This is a bit weird to me. We're doing R and S configurations and I think of it as a steering wheel - steering to the right is an R configuration and steering to the left is an S configuration.

These questions are drawn out as molecules in our book and I listed them going clockwise.
So..

If a chiral center has an H, OH, C-CH3 and CH3 shouldn't it be an R configuration? Why is it S..(according to the solutions manual)

If a chiral center has a H, OCH3, CO2H, HOCH2, then shouldn't that be R as well.. Why is it S?

In the compound Prostaglandin E1 there are 4 chiral centers. Apparently there are 3 Rs and 1 S. I don't understand the S. Shouldn't that be an R?

Is there anyway anyone can explain the priority thing to me because that's where I'm confused when it comes to bigger molecules. Thanks!

You need to be able to visulaise the molecule or get yourself a set of models.

Identify the chirality centres (most commonly an sp3 C with 4 different groups attached)
Assign the priority to each group (high = 1, low = 4) based on atomic number (or mass if same atomic number) of the atom attached to the chirality center (remember the first point of difference rule)
Position the lowest priority group away from you as if you were looking along the bond, C nearest to you.

For the other 3 groups, determine the direction of high to low priority (1 to 3)
If this is clockwise, then the center is R (Latin: rectus = right)
If this is counter clockwise, then it is S (Latin: sinister = left)

In you first example with the H away from you the order would need to be

OH, C-CH3 and CH3
anticlockwise for S - hard to draw on here
C-CH3
\
H3C-C-OH

For PE1 you need to make a model. Yes, there are 4 chiral centres.

Understanding the R and S configurations in organic chemistry can be confusing at first, but let's break it down step by step and I'll explain how to determine the configuration.

To assign the R and S configuration, we need to use the Cahn-Ingold-Prelog (CIP) priority rules. These rules are based on assigning priorities to the substituents attached to the chiral center based on atomic number.

Step 1: Identify the chiral center in the molecule. A chiral center is a carbon atom bonded to four different groups/substituents.

Step 2: Assign priorities to the substituents based on atomic number. The higher the atomic number, the higher the priority. Look at the atoms directly bonded to the chiral center and compare their atomic numbers.

Step 3: If two substituents have the same atom directly bonded to the chiral center, compare the atomic numbers of the next atoms in the substituents until a difference is found.

Step 4: Once priorities are assigned, orient the molecule so that the lowest priority substituent (H in most cases) is pointing away from you.

Step 5: Now, visualize the remaining three substituents and mentally trace a curve from the highest priority (1) to the second highest (2) to the third highest (3). If this curve is clockwise, it is assigned the R configuration. If this curve is counterclockwise, it is assigned the S configuration.

Now, let's apply these rules to your specific examples:

Example 1: Chiral center with H, OH, C-CH3, and CH3 substituents
To determine the R or S configuration, assign priorities to each substituent based on atomic number. Usually, oxygen (O) has a higher atomic number than carbon (C), which is higher than hydrogen (H). In this case:

1. H (lowest priority)
2. CH3
3. C-CH3
4. OH (highest priority)

Now, mentally trace a curve from 1 to 2 to 3. If the curve is clockwise, it is assigned the R configuration. If the curve is counterclockwise, it is assigned the S configuration. In this case, it should be R.

Example 2: Chiral center with H, OCH3, CO2H, and HOCH2 substituents
Following the same steps as above:

1. H (lowest priority)
2. OCH3
3. HOCH2
4. CO2H (highest priority)

Mentally trace a curve from 1 to 2 to 3. If the curve is clockwise, it is assigned the R configuration. If the curve is counterclockwise, it is assigned the S configuration. In this case, it should be S.

Example 3: Prostaglandin E1 with 4 chiral centers (3 R and 1 S)
Without the specific structure of Prostaglandin E1, it's difficult to explain each chiral center individually. However, keep in mind that each chiral center is independent, and its configuration is determined by the substituents directly attached to it.

If you can provide the structure of Prostaglandin E1 or specific chiral centers, I can help explain their configurations.

Remember, the priority of substituents is determined by comparing their atomic numbers. If you're confused about larger molecules, it often helps to draw them in 2D and prioritize the substituents based on atomic number, just as we did in the examples above.