Cambridge International AS & A Level Chemistry 9701 · Topic 3, with 4.2 Bonding and structure

Chemical bonding

Everything in this page comes back to one idea: electrostatic attraction between positive nuclei and negative electrons. Ionic, covalent and metallic bonding are three ways of arranging that attraction, and every physical property that follows — melting point, hardness, conductivity, solubility, molecular shape — is a consequence of which arrangement you have and how strongly it holds.

Why atoms bond3.1–3.3

An isolated atom has a certain energy. If two atoms can arrange their electrons so that the system's total energy is lower than the two separate atoms, they will do so, and the energy difference is released. That lowered-energy arrangement is a chemical bond. Bonds do not form because atoms "want a full outer shell" — the full-shell rule is a useful bookkeeping shortcut that works because filled shells usually happen to be the low-energy arrangement for the first two rows of the periodic table. It fails often enough that you should hold it loosely: Fe³⁺, Cu²⁺, Pb²⁺, SF₆ and PCl₅ all exist.

Three ways to lower the energy

Ionic bonding3.2.1–3.2.2

Sodium has one electron outside a stable 2,8 core, and losing it costs relatively little (first ionisation energy 496 kJ mol⁻¹). Chlorine is one electron short of 2,8,8 and gains one exothermically. Neither of those steps, on its own, releases enough energy to make the reaction worthwhile — the transfer Na(g) + Cl(g) → Na⁺(g) + Cl⁻(g) is actually endothermic by about +147 kJ mol⁻¹. What pays for the whole process is the lattice energy: the enormous release of energy when those gaseous ions pack into a three-dimensional lattice, about −787 kJ mol⁻¹ for NaCl.

Working out the charge on an ion

For s- and p-block elements the charge follows from the group: the atom loses or gains the smallest number of electrons that reaches the nearest noble gas configuration.

Why ionic compounds behave as they do

Every property comes from "giant lattice of charged particles, each strongly attracted to several neighbours":

• High melting and boiling points — melting means separating ions against the full lattice attraction. NaCl melts at 801 °C, MgO at 2852 °C.
• Hard but brittle — hard because the lattice resists deformation; brittle because a small displacement of one layer brings like charges face to face and the crystal splits along the plane.
• Conduct only when molten or in solution — the ions carry the charge and must be free to move. A solid ionic crystal is an insulator.
• Often soluble in water — the ion–dipole attraction to polar water molecules (hydration) can repay the lattice energy. Non-polar solvents cannot, so ionic solids are insoluble in hexane.

Lattice energy depends on charge and size

Lattice energy is roughly proportional to (q₊ × q₋) / (r₊ + r₋). Doubling both charges quadruples the attraction; that is why MgO (2+/2−) melts more than 2000 °C above NaCl (1+/1−) despite having almost identical ionic radii and the same lattice type.

Covalent bonding3.4.1(a)–(b)

The shared pair sits in the region between the two nuclei, where it is attracted by both. That attraction pulls the nuclei together; nuclear–nuclear repulsion pushes them apart. The bond length is the separation at which those balance, and the depth of the energy well at that separation is the bond energy.

Single, double and triple bonds

Expanded octets3.4.1(b)

Elements in Period 3 and below can accommodate more than eight electrons in their outer shell because d orbitals of similar energy are available. You are expected to know these:

Dative covalent (co-ordinate) bonding3.4.1(c)

The two requirements are a lone pair on the donor and a vacant orbital on the acceptor. Once formed, the bond is indistinguishable from any other covalent bond of the same type — all four N–H bonds in NH₄⁺ have identical length and strength, and the ion is a perfect tetrahedron.

Metallic bonding3.3.1

A metal atom cannot lower its energy by transferring electrons to another metal atom — neither is electronegative enough to hold them. Instead the outer-shell orbitals of every atom in the crystal overlap into one continuous set of orbitals spanning the whole piece of metal, and the outer electrons occupy those. Each electron is no longer associated with a particular nucleus; the ibchem page describes the result as marbles stuck into blu-tack, the cations being the marbles and the delocalised electrons the blu-tack holding them.

What makes metallic bonding strong?

Two factors, and both are about how much charge is packed into how small a space:

1. Number of delocalised electrons per atom (equivalently, the charge on the cation). Sodium contributes one, magnesium two, aluminium three.
2. Size of the cation. A smaller ion puts its charge closer to the electron sea, so the attraction is stronger.

Properties explained

• Electrical conductivity — an applied potential difference makes the delocalised electrons drift; they enter at one end and leave at the other. The metal is unchanged chemically.
• Thermal conductivity — heat is carried both by lattice vibrations and, far more effectively, by the mobile electrons. Silver 430, copper 400, aluminium 235, brass 109 W m⁻¹ K⁻¹.
• Malleable and ductile — the bonding is non-directional, so one layer of cations can slide over another and the electron sea simply flows with it. Contrast the brittleness of an ionic lattice, where the same displacement brings like charges together.
• High melting point, high density, shiny — strong bonding, efficient close packing, and delocalised electrons that absorb and re-emit light across the visible range.
• Exceptions exist — mercury is liquid at room temperature and the Group 1 metals are soft enough to cut with a knife, because their metallic bonding is weak.

Comparing the three strong bonds

σ and π bonds, and hybridisation3.4.2

A covalent bond is an overlap of atomic orbitals. How they overlap divides bonds into two kinds.

Hybridisation

Carbon's ground state is 1s²2s²2p² — only two unpaired electrons, yet it forms four bonds. Promoting one 2s electron to the empty 2p orbital costs energy but is repaid four times over by the extra bonds. The 2s and 2p orbitals then mix into equivalent hybrid orbitals.

The syllabus examples in detail

• H₂ — plain 1s–1s overlap. No hybridisation is involved or needed.
• Ethane, C₂H₆ — each carbon sp³. Seven σ bonds (one C–C, six C–H) and no π bonds, so the C–C bond rotates freely.
• Ethene, C₂H₄ — each carbon sp², with one unhybridised 2p orbital perpendicular to the molecular plane. Sideways overlap of those two p orbitals gives the π bond. Five σ + one π; the molecule is planar and cannot rotate about C=C, which is the origin of cis–trans isomerism.
• Ethyne, C₂H₂ — each carbon sp, two unhybridised p orbitals each, giving two mutually perpendicular π bonds. Three σ + two π; linear.
• HCN — the nitrogen (1s²2s²2p_x¹2p_y¹2p_z¹) is sp hybridised, giving two sp hybrids of which one holds the lone pair; the other forms the σ bond to carbon, and two p orbitals form the two π bonds of the triple bond.
• N₂ — exactly the same orbital arrangement as ethyne and HCN, but with a lone pair at each end instead of a hydrogen. The N≡N bond energy of 944 kJ mol⁻¹ is why nitrogen is so unreactive.
• Benzene — six sp² carbons in a planar ring; the six unhybridised p orbitals overlap all the way round, giving a delocalised π system above and below the ring rather than three localised double bonds. Studied in full in the organic half of the course, but the orbital picture belongs here.

Bond energy and bond length3.4.3

The two trends, and why they run opposite ways

Larger atoms have more electron shells, so their nuclei end up further apart and the bond is longer. In a longer bond the shared pair is further from each nucleus and better shielded by the inner shells, so it is held less tightly — the bond is weaker. Shorter therefore usually means stronger.

Multiple bonds are shorter and stronger

Electronegativity3.1.1–3.1.3 · 3.6.2

It is a property of an atom within a bond, not of an isolated atom — which is why it is measured on a relative scale rather than in joules. The usual scale is Pauling's, running from caesium at 0.79 to fluorine at 3.98, the most electronegative element.

What electronegativity depends on

Two factors, and they are the same two that control atomic radius and ionisation energy:

1. Nuclear charge — more protons pull the bonding pair harder.
2. Distance and shielding — the further the bonding pair is from the nucleus, and the more inner shells lie between, the weaker the pull. The relevant quantity is the number of unshielded protons, i.e. the effective nuclear charge felt by the bonding pair.

Across a period (Na → Cl): electronegativity increases

Nuclear charge rises by one proton each step. The added electron goes into the same shell, so shielding is essentially unchanged and the atomic radius falls. Effective nuclear charge on a bonding pair rises sharply, so the pull increases.

Down a group (F → I): electronegativity decreases

Nuclear charge also rises, but each step adds a complete inner shell. The bonding pair is now much further from the nucleus and much more shielded, and those effects outweigh the extra protons.

Bond polarity, and bond type from Δχ3.1.4

If the two bonded atoms have equal electronegativity the shared pair sits centrally: the bond is pure (non-polar) covalent. If one atom pulls harder, the pair is displaced towards it, giving that atom a partial negative charge δ− and leaving the other δ+: a polar covalent bond with a permanent dipole. Push the difference far enough and the pair is transferred outright, which is an ionic bond.

Polarising power and polarisability3.1.4

Coming from the ionic side: a small, highly charged cation distorts the electron cloud of a large anion, dragging electron density back into the space between the ions. That is covalent character in an ionic compound. The cation's ability to do this is its polarising power (high for small, highly charged ions such as Al³⁺ and Be²⁺); the anion's susceptibility is its polarisability (high for large, highly charged ions such as I⁻).

This is why AlCl₃ sublimes at 178 °C and dissolves in organic solvents, behaving as a covalent molecule, while NaCl is a classic high-melting ionic solid — despite both being "metal + chlorine".

Polar bonds vs polar molecules

A molecule has a net dipole only if its individual bond dipoles do not cancel. Because a dipole is a vector, cancellation depends entirely on the shape. So a molecule can be full of strongly polar bonds and still be completely non-polar.

Intermolecular forces: the overview3.6.3

Simple molecular substances have two completely different kinds of attraction in them, and the whole topic depends on not confusing the two.

Instantaneous dipole–induced dipole forces

Electrons in a molecule are in constant motion. At any instant they are, by chance, unevenly distributed, so the molecule has a fleeting instantaneous dipole. That dipole repels the electrons of a neighbouring molecule, inducing a dipole in it that is aligned to attract. The instantaneous dipole vanishes and reappears elsewhere within about 10⁻¹⁵ s, but the correlation between neighbours persists, and the time-averaged result is a real, always-attractive force.

What makes them stronger

1. More electrons (which usually means larger M_r). A bigger, more diffuse electron cloud is more polarisable: it distorts more easily, so the instantaneous dipoles are larger. This is the dominant factor.
2. Greater surface contact. Long, thin molecules can lie alongside each other over their whole length; compact, spherical ones touch at fewer points. Branching reduces contact and therefore lowers the boiling point.

Permanent dipole–dipole forces

A polar molecule has a permanent δ+ end and δ− end. Neighbouring molecules line up δ+ to δ−, and the attraction is extra to the id–id forces that are always present. Because it requires alignment, it is strongly weakened by thermal motion, which is why its contribution is smaller than people expect.

Hydrogen bonding3.6.1

Both halves of that definition are needed. Hydrogen bonded to N, O or F is unusually δ+ because those atoms are very electronegative and because hydrogen has no inner shell — strip away most of its single electron and what is exposed is a bare proton, an extremely concentrated positive charge. A lone pair on a small, electronegative neighbour can approach that charge very closely. The bond is directional: it is strongest when X–H···Y is linear.

The evidence: boiling points of the hydrides

Down each group the hydrides get heavier, gain electrons, and boil at steadily higher temperatures — exactly as dispersion forces predict. Group 14 does this cleanly all the way. In Groups 15, 16 and 17 the first member breaks the pattern violently, and in every case that first member is the one that can hydrogen bond.

Why water is strange3.6.4

Ice is less dense than water

Each water molecule can form four hydrogen bonds, arranged tetrahedrally. On freezing, the molecules take up the arrangement that satisfies all four, and that arrangement is an open, cage-like lattice containing large hexagonal holes. In liquid water the hydrogen bonds are constantly breaking and re-forming, so molecules can pack more closely — about 9% more closely. Ice therefore floats, and water reaches its maximum density at 4 °C rather than at its freezing point.

The rest of the list

• High melting and boiling point — 0 °C and 100 °C, against −85 and −60 °C for H₂S, which is a heavier molecule.
• High surface tension — a molecule at the surface has no neighbours above it, so the net hydrogen bonding pulls it inward. The surface behaves like an elastic membrane, which is why small insects can stand on water and why droplets are spherical.
• High specific heat capacity and enthalpy of vaporisation — a great deal of energy goes into breaking hydrogen bonds, which is what makes sweating an effective coolant and oceans a thermal buffer.
• Solvent for ionic and polar substances — the molecular dipole lets water surround ions and hydrogen bond to sugars, alcohols and proteins.
• Ethanol mixes with water in all proportions, while ethane does not dissolve at all: the O–H group can hydrogen bond into the water network, a C–H group cannot.

Deciding which forces act

Topics 4.2 and 3.5

Bonding and structure · Shapes of molecules

Bonding decides what holds the particles together. Structure decides how they are arranged, and between them they fix every physical property. Then, for molecules, shape decides polarity, packing and — later in the course — reactivity.

The four types of crystal

Ionic and metallic lattices in detail

Sodium chloride: 6:6 coordination

Each Na⁺ is surrounded octahedrally by six Cl⁻ ions, and each Cl⁻ by six Na⁺ — a face-centred cubic arrangement. The formula NaCl states the ratio, 1:1; there is no such thing as an NaCl molecule. Caesium chloride, whose cation is larger, achieves 8:8 coordination instead, showing that the packing arrangement is set by the relative sizes of the ions.

Why ionic solids are brittle

Apply enough force to slide one plane of ions over the next by half a lattice spacing and every ion is now adjacent to an ion of the same charge. The lattice does not deform, it repels itself apart, and the crystal cleaves along a flat plane. Compare a metal, where sliding one plane over another changes nothing because the electron sea is indifferent to where the cations are.

Close packing in metals

Metal atoms are effectively spheres of equal size with non-directional bonding, so they pack as efficiently as spheres can — 74% of space filled. There are two ways to stack the layers:

• ABAB… — hexagonal close packing (hcp): Mg, Zn, Ti.
• ABCABC… — cubic close packing (ccp, = face-centred cubic): Cu, Ag, Au, Al.

Both give each atom 12 nearest neighbours. Some metals adopt the slightly less efficient body-centred cubic arrangement (68%, 8 nearest neighbours): the Group 1 metals, and iron at room temperature.

Giant covalent structures

Diamond

• Every carbon is sp³ hybridised and bonded to four others, tetrahedrally, at 109.5°, with C–C = 0.154 nm.
• The covalent network extends through the whole crystal — a diamond is, in effect, one molecule.
• Extremely hard and melting above 3500 °C: melting or scratching it means breaking covalent bonds.
• Does not conduct electricity — all four outer electrons of every atom are localised in σ bonds, so there are no mobile charge carriers.
• Conducts heat superbly (better than any metal at room temperature) because the stiff, perfectly ordered lattice transmits vibrations extremely efficiently.
• Insoluble in every solvent; there is nothing a solvent could detach.

Graphite

• Every carbon is sp² hybridised and bonded to three others in flat hexagonal layers, at 120°, with C–C = 0.142 nm — shorter and stronger than in diamond because of the partial π character.
• The fourth electron of each atom occupies an unhybridised p orbital perpendicular to the layer. These overlap sideways across the whole sheet, producing a delocalised π system.
• Conducts electricity along the layers because those delocalised electrons are mobile — and much less well perpendicular to them. This is the exception to "covalent substances do not conduct".
• Soft, slippery, used as a lubricant and in pencils: the layers are 0.335 nm apart, held only by dispersion forces, so they slide over one another easily.
• Melting point is still enormous (sublimes above 3600 °C) because melting requires breaking the covalent bonds within the layers.
• Less dense than diamond (2.27 vs 3.51 g cm⁻³) because the layered structure wastes space.

Other allotropes and networks

Simple molecular crystals

The lattice points are whole molecules, and only intermolecular forces hold them in place. Everything follows: low melting and boiling points, softness, no conductivity in any state, and solubility governed by whether the solvent can offer similar forces.

Iodine

I₂ molecules sit at the points of a face-centred cubic lattice, held by dispersion forces only. Iodine still melts at 114 °C — high for a molecular solid — because each molecule has 106 electrons and is highly polarisable. It sublimes readily to a violet vapour, and dissolves in hexane (dispersion forces on both sides) far better than in water.

Ice

Water molecules held in an open tetrahedral network of hydrogen bonds, four per molecule. Compared with iodine, ice melts at a much lower temperature (0 °C) even though hydrogen bonds are individually stronger than iodine's dispersion forces — because a water molecule has only 10 electrons, and there are far fewer forces per unit volume to break.

Shapes of molecules and ions3.5.1–3.5.2

The method, in four steps

1. Count the outer-shell electrons of the central atom.
2. Add one electron per single bond to a monovalent atom such as H or a halogen. For a double bond, add nothing extra — a double bond counts as one region of electron density and the two electrons the central atom contributes are already counted. For a dative bond in which the central atom is the acceptor, add two.
3. Adjust for charge: subtract one electron per positive charge, add one per negative charge.
4. Divide by two to get the total number of electron pairs; subtract the number of bonded atoms (bonding regions) to find the lone pairs. Then read the shape off the table.

The complete table

The effect of lone pairs on bond angles

Within one electron-pair geometry, each lone pair you add closes the bond angle by roughly 2.5°. The classic series is the isoelectronic set of four-pair molecules:

Double bonds, ions and unfamiliar molecules3.5.2

A double bond is one region of electron density

For shape purposes, treat C=O exactly as you would treat C–O. CO₂ has two regions, so it is linear. SO₃ has three, so it is trigonal planar.

SO₂: the one you must know

Sulfur contributes 6 outer electrons. Two S=O double bonds add nothing (the double bond uses the sulfur's own electrons), so 6 electrons → 3 pairs: two bonding regions and one lone pair. Three regions are trigonal planar; with one being a lone pair the molecule is bent at about 119° — and therefore polar, unlike the linear, non-polar CO₂.

ClO₂: why understanding beats memorising

Chlorine dioxide looks like carbon dioxide on paper, yet it is bent, not linear. Chlorine has seven outer electrons; two are used in the double bonds, leaving five — two lone pairs and one unpaired electron on the central atom. That gives three regions of electron density round chlorine, so the electron geometry is trigonal planar and the molecule is bent, at about 117°. A molecule with an odd number of electrons cannot have a symmetrical pair arrangement.

Shapes of ions

Review

Review and data

Self-test30 questions

Written to the style of 9701 Paper 1 and the short-answer parts of Paper 2. Answers explain the reasoning, not just the letter.

Definitions to learn word for word

Data used on this page

All numerical values quoted here are reference data taken from standard tabulations, given so that trends can be compared. They are not a substitute for the Cambridge data booklet you are given in the examination, and any calculation you submit should use the booklet's values.