Gone Fishin’!

As an example:

Simple amines, molecules containing a nitrogen, are hybridized approximately sp3 at nitrogen and thus are pyramidal. The bond angles are close to the tetrahedral angle of 109.5, but, of course, cannot be exactly the tetrahedral angle. Why?

Understanding the logic and not just the facts behind it would be really helpful. Thanks in advance.

Well, NH3 for example is asymmetric, unlike CH4 – it has a lone pair of electrons instead of an atom as the fourth "group" sticking off of the central atom. Electrons that are present as lone pairs take up slightly more space because they are not confined in a bond, so they "push" the three H-N-H bonds down a little, causing the N-H angles to decrease slightly. CH4, on the other hand, also has four "groups" sticking off of the central atom, but they’re all the same – single bonded H atoms. Since each of the C-H bonds is identical*, they take up exactly the same amount of space and therefore the bond angles are identical as well.

* for this application, this is true, but if you get into molecular orbital theory in more detail in organic chemistry, you will see that the four C-H bonds are actually NOT exactly the same. Or so the current theory says!