S2.2 The covalent model

Most of the substances around us, from the gases of the air and the water in the oceans to plastics, medicines and DNA, are made of atoms joined by covalent bonds. The covalent model explains how atoms share electrons, why molecules have particular shapes and polarities, and why some covalent substances are gases at room temperature while others, such as diamond, are among the hardest materials known.

Covalent bonds and the octet rule

Atoms of non-metals have high ionization energies and high electronegativities. When two such atoms meet, neither can remove an electron from the other, so instead they share electrons. Each atom contributes one electron to a pair that sits between the two nuclei, and both nuclei attract that pair.

The attraction acts in both directions at once: the negative pair is pulled towards each positive nucleus, so it holds the two nuclei together. The covalent bond in a hydrogen molecule is the simplest case, with one pair of electrons shared between two protons.

Because the bond involves sharing rather than transfer, covalent bonds form between atoms of the same element, as in ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}}}$, ${{\mathrm{Cl}{\vphantom{X}}_{\smash[t]{2}}}}$ and ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$. An ionic bond needs one atom to lose electrons and another to gain them, which happens only between elements with very different electronegativities. Identical atoms have identical electronegativities, so they can only share.

Covalent bonding typically occurs between non-metal atoms. Water, carbon dioxide, ammonia, methane and hydrogen chloride are all covalent: every bond joins two non-metal atoms. The same model also describes the bonds inside polyatomic ions such as ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{4}}{\vphantom{X}}^{+}}}$, ${{\mathrm{OH}{\vphantom{X}}^{-}}}$ and ${{\mathrm{SO}{\vphantom{X}}_{\smash[t]{4}}{\vphantom{X}}^{2-}}}$.

The octet rule

The electrons in the outermost occupied energy level, the valence electrons, are the ones that take part in bonding. For the main-group elements their number follows from the group number: one for group 1, two for group 2, and three to eight for groups 13 to 18.

An octet matches the electron configuration of a noble gas. A chlorine atom has seven valence electrons; by sharing one pair with another chlorine atom, each atom counts eight electrons around itself (six in its own lone pairs and two in the shared pair). Both electrons of a shared pair count towards the octet of each atom in the bond.

The octet rule also explains why the noble gases form so few compounds. Their atoms already have a full valence shell and very high first ionization energies, so they gain nothing by sharing electrons. Helium, neon and argon form no stable compounds at all. The heavier noble gases, with outer electrons further from the nucleus, can bond to very electronegative atoms: xenon forms fluorides such as ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{2}}}}$ and ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{4}}}}$.

Limitations of the octet rule

The octet rule is a model: it predicts the formulas of most compounds of carbon, nitrogen, oxygen and the halogens, but several kinds of molecule break it.

• Incomplete octets. Beryllium, boron and aluminium have only two or three valence electrons to share. In ${{\mathrm{BeCl}{\vphantom{X}}_{\smash[t]{2}}}}$ the beryllium atom has four electrons around it, and in ${{\mathrm{BF}{\vphantom{X}}_{\smash[t]{3}}}}$, ${{\mathrm{BCl}{\vphantom{X}}_{\smash[t]{3}}}}$ and ${{\mathrm{AlCl}{\vphantom{X}}_{\smash[t]{3}}}}$ the central atom has six. Such molecules are electron-deficient and react readily with species that can donate a pair of electrons.

• Odd numbers of electrons. Nitrogen monoxide, ${{\mathrm{NO}}}$ (11 valence electrons), and nitrogen dioxide, ${{\mathrm{NO}{\vphantom{X}}_{\smash[t]{2}}}}$ (17), cannot give every atom an octet, because an odd number of electrons cannot all be paired. Species with an unpaired electron are called radicals and are usually very reactive.

• Expanded octets. Atoms of period 3 and beyond, such as phosphorus and sulfur, can have more than eight electrons around them, as in ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{5}}}}$ and ${{\mathrm{SF}{\vphantom{X}}_{\smash[t]{6}}}}$

Lewis formulas

A Lewis formula (also called a Lewis structure or electron-dot structure) is a map of where the valence electrons are. A bonding pair is shared between two atoms; a lone pair belongs to one atom only and takes no part in a bond. Any combination of dots, crosses and lines is acceptable, provided every electron is shown: a line counts as two electrons. Ions are drawn inside square brackets with the charge at the top right.

Drawing a Lewis formula step by step

1. Count the valence electrons of all the atoms. For an anion add one electron per negative charge; for a cation subtract one per positive charge. Divide by two to get the number of electron pairs to place.

2. Choose the central atom. It is usually the atom that forms the most bonds, which is usually the least electronegative atom other than hydrogen. Hydrogen forms only one bond, so it is never central. In oxyacids such as ${{\mathrm{HNO}{\vphantom{X}}_{\smash[t]{3}}}}$ and ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{SO}{\vphantom{X}}_{\smash[t]{4}}}}$ the hydrogen atoms are bonded to oxygen, not to the central atom.

3. Join each outer atom to the central atom with a single bond (one pair).

4. Complete the octets of the outer atoms with lone pairs (hydrogen needs none).

5. Place any remaining pairs on the central atom as lone pairs.

6. Check the central atom. If it has fewer than eight electrons, move a lone pair from an outer atom into a second bond to make a double bond, and repeat if needed (a triple bond). Atoms such as B and Be are left with an incomplete octet instead.

7. Check the total: the number of electrons drawn must equal the count from step 1, and an ion needs brackets and its charge.

The Lewis formulas of simple molecules with single bonds show the common patterns. Every atom other than hydrogen has eight electrons around it: halogen atoms with one bond carry three lone pairs, oxygen with two bonds carries two, nitrogen with three bonds carries one, and carbon with four bonds carries none.

Double and triple bonds appear wherever single bonds would leave an atom short of an octet. In ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$ each oxygen atom shares two pairs; in ${{\mathrm{N}{\vphantom{X}}_{\smash[t]{2}}}}$ each nitrogen shares three. Carbon dioxide has two ${{\mathrm{C}{=}\mathrm{O}}}$ double bonds, so carbon has its octet from four shared pairs and each oxygen keeps two lone pairs.

Central atoms with lone pairs

Elements of the same group form the same number of bonds, so their compounds have Lewis formulas of the same pattern. Sulfur, in group 16 like oxygen, forms two bonds and keeps two lone pairs in ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{S}}}$ and ${{\mathrm{SCl}{\vphantom{X}}_{\smash[t]{2}}}}$; oxygen does the same in ${{\mathrm{OF}{\vphantom{X}}_{\smash[t]{2}}}}$. Phosphorus, in group 15 like nitrogen, forms three bonds and keeps one lone pair in ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{3}}}}$, as nitrogen does in ${{\mathrm{NF}{\vphantom{X}}_{\smash[t]{3}}}}$ and ${{\mathrm{NCl}{\vphantom{X}}_{\smash[t]{3}}}}$. The lone pairs on the central atom are the ones most often left out, and they decide the shape of each molecule.

Each halogen atom in these molecules forms one bond and carries three lone pairs, so a molecule such as ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{3}}}}$ has ten lone pairs in all: one on phosphorus and nine on the chlorine atoms. Counting confirms it: $5 + 3(7) = 26$ valence electrons, or 13 pairs, of which 3 are bonding pairs.

Tetrachloromethane, ethane, carbon monoxide and white phosphorus complete the set of small molecules whose Lewis formulas are most often asked for. In carbon monoxide each atom has one lone pair and the two atoms share three pairs, as in ${{\mathrm{N}{\vphantom{X}}_{\smash[t]{2}}}}$, with which ${{\mathrm{CO}}}$ is isoelectronic.

Organic and inorganic molecules

The same rules apply to larger molecules, where each atom in turn can be treated as a centre. In organic molecules carbon forms four bonds, hydrogen one, oxygen two (with two lone pairs) and nitrogen three (with one lone pair). In ethanoic acid one oxygen atom is joined to carbon by a double bond and the other by single bonds to both C and H; each oxygen keeps two lone pairs.

Lewis formulas of ions

For an ion, the charge changes the electron count. The ammonium ion, ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{4}}{\vphantom{X}}^{+}}}$, has $5 + 4(1) - 1 = 8$ electrons, or four bonding pairs and no lone pairs. The hydroxide ion, ${{\mathrm{OH}{\vphantom{X}}^{-}}}$, has $6 + 1 + 1 = 8$ electrons: one bonding pair and three lone pairs on oxygen. The whole structure is placed in square brackets with the charge outside, because the charge belongs to the ion as a whole.

The double bond in the nitrate and carbonate ions could equally be drawn to any of the three oxygen atoms. Measured bond lengths show that all three bonds in each ion are in fact the same length; resonance, an HL idea, explains this.

Single, double and triple bonds

A single bond is one shared pair of electrons, a double bond two shared pairs and a triple bond three. The number of shared pairs between two atoms affects how far apart the nuclei sit and how much energy is needed to separate them.

More shared pairs put more electron density between the two nuclei. Both nuclei are attracted to this larger negative charge, so they are pulled closer together and held more tightly. A triple bond is therefore shorter and stronger than a double bond, which is shorter and stronger than a single bond between the same two atoms. The data booklet values for bonds between carbon, nitrogen and oxygen follow this pattern in every series.

Data: IB Chemistry data booklet (2025), sections 11 (lengths) and 12 (enthalpies). ${{\mathrm{C}{\equiv}\mathrm{O}}}$ is the bond in carbon monoxide.

The strength of the triple bond in nitrogen, $945\ \text{kJ mol}^{-1}$, makes ${{\mathrm{N}{\vphantom{X}}_{\smash[t]{2}}}}$ very unreactive, even though it makes up about 78% of the air. Breaking it needs a great deal of energy, which is why nitrogen is used as an inert atmosphere for packaging food and why converting it into ammonia or nitrates needs high temperatures, catalysts or lightning. In contrast, the ${{\mathrm{O}{-}\mathrm{O}}}$ single bond in hydrogen peroxide ($144\ \text{kJ mol}^{-1}$) breaks easily, and hydrogen peroxide decomposes slowly even at room temperature.

Exceptions and reactivity

A shorter bond is usually stronger, but not always. The ${{\mathrm{F}{-}\mathrm{F}}}$ bond is short (142 pm) yet weak ($159\ \text{kJ mol}^{-1}$), weaker than ${{\mathrm{Cl}{-}\mathrm{Cl}}}$ (199 pm, $242\ \text{kJ mol}^{-1}$). Fluorine atoms are so small that the lone pairs on the two atoms are close together and repel each other, which weakens the bond.

A double bond is stronger than a single bond, yet alkenes react much more readily than alkanes. The bond enthalpy of ${{\mathrm{C}{=}\mathrm{C}}}$ ($614\ \text{kJ mol}^{-1}$) is less than twice that of ${{\mathrm{C}{-}\mathrm{C}}}$ ($346\ \text{kJ mol}^{-1}$), so the second pair of a double bond is held less strongly than the first, and its electrons are more exposed. Reactions of alkenes break only this second part of the double bond. (The two parts of a double bond are the sigma and pi bonds of HL.)

Coordination bonds

In most covalent bonds each atom supplies one electron of the shared pair. In a coordination bond (also called a dative covalent bond) one atom supplies both. The donor atom must have a lone pair, and the acceptor must have an empty orbital in its valence shell that can take the pair.

The ammonium ion forms when ammonia meets a hydrogen ion. The ${{\mathrm{H}{\vphantom{X}}^{+}}}$ ion has no electrons at all, and the nitrogen atom of ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}}}$ has a lone pair. The lone pair becomes the shared pair of a new N–H bond:

A coordination bond can be shown in a structure as an arrow pointing from the donor atom to the acceptor atom. The hydronium ion forms in the same way when a water molecule uses one of its lone pairs to bond to ${{\mathrm{H}{\vphantom{X}}^{+}}}$: ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O} {}+{} \mathrm{H}{\vphantom{X}}^{+}\xrightarrow{}\mathrm{H}{\vphantom{X}}_{\smash[t]{3}}\mathrm{O}{\vphantom{X}}^{+}}}$. Any acid dissolved in water forms hydronium ions by this reaction.

Once it has formed, a coordination bond is identical to any other covalent bond between the same two atoms. All four N–H bonds in ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{4}}{\vphantom{X}}^{+}}}$ have the same length and strength, and there is no way to tell which one was formed by coordination. The arrow describes how the bond formed, not a different kind of bond.

Identifying coordination bonds

A coordination bond is present wherever an atom has more bonds than its usual number and its bonding partner has fewer than its usual share of electrons. Common examples:

• ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{4}}{\vphantom{X}}^{+}}}$ and ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{3}}\mathrm{O}{\vphantom{X}}^{+}}}$: nitrogen with four bonds and oxygen with three, each having donated a lone pair to ${{\mathrm{H}{\vphantom{X}}^{+}}}$.

• Carbon monoxide, ${{\mathrm{C}{\equiv}\mathrm{O}}}$: carbon brings 4 valence electrons and oxygen 6. To give both atoms an octet, the two atoms share three pairs, of which two pairs come one electron from each atom and the third comes entirely from oxygen.

• Adducts of electron-deficient molecules: the boron atom of ${{\mathrm{BF}{\vphantom{X}}_{\smash[t]{3}}}}$ has an empty orbital and accepts the lone pair of ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}}}$

• Octet Lewis formulas of ozone, nitric acid and the nitrate ion: in ozone, ${{\mathrm{O}{=}\mathrm{O}{-}\mathrm{O}}}$, the central oxygen atom uses two of its six valence electrons in the double bond and keeps two as a lone pair; the last two form the single bond to the third oxygen atom, which supplies none. In nitric acid, ${{\mathrm{HNO}{\vphantom{X}}_{\smash[t]{3}}}}$, nitrogen uses one electron in the bond to the OH group and two in the ${{\mathrm{N}{=}\mathrm{O}}}$

Metal ions in solution also form coordination bonds, with water molecules, ammonia molecules or anions donating lone pairs to the metal ion. These complex ions of the transition elements are studied at HL, where reactions that form coordination bonds are also described as Lewis acid–base reactions.

Predicting the shape of a molecule: the VSEPR model

Molecules have definite three-dimensional shapes, measured by techniques such as X-ray crystallography and spectroscopy. The shape decides whether a molecule is polar, how it packs and how it reacts. The valence shell electron pair repulsion (VSEPR) model predicts the shape from the Lewis formula.

The VSEPR model rests on one idea: electron domains around a central atom all contain negative charge, so they repel each other and take up positions as far apart as possible. The number of domains fixes their arrangement in space.

• Two domains point in opposite directions: linear, $180^\circ$ apart.

• Three domains point to the corners of an equilateral triangle in one plane: trigonal planar, $120^\circ$ apart.

• Four domains point to the corners of a tetrahedron: tetrahedral, $109.5^\circ$ apart.

A multiple bond counts as one domain because all its electrons lie between the same two atoms and point in the same direction. In ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ the carbon atom has two double bonds, so two domains, and the molecule is linear.

Electron domain geometry and molecular geometry

When every domain is a bond, the two geometries are the same. When some domains are lone pairs, the molecular geometry describes only the positions of the atoms. Ammonia has four domains around nitrogen (three bonds and one lone pair), so its electron domain geometry is tetrahedral, but its atoms form a pyramid with N at the top: its molecular geometry is trigonal pyramidal. Water has four domains (two bonds and two lone pairs) and a bent molecular geometry.

How lone pairs and multiple bonds change bond angles

A lone pair is held by only one nucleus, so its electron density sits closer to the central atom and spreads out more widely than a bonding pair, which is pulled out between two nuclei. Lone pairs therefore repel more strongly than bonding pairs. The order of repulsion is:

Each lone pair pushes the bonding pairs closer together and reduces the bond angle between them by roughly $2$ to $3^\circ$. Methane (no lone pairs) has H–C–H angles of $109.5^\circ$, ammonia (one lone pair) $107^\circ$ and water (two lone pairs) $104.5^\circ$, even though all three have four electron domains.

Multiple bonds have a similar effect. A double bond contains four electrons in one domain, so it repels the neighbouring domains more than a single bond does. In methanal, ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{C}{=}\mathrm{O}}}$, the three domains around carbon are not equal: the H–C–O angles open to about $122^\circ$ and the H–C–H angle closes to about $116^\circ$, compared with the perfect $120^\circ$ of ${{\mathrm{BF}{\vphantom{X}}_{\smash[t]{3}}}}$.

Explaining a shape

An explanation of a molecular shape follows the same chain each time: the Lewis formula, the number of electron domains and how many of them are lone pairs, repulsion to maximum separation, the electron domain geometry, then the molecular geometry and bond angle. The name of the shape alone is not an explanation.

In larger molecules, each atom with two or more neighbours is a centre with its own geometry. In ethanoic acid, ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{3}}\mathrm{COOH}}}$, the carbon of the ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{3}}}}$ group has four domains (tetrahedral, $109.5^\circ$); the carbon of the ${{\mathrm{COOH}}}$ group has three domains, one of them a double bond (trigonal planar, about $120^\circ$); and the oxygen of the O–H group has four domains, two of them lone pairs (bent, about $104.5^\circ$). In methylamine, ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{3}}\mathrm{NH}{\vphantom{X}}_{\smash[t]{2}}}}$, the nitrogen atom has three bonds and a lone pair, so the geometry around N is trigonal pyramidal.

How good is the VSEPR model?

The VSEPR model predicts the shapes of most molecules of the main-group elements correctly, using nothing more than a Lewis formula, and it explains the order of bond angles in series such as ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{4}}}}$, ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}}}$ and ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$. Molecular model kits and computer modelling programs build the same shapes, and measured structures confirm them.

It is still a model with limits. Its bond angles are approximate: the measured H–S–H angle in ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{S}}}$ is about $92^\circ$, and the H–P–H angle in ${{\mathrm{PH}{\vphantom{X}}_{\smash[t]{3}}}}$ about $93^\circ$, far below the $104.5^\circ$ and $107^\circ$ suggested by comparison with water and ammonia. VSEPR treats electron domains as simple charged clouds and says nothing about why bonds form or how strong they are; the orbital models of HL (hybridization and sigma and pi bonds) describe the bonding itself. It also works poorly for many compounds of the transition elements.

Bond polarity and electronegativity

When two identical atoms share a pair of electrons, the pair is shared equally. When the atoms are different, the atom with the greater attraction for electrons pulls the shared pair towards itself.

Electronegativity increases across a period and decreases down a group; fluorine (4.0) is the most electronegative element, followed by oxygen (3.4), then chlorine (3.2) and nitrogen (3.0). These trends are explained by nuclear charge and atomic radius in the periodic table. The values in the table are those of the data booklet.

Data: Pauling electronegativities, IB Chemistry data booklet (2025), section 9.

Polar and non-polar bonds

The difference in electronegativity, $\Delta\chi$, between two bonded atoms decides how unequally the pair is shared. If $\Delta\chi = 0$, as in ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}}}$ or ${{\mathrm{Cl}{\vphantom{X}}_{\smash[t]{2}}}}$, the bond is a non-polar covalent bond. If the atoms differ, the electron density is pulled towards the more electronegative atom, which gains a small negative charge, written $\delta-$ ("delta negative"), while the other atom is left with a small positive charge, $\delta+$. Such a bond is a polar covalent bond, and the separation of charge is a bond dipole.

Bond dipoles are shown either with partial charges or with a vector arrow along the bond that points towards the $\delta-$ end, with a short cross-line at the $\delta+$ end. In hydrogen chloride, chlorine (3.2) is more electronegative than hydrogen (2.2), so the bond is polar with $\delta-$ on Cl.

The larger the electronegativity difference, the more polar the bond. Polarity forms a continuum: at one end are non-polar bonds between identical atoms, in the middle polar covalent bonds, and at the far end ionic bonding, where the difference is so large (sodium chloride, $\Delta\chi = 2.3$) that the electron is effectively transferred. The bonding triangle places compounds along this continuum using electronegativity values.

Compounds with very polar covalent bonds share some properties with ionic compounds. Hydrogen chloride is a covalent gas, but its strongly polar molecules dissolve in water and break up into ions, so the solution conducts electricity. Polar molecules also dissolve better in polar solvents such as water than non-polar ones do.

Molecular polarity

A molecule with polar bonds is not necessarily polar itself. Each bond dipole has a size and a direction, so the dipoles add up like vectors. If they cancel, the molecule has no net dipole and is non-polar; if they do not cancel, the molecule has a net dipole and is polar.

Whether bond dipoles cancel depends on the molecular geometry. In carbon dioxide the two ${{\mathrm{C}{=}\mathrm{O}}}$ bonds are polar, but they point in exactly opposite directions, so their effects cancel and ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ is a non-polar molecule. In water the two O–H dipoles point partly in the same direction because the molecule is bent, so they reinforce each other and water is a polar molecule.

Polar bonds cancel only when they are identical and arranged symmetrically around the central atom with no lone pairs: linear ${{\mathrm{AB}{\vphantom{X}}_{\smash[t]{2}}}}$, trigonal planar ${{\mathrm{AB}{\vphantom{X}}_{\smash[t]{3}}}}$ and tetrahedral ${{\mathrm{AB}{\vphantom{X}}_{\smash[t]{4}}}}$ molecules. Two things break the symmetry:

• Lone pairs on the central atom, which make the shape bent or pyramidal (${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$, ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}}}$, ${{\mathrm{SO}{\vphantom{X}}_{\smash[t]{2}}}}$, ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{3}}}}$, ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{2}}\mathrm{Cl}}}$).

• Different outer atoms, which give bond dipoles of different sizes even in a symmetrical shape (${{\mathrm{CHCl}{\vphantom{X}}_{\smash[t]{3}}}}$, ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{2}}\mathrm{Cl}{\vphantom{X}}_{\smash[t]{2}}}}$

The same reasoning applies to ions. The three bond dipoles of the trigonal planar carbonate and nitrate ions cancel, so these ions have no dipole moment, although each ion carries a charge.

Molecular polarity matters in two further ways. It decides the type of force that acts between the molecules, and so their boiling points and solubility. It also decides how molecules absorb infrared radiation: a vibration absorbs infrared only if it changes the dipole moment, which is why ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ and ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$ are greenhouse gases but ${{\mathrm{N}{\vphantom{X}}_{\smash[t]{2}}}}$ and ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$ are not, a topic of infrared spectroscopy at HL.

Covalent network structures

Most covalent substances are made of separate molecules. A few elements and compounds instead form a continuous network in which every atom is covalently bonded to its neighbours, throughout the whole crystal. There are no separate molecules, so the formula gives only the ratio of atoms. These covalent network structures (also called giant covalent structures) include silicon, silicon dioxide and two of the forms of carbon.

Melting a covalent network structure means breaking strong covalent bonds, not overcoming weak forces between molecules, so these substances have very high melting points. They are hard, insoluble in all solvents, and, with the important exceptions of graphite and graphene, do not conduct electricity.

Allotropes of carbon

Carbon has several allotropes. In each one a carbon atom uses its four valence electrons in a different way, and the structure that results explains the properties.

Diamond

In diamond every carbon atom forms four single covalent bonds to four other carbon atoms, arranged tetrahedrally at $109.5^\circ$. The bonds extend in three dimensions through the whole crystal. Diamond is the hardest natural substance and has a very high melting point (about $3500\ ^\circ\text{C}$), because many strong ${{\mathrm{C}{-}\mathrm{C}}}$ bonds must be broken to deform or melt it. All four valence electrons of each atom are held in localized bonds, so there are no mobile electrons and diamond does not conduct electricity. It does conduct heat very well, better than copper, because the stiff, strongly bonded lattice passes vibrations quickly from atom to atom. Diamond is used in jewellery and in the tips of drills and saws that cut rock, glass and concrete.

Graphite

In graphite each carbon atom forms three covalent bonds to three other carbon atoms, at $120^\circ$ in a flat sheet of hexagonal rings. The fourth valence electron of each atom is not used in these bonds; it is delocalized, free to move across the whole layer. The layers are stacked 335 pm apart and held together only by weak London forces.

• Electrical conductor. The delocalized electrons move along the layers when a voltage is applied, so graphite conducts electricity (much better along the layers than across them). It is used for electrodes in electrolysis.

• Soft and slippery. The weak forces between layers let the layers slide over each other, so graphite is used as a lubricant and in pencil "leads", where layers rub off onto the paper.

• Very high melting point. Melting breaks the strong covalent bonds within the layers, so graphite, like diamond, melts or sublimes only at well over $3500\ ^\circ\text{C}$.

• Less dense than diamond ($2.2\ \text{g cm}^{-3}$ against $3.5\ \text{g cm}^{-3}$), because of the wide gaps between the layers.

Graphene

Graphene is a single layer of graphite: a two-dimensional sheet of hexagonal rings one atom thick, in which each carbon atom is bonded to three others and has one delocalized electron. It was first isolated in 2004 by Andre Geim and Konstantin Novoselov at the University of Manchester, who peeled flakes off graphite with adhesive tape, and the two shared the 2010 Nobel Prize in Physics for the work.

Graphene is an excellent conductor of electricity (delocalized electrons) and of heat. Its network of strong ${{\mathrm{C}{-}\mathrm{C}}}$ bonds makes it one of the strongest materials known for its mass, many times stronger than steel, yet it is flexible and almost transparent. Every atom is on the surface, so it has an enormous surface area for its mass. These properties are being developed for flexible screens, sensors, lightweight composites and battery electrodes.

Fullerenes

Fullerenes are molecular forms of carbon: closed cages of carbon atoms. The best known, buckminsterfullerene, ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{60}}}}$, was discovered in 1985 by Harold Kroto, Robert Curl and Richard Smalley (Nobel Prize in Chemistry, 1996). Its 60 atoms form a hollow sphere of 12 pentagons and 20 hexagons, the pattern of a football. Each carbon atom is bonded to three others, and the remaining electrons are delocalized over the cage.

Because ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{60}}}}$ is a molecule, its solid is held together only by London forces between the cages. Fullerene therefore has a much lower melting point than diamond or graphite: it sublimes on heating at a few hundred degrees Celsius, while diamond needs well over $3000\ ^\circ\text{C}$. It is a poor conductor of electricity, because although the electrons are delocalized within each cage, they cannot move easily from one molecule to the next. Unlike diamond and graphite, ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{60}}}}$ dissolves in some non-polar solvents, such as methylbenzene, giving a purple solution, and it reacts more readily than the other allotropes.

Silicon and silicon dioxide

Silicon is in group 14 below carbon and has the same structure as diamond: each Si atom is bonded tetrahedrally to four others in a three-dimensional network. Silicon is hard, brittle and has a high melting point ($1414\ ^\circ\text{C}$). It is a semiconductor: its conductivity is low at room temperature but rises with temperature and with tiny amounts of added elements, which makes it the basic material of computer chips and solar cells.

The melting point of silicon is far lower than that of diamond because ${{\mathrm{Si}{-}\mathrm{Si}}}$ bonds are weaker than ${{\mathrm{C}{-}\mathrm{C}}}$ bonds. Silicon atoms are larger, so the bonding pair is further from the two nuclei and the bonds are longer (232 pm against 154 pm) and weaker ($226\ \text{kJ mol}^{-1}$ against $346\ \text{kJ mol}^{-1}$). The same weakness is why silicon, unlike carbon, does not form long chains of atoms bonded to each other.

Silicon dioxide, ${{\mathrm{SiO}{\vphantom{X}}_{\smash[t]{2}}}}$, which occurs naturally as quartz and as most sand, is also a covalent network. Each silicon atom is bonded to four oxygen atoms arranged tetrahedrally, and each oxygen atom is bonded to two silicon atoms. The formula ${{\mathrm{SiO}{\vphantom{X}}_{\smash[t]{2}}}}$ gives the 1 : 2 ratio of atoms; there are no ${{\mathrm{SiO}{\vphantom{X}}_{\smash[t]{2}}}}$ molecules.

Quartz is hard and melts only at about $1700\ ^\circ\text{C}$, because melting it breaks strong ${{\mathrm{Si}{-}\mathrm{O}}}$ bonds. It has no mobile electrons or ions, so it does not conduct electricity, and it is insoluble in water. Carbon dioxide, with the same type of formula, is completely different: its molecules are separate ${{\mathrm{O}{=}\mathrm{C}{=}\mathrm{O}}}$ units held together by weak London forces, so it is a gas at room temperature and solid ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ sublimes at $-78\ ^\circ\text{C}$.

Intermolecular forces

Covalent bonds hold the atoms together inside a molecule. Separate molecules are attracted to each other by much weaker intermolecular forces. The two must be kept apart: the strong bonds within molecules are intramolecular, and the weak attractions between molecules are intermolecular.

When a molecular substance melts or boils, the molecules move apart but stay intact: only intermolecular forces are overcome, and no covalent bonds break. Steam is made of the same ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$ molecules as ice. The energy needed to boil water ($41\ \text{kJ mol}^{-1}$ at $100\ ^\circ\text{C}$) is only a small fraction of the energy needed to break the two O–H bonds in each molecule ($2 \times 463\ \text{kJ mol}^{-1}$).

The strength of the force between molecules depends on their size and polarity. There are four types, described in order of increasing strength for molecules of similar size.

London (dispersion) forces

The electrons in an atom or molecule are always moving. At any instant they may be spread a little unevenly, making one side slightly negative and the other slightly positive: a temporary dipole (an instantaneous dipole). This dipole repels electrons in a neighbouring particle and creates an induced dipole in it, with opposite charges facing. The two dipoles attract. A moment later the electrons have moved and the dipoles have changed, but neighbouring dipoles keep forming in step, so on average there is a net attraction.

London (dispersion) forces are the only forces between non-polar molecules such as ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}}}$, ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{4}}}}$, ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ and ${{\mathrm{Cl}{\vphantom{X}}_{\smash[t]{2}}}}$, and between the atoms of the noble gases. Their strength depends on two things:

• The number of electrons. A particle with more electrons, usually a larger molar mass, has a larger, more easily distorted electron cloud (it is more polarizable), so larger temporary dipoles form. Down group 17 the boiling points rise from fluorine ($-188\ ^\circ\text{C}$) and chlorine ($-34\ ^\circ\text{C}$), which are gases, to bromine ($59\ ^\circ\text{C}$), a liquid, and iodine ($184\ ^\circ\text{C}$), a solid at room temperature.

• The shape of the molecule. Long, straight molecules can lie alongside each other and touch over a large surface area; compact, branched molecules touch over a smaller area, so the forces between them are weaker.

London forces between individual molecules are weak, but they add up. A gecko can run up a glass window and hang from a ceiling because each foot carries hundreds of thousands of microscopic hairs, each split into hundreds of even finer tips. Every tip comes so close to the surface that London forces act between them, and the total over millions of contacts is enough to hold the animal's weight. Adhesives and tapes modelled on gecko feet use the same principle.

Dipole-induced dipole forces

A polar molecule has a permanent dipole. When it comes close to a non-polar molecule or atom, its charged ends distort the electron cloud of the neighbour and induce a dipole in it, and the two attract. These dipole-induced dipole forces act, for example, between water and oxygen molecules, and help a small amount of oxygen to dissolve in water, the oxygen that fish breathe. They also act between hydrogen chloride and argon atoms in a mixture of the two gases.

Dipole–dipole forces

Polar molecules have permanent dipoles, and they line up so that the $\delta+$ end of one molecule is near the $\delta-$ end of the next. The attraction between these permanent dipoles is a dipole–dipole force. It acts in addition to London forces, which act between all molecules.

For molecules with similar numbers of electrons, dipole–dipole forces make a polar substance less volatile than a non-polar one. Propane, ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{3}}\mathrm{CH}{\vphantom{X}}_{\smash[t]{2}}\mathrm{CH}{\vphantom{X}}_{\smash[t]{3}}}}$ ($M = 44\ \text{g mol}^{-1}$), is non-polar and boils at $-42\ ^\circ\text{C}$; ethanal, ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{3}}\mathrm{CHO}}}$ ($M = 44\ \text{g mol}^{-1}$), has a polar ${{\mathrm{C}{=}\mathrm{O}}}$ group and boils at $20\ ^\circ\text{C}$. Hydrogen cyanide (boiling point $26\ ^\circ\text{C}$) boils far higher than hydrogen chloride ($-85\ ^\circ\text{C}$), although it has a smaller molar mass, because the HCN molecule is much more polar.

The term van der Waals forces is used as a general name for London forces, dipole-induced dipole forces and dipole–dipole forces together. It does not include hydrogen bonding.

Hydrogen bonding

When a hydrogen atom is covalently bonded to a very electronegative atom, the bonding pair is pulled strongly away from the hydrogen. Hydrogen has no inner electrons, so its nucleus, a single proton, is left almost exposed with a large $\delta+$ charge. This small, strongly positive hydrogen atom is attracted to a lone pair on an electronegative atom of a neighbouring molecule. The result is a hydrogen bond, the strongest type of intermolecular force.

A hydrogen bond is drawn as a dashed line from the hydrogen atom to the lone pair it is attracted to. The three atoms involved, such as O–H···O, lie close to a straight line, because the lone pair points towards the hydrogen atom. Hydrogen bonds form between molecules containing N–H, O–H or H–F bonds: water, ammonia, hydrogen fluoride, alcohols, carboxylic acids, amines and many molecules in living things.

Hydrogen bonds are typically about a tenth as strong as a covalent bond, roughly 5 to $40\ \text{kJ mol}^{-1}$ compared with $463\ \text{kJ mol}^{-1}$ for the O–H bond itself, but they are strong enough to change the properties of a substance dramatically.

• Water's high boiling point. Water ($M = 18\ \text{g mol}^{-1}$) boils at $100\ ^\circ\text{C}$, while hydrogen sulfide ($M = 34\ \text{g mol}^{-1}$), with no hydrogen bonding, boils at $-60\ ^\circ\text{C}$. Without hydrogen bonding, water would be a gas at room temperature and there would be no liquid oceans.

• Ice floats. In ice each water molecule is hydrogen bonded to four others in a tetrahedral arrangement, which holds the molecules in an open lattice with a lot of empty space. When ice melts, some hydrogen bonds break and the molecules pack more closely, so liquid water ($1.00\ \text{g cm}^{-3}$) is denser than ice ($0.92\ \text{g cm}^{-3}$). Ice therefore forms on the top of lakes and insulates the water below, where aquatic life survives the winter.

• DNA. The two strands of the DNA double helix are held together by hydrogen bonds between pairs of bases: adenine pairs with thymine through two hydrogen bonds, and guanine with cytosine through three. Each hydrogen bond is weak, so the strands can be separated when DNA is copied, but together millions of them hold the helix firmly.

The definition of a hydrogen bond has changed as experimental techniques have improved. Spectroscopic and diffraction measurements showed similar, weaker attractions involving hydrogen atoms bonded to carbon and acceptor atoms other than N, O or F. In 2011 IUPAC adopted a broader definition: an attraction between a hydrogen atom bonded to an atom more electronegative than hydrogen and an atom or group in the same or another molecule, where there is evidence of bond formation. For most purposes in introductory chemistry, hydrogen bonding is still limited to H bonded to N, O or F.

Deducing the forces between molecules

The forces between the molecules of a substance follow from its structure. Every substance has London forces; polar molecules also have dipole–dipole forces; molecules with H bonded to N, O or F also form hydrogen bonds.

Comparing the strengths of the forces

For molecules of comparable molar mass, the strengths of the intermolecular forces are generally:

All three are much weaker than covalent bonds. The order holds only when the molecules have similar numbers of electrons. London forces grow steadily with molecular size, so for large molecules they can outweigh the dipole–dipole forces or even the hydrogen bonding of much smaller ones. Iodine, held only by London forces between its large, electron-rich molecules, is a solid that boils at $184\ ^\circ\text{C}$, higher than water. A long-chain alkane such as octane ($126\ ^\circ\text{C}$) boils higher than methanol ($65\ ^\circ\text{C}$).

Intermolecular forces also explain why real gases do not behave ideally. The ideal gas model assumes no forces between particles; at high pressure and low temperature the particles of a real gas are close enough for these forces to matter, and gases with stronger intermolecular forces, such as ammonia, deviate more than helium or hydrogen.

Physical properties of covalent substances

The properties of a covalent substance follow from its structure. For a covalent network the strong bonds throughout the lattice decide everything. For a molecular substance, the properties that involve separating molecules (melting, boiling, dissolving) depend on the intermolecular forces.

Volatility and boiling point

Volatility is the tendency of a substance to evaporate. Molecular substances with weak intermolecular forces are volatile, with low melting and boiling points: many are gases or liquids at room temperature. The stronger the intermolecular forces, the more energy is needed to separate the molecules, and the higher the boiling point. The boiling points of the hydrides of groups 14 to 17 show both effects at once.

Down each group the hydrides have more electrons, so London forces increase and the boiling point rises, for example ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{S}}} < {{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{Se}}} < {{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{Te}}}$. The group 14 hydrides follow this trend all the way from ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{4}}}}$, because their tetrahedral molecules are non-polar. In groups 15, 16 and 17, the first members, ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}}}$, ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$ and ${{\mathrm{HF}}}$, boil far higher than the trend predicts: N, O and F are electronegative enough for hydrogen bonding. Water is furthest above the trend, because each molecule has two H atoms and two lone pairs and can form up to four hydrogen bonds, while ${{\mathrm{HF}}}$ and ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}}}$ are limited by having only one H atom or one lone pair.

Comparing compounds of similar molar mass

When molar masses are similar, London forces are similar too, and the type of polar group decides the order of boiling points. Organic compounds with about $58$–$60\ \text{g mol}^{-1}$ show the full sequence.

Data: CRC Handbook of Chemistry and Physics (values rounded).

Ethanoic acid boils highest because its ${{\mathrm{COOH}}}$ group has both an O–H group to donate a hydrogen bond and a ${{\mathrm{C}{=}\mathrm{O}}}$ oxygen to accept one; pairs of molecules hydrogen bond to each other through both groups, forming dimers even in the vapour. The same pairing explains why the molar mass of benzoic acid measured in a non-polar solvent such as hexane comes out at about twice its true value: the molecules exist there as hydrogen-bonded pairs.

Chain length and branching

Within a homologous series each extra ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{2}}}}$ group adds electrons and surface area, so London forces increase and the boiling point rises steadily. Alcohols boil far higher than alkanes of the same chain length because of hydrogen bonding through the –OH group, but the difference becomes proportionally smaller as the chain grows and the London forces of the hydrocarbon part become more important.

Isomers have the same molar mass, so differences in their boiling points come from shape. The three isomers of ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{5}}\mathrm{H}{\vphantom{X}}_{\smash[t]{12}}}}$ are all non-polar alkanes with only London forces between their molecules. The straight-chain isomer, pentane, can lie alongside its neighbours over its whole length. The more branched the molecule, the more nearly spherical it is, the smaller its area of contact with neighbouring molecules, and the weaker the London forces.

Electrical conductivity

A substance conducts electricity when it contains charged particles that are free to move: delocalized electrons or mobile ions.

• Molecular substances do not conduct in any state. Their molecules are uncharged, and all their electrons are held in bonds or lone pairs within each molecule. Pure water, ethanol, sugar and solid iodine are non-conductors.

• Some molecular substances react with water to form ions, and their solutions conduct. Hydrogen chloride gas does not conduct, but its solution in water, hydrochloric acid, conducts well because ${{\mathrm{HCl}}}$ ionizes completely to ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{3}}\mathrm{O}{\vphantom{X}}^{+}}}$ and ${{\mathrm{Cl}{\vphantom{X}}^{-}}}$ ions. Ethanoic acid ionizes only slightly, so its solution conducts weakly, a difference explained by the strengths of acids.

• Covalent networks do not conduct, with two exceptions: graphite and graphene conduct because of their delocalized electrons. Silicon is a semiconductor, conducting slightly at room temperature and better as it gets warmer.

Solubility

A substance dissolves when the attractions between its particles and the solvent molecules can replace the attractions that hold the particles together and that hold the solvent molecules together. Dissolving is favoured when the solute and the solvent form similar kinds of intermolecular force. This is often summarized as "like dissolves like", but an explanation must name the forces involved.

• Polar substances that can form hydrogen bonds dissolve in water. Short-chain alcohols, carboxylic acids, amines and sugars all dissolve, because their –OH, –COOH or ${{{-}\mathrm{NH}{\vphantom{X}}_{\smash[t]{2}}}}$ groups form hydrogen bonds with water molecules. Methanol, ethanol and propan-1-ol mix with water in any proportion: they are miscible.

• Non-polar substances dissolve in non-polar solvents. Iodine and fats dissolve in hexane, because they form London forces with the hexane molecules similar to those they break. Iodine dissolves only slightly in water: its non-polar molecules cannot form hydrogen bonds with water and cannot make up for the hydrogen bonds between water molecules that they would break apart.

• Covalent networks are insoluble in every solvent. Dissolving diamond or quartz would mean breaking strong covalent bonds, which no attraction to a solvent can repay.

In a homologous series, solubility in water falls as the non-polar hydrocarbon chain gets longer. The –OH group of an alcohol forms hydrogen bonds with water, but the hydrocarbon chain cannot; it only disrupts the hydrogen bonding between water molecules. As the chain lengthens, this effect wins. At $20\ ^\circ\text{C}$ about 8 g of butan-1-ol dissolves in $100\ \text{g}$ of water, about 2 g of pentan-1-ol and less than 1 g of hexan-1-ol, while the first three alcohols are miscible.

The same reasoning explains the difference between water-soluble and fat-soluble vitamins. Vitamin C (ascorbic acid) is a small molecule with several –OH groups, which form hydrogen bonds with water, so it dissolves in water and is not stored in the body. Vitamin A (retinol) has only one –OH group on a long non-polar hydrocarbon chain; it forms London forces with fat molecules, dissolves in fats and is stored in fatty tissue.

Comparing structures and properties

Experimental data distinguish the main types of structure: a melting-point measurement, a conductivity test of the solid, the melt and any solution, and solubility tests in water and in a non-polar solvent such as hexane. Each type of structure gives its own pattern of results.

Chromatography

Chromatography separates and identifies the components of a mixture, even when only tiny amounts are present. It is used to identify the dyes in inks and foods, check the purity of medicines, detect drugs in blood and urine, and follow the progress of a reaction in the laboratory. The separations depend on intermolecular forces between the components and the two phases.

How chromatography separates a mixture

Every form of chromatography uses two phases. The stationary phase does not move; the mobile phase, a liquid or gas, moves through or over it and carries the mixture with it. Each component is attracted to both phases and spends part of its time held by the stationary phase and part carried by the mobile phase. A component that is more strongly attracted to the mobile phase (more soluble in it) spends more time moving and travels further. A component more strongly attracted to the stationary phase lags behind. Because different substances form different intermolecular forces with the two phases, they travel different distances and separate.

The surface of silica is covered with –OH groups, so it is very polar and can form hydrogen bonds. When a fairly non-polar solvent is used, polar components are held strongly by the silica and move little, while non-polar components dissolve well in the solvent and move far. Changing to a more polar solvent carries polar components further. Choosing the solvent is therefore the way to improve a separation.

Carrying out paper chromatography or TLC

1. Draw a baseline (origin) in pencil about 1–2 cm from the bottom of the paper or plate. Pencil is graphite, which does not dissolve in the solvent or move up the plate; ink would separate along with the samples.

2. Use a capillary tube to put a small, concentrated spot of each sample on the baseline, letting each spot dry and adding more to the same place if needed. Small spots give sharp, separate results.

3. Stand the paper or plate in a container holding a shallow layer of solvent, with the solvent level below the baseline, so the spots are not washed off into the solvent. Cover the container with a lid so that the air inside is saturated with solvent vapour and the solvent does not evaporate from the plate.

4. Let the solvent rise until it is close to the top. Remove the plate and immediately mark the solvent front in pencil before the solvent evaporates.

5. Dry the plate and mark the centre of each spot. Coloured substances, such as dyes and plant pigments, are visible directly; colourless ones are made visible by other methods.

The retardation factor

The distance a component travels depends on how far the solvent went, so results are compared using a ratio rather than a raw distance.

The retardation factor has no units and lies between 0 (the component stays on the baseline) and 1 (it moves with the solvent front). Under the same conditions (the same stationary phase, the same solvent and the same temperature) each substance has its own $R_\text{F}$ value, so $R_\text{F}$ values can be used to identify components.

Interpreting chromatograms

• Number of components. Each spot is at least one substance. A mixture gives several spots; a pure substance gives one.

• Identification. A spot is identified by comparison with known substances run under the same conditions, preferably on the same plate. A sample and a standard with the same $R_\text{F}$, or a single spot when the two are applied on top of each other ("co-spotting"), are probably the same substance.

• Limits. Two different substances can have the same $R_\text{F}$ in one solvent, so a single spot does not prove purity. Running the chromatogram again with a different solvent usually separates them.

• Polarity. On silica or paper with a non-polar solvent, more polar components have lower $R_\text{F}$ values, because they are held more strongly by the polar stationary phase. Changing the solvent changes every $R_\text{F}$ value, which is why the solvent must be stated with each value.

The pigments of green leaves are a classic separation. An extract of leaves ground with propanone, run on a TLC plate in a non-polar solvent mixture, separates into several coloured bands. Carotene, a hydrocarbon with no polar groups, has an $R_\text{F}$ close to 1, while the chlorophylls and xanthophylls, whose molecules contain oxygen atoms, are held more strongly by the silica and travel less far.

Gas chromatography (GC) and high-performance liquid chromatography (HPLC) use the same principle in instruments: the mobile phase is a gas or a liquid pumped through a narrow column packed with the stationary phase, and components are detected as they come out. They separate and measure very small amounts and are used in drug testing, food analysis and forensic science.

Coordination bonds in transition element complexes (HL)

Transition element ions are small and highly charged, and they have empty orbitals of suitable energy. Molecules and ions with a lone pair, such as water, ammonia, chloride ions and cyanide ions, are attracted to them and donate that lone pair into an empty orbital on the metal ion. This is the same donor–acceptor bonding as in the ammonium ion, repeated several times around one metal ion.

The number of coordination bonds to the central ion is its coordination number. Six is the most common, and six ligands are arranged octahedrally around the metal ion, with every neighbouring pair of ligands at 90°. Four ligands give either a tetrahedral or a square planar complex. In the hexaamminecobalt(III) ion, ${{[\mathrm{Co}(\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}){\vphantom{X}}_{\smash[t]{6}}]{\vphantom{X}}^{3+}}}$, each ammonia molecule bonds to the cobalt(III) ion through the lone pair on its nitrogen atom.

A complex ion is written in square brackets, with the metal first and the charge of the whole ion outside. The charge of the complex is the charge of the metal ion plus the charges of the ligands. Neutral ligands such as ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$ and ${{\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}}}$ add nothing, while each anionic ligand such as ${{\mathrm{Cl}{\vphantom{X}}^{-}}}$ or ${{\mathrm{CN}{\vphantom{X}}^{-}}}$ adds −1:

• ${{[\mathrm{Cu}(\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}){\vphantom{X}}_{\smash[t]{6}}]{\vphantom{X}}^{2+}}}$: ${{\mathrm{Cu}{\vphantom{X}}^{2+}}}$ with six neutral water ligands, charge 2+ (the blue ion in copper(II) sulfate solution);

• ${{[\mathrm{Fe}(\mathrm{CN}){\vphantom{X}}_{\smash[t]{6}}]{\vphantom{X}}^{3-}}}$: ${{\mathrm{Fe}{\vphantom{X}}^{3+}}}$

• ${{[\mathrm{CuCl}{\vphantom{X}}_{\smash[t]{4}}]{\vphantom{X}}^{2-}}}$: ${{\mathrm{Cu}{\vphantom{X}}^{2+}}}$

The ligand always supplies both electrons, so every metal–ligand bond in a complex is a coordination bond. In cyanide the donor atom is carbon, which carries a lone pair in the Lewis formula ${{[:\mathrm{C}{\equiv}\mathrm{N}:]{\vphantom{X}}^{-}}}$. The anticancer drug cisplatin, ${{[\mathrm{Pt}(\mathrm{NH}{\vphantom{X}}_{\smash[t]{3}}){\vphantom{X}}_{\smash[t]{2}}\mathrm{Cl}{\vphantom{X}}_{\smash[t]{2}}]}}$, is a neutral complex: a platinum(II) ion bonded to two ammonia ligands and two chloride ligands, which together cancel the 2+ charge of the metal.

Forming a complex is a reaction between an electron-pair donor (the ligand, a Lewis base) and an electron-pair acceptor (the metal ion, a Lewis acid), so every coordination bond can be seen as the product of a Lewis acid–base reaction. The colours of transition element complexes and the reasons these elements form so many of them belong to the chemistry of the transition elements.

Expanded octets: five and six electron domains (HL)

Boron and beryllium compounds have fewer than eight electrons around the central atom. Many compounds of heavier non-metals break the octet rule in the other direction. In phosphorus pentachloride, ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{5}}}}$, phosphorus forms five P–Cl bonds and so has ten electrons in its valence shell; in sulfur hexafluoride, ${{\mathrm{SF}{\vphantom{X}}_{\smash[t]{6}}}}$, sulfur has twelve. Such a central atom has an expanded octet.

Which atoms can expand their octet

The second shell ($n = 2$) has only one s orbital and three p orbitals, so it can hold at most eight electrons. Nitrogen, oxygen and fluorine therefore never have more than eight valence electrons. From period 3 onwards the valence shell also contains d orbitals ($n = 3$ has 3s, 3p and 3d), which are empty in phosphorus, sulfur and chlorine but close enough in energy to be used. In a simple model, these d orbitals allow the atom to accommodate extra electron pairs.

Atomic size matters as well. A phosphorus or sulfur atom is larger than a nitrogen or oxygen atom, so five or six other atoms can fit around it without the bonded atoms crowding each other. Expanded octets are most common when the outer atoms are small and very electronegative, such as fluorine, chlorine and oxygen. This explains pairs such as these:

The xenon fluorides, ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{2}}}}$, ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{4}}}}$ and ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{6}}}}$, are expanded-octet species too, as is the oxide ${{\mathrm{XeO}{\vphantom{X}}_{\smash[t]{4}}}}$. In each, xenon keeps its own eight valence electrons and gains a share of further electrons from the bonded atoms, so its valence shell holds ten, twelve or more.

Drawing Lewis formulas with expanded octets

The method is the same as for any Lewis formula, except that the central atom may finish with more than eight electrons:

1. Count the total number of valence electrons, adding one for each negative charge and subtracting one for each positive charge.

2. Put the least electronegative atom in the centre (never hydrogen or fluorine) and join each outer atom to it with a single bond.

3. Complete the octet of every outer atom with lone pairs.

4. Place any electrons that remain on the central atom as lone pairs, even if this takes it beyond eight.

Five electron domains: the trigonal bipyramid

Five electron domains around a central atom repel each other to the arrangement that keeps them furthest apart, a trigonal bipyramid: three domains around the middle at 120° to each other, and one above and one below at 90° to the middle three. Unlike the tetrahedron, its positions are not all equivalent.

• The two axial positions lie on the vertical axis, 180° apart. Each has three neighbouring domains at 90°.

• The three equatorial positions lie in a plane around the centre. Each has only two neighbouring domains at 90°, and two at 120°.

Repulsion between electron domains falls off very steeply with distance, so the repulsions between domains at 90° dominate. A lone pair is held closer to the central atom and repels more strongly than a bonding pair, so it takes the position with the fewest neighbours at 90°: an equatorial position. Lone pairs in a trigonal bipyramidal arrangement are therefore always equatorial, and this fixes the molecular geometry when one, two or three domains are lone pairs.

The see-saw shape of ${{\mathrm{SF}{\vphantom{X}}_{\smash[t]{4}}}}$ comes from one equatorial lone pair. It pushes the two axial S–F bonds away from it, so the axial F–S–F angle is about 173° instead of 180°, and it squeezes the two equatorial bonds together to about 102° instead of 120°. In the T-shaped ${{\mathrm{ClF}{\vphantom{X}}_{\smash[t]{3}}}}$ molecule two equatorial lone pairs leave the three fluorine atoms in a T, with F–Cl–F angles of about 87.5°, just under 90°. In ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{2}}}}$ all three equatorial positions are lone pairs, so the two fluorine atoms are axial and the molecule is exactly linear.

Six electron domains: the octahedron

Six electron domains point to the corners of an octahedron: four in a square around the middle and one above and one below, with every pair of neighbouring domains at 90°. All six positions are equivalent, so the first lone pair can go anywhere. A second lone pair goes opposite the first, at 180°, where the two lone pairs repel each other least.

In the square pyramidal molecule ${{\mathrm{BrF}{\vphantom{X}}_{\smash[t]{5}}}}$ the lone pair below the bromine atom pushes the four basal fluorine atoms slightly upwards, so the angle between the apical and basal bonds is about 85°, a little less than 90°. In the square planar ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{4}}}}$ molecule the two lone pairs are opposite each other, their effects cancel, and the four F–Xe–F angles are exactly 90°.

Sulfur hexafluoride is a dense, colourless and very unreactive gas, and an excellent electrical insulator. About 80% of the world's ${{\mathrm{SF}{\vphantom{X}}_{\smash[t]{6}}}}$ is used in high-voltage switchgear in electricity networks. The six fluorine atoms surround the sulfur atom so completely that there is no easy route for other molecules to attack it. The same stability makes ${{\mathrm{SF}{\vphantom{X}}_{\smash[t]{6}}}}$ the most potent greenhouse gas assessed by the IPCC. Its atmospheric lifetime is about 3200 years, and over 100 years one kilogram traps about 25 200 times as much heat as one kilogram of carbon dioxide.

Molecules with double bonds and ions

The same rules apply to ions and to molecules with double bonds; a double bond still counts as one electron domain. Two contrasting examples:

• ${{\mathrm{XeO}{\vphantom{X}}_{\smash[t]{4}}}}$: xenon forms four Xe=O double bonds, which use all eight of its valence electrons. Four domains and no lone pairs make it tetrahedral, even though xenon has an expanded octet (16 electrons).

• ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{4}}{\vphantom{X}}^{+}}}$ and ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{6}}{\vphantom{X}}^{-}}}$: in the cation, $(5 + 4 - 1)/2 = 4$ domains give a tetrahedron; in the anion, $(5 + 6 + 1)/2 = 6$ domains give an octahedron. Solid phosphorus pentachloride is in fact made of these two ions, ${{[\mathrm{PCl}{\vphantom{X}}_{\smash[t]{4}}]{\vphantom{X}}^{+}[\mathrm{PCl}{\vphantom{X}}_{\smash[t]{6}}]{\vphantom{X}}^{-}}}$, while gaseous ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{5}}}}$ consists of trigonal bipyramidal molecules.

Polarity of molecules with five and six domains

Molecular polarity follows the same reasoning as for smaller molecules: polar bonds arranged symmetrically, with identical outer atoms and no asymmetric lone pairs, cancel. ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{5}}}}$, ${{\mathrm{SF}{\vphantom{X}}_{\smash[t]{6}}}}$, ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{2}}}}$ and ${{\mathrm{XeF}{\vphantom{X}}_{\smash[t]{4}}}}$ are non-polar. ${{\mathrm{SF}{\vphantom{X}}_{\smash[t]{4}}}}$, ${{\mathrm{ClF}{\vphantom{X}}_{\smash[t]{3}}}}$ and ${{\mathrm{BrF}{\vphantom{X}}_{\smash[t]{5}}}}$ are polar, because the lone pairs make their shapes unsymmetrical and the bond dipoles do not cancel.

Changing one outer atom also breaks the symmetry. In ${{\mathrm{PCl}{\vphantom{X}}_{\smash[t]{4}}\mathrm{F}}}$ the shape is still trigonal bipyramidal, but the P–F bond is more polar than the P–Cl bonds (fluorine is more electronegative than chlorine), so the bond dipoles no longer cancel and the molecule is polar.

Formal charge and the preferred Lewis formula (HL)

For many species more than one valid Lewis formula can be drawn. Carbon dioxide could be ${{\mathrm{O}{=}\mathrm{C}{=}\mathrm{O}}}$ or ${{\mathrm{O}{\equiv}\mathrm{C}{-}\mathrm{O}}}$, and the sulfate ion can be drawn with four S–O single bonds or with two of them double. All of these contain the right number of electrons, but the real species is best described by one of them. Formal charge gives a simple way to decide which.

Because each bond contains two electrons, $\tfrac{1}{2}B$ is simply the number of bonds to the atom, counting a double bond as two and a triple bond as three. An equivalent form is therefore:

The formal charges of all the atoms in a species always add up to the charge on the species: zero for a molecule, −2 for the sulfate ion. This is a useful check on the arithmetic.

Choosing the preferred Lewis formula

A Lewis formula in which charge is separated (positive on one atom, negative on another) is higher in energy than one without separation. The preferred Lewis formula is therefore the one that:

1. has formal charges closest to zero (the smallest values, and the fewest atoms with a non-zero formal charge);

2. if two structures are equally good by the first rule, has any negative formal charge on the most electronegative atom.

Formal charge also explains why some species are best drawn with an expanded octet. In the sulfate ion the octet structure puts +2 on sulfur and −1 on every oxygen atom. Moving lone pairs from two oxygen atoms into S=O double bonds reduces the charge on sulfur to zero and leaves −1 on only two oxygen atoms, so the expanded-octet structure is preferred.