One important property of molecules is their polarity. A polar molecule has positive and negative poles, areas where there is a partial charge along the molecule. Polar molecules orient themselves in an electric field, with the negative ends towards the + end of the field and vice versa.

Polarity in molecules is due to a combination of polar bonds and molecular geometry. (Gotten from VSEPR theory or more sophisticated methods.)

For diatomic molecules, determining polarity is easy. Since there is only one bond, decide if the bond is polar. (All bonds except those between like atoms are polar.) If it is, the molecule is polar.

For molecules with more than two atoms, it's a bit more complicated. Consider two molecules, BeH₂ and H₂O. Both of these contain polar bonds, since the Be-H and H-O bonds are between unlike atoms. Drawing the Lewis structures for each and using VSEPR theory, we can see that the BeH₂ molecule is linear (Type AX₂), while the H₂O molecule is bent. (Type AX₂E₂)

BeH2
H2O

Since hydrogen is more electronegative than beryllium, the bond dipole will have a negative charge on the hydrogen and a positive one on beryllium. However, for the molecule, the two dipoles are in opposite directions with equal magnitude: they will thus cancel out. (For those who've had vector math, each of the bond dipoles is a vector in 3-space. Simply adding them gives a zero vector.) The BeH₂ molecule is nonpolar, even though it contains polar bonds.

For water, on the other hand, the dipole has oxygen negative and hydrogen positive. Since the molecule is bent, the two vectors do not add up to zero, and the molecule has an overall dipole: it is polar.

This sort of analysis can be used for more complex molecules as well. In general, if a molecule has polar bonds arranged symmetrically around the central atom, the molecule is non-polar.

Example 1: Is the N₂ molecule polar?

Solution 1: No. The N₂ molecule has only one bond, and since it's between two of the same atoms that bond is non-polar, thus the N₂ molecule is non-polar.

Example 2: Is the AlH₃ molecule polar?

Solution 2: The Al-H bond is polar, with the hydrogen being the negative end. If we draw the AlH₃ Lewis structure, we realize it is of type AX₃, trigonal planar. The polar bonds are arranged symmetrically around the central aluminum atom, thus, the AlH₃molecule is non-polar

Example 3: Is the CHCl₃ molecule polar?

Solution: The molecule contains two types of polar bonds: C-Cl and C-H. In both cases the hydrogen is the negative end, but the C-Cl bond is much more polar than the C-H bond since Cl is much more electronegative than H. The molecule is of type AX₄, tetrahedral. The polar bonds are not arranged symmetrically around the center, however: there is one bond that is only weakly polar around three that are strongly polar. 
Thus, the CHCl₃ molecule is polar

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