Why does Carbon form 4 covalent bonds instead of 2?

Most people are not in the slightest bit interested in the answer to this question. For the 1% who are though, this vexing little question is at the heart of organic chemistry - that bitch of subject that seems to drive people alternately mad/ecstatic. I always knew C formed 4 bonds, and got through uni organic chem and some other stuff without really knowing/remembering why. So....years later, I decided to sort myself out, with a particular interest in why the 4 single bonds carbon makes are done with 'sp3' orbitals and why a carbon double bond uses 'sp2' etc. The numbers 3 and 2 didn't seem to have anything to do with anything - but they do, as you can see below.

Here's the answer to why carbon forms 4 covalent bonds instead of 2:

The trivial answer is that a carbon atom that forms 4 covalent bonds is in a lower energy state that one that forms 2. But what happens when this occurs? Carbon's valence shell is configured 2s2 2p2 (remember the p shell can contain up to 6 electrons, in a 3-D 2px, 2py, 2pz shape). Two half-filled p orbitals should mean stable molecules like CH2 - the 2 electrons from the H filling the 2px and 2py subshells. But....these don't normally exist ...instead carbon likes to form 4 covalent bonds with other atoms. Why 4 and not 2? Because the 2s2 2p2 shell hybridizes. Why does it hybridise? Because it results in a lower energy state. After hybridization there are NO LONGER any s or p shells, and we're left with 4 hybrid orbitals that are 'a little bit s and a little bit p'. This is really important to understand. They've gone forever! Why are the 4 hybrid orbitals called 'sp3'? Because the new hybrid effectively replaces 1 s and 3 p orbitals, to give 4 single bonding opportunities.

2s2 2p2 becomes : sp3 sp3 sp3 sp3 (the hybrid).

What's an sp3 shell look like? sp3 shells look nothing like s or p shells...more like a short stocky baseball bat (whereas an s orbital is a sphere, and a p orbital is like 3 double baseball bats without the handles!). They're called sp3 because the s and the 3 p shells combine to make 4 sp3 orbitals. Because there are 4 of them, and they like to be as far away from each other as possible, C forms (single bonding) tetrahedral shapes ie. 4 triangle surface planes.

Here's a picture of the unhybridized orbitals (s and p):

And here's a picture of the orbitals hybridizing:

I admit that wasn't a great job explaining one of organic chemistry's most fundamental concepts, but hopefully it helped. The most important thing I realised was that sp3 orbitals are not s and not p. They are completely different, and the old s and p orbitals have gone.

Carbon and double bonds

How does a double bond work? Think of a carbon double bond in a molecule like ethylene as a carbon with 3 bonds. The hybridization logic is the same as for sp3, but this time we end up with 2 single bonds, and 1 double bond. Using ethylene as an example:

H2C=CH2

1 x s and 2 p orbitals create 3 x sp2 orbitals. The remaining p orbital on the 2 C atoms forms a pi bond. In conjunction with a sigma bond, the pi+sigma form the double bond between the carbons. The hybrids are called sp2 because they're made up of 1 x s orbital, and 2 of the p orbitals (as opposed to 3 of the p orbitals in sp3 hybridization).

A triple bond's no different: 1 x s and 1 x p form an sp orbital. 2 p's then form 2 pi bonds (used for the triple bond in conjunction with the remaining sigma bond). Between the carbon atoms, you've got one sigma bond (from the sp's touching), and 2 pi bonds to make 3! (the sp hybrid has nothing to do with the normal p pi bonding). Easy eh?

Ethyne (acetylene):

Hopefully this explanation also clears up that confusing issue of naming the hybrid orbitals. sp3 for 4 bonds, sp2 for double, and sp for triple never made any sense to me, until I realised they're just the formula that represents how many of the old s and p bonds combined. And a quick note on terminology: the orbitals are named 's', 'p' and 'sp3' etc. but the bonds are called 'sigma' or 'pi', depending on their source.

* A more advanced description is available at: UC Davis - Hybrid Orbitals And a good explanation is also available at: Organic Chemistry (Carey). The Carey book is an excellent resource for organic chemistry.