Covalent bonding and coordinate (dative covalent) bonding

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

Both nuclei attract the shared pair, holding the atoms together. Non-metals share electrons to reach a (usually) full outer shell.

Single, double and triple bonds:

• Single (1 shared pair): H₂, Cl₂, HCl, CH₄, C₂H₆.
• Double (2 shared pairs): O₂ (O=O), CO₂ (O=C=O), C₂H₄ (C=C).
• Triple (3 shared pairs): N₂ (N≡N).

In NH₃ the nitrogen also keeps a lone pair (an unshared pair) — important for shape and for dative bonding.

Period 2 atoms are limited to 8 outer electrons. Period 3 atoms can expand the octet because they have energetically accessible 3d orbitals, accommodating more than 8 electrons around the central atom:

• SO₂ — sulfur with double bonds (10 electrons around S).
• PCl₅ — phosphorus with 5 bonding pairs (10 electrons).
• SF₆ — sulfur with 6 bonding pairs (12 electrons).

This is why phosphorus and sulfur form compounds (PCl₅, SF₆) that nitrogen and oxygen cannot.

A coordinate (dative covalent) bond is a covalent bond in which both electrons of the shared pair come from the same atom (a lone pair donated to an atom/ion short of electrons). Once formed, it is identical to an ordinary covalent bond.

It is drawn with an arrow (→) pointing from the donor (lone pair) to the acceptor.

Examples:

• Ammonium ion, NH₄⁺. The N lone pair in NH₃ is donated to an H⁺ (which has no electrons): $\text{NH}_3 + \text{H}^+ \rightarrow \text{NH}_4^+$. All four N–H bonds are then equivalent.
• Al₂Cl₆. Aluminium chloride dimerises: a lone pair on a chlorine of one AlCl₃ is donated into the electron-deficient Al of the other, forming two dative bonds that bridge the two units.

Covalent bonds form by orbital overlap:

• σ (sigma) bond — formed by direct, end-on overlap of orbitals along the line between the two nuclei. Strong; allows free rotation.
• π (pi) bond — formed by the sideways overlap of adjacent p orbitals, with electron density above and below the σ bond. Weaker than σ; prevents rotation.

Counting bonds:

• Single bond = 1 σ.
• Double bond = 1 σ + 1 π (e.g. C=C in ethene).
• Triple bond = 1 σ + 2 π (e.g. N≡N in N₂; C≡N in HCN).

Worked examples of σ/π:

• Ethane C₂H₆ — all single bonds → all σ.
• Ethene C₂H₄ — the C=C is 1 σ + 1 π; C–H bonds are σ.
• N₂ — N≡N is 1 σ + 2 π.
• HCN — H–C is σ; C≡N is 1 σ + 2 π.

Hybridisation mixes atomic orbitals on the central atom to give equivalent orbitals that point towards the bonded atoms:

Hybridisation	Orbitals mixed	σ bonds	Shape	Example
sp³	1 s + 3 p	4	Tetrahedral (109.5°)	CH₄, C₂H₆ (each C)
sp²	1 s + 2 p	3 (+1 p left for π)	Trigonal planar (120°)	C₂H₄ (each C)
sp	1 s + 1 p	2 (+2 p left for π)	Linear (180°)	HCN, the C in C≡N

Pattern: count the σ bonds (and lone pairs) on the atom → 4 = sp³, 3 = sp², 2 = sp. The leftover unhybridised p orbitals form the π bonds of double/triple bonds.

Bond energy — the energy required to break one mole of a particular covalent bond in the gaseous state.

Bond length — the internuclear distance between two covalently bonded atoms.

The relationship. More shared pairs pull the nuclei closer: $\text{bond length: } \text{C–C} > \text{C=C} > \text{C≡C}$ $\text{bond energy: } \text{C–C} < \text{C=C} < \text{C≡C}$ A shorter bond is stronger (higher bond energy) because the bonding electrons are closer to, and more strongly attracted by, the nuclei.

Using this to compare reactivity:

• N₂ is very unreactive because the N≡N triple bond is exceptionally strong (high bond energy) — a lot of energy is needed to break it (links to 12.1).
• Halogenoalkane reactivity depends on C–X bond strength: C–F is strongest (shortest) → least reactive; C–I is weakest → most reactive (links to 15.1).