Covalent bonds are formed when two atoms share one or more pairs of electrons.
We now want to examine the nature of that sharing in greater detail.
First, we will consider the question of whether two atoms share a pair of electrons equally, i.e. is the electron density in the inter-nuclear region symmetrically distributed or not?
Bonds in which the electron density is symmertically distributed between the nuclei are called non-polar bonds, while those in which the electron density is unsymmetrically distributed are called polar bonds.
Any bond between two identical atoms is non-polar since the electronegativities of the two atoms is identical. The simplest examples are the diatomic molecules such as H2, N2, and F2. The C-C bond in ethane, H3C-CH3, is also non-polar.
Any bond between two non-identical atoms is polar.
The bond in HF is polar.
So are the C-H bonds in CH4.
Both C-C bonds in propane CH3CH2CH3 are polar.
This is because the terminal carbon atoms and the central carbon are not identical. The terminal carbon atoms are both bonded to three hydrogen atoms and the central carbon atom. The central carbon, however, is bonded to two hydrogen atoms and two carbon atoms.
An alternative way to think about this is to identify the groups that are attached to each carbon in propane. The left-hand carbon is attached to three hydrogen atoms and a CH2CH3 (ethyl) group. The central carbon is attached to two hydrogen atoms and two CH3 (methyl) groups. Since the right-hand carbon is attached to three hydrogen atoms and an ethyl group, it is identical to the left-hand carbon. Looking at propane in this way allows us to introduce the idea of group electronegativities.
In the same way that the electronegativity of an atom is a measure of the tendency of that atom to attract electrons, group electronegativity is a measure of the tendency of a polyatomic group to attract electrons.
Propane contains two CH3 groups and one CH2 group (methylene group). Since these two groups are not identical, they have different group electronegativities. Even though the H3C-CH2 bond is a bond between two carbon atoms, the carbons are not identical because they have different atoms attached to them.
As far as the pair of electrons that the two carbons share goes, they experience a different Coulombic attraction from the CH3 group than they do from the CH2 group.
One way to investigate group electronegativities experimentally involves nuclear magnetic resonance (NMR) spectroscopy.
Polar and Non-Polar Molecules
The C-H bonds in methane are polar. However, a molecule of methane is non-polar. Specifically, the dipole moment of methane is zero.
A dipole moment of zero means that the "center of negative charge" in the molecule corresponds to the "center of positive charge". In the case of methane, the "center of positive charge" and the "center of negative charge" are focused on the carbon atom. Think of the "center of charge", whether positive or negative, in the same way that you think of the "center of mass". From that perspective, a molecule with a dipole moment of zero is like a perectly balanced see-saw.