This question involves determining the absolute configuration (R/S notation) at two chiral centers in a molecule. The given structure is a Fischer projection, which is a 2D representation used for stereochemistry.

Step 1: Understand Fischer Projection Rules
In a Fischer projection:

Horizontal lines represent bonds coming out of the plane (toward you).
Vertical lines represent bonds going into the plane (away from you).

The carbon chain is drawn vertically with the most oxidized carbon at the top.

Step 2: Identify the Chiral Centers
The molecule has two chiral centers: carbon 2 and carbon 3 (numbering from the top).

Step 3: Assign Priorities Using Cahn-Ingold-Prelog (CIP) Rules
For each chiral center, assign priorities 1 to 4 to the substituents based on atomic number (higher atomic number = higher priority).

For Carbon 2 (the second carbon from top):
Substituents are:

Top: -OH (O, H, H) → priority 1 (O has highest atomic number)
Right: -H → priority 4 (lowest)
Left: -CH(OH)CH₃ (C, O, H, H) → priority 2 (C connected to O)
Bottom: -CH₃ (C, H, H, H) → priority 3

Now, orient the molecule so the lowest priority (H) is pointing away. The order of priorities 1→2→3 is clockwise, which would normally be R. But since the H is on a horizontal bond (coming out), we reverse the assignment. So, carbon 2 is S.

For Carbon 3 (the third carbon from top):
Substituents are:

Top: -CH(OH)CH₃ (C, O, H, H) → priority 1 (C connected to O)
Right: -H → priority 4
Left: -OH (O, H, H) → priority 2
Bottom: -CH₃ (C, H, H, H) → priority 3

Orient with H away. The order 1→2→3 is counterclockwise, which would be S. But again, H is on horizontal (coming out), so reverse: carbon 3 is R.

Final Answer: The absolute configuration is (2S,3R).

Related Topics & Formulae

Stereochemistry: The study of the spatial arrangement of atoms in molecules. Key concepts include chiral centers, enantiomers, diastereomers, and R/S notation.

Cahn-Ingold-Prelog (CIP) Rules: Used to assign R/S configuration:

Assign priorities based on atomic number.
Orient the molecule so the lowest priority group is away.
Determine the direction (clockwise = R, counterclockwise = S).
If the lowest priority is not away, reverse the assignment.

Fischer Projection: A convention to represent 3D molecules in 2D. Remember: horizontal = out, vertical = in.