Convert the Fischer projections into line-angle drawings and assign (R) and (S) at each chiral center.
(a)

Verified step by step guidance

1. Step 1: Understand the Fischer projection. In a Fischer projection, horizontal lines represent bonds coming out of the plane (toward the viewer), and vertical lines represent bonds going behind the plane (away from the viewer). Identify the groups attached to each chiral center in the molecule.
2. Step 2: Convert the Fischer projection into a line-angle drawing. To do this, visualize the molecule in 3D and redraw it using wedge-and-dash notation. Assign the correct spatial orientation to each substituent based on the Fischer projection.
3. Step 3: Assign priorities to the substituents at each chiral center using the Cahn-Ingold-Prelog (CIP) priority rules. The rules are based on atomic number, with higher atomic numbers receiving higher priority. If two atoms are the same, move outward to the next set of atoms until a difference is found.
4. Step 4: Determine the configuration (R or S) at each chiral center. Arrange the molecule so that the lowest priority group is pointing away from you. Then, trace a path from the highest priority group to the second and third highest priority groups. If the path is clockwise, the configuration is (R); if counterclockwise, it is (S).
5. Step 5: Verify your assignments by double-checking the spatial arrangement of the substituents and the priority order. Ensure that the line-angle drawing accurately represents the Fischer projection and that the (R) and (S) configurations are correctly assigned.

Key Concepts

Fischer Projections

Fischer projections are a two-dimensional representation of three-dimensional organic molecules, particularly useful for depicting carbohydrates and amino acids. In these projections, vertical lines represent bonds that extend away from the viewer, while horizontal lines indicate bonds that come towards the viewer. Understanding how to interpret Fischer projections is essential for converting them into other representations, such as line-angle drawings.

Line-Angle Drawings

Line-angle drawings, also known as skeletal structures, are a simplified way of representing organic molecules where vertices represent carbon atoms and lines represent bonds. This format omits hydrogen atoms attached to carbons for clarity, making it easier to visualize complex structures. Mastery of converting Fischer projections to line-angle drawings is crucial for accurately depicting molecular geometry.

Cahn-Ingold-Prelog (CIP) Priority Rules

The Cahn-Ingold-Prelog priority rules are a set of guidelines used to assign (R) and (S) configurations to chiral centers in organic molecules. These rules involve ranking the substituents attached to the chiral carbon based on atomic number and connectivity. Correctly applying these rules is vital for determining the stereochemistry of a molecule, which is essential in understanding its reactivity and interactions.