How Carbon Mixes Its Orbitals to Build Methane, Ethene and Ethyne

A Lewis structure shows that atoms share electrons, but not how. Valence bond theory pictures a bond as two atomic orbitals overlapping, and hybridisation explains how an atom such as carbon can form four identical bonds pointing to the corners of a tetrahedron.

This lesson covers valence bond theory, hybridisation and molecular shape, and how s-character affects bonds.

Valence bond theory states that a covalent bond forms when half-filled atomic orbitals of two atoms overlap and their electrons pair with opposite spins, and the greater the overlap, the stronger the bond.

Energy of bond formation. As two hydrogen atoms approach, each nucleus attracts the other atom's electron and the energy falls, until attractions and repulsions balance at the bond length, 74 pm, where energy is lowest. The energy released, 435.8 kJ mol${}^{-1}$, is the bond enthalpy.

Types of overlap:

- s-s overlap — as in hydrogen, ${\mathrm{H}}_2$
- s-p overlap — as in hydrogen chloride
- p-p overlap — as in chlorine, $\mathrm{C}{\mathrm{l}}_2$
- Only in-phase (positive) overlap forms a bond

Sigma and pi bonds:

- Sigma bond — head-on overlap along the line joining the nuclei; strong, and allows free rotation about the bond
- Pi bond — sideways overlap of parallel p orbitals above and below that line; weaker, and prevents rotation
- A single bond is one sigma bond, a double bond is one sigma and one pi, and a triple bond is one sigma and two pi

Worked example. Ethyne, $\mathrm{HC}\equiv \mathrm{CH}$, has 3 sigma bonds — two C-H and one C-C — and 2 pi bonds.

An everyday example. The LPG in a kitchen cylinder is mostly propane and butane, whose atoms are held together entirely by strong sigma bonds that need a flame to break.

The substance. Valence bond theory alone cannot explain methane's shape — carbon's unhybridised orbitals would give bonds at 90°, not 109.5°, which is why hybridisation is needed.

Hybridisation is the mixing of atomic orbitals of similar energy on one atom to form an equal number of identical hybrid orbitals, and the type of hybridisation fixes the arrangement of bonds and hence the shape of the molecule.

Features:

- Only orbitals of similar energy mix, and the number of hybrid orbitals equals the number of orbitals mixed
- Hybrid orbitals are identical in energy and shape and point as far apart as possible
- Hybrid orbitals form sigma bonds or hold lone pairs; pi bonds use unhybridised p orbitals

Finding the hybridisation. Count the sigma bonds and lone pairs on the central atom to get the steric number:

$$\text{Steric number}=\text{sigma bonds}+\text{lone pairs}$$

Types and shapes:

- sp (steric number 2) — linear, 180°; $\mathrm{BeC}{\mathrm{l}}_2$ and each carbon in ethyne
- $\mathrm{s}{\mathrm{p}}^2$ (3) — trigonal planar, 120°; $\mathrm{B}{\mathrm{F}}_3$ and each carbon in ethene
- $\mathrm{s}{\mathrm{p}}^3$ (4) — tetrahedral, 109.5°; $\mathrm{C}{\mathrm{H}}_4$, and ammonia and water with lone pairs
- $\mathrm{s}{\mathrm{p}}^3\mathrm{d}$ (5) — trigonal bipyramidal; $\mathrm{PC}{\mathrm{l}}_5$
- $\mathrm{s}{\mathrm{p}}^3{\mathrm{d}}^2$ (6) — octahedral; $\mathrm{S}{\mathrm{F}}_6$

Worked example 1 — ethene. Each carbon forms 3 sigma bonds (two C-H and one C-C) and has no lone pair, so it is $\mathrm{s}{\mathrm{p}}^2$; its unhybridised p orbitals overlap sideways to form the pi bond.

Worked example 2 — water. Oxygen has 2 sigma bonds and 2 lone pairs, a steric number of 4, so it is $\mathrm{s}{\mathrm{p}}^3$, with a bent shape.

An everyday example. Polythene sheets used in farm greenhouses are made by opening the double bonds of ethene, turning each $\mathrm{s}{\mathrm{p}}^2$ carbon into an $\mathrm{s}{\mathrm{p}}^3$ carbon in a long chain.

The substance. Hybridisation is a model that explains observed shapes, not a step atoms go through — the shape is measured first, and hybridisation describes it.