I thought that it was about four bonds to carbon! We were told that if a molecule had a C atom with four different groups, the molecule was chiral!
Yeah, your mom told you Santa Claus was real, too.
The four different groups thing is a good trick, but it's obviously only useful for organic compounds, and even then it doesn't always work. Four different groups at a C atom -- a so-called stereogenic carbon or stereocentre -- is neither a necessary nor sufficient condition for chirality. In other words: A) chirality can occur in the
absence of such carbon, and B) the presence of such a carbon isn't a guarantee for chirality.
Case A: chirality in the absence of a stereogenic carbon.
None of the structures below has four different groups at any carbon. In fact, none has four bonds at any carbon: all the C atoms are sp2 hybridized. The compounds at left are helicenes, complexes that consist of helical spirals of aromatic rings. The resulting corkscrew shape means that the clockwise and anti-clockwise spirals are non-superimposable mirror images. The compounds at right are coordination compounds, in which three bidentate bipyridine ligands form a pinwheel. Again, the pinwheel can either be clockwise or anti-clockwise, so the two compounds are enantiomers.
Case B: no chirality in the presence of a stereogenic carbon.
Compounds with multiple stereocentres can remain achiral if pairs of stereocentres cancel each other out. Below are various isomers of 2,3-dibromobutane, where in each case there are two C atoms connected to four different groups: -H, -CH3, -Br, and -CH(Br)CH3. Two of the isomers are enantiomers -- the (R,R) and (S,S) are non-superimposable mirror images. However, the (R,S) isomer is identical to its mirror image -- it is not chiral, despite the presence of two potential stereocentres. Because the two stereocentres are mirrors of each other, the potential chirality of the molecule as a whole is negated.
RR and SS are enantiomers
RS is its own mirror: achiral!
The trouble is that chirality is a molecular property, not an atomic one. Atoms aren't chiral, and the bonds at a single atom don't determine chirality. The geometry and symmetry of the entire molecule must be considered. A common feature of the compounds above is this: the chiral compounds lack a mirror plane of symmetry, while the achiral isomer possesses one, as seen is clearer in the fully eclipsed conformation shown at right. A compound with multiple stereocentres that remains achiral due to an internal mirror plane is called a meso compound (from Greek meso = middle). If a molecule has a mirror plane, then its mirror image must be identical, so it isn't chiral; if a molecule lacks the mirror plane, the mirror image must be different, so the two compounds are enantiomers.
So, forget four groups at carbon. The real test is the absence of a mirror plane. Mirror plane = not chiral, no mirror plane = chiral.
Almost. More than 99% of the time, that will be true. But it's not always the case, as we see in Part II.