Covalent and Coordinate Bonding

When two non-metal atoms bond, neither can pull an electron completely away from the other, so instead they share electrons. This note defines covalent bonding in the syllabus wording, shows how to draw dot-and-cross diagrams for every molecule the syllabus names (including multiple bonds, expanded octets and odd-electron species), explains coordinate (dative covalent) bonding in the ammonium ion and in $\ce{Al2Cl6}$, and defines bond energy and bond length so you can use them to compare how reactive molecules are. Dot-and-cross diagrams and the two bond definitions appear in Paper 2 almost every series.

What a covalent bond is

Think of two hydrogen atoms approaching each other. Each nucleus attracts its own electron, but also the other atom's electron. When the atoms are close enough, the two electrons settle in the region between the nuclei, where both nuclei attract them. The shared pair acts like glue: each positive nucleus is attracted to the negative pair sitting between them.

Three points follow from this definition.

• The bond is electrostatic, just like ionic and metallic bonding. What differs is what is attracted to what: here, two nuclei to one shared pair.
• A single bond is one shared pair, a double bond two shared pairs and a triple bond three shared pairs.
• A covalent bond is directional: it points from one nucleus to the other. That is why covalent molecules have definite shapes, unlike ionic lattices.

Covalent bonds form between atoms whose electronegativities are similar, usually two non-metals. When the electronegativities are equal (as in $\ce{Cl2}$) the pair is shared equally; when they differ (as in $\ce{HCl}$) the pair is pulled towards the more electronegative atom and the bond is polar. You will use bond polarity in the note on intermolecular forces.

Lone pairs and bonding pairs

The outer-shell electrons of a covalently bonded atom are in two kinds of pair:

• a bonding pair is shared between two atoms;
• a lone pair (non-bonding pair) belongs to one atom only.

In ammonia, nitrogen has three bonding pairs (one to each hydrogen) and one lone pair. Counting these pairs is the key to working out molecular shapes in the next notes.

Dot-and-cross diagrams for molecules

A dot-and-cross diagram for a molecule shows the outer-shell electrons of each atom. Electrons that came from one atom are drawn as dots, electrons from the other atom as crosses, and shared pairs sit where the atoms' circles overlap.

The diagrams below cover the molecules the syllabus names. Circles are optional in an exam (you may draw the atoms' symbols with electrons around them), but shared pairs must be clearly between the two atoms and every outer electron must be shown.

Hydrogen chloride looks like chlorine but with one of the chlorine atoms replaced by a hydrogen with no lone pairs: one shared pair, and three lone pairs on chlorine. Hydrogen, $\ce{H2}$, is simply two overlapping circles with one dot and one cross between them.

Multiple bonds

When an atom still has too few electrons after forming single bonds, it shares a second or third pair with the same neighbour.

For the two hydrocarbons in the list:

molecule	bonding pairs	lone pairs	key feature
ethane, $\ce{C2H6}$	7 (one C–C, six C–H)	0	every carbon has four single bonds
ethene, $\ce{C2H4}$	6 (two shared between the carbons, four C–H)	0	a $\ce{C=C}$ double bond: four electrons, two dots and two crosses, between the carbons

Exceptions to the octet rule

Most atoms in molecules have eight outer electrons, but the syllabus expects you to know three kinds of exception.

Expanded octets in Period 3

Elements in Period 3 and beyond can have more than eight electrons in their outer shell. Their outer shell is the third shell, which contains empty 3d orbitals of fairly similar energy to the 3s and 3p orbitals. Electrons can be promoted into these, so more electrons are available to pair up in bonds. Period 2 elements (such as nitrogen and oxygen) cannot do this: their second shell has no d sub-shell, so it holds at most eight electrons.

molecule	central atom's outer electrons	electrons around central atom	arrangement
$\ce{SO2}$	S: 6	10	two $\ce{S=O}$ double bonds and one lone pair
$\ce{PCl5}$	P: 5	10	five P–Cl single bonds, no lone pairs
$\ce{SF6}$	S: 6	12	six S–F single bonds, no lone pairs

In $\ce{PCl5}$, all five of phosphorus's outer electrons are paired with one electron from each of five chlorine atoms; each chlorine keeps three lone pairs. In $\ce{SF6}$, all six of sulfur's outer electrons pair with one electron from each of six fluorine atoms.

Electron-deficient molecules

Some central atoms have fewer than eight electrons. Boron has three outer electrons, so in $\ce{BF3}$ it forms three single bonds and has only six electrons around it. Aluminium chloride, $\ce{AlCl3}$, is the same: aluminium has six electrons. These molecules can accept a lone pair from another species, which leads to coordinate bonding below.

Odd-electron species

A molecule with an odd total number of outer electrons cannot have every electron paired. Nitrogen monoxide, $\ce{NO}$, has $5 + 6 = 11$ outer electrons. Drawn with an $\ce{N=O}$ double bond, oxygen has two lone pairs (8 electrons) but nitrogen has one lone pair and one unpaired electron, so only 7 electrons. Nitrogen dioxide, $\ce{NO2}$, is also an odd-electron molecule ($5 + 6 + 6 = 17$). Species with an unpaired electron are called radicals, and they are typically very reactive, which you will meet again in organic chemistry.

Coordinate (dative covalent) bonding

In an ordinary covalent bond, each atom provides one electron of the shared pair. In a coordinate bond, also called a dative covalent bond, both electrons of the shared pair come from the same atom.

Two conditions are needed:

1. one atom has a lone pair to donate;
2. the other atom has an empty orbital in its outer shell that can accept the pair (it is electron deficient).

A coordinate bond is drawn as an arrow from the donor atom to the acceptor atom, for example $\ce{H3N -> H+}$. Once formed, a coordinate bond is identical to any other covalent bond of the same type: the four N–H bonds in the ammonium ion are indistinguishable.

The ammonium ion

When ammonia gas and hydrogen chloride gas meet, white fumes of ammonium chloride form:

$$\ce{NH3(g) + HCl(g) -> NH4Cl(s)}$$

The hydrogen chloride transfers $\ce{H+}$ to ammonia. The $\ce{H+}$ ion has no electrons at all, so it has an empty 1s orbital. The nitrogen lone pair is donated into it, forming a coordinate bond and the ammonium ion, $\ce{NH4+}$. The chloride ion keeps the electron from the original H–Cl bond, so ammonium chloride is an ionic compound made of $\ce{NH4+}$ and $\ce{Cl-}$ ions.

The same thing happens when an acid dissolves in water: a lone pair on the oxygen of water forms a coordinate bond to $\ce{H+}$, giving the oxonium ion, $\ce{H3O+}$.

Aluminium chloride and Al2Cl6

At about $180\ ^\circ\text{C}$ aluminium chloride sublimes, and in the vapour (and in the solid at lower temperature) it exists largely as dimers, $\ce{Al2Cl6}$:

$$\ce{2AlCl3 <=> Al2Cl6}$$

In $\ce{AlCl3}$ the aluminium has only six outer electrons and an empty orbital. A chlorine atom on one $\ce{AlCl3}$ unit has three lone pairs. One lone pair from a chlorine on each $\ce{AlCl3}$ unit is donated to the aluminium of the other unit, so the dimer contains two coordinate bonds. The two "bridging" chlorine atoms each bond to both aluminium atoms; the other four chlorines are "terminal".

After dimerisation, each aluminium atom has four bonding pairs (three ordinary covalent bonds and one coordinate bond), so it has eight electrons: a full octet. The arrangement around each aluminium is roughly tetrahedral.

feature of $\ce{Al2Cl6}$	detail
total Al–Cl bonds	8
coordinate bonds	2 (from bridging Cl to Al)
electrons around each Al	8
lone pairs on each bridging Cl	2
lone pairs on each terminal Cl	3

Bond energy and bond length

How strong is a covalent bond, and how does that relate to reactivity? Two measurable quantities answer this.

Bond energies are always positive, because breaking a bond always needs energy. The phrase "in the gaseous state" matters: breaking bonds in a liquid or solid would also involve overcoming intermolecular forces.

For a diatomic molecule, the bond energy is exact: there is only one bond to break. For a bond such as C–H, the energy needed depends slightly on the molecule it is in, so the data booklet quotes an average bond energy over many compounds. You will use this distinction in the note on bond energies and enthalpy changes.

How bond length and bond energy are linked

The more electrons shared between two nuclei, the more strongly the nuclei are attracted to the pairs and the closer they are pulled together. So, for the same pair of atoms, multiple bonds are shorter and stronger:

bond	bond energy / kJ mol⁻¹	bond length / nm
C–C	350	0.154
C=C	610	0.134
C≡C	840	0.120

Down a group, atoms get larger, the bonding pair is further from the nuclei and more shielded, so the attraction is weaker. Bonds get longer and weaker:

bond	bond energy / kJ mol⁻¹	bond length / nm
H–F	562	0.092
H–Cl	431	0.127
H–Br	366	0.141
H–I	299	0.161

Bond energy and reactivity

Most reactions start by breaking a bond. A molecule with only strong bonds is hard to break apart, so it tends to be unreactive; a molecule with a weak bond reacts more readily.

• Nitrogen, $\ce{N2}$, has a triple bond with bond energy $944\ \text{kJ mol}^{-1}$, among the strongest known. That is why nitrogen is so unreactive and makes up most of the atmosphere, and why the Haber process needs a catalyst, high temperature and high pressure.
• Hydrogen halides: thermal stability decreases from HF to HI because the H–X bond gets longer and weaker. A hot wire plunged into hydrogen iodide produces violet iodine vapour; hydrogen chloride is unaffected.
• Halogenoalkanes (organic chemistry): the C–I bond is the longest and weakest carbon–halogen bond, so iodoalkanes react fastest in substitution reactions.

Worked examples

Practice

Answers

1. The electrostatic attraction between the nuclei of two atoms and a shared pair of electrons.
2. Each carbon forms single bonds to two hydrogens (one dot, one cross each) and a double bond to the other carbon (two dots and two crosses between the carbons). No lone pairs. Each carbon has 8 outer electrons; each hydrogen has 2.
3. (a) $\ce{H2O}$: 2 bonding pairs, 2 lone pairs. (b) $\ce{PCl5}$: 5 bonding pairs, 0 lone pairs. (c) $\ce{SO2}$: 4 bonding pairs (two double bonds), 1 lone pair. (d) $\ce{BF3}$: 3 bonding pairs, 0 lone pairs.
4. $\ce{HCl}$ transfers $\ce{H+}$ to ammonia. The lone pair on nitrogen is donated into the empty 1s orbital of $\ce{H+}$, forming a coordinate (dative covalent) bond: $\ce{NH3 + H+ -> NH4+}$. Once formed, the coordinate bond is a shared pair between N and H exactly like the other three, so all four bonds have the same length and strength.
5. The energy required to break one mole of a particular covalent bond in the gaseous state. Breaking a bond means separating the nuclei from the shared pair against their electrostatic attraction, which always requires energy (endothermic, positive).
6. The $\ce{N#N}$ triple bond is very strong, so a large amount of energy is needed to break it before nitrogen can react: nitrogen is very unreactive. The F–F bond is very weak, so it breaks easily and fluorine is extremely reactive.
7. Oxygen (6 outer electrons, dots) shares one pair with hydrogen (one dot, one cross from H). Oxygen has three lone pairs, one of which contains the extra electron gained to make the ion (shown with a different symbol, for example a triangle or open circle). The whole ion is drawn in square brackets with a $-$ charge.
8. Oxygen is in Period 2. It has six outer electrons and needs two more to complete an octet; its second shell cannot hold more than eight electrons, so it forms two bonds and keeps two lone pairs. Sulfur is in Period 3 and has empty 3d orbitals in its outer shell, so it can expand its octet: all six outer electrons can be used to form six bonds, giving 12 electrons around sulfur.
9. Two of the shared pairs are ordinary covalent bonds (one electron from C and one from O in each). The third is a coordinate bond in which oxygen donates a lone pair to carbon. Carbon then has 6 electrons in bonds plus one lone pair (8); oxygen has 6 electrons in bonds plus one lone pair (8). Each atom has one lone pair.
10. In $\ce{AlCl3}$ the aluminium atom has only six outer electrons and so has an empty orbital. A lone pair on a chlorine atom of one $\ce{AlCl3}$ molecule is donated into the empty orbital of aluminium in a second molecule, and vice versa, forming two coordinate bonds. Lone pairs: four terminal chlorines with three each ($4 \times 3 = 12$) and two bridging chlorines with two each ($2 \times 2 = 4$), so 16 lone pairs in total.