Step 1: Concept:
We are tasked with determining the absolute stereochemical configuration (R or S) for two chiral centers (C-2 and C-3) in a molecule drawn in a Fischer projection. The molecule is 2,3-dichloropentane.
Step 2: Key Formula or Approach:
Use the Cahn-Ingold-Prelog (CIP) priority rules:
1. Assign priorities (1 to 4) to the four groups attached to each chiral center based on atomic number.
2. Determine the direction of the curve tracing priority 1 $\rightarrow$ 2 $\rightarrow$ 3.
3. In a Fischer projection, if the lowest priority group (usually H) is on a horizontal bond, the apparent configuration is reversed (Clockwise becomes S, Counter-clockwise becomes R).
Step 3: Step-by-step Explanation:
• Configuration at C-2:
The groups attached to C-2 are: $-Cl$, $-CH(Cl)CH_2CH_3$ (C-3 group), $-CH_3$, and $-H$.
- Priority 1: $-Cl$ (highest atomic number, 17).
- Priority 2: $-CH(Cl)CH_2CH_3$ (C-3 has a Cl attached, making it higher priority than C-1).
- Priority 3: $-CH_3$.
- Priority 4: $-H$ (lowest atomic number).
In the drawn projection, $-Cl$ is on the right, $-CH_3$ is up, and C-3 is down. The path from 1($-Cl$) $\rightarrow$ 2(C-3 down) $\rightarrow$ 3($-CH_3$ up) traces a clockwise direction.
However, the lowest priority group ($-H$) is situated on a horizontal line.
Therefore, we reverse the apparent clockwise (R) configuration to S. So, C-2 is 2S.
• Configuration at C-3:
The groups attached to C-3 are: $-Cl$, $-CH(Cl)CH_3$ (C-2 group), $-CH_2CH_3$, and $-H$.
- Priority 1: $-Cl$ (atomic number 17).
- Priority 2: $-CH(Cl)CH_3$ (C-2 is attached to Cl, whereas the ethyl group is only attached to C).
- Priority 3: $-CH_2CH_3$ (ethyl group).
- Priority 4: $-H$.
In the Fischer projection, $-Cl$ is on the right, C-2 is up, and $-CH_2CH_3$ is down. The path from 1($-Cl$ right) $\rightarrow$ 2(C-2 up) $\rightarrow$ 3($-CH_2CH_3$ down) traces a counter-clockwise direction.
Since the lowest priority group ($-H$) is on a horizontal line, we reverse the apparent counter-clockwise (S) configuration to R. So, C-3 is 3R.
Step 4: Final Answer:
The absolute configuration is (2S, 3R), which corresponds to option (C).