Chirality is the name given to the phenomenon where two or more molecules with the same chemical formula and atomic connectivity are non-superimposable. These molecules with the same molecular formula and atomic connectivity but different spatial arrangements are called stereoisomers. Chiral molecules rotate polarized light as a result of the property called optical activity.
What does it take to be chiral?
In order for a carbon to be chiral, it needs to have four unique groups. Let’s say we’ve got a carbon with these groups attached to it: NH2, OH, CH3, and H. That’s four unique groups, so we’d say that carbon is a chiral center (aka stereogenic center). If the groups are NH2, OH, CH3, and CH3 the carbon would not be chiral because it only has three types of groups; two of them are the same.
Chiral and achiral molecules
It’s pretty easy to see how many unique groups are attached to the carbons in the examples above, but what happens when all of the groups are R groups (carbon chains)? As long as the lengths or connectivity of the chains are different, the center carbon will be chiral.
Chiral molecule with only alkyl groups
The center carbon in the above molecule has alkyl groups as all four substituents, but all are different! The substituents attached—in order of 1-4—are isopropyl, propyl, ethyl, and methyl. A molecule, like the one above with just one chiral center, is said to have point chirality.
Identifying chiral centers
Let’s go ahead and see how many chiral centers we can find in the molecule below!
Vitamin D3
Try to find where all the chiral centers are on your own before looking at the answer below. Remember: in order for a carbon to be a chiral center, it needs to have four unique groups.
Vitamin D3 labeled
There are five different chiral centers in Vitamin D3. Each colored dot is a chiral center, and the numbers drawn in the same color are the unique groups. Depending on the wedge and dash information at each chiral center, different stereoisomers can be formed. Stereoisomers are molecules with the same atomic connectivity and molecular formula but with different spatial arrangement.
Number of stereoisomers possible (non-meso)
Once we’ve determined the number of chiral centers, determining the total number of possible stereoisomers is generally pretty simple. Let’s take a look at the blue chiral center with the alcohol above.
Right now the bond to the alcohol is drawn in plane to not imply any stereochemistry, but that OH is either facing toward us (on wedge) or facing away from us (on dash). It’s binary, so all we need to do is take 2 and raise it to the nth power, where n is equal to the number of chiral centers we have. We’ve got five chiral centers, so it would be 2n = 25 = 32 total possible stereoisomers.
Total stereoisomers
Absolute configuration
1-aminoethanol blank
The two molecules above are mirror images of each other. Molecules that are mirror images of each other are called enantiomers. Enantiomers have the exact opposite stereochemistry. Some real-world examples of enantiomeric objects include hands, feet, and shoes. The word chiral is actually derived from the Greek word for hand.
It’s pretty easy to identify mirror images of each other when they’re rotated so their groups-in-common are facing each other, but molecules rotate all the time! How on Earth can we tell which enantiomer we’re looking at when the molecules rotate or if there’s just one given? Enter the Cahn-Ingold-Prelog system for assigning absolute configuration. We’ll just call it assigning R and S for short.
The first step is to identify a chiral center. Once we’ve found our four unique groups, it’s time to order them in terms of the mass of the atom directly attached to the center carbon. The heaviest atom gets priority 1, and the lightest atom gets priority 4. 
1-aminoethanol with labeled priorities
Oxygen is the heaviest atom attached to the carbon, so it gets priority 1. Nitrogen gets priority 2, carbon gets 3, and hydrogen gets 4. In both cases, the group with the lowest priority is already in the back (on dash), so all we have to do now is trace a circle around priorities 1, 2, and 3 in that order. If it’s clockwise, the chiral center is said to be “R”; if it’s counter-clockwise, it’s said to be S. 
R and S of 1-aminoethanol
Check it out! The mirror images of 1-aminoethanol have opposite R and S configurations. Okay, it’s not so bad when the lowest-priority group is in the back. What happens when it’s not on dash? Do we have to re-draw it to put it there? Nope! All we have to do is assign the priorities just like before, but there’s a bit of a trick. 
1-aminoethanal
The molecule on the left has the hydrogen in the back, so it’s easy to solve. The one on the right, though, has the oxygen in the back. What we need to do from here is a) swap the priority values {1 and 4 here}, b) trace a circle around 1, 2, and 3, and c) take the opposite result from the trace. For example: if, after the swap, the trace is counterclockwise the actual configuration is an R.
S-1-aminoethanol and R-1-aminoethanol
Check it out! After swapping priorities, the circle traced is counterclockwise. It looks like an S, but it’s actually an R because we swapped priorities.
Fischer projection
Before we get into stereoisomers beyond enantiomers, let’s learn how to find the R and S of chiral centers in Fischer projections. Good news: it’s actually easier!
Fischer projection
All we have to do is, just like before, assign our priorities based on atomic mass and trace around the top three priorities. If the lowest-priority group is on the vertical like in the molecule on the left, the stereochemistry is as it looks; if the lowest-priority group is on the horizontal like in the molecule on the right, stereochemistry is flipped! Let’s see what it looks like before trying on our own.
Fischer projection R and S
Not bad at all, right? The chiral center on top is an S for the molecule on the left and an R for the molecule on the right. Why don’t we apply this new skill on this molecule right below. There are three chiral centers, and we’re going to have to use the playoff system to assign the priorities since many atoms directly attached are carbon.
3-chloro-2,3,4,5-tetrahydroxypentanal without stereochemistry
3-chloro-2,3,4,5-tetrahydroxypentanal with stereochemistry
From top down, the chiral centers are R, S, and R. Including stereochemistry, the name of this molecule is (2R,3S,4R)-3-chloro-2,3,4,5-tetrahydroxypentanal.
Stereoisomers
Enantiomers
We’ve already talked a bit about enantiomers, but that was only with molecules with only one chiral center. If a molecule has more than one chiral center, all of them swap wedge/dash information (R and S) between the enantiomers. Let’s use 3-chloro-butan-2-ol as our example molecule.
Enantiomers
Notice that both the alcohol and chlorine switch from wedged bonds to dashed bonds. Both chiral centers switched from R to S. What happens if not all chiral centers are swapped? Well, that’s when we end up with diastereomers.
Diastereomers
Diastereomers
In this case, only one of our chiral centers swapped R and S configuration. That leaves us with diastereomers. Something to think about: the enantiomer of the molecule on the right is still a diastereomer of the molecule on the left. Check it out:
Relationships between stereoisomers
Meso compounds
Here’s a riddle for you: what’s got at least two chiral centers but is itself achiral? Here’s a hint: it’s got diastereomers but no enantiomer; it’s actually superimposable on its mirror image. Nope, it’s not a vampire! Meso compounds have a plane of symmetry and an even number of chiral centers with opposite R & S configurations.
Cyclohexa-1,3-diol
Chiral molecules rotate polarized light. Their enantiomers (aka optical isomers) rotate light in equal magnitude and opposite direction. If we know how much a molecule rotates light (specific rotation), we can actually determine the concentration of each enantiomer based on the observed rotation of the light as it passes through the solution.
Rotation of light
If two enantiomers are known to be in solution and polarized light is not rotated as it passes through, the solution is racemic—that is, it has equal concentrations of each enantiomer.
Quick question: would a meso compound rotate polarized light? It’s got chiral centers, so the answer should be yes, right? Nope, they won’t due to their overall achirality. Here’s a nice way to think about it: meso compounds have a plane of symmetry with respect to atomic connectivity and two chiral centers with opposite R and S configurations. That means that if the “R” chiral center rotates light just a bit one way, the “S” chiral center will rotate it back to its initial starting point immediately after. That happens because enantiomers (molecules with opposite R and S configurations) rotate light in opposite directions with equal magnitude.
Why does chirality matter?
Back in the 1960s, anti-morning sickness drug caused widespread birth defects in the Germany and across Europe. The drug thalidomide, a molecule with just one chiral center, was prepared and sold as a racemic mixture of S-thalidomide and R-thalidomide.
Thalidomide
Soon after it was released as an over-the-counter drug, it was discovered that one of the enantiomers was a mild sedative safe enough for use during pregnancy that helped with nausea while the other enantiomer was extremely toxic to the forming embryos. More than 10,000 children were born with severely deformed limbs as a result of the use of thalidomide.
Chirality is also important in less horrid ways. Get this: all of the amino acids that your body (and the rest of the eukaryotic world) uses are left-handed! They're all, except for achiral glycine, of the S or "L" absolute configuration. Amino acids and sugars use D and L in place of R and S, but they mean the same thing.
