Sigma bonds come in six varieties: Pi bonds come in one

You may recall from Gen chem (and no doubt your first week of o-chem as well), that orbitals on carbon come in two flavors: s and p.

s orbitals should be familiar as the spherical-shaped orbitals. The electrons of hydrogen, for instance, are in a 1s orbital.

p orbitals are shaped like figure-eights, or loops. The electrons in p orbitals are slightly farther away from the nucleus than those in s orbitals, so they are a little bit higher in energy. The p orbitals therefore fill with electrons only after the s orbitals are filled.

Hybridization is a concept that  we address here.

What’s observed from analyzing the structure of molecules such as CH₄ is that the shapes cannot result from the electrons being in s or p orbitals alone, but instead are a consequence of the electrons in s and p orbitals mixing to form hybrid orbitals. If you draw an analogy to how we could make a “hybrid” soft drink by  mixing different proportions of Sprite and Pepsi, these new orbitals aren’t fully s or fully p, but are a combination of both. The “flavor” of each bond depends on the relative proportions of s orbital and p orbital content:

• sp³ = 25% s character, 75% p character
• sp² = 33% s character, 66% p character
• sp = 50% s character, 50% p character.

It is these hybrid orbitals that form sigma bonds (σ bonds). Sigma bonds are created from the head-on overlap of orbitals. Those orbitals will be some combination of s orbitals and p orbitals.

[What’s happened to the missing p orbitals for sp² and sp hybridized carbon? Well, these p orbitals aren’t involved in hybridization or in  sigma bonding –  instead, they maintain 100% p character,  are available to form π bonds, which are created by the side-by-side overlap of orbitals. π bonding involves p orbitals exclusively. ]

Since carbon can exist in one of these three hybridization states, we can therefore have six varieties of carbon-carbon sigma bonds:

Now, recall that for any given quantum number, s orbitals are lower in energy than p orbitals. The electrons in s orbitals are held more closely to the nucleus than electrons in p orbitals. Take a look at the relative bond lengths and strengths for each of these six situations.

General principle – the more s character the bond has, the more tightly held the electrons will be. [Note 1]

Now, the number of π bonds that can form will be dependent on the number of unhybridized p orbitals available – 1 for sp² hybridized carbons, 2 for sp hybridized carbons (the two π bonds will be at right angles to each other in the latter case).

In contrast to sigma orbitals, there is only one way to form a C-C π bond – from the overlap of two p orbitals.

Question:  Relative to sigma bonds, do you think p-p bonds (π bonds) would be stronger or weaker?

1) What’s their % s-character?

2) Energy required to break C-C bond in ethane:

Energy required to break apart the C=C bond in ethene:

Notes

Note 1. This is also why the protons in acetylene are more acidic than those in ethene and ethane – the electrons in the conjugate base are more tightly held, making them more stable. If it seems contradictory that the bond is both stronger and yet more easily broken, remember that bond energies measure homolytic cleavage]

(Advanced) References And Further Reading

1. Tables of bond lengths determined by X-ray and neutron diffraction. Part 1. Bond lengths in organic compounds. Allen, F. H.; Kennard, O.; Watson, D. G. ; Brammer, L.; Orpen, A. G.; Taylor, R. J. Chem. Soc., Perkin Trans. 2, 1987, S1-S19
   DOI: 10.1039/P298700000S1
   A useful reference, this paper collects bond lengths of various organic compounds determined from X-ray crystal diffraction data.