Concepts: tetravalency, hybridisation and shapes

2.1 Tetravalency and the tetrahedral carbon

Carbon has four valence electrons and needs four more to complete its octet, so it forms four covalent bonds. This tetravalency is why carbon can form long chains and rings in which each carbon is bonded to four neighbours. In methane the four bonds point toward the corners of a tetrahedron, giving bond angles of about 109.5 degrees, and the carbon is described as sp three hybridised.

The hybridisation model explains the geometry by mixing one s orbital and three p orbitals into four equivalent sp three orbitals. Each hybrid orbital points to a corner of the tetrahedron and overlaps with an orbital of another atom to form a sigma bond. The model works for ethane, in which each carbon forms four sigma bonds, and for the saturated rings of cycloalkanes.

A simpler description uses models. The ball and stick model shows the positions of the atoms and the bonds as sticks, while the space filling model shows the volume occupied by each atom and therefore the actual shape of the molecule. Both models are used to visualise organic structures, and the space filling model shows why crowded molecules have difficulty approaching each other.

2.2 sp two and sp hybridisation

When carbon forms a double bond it uses sp two hybridisation, in which three hybrid orbitals lie in a plane at 120 degrees and the remaining p orbital is perpendicular to that plane. The sigma bonds of ethene use the three sp two orbitals of each carbon, and the two unhybridised p orbitals overlap sideways to form the pi bond. The result is a planar molecule with bond angles close to 120 degrees.

For a triple bond the carbon is sp hybridised, with two hybrid orbitals at 180 degrees and two p orbitals left over. The sigma bond lies along the internuclear axis and the two pi bonds are perpendicular to each other around it, giving the linear geometry of ethyne. The same pattern applies to the nitrile group, in which the carbon and nitrogen are both sp hybridised and the group is linear.

The number and strength of bonds explain reactivity. A sigma bond is strong and free to rotate, so single bonded chains are flexible. The pi bonds of double and triple bonds are weaker and cannot rotate without breaking, which locks the geometry and makes those bonds the site of addition reactions. This is why alkenes and alkynes decolourise bromine water while alkanes do not.

2.3 Worked examples

In ethane, each carbon has four sigma bonds, so each is sp three and the carbon-carbon bond is free to rotate. The molecule has staggered and eclipsed conformations, and the staggered one is slightly lower in energy because the hydrogens are farther apart. Rotation is fast at room temperature, so the two conformations interconvert continuously.

In ethene, each carbon has three sigma bonds and one pi bond, so each is sp two. The molecule is planar, the hydrogen-carbon-hydrogen angle is about 117 degrees and the carbon-carbon bond length is shorter than in ethane because of the extra bond. The restricted rotation around the double bond is the basis of geometrical isomerism, and a substituent must have a partner on the other carbon for cis and trans forms to exist.

In ethyne, each carbon has two sigma bonds, so it is sp and the molecule is linear. The carbon-carbon bond is the shortest of the three because it has one sigma and two pi bonds. The linear shape is retained in larger alkynes, which is why the alkyne unit is a straight segment in a longer chain. The same counting rule explains the shapes of groups such as the carbonyl group, in which the carbon is sp two and the oxygen is also described with sp two hybridisation, giving the group a planar arrangement with angles near 120 degrees. The planar carbonyl group is important because it allows reagents to approach from either face and it participates in resonance with adjacent pi systems.

2.4 Why the geometry matters

The shape of a molecule controls its physical properties and its reactions. A planar alkene can approach a reagent only from the two faces of the plane, while a tetrahedral carbon presents three different directions. The three dimensional arrangement also decides whether a molecule is chiral, because a carbon with four different groups has two mirror image arrangements that are not superimposable.

The concept of hybridisation is a model, not a physical process, and the mixing of orbitals happens only in the description. What is real is the geometry that experiments show, and the model is judged by how well it predicts bond angles, bond lengths and the planarity of double bonded systems. Once the model is understood, most questions about shapes, angles and reactivity become a matter of counting the sigma bonds and lone pairs around each atom.