monoxide, oxygen supplies both electrons of the third bond. The bond is drawn as an arrow pointing away from the atom that supplied the pair. Once formed it is an ordinary covalent bond: all four N–H bonds in NH₄⁺ are identical.

6VSEPR: predicting the shape

The valence shell electron pair repulsion (VSEPR) model predicts shape from one principle: the groups of electrons round a central atom repel each other and get as far apart as possible.

Each group is an electron domain. A lone pair is one domain, a single bond is one, and a double or triple bond is also one, because all its electrons lie between the same two atoms. So carbon in CO₂ has two domains.

Draw the Lewis formula; count the domains round the central atom, which gives the electron domain geometry; then look only at where the atoms are, which gives the molecular geometry, the shape you name.

Lone pairs close the angle. A lone pair is held by one nucleus only, so it sits closer to that atom and spreads wider than a bonding pair, and repels more: lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair. In ammonia one lone pair squeezes the N–H bonds from 109.5° to about 107°; in water two squeeze to about 104.5°. Both still have four domains, a tetrahedral electron domain geometry; only the molecular geometry differs.

Multiple bonds do the same, a little. A double bond puts four electrons in one domain and repels more than a single bond. In methanal, H₂C=O, the C=O domain pushes the C–H bonds together, so H–C–H is slightly less than 120°, about 116°.

How useful is VSEPR? Very, for a model this simple: it gets almost every shape right and every angle change in the right direction. It does not give exact angles (it cannot say why H₂S is about 92° while H₂O is 104.5°), and it says nothing about why the pairs form. It is a model of repulsion, not a theory of bonding.

7Polar bonds and polar molecules

Electronegativity is the ability of an atom to attract a shared pair towards itself. Data booklet values include F 4.0, O 3.4, Cl 3.2, N 3.0, C 2.6 and H 2.2. When bonded atoms differ, the pair is pulled towards the more electronegative one, which carries a small negative charge, δ−, leaving the other δ+. The bond is a polar covalent bond with a bond dipole, and the larger the difference, Δχ, the more polar it is.

A bond dipole is shown with δ+ and δ−, or with a dipole arrow pointing from δ+ to δ− with a cross stroke at the δ+ end.

A molecule can have polar bonds and still be non-polar. Bond dipoles have direction, and a molecule has a net dipole moment only if they do not cancel. Figure 6 shows the four cases to learn.

Linear CO₂: two equal dipoles in opposite directions cancel, so it is non-polar. Bent H₂O: both dipoles point partly the same way and add, so it is polar. Tetrahedral CCl₄ cancels; CHCl₃, with one bond different, does not. BF₃ is non-polar and NH₃ polar for the same reasons. Ions work the same way: the three N–O dipoles in nitrate cancel by symmetry. Ask two questions in order: are there polar bonds, and if so, does the shape cancel them?

8Covalent network structures

Carbon and silicon form four covalent bonds and can keep doing so in every direction. A covalent network structure has no separate molecules: the whole crystal is held by covalent bonds. Carbon's allotropes, different structural forms of one element, have different bonding patterns and so different properties. Figure 7 shows them with silicon and silicon dioxide.

SiO₂ looks like CO₂ on paper, but CO₂ is a gas of small molecules and SiO₂ a mineral. Its formula is only the 1 : 2 ratio in a network, like an ionic empirical formula.

9Intermolecular forces

The bonds inside a molecule are strong. The forces between molecules, intermolecular forces, are much weaker, and they are what you overcome when a molecular substance melts or boils: steam is still H₂O. Keep the words apart. A bond holds atoms together within a molecule or network; the forces here act between separate molecules.

London (dispersion) forces act between all molecules. Moving electrons make a molecule's cloud momentarily uneven, an instantaneous dipole, which distorts a neighbour's cloud into an induced dipole, and the two attract. More electrons make a more easily distorted cloud, so London forces grow with size. Shape matters too: pentane (36 °C) boils above its compact isomer 2,2-dimethylpropane (about 10 °C), because long molecules touch over more surface.

Dipole–induced dipole forces act when a polar molecule meets a non-polar one and distorts its cloud: mainly in mixtures.

Dipole–dipole forces act between polar molecules: the δ+ end of one attracts the δ− end of the next.

Hydrogen bonding occurs when hydrogen, covalently bonded to N, O or F, is attracted to a lone pair on an N, O or F atom of a neighbouring molecule (Figure 9). The bond to H is so polar that the hydrogen is left almost a bare proton, and the lone pair can approach it closely. IUPAC revised its definition of the hydrogen bond in 2011, as better instruments revealed a wider family of these interactions: definitions change when science can see more.

Van der Waals forces is the umbrella term for London, dipole–induced dipole and dipole–dipole forces. Figure 8 is the decision you make in an exam.

The condition catches students both ways. Methane has H, but on carbon: no hydrogen bonding. Methoxymethane, CH₃OCH₃, has O with lone pairs but no H on it, so its molecules cannot hydrogen bond with each other.

10Comparing forces, and the properties of covalent substances

For molecules of comparable molar mass:

London forces < dipole–dipole forces < hydrogen bonding

The condition matters. Iodine, I₂, with 106 electrons and London forces only, is a solid at room temperature, while water, with 10 electrons, is a liquid. Compare types of force only between molecules of similar size, and size only between molecules with the same type of force. Figure 10 does each.

In (a) the molar masses are 44 to 46 g mol⁻¹, so London forces are similar. Methoxymethane adds dipole–dipole forces and boils 18 °C above propane; ethanol adds hydrogen bonding and boils over 100 °C above methoxymethane. In (b) the alkanes are all non-polar, and the steady rise is London forces growing with the number of electrons.

Volatility. Simple molecular substances have low melting and boiling points, because only weak intermolecular forces are overcome. Network substances have very high ones, because covalent bonds must break.

Electrical conductivity. Almost all covalent substances are non-conductors in every state: no ions and no mobile delocalized electrons. Graphite and graphene are the exceptions. A few polar molecules react with water to form ions: HCl gas does not conduct, hydrochloric acid does.

Solubility. "Like dissolves like": a substance dissolves when it can form attractions with the solvent comparable to those it breaks. Small molecules that hydrogen bond, such as ethanol, glucose and ammonia, dissolve in water. Non-polar substances, such as iodine, hexane and oils, dissolve in non-polar solvents but barely in water, since they cannot replace the hydrogen bonds they would break between water molecules. Along the alcohols, solubility in water falls as the non-polar chain grows. Network structures dissolve in nothing.

11Chromatography

Chromatography separates a mixture using a stationary phase that stays put and a mobile phase that moves. Each component is attracted to both through intermolecular forces, and the balance decides how far it travels. In paper chromatography the stationary phase is water held in the cellulose fibres; in thin-layer chromatography (TLC) it is a thin layer of silica or alumina. Both are polar. The mobile phase is the solvent.

The mixture is spotted on a pencil baseline (ink would itself separate), the plate stands in solvent below the baseline, and the solvent rises until it is stopped and its solvent front marked. A component attracted more to the mobile phase than the stationary phase travels further; with a polar stationary phase, less polar components usually travel further.

RF = distance travelled by the component ÷ distance travelled by the solvent front

Both distances are measured from the baseline, the first to the centre of the spot. RF has no units and lies between 0 and 1 (Figure 11).

A component is identified by matching its RF with a known substance run under the same conditions: same stationary phase, solvent and temperature. Two substances can share an RF in one solvent, so a match is evidence, not proof; a second solvent strengthens it.