Carbon dioxide

In carbon dioxide the central carbon is double-bonded to two oxygens. It bonds to only two atoms, so like the carbons in ethyne it is sp hybridized: its two sp orbitals point in opposite directions and the molecule is a straight line, with an O=C=O angle of 180°. Turn on Angles & lengths to check.

Each C=O double bond needs its own π bond, and carbon has two leftover p orbitals for the job, at right angles to each other. Turn on p orbitals: one of carbon’s p orbitals lines up with a p orbital on the left oxygen, and the other lines up with a p orbital on the right oxygen, rotated 90°. So the two π bonds are perpendicular, just like the two π bonds in ethyne. They’re simply shared out between two different oxygens.

Now turn on π electrons. Instead of two separate bonds you’ll see one smooth tube wrapped around the whole O=C=O axis. Two things blend into that tube: the electrons of the two π bonds, and some of the oxygens’ lone-pair electrons, which sit in p orbitals of the same shape. Like ethyne’s, the tube has no density along the axis itself.

Each C=O bond is polar, because oxygen pulls electrons toward itself. But the two bonds point in exactly opposite directions, so their pulls cancel and CO₂ as a whole is nonpolar. That’s a good example of shape deciding a molecule’s properties. Water has polar bonds too, but its bent shape means they don’t cancel.