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Chiral Carbon
A chiral carbon (also called a stereogenic center) is a carbon atom attached to four different groups. Basically, a sp3 carbon with 4 different groups attached.

R and S
R and S are labels that describe the 3D spatial arrangement of groups around a chiral carbon. They tell you the configuration: If a carbon is chiral, it can exist in two different spatial forms:
One is labeled R: Clockwise (right)
The other is labeled S: Counterclockwise (left)
EX: (S)-2-Bromobutane and (R)-2-Bromobutane are enantiomers.

How R and S are assigned
Look at atoms directly connected to the Chiral Carbon, then give them their respective atomic numbers.
Look for differences in atom placement
Assign numbers (highest-lowest, highest being 1) based on the highest atomic number to the lowest (ranking).
If you have two different groups with the same atom, look at the next atom next to it and compare it to the other to see which has a higher priority. EX: OH or OCH, OCH is higher priority because of the Carbon attached.
Lowest group will go away from you (wedge), and will be #4.
Look at your first 3 numbers based on your priority list, look for where 1 and 2 are placed, and based on the direction it goes in will tell you if it is S or R.
if your first 3 are clockwise (right) it is R
if your first 3 are counterclockwise (left), it is S
If you have a methyl or ethyl group, ethyl is a higher priority.
When writing R or S in the name, make sure to write it in parenthesis and a dash to separate it from a number.
Its mirror image will be the opposite, so if R is assigned to a chiral carbon, then its enantiomer is S.

In double bonds, for bookkeeping purposes, i.e. priority rank…
Both atoms are accounted for twice for priority ranking. EX: see image, the top Carbon is #1 because it contains (for bookkeeping purposes) two carbon-oxygen bonds, as opposed to the other CO, with an H attached.

To properly look at a Chiral Carbon & determine R or S…
To determine R or S, you must view the chiral carbon so that the lowest-priority group (4) is pointing away from you.
If the lowest group is coming towards you
flip the R or S that you assigned to the opposite. EX: If you assigned R to a chiral carbon, but your lowest group (4) is coming towards you (wedged), flip to S.