Covalent, dative covalent and metallic bonding

A shared pair held by two nuclei

Hydrogen gas is made of H₂ molecules, and the two atoms in each are held together firmly: breaking one mole of H–H bonds takes 436 kJ. Neither atom has given its electron to the other, since both attract electrons equally. The two electrons spend most of their time in the region between the nuclei, and each positive nucleus is attracted to that negative pair. The pair is attracted to both nuclei at once, and that attraction is the covalent bond.

Covalent bonds form between non-metal atoms, where neither atom loses electrons easily. Each atom usually supplies one electron to each bond, and forms as many bonds as it needs to fill its outer shell: hydrogen forms one, oxygen two, nitrogen three and carbon four. Outer electrons that are not used in bonding stay on their atom in pairs. These lone pairs decide the shapes of molecules, form dative bonds and take part in hydrogen bonding.

Covalent bond

A shared pair of electrons between two atoms, attracted electrostatically to the nuclei of both.

Bonding pair

A pair of electrons shared between two atoms in a covalent bond.

Lone pair

A pair of outer-shell electrons on one atom that is not used in bonding.

Drawing molecules

In a dot-and-cross diagram for a molecule, the outer shells of the bonded atoms overlap and the shared electrons sit in the overlap. One atom's electrons are dots and the other's crosses, so each shared pair is one dot and one cross. Circles for the shells are optional; what must be right is the number of electrons in each overlap and the lone pairs on each atom.

Count before drawing. In ammonia, nitrogen has five outer electrons and each hydrogen one. Nitrogen shares one electron with each of three hydrogen atoms, giving three bonding pairs, and its remaining two electrons form a lone pair. Each hydrogen now has two electrons and nitrogen has eight. Water follows the same count: oxygen's six outer electrons give two bonding pairs and two lone pairs. Methane has four bonding pairs and no lone pair. In hydrogen chloride the single bonding pair leaves three lone pairs on chlorine.

Describe the drawing

Two dot-and-cross diagrams with outer shells drawn as overlapping circles. Ammonia: a nitrogen circle overlapped by three hydrogen circles, each overlap holding one cross from nitrogen and one dot from hydrogen, and a lone pair of two crosses at the top of nitrogen. Carbon dioxide: oxygen, carbon and oxygen in a row, each overlap holding two crosses and two dots as a double bond, and two lone pairs of dots on the outer side of each oxygen. Beneath each, its displayed formula.

A dot-and-cross diagram is a count, not a picture. It shows how many electrons each atom supplies and where the lone pairs are, but it is drawn flat, so it says nothing about the angles between the bonds. Ammonia drawn this way looks like a flat T; the real molecule is a pyramid. The shape comes from the number of bonding pairs and lone pairs the diagram reveals. Draw the shared pair in the overlap and write 'shared pair of electrons' in words; a scheme accepts 'shared pair' but not 'shared electrons', which could be one electron or three.

Double and triple bonds

Two atoms can share more than one pair. In an oxygen molecule each atom has six outer electrons and needs two more, so the atoms share two pairs: a double bond, O=O, with two lone pairs left on each atom. Nitrogen needs three, so N₂ has a triple bond, N≡N, and one lone pair on each atom. In carbon dioxide, carbon shares two pairs with each oxygen, O=C=O, and has no lone pairs of its own.

More shared pairs pull the two nuclei closer and hold them more strongly, so multiple bonds are shorter and stronger than single bonds between the same atoms. The triple bond in N₂, at 945 kJ mol⁻¹, is one of the strongest bonds there is, and the nitrogen in the air reacts with almost nothing.

The same link between length and strength runs down a group. As the halogen atom gets larger, the shared pair in its bond to hydrogen is further from the halogen nucleus, the bond is longer, and it is weaker: H–F 562, H–Cl 432, H–Br 366 and H–I 298 kJ mol⁻¹. A hot wire pushed into hydrogen iodide gives violet fumes of iodine at once, while hydrogen chloride is unchanged. The weaker bond breaks more readily, so here bond enthalpy, not polarity, accounts for which of the two reacts.

The full outer shell of eight is a pattern, not a law. Boron in BF₃ shares its three electrons and ends with only six. Elements in Period 3 and below can hold more than eight, because their outer shell has room beyond the s and p orbitals: phosphorus shares all five outer electrons in PCl₅, giving it ten, and sulfur shares all six in SF₆, giving it twelve. Nitrogen, in Period 2, can never do this, so there is NCl₃ but no NCl₅.

Double bond

Two shared pairs of electrons between the same two atoms, shorter and stronger than a single bond between them.

Bond length

The distance between the nuclei of two covalently bonded atoms; for the same pair of atoms, the shorter the bond, the stronger it is.

Dative covalent bonds

Ammonia dissolves in acid to form the ammonium ion. The nitrogen in NH₃ has a lone pair, and a hydrogen ion, H⁺, has no electrons at all. The lone pair forms a bond to the H⁺, both electrons coming from nitrogen. A covalent bond in which both shared electrons come from the same atom is a dative covalent bond, also called a co-ordinate bond.

NH₃(aq) + H⁺(aq) → NH₄⁺(aq)

A dative bond is drawn as an arrow from the atom that supplies the pair to the atom that accepts it, N→H. The arrow records how the bond formed. Once the ion exists, its four N–H bonds are identical in length and strength, the ion is a regular tetrahedron, and nothing distinguishes the hydrogen that arrived last. The charge belongs to the whole ion and is written outside square brackets.

Describe the drawing

Two panels. In the first, ammonia drawn as dot-and-cross with nitrogen's lone pair of two crosses at the top, plus an empty-shelled H⁺, react to give the ammonium ion in square brackets with a plus charge, whose top overlap holds two crosses; beneath it the ammonium displayed formula with one N–H bond drawn as an arrow from N to H. In the second, Al₂Cl₆: two aluminium atoms with two terminal chlorines each, bridged by two chlorine atoms, each with an ordinary bond to one aluminium and an arrow to the other.

A dative bond needs an atom with a lone pair to give and an atom with an empty orbital to receive it. Water likewise gives a lone pair to H⁺, forming the oxonium ion, H₃O⁺, which is present in every acidic solution. Aluminium chloride is the third example. In AlCl₃ the aluminium has only six outer electrons. In the vapour just above its sublimation temperature, two molecules join: a lone pair on one chlorine of each molecule forms a dative bond to the aluminium of the other, giving Al₂Cl₆, in which each aluminium has eight.

Dative covalent bond

A covalent bond in which both electrons of the shared pair come from the same atom; also called a co-ordinate bond.

Metallic bonding

A copper wire bends without snapping and carries a current, and neither fact fits ionic or simple covalent bonding. In a metal, each atom releases its outer electrons into the structure as a whole. What remains is a regular lattice of positive ions, and the released electrons are delocalised: not tied to any one atom, and free to move through the whole lattice. Metallic bonding is the electrostatic attraction between the positive ions and this sea of delocalised electrons.

Describe the drawing

Two panels of a close-packed array of sixteen magnesium ions, each a cyan disc marked 2+, on a lightly shaded background with thirty-two small amber electrons spread evenly between them, two per ion. In the right panel a force has slid the top two rows one ion spacing to the right; the array is still close-packed, the electrons are still spread evenly through it including along the slip, and every ion is still 2+.

The strength of metallic bonding depends on three things that change together across a period. Sodium releases one electron per atom, magnesium two and aluminium three, so the ions carry larger charges, there are more delocalised electrons per ion, and the ions are smaller. The attraction rises along the series, and so does the boiling point: sodium 883 °C, magnesium 1090 °C, aluminium 2519 °C.

Down Group 1 the charge stays at +1 but the ions get larger, so the delocalised electrons are further from the nuclei and the attraction is weaker. The melting point falls: lithium 181 °C, sodium 98 °C, potassium 63 °C. Boiling points show the trend across a period more cleanly than melting points, because melting only loosens a metal lattice and the ions in the liquid are still held in the sea of electrons. Magnesium melts at 650 °C and aluminium at 660 °C, almost the same, while their boiling points differ by over 1400 °C.

The properties follow from the structure. Metals conduct electricity because the delocalised electrons move through the lattice when a potential difference is applied, and the same mobile electrons carry heat. They are malleable and ductile because layers of ions can slide over one another while the electrons move with them, so no bonds break and no like charges are forced together. Most have high melting points because the attraction between ions and electrons is strong and extends through the whole giant lattice.

Metallic bonding

The electrostatic attraction between a lattice of positive metal ions and the delocalised electrons around them.

Delocalised electrons

Electrons that are not associated with any single atom or bond and are free to move through a structure.

Other boards: σ and π bonds, hybridisation and bond strength

OCR, Edexcel and Cambridge describe a covalent bond by the orbitals that overlap to make it. A σ bond forms when two orbitals overlap end-on, so the shared pair lies directly between the two nuclei. Every single bond is a σ bond: s with s in H₂, s with p in HCl, p with p in Cl₂. Turning one atom about the bond does not change that overlap, so groups joined by a single bond rotate freely.

A π bond forms when two parallel p orbitals overlap sideways, above and below the line between the nuclei. It forms only alongside a σ bond that already holds the atoms close. A double bond is one σ and one π bond; a triple bond is one σ and two π, the two π bonds at right angles to each other. Twisting about a double bond would pull the p orbitals out of line and break the π overlap, which is why a C=C bond does not rotate. AQA does not ask for σ and π in this topic.

Cambridge takes one step further and explains the directions of the bonds by hybridisation. Carbon's outer shell has one 2s and three 2p orbitals, and none of them points to the corners of a tetrahedron. In methane and ethane the 2s and all three 2p orbitals mix into four identical sp³ hybrid orbitals that do, at 109.5°, and each forms a σ bond. In ethene each carbon mixes the 2s with two 2p orbitals into three sp² orbitals, in a plane at 120°, which form three σ bonds. The third 2p orbital is left unmixed, at right angles to that plane, and overlaps sideways with its neighbour's to make the π bond.

In ethyne, HC≡CH, and hydrogen cyanide, HC≡N, carbon mixes the 2s with one 2p into two sp orbitals at 180°, and its two unmixed 2p orbitals make the two π bonds of the triple bond. HCN therefore has two σ bonds, C–H and the σ part of C≡N, and two π bonds. The number of regions of electron density round the atom fixes the hybridisation, and the angles are the ones electron-pair repulsion predicts: hybridisation describes the same shapes in terms of orbitals.

Sigma (σ) bond

A covalent bond formed by end-on overlap of two orbitals, with the shared pair lying directly between the two nuclei.

Pi (π) bond

A covalent bond formed by sideways overlap of two parallel p orbitals, with electron density above and below the line between the nuclei.

Hybridisation

The mixing of an atom's s and p orbitals to give a set of identical hybrid orbitals, sp³, sp² or sp, that point along its σ bonds.

Cambridge also asks for two reasons why the nitrogen in the air reacts with almost nothing: the triple bond is very strong, and the molecule is non-polar, with no δ+ or δ− end to attract a reagent. Both are why making ammonia from it needs an iron catalyst, a high temperature and a high pressure. Cambridge and Edexcel ask for bond lengths and bond enthalpies to be used, as with the hydrogen halides, to compare how readily covalent molecules react.