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Question

Question: Which is correct...

Which is correct

A

P and Q are diastereomers

B

P and R are homomers

C

Q and R are enantiomers

D

P and Q are enantiomers

Answer

P and Q are diastereomers

Explanation

Solution

The problem requires us to determine the relationship between three given stereoisomers P, Q, and R. All three structures represent 2-bromo-3-chlorobutane, which has two chiral centers at C2 and C3. To establish the relationship, we will assign the R/S configuration to each chiral center in all three structures.

1. Assigning R/S Configuration for Structure P: Structure P is given as a Fischer projection.

  CH3
  |
H-C2-Cl
  |
H-C3-Br
  |
  CH3

  • For C2 (top chiral carbon):

    • Priorities of groups attached to C2: Cl (1), -CH(Br)CH3 (C3 carbon, 2), -CH3 (3), H (4).
    • H is on a horizontal line (coming out).
    • Path 1 -> 2 -> 3 (Cl -> C3 -> CH3) is clockwise (R).
    • Since H is on a horizontal line, the actual configuration is the opposite.
    • Therefore, C2 is (S).

  • For C3 (bottom chiral carbon):

    • Priorities of groups attached to C3: Br (1), -CH(Cl)CH3 (C2 carbon, 2), -CH3 (3), H (4).
    • H is on a horizontal line (coming out).
    • Path 1 -> 2 -> 3 (Br -> C2 -> CH3) is clockwise (R).
    • Since H is on a horizontal line, the actual configuration is the opposite.
    • Therefore, C3 is (S).

So, Structure P is (2S, 3S)-2-bromo-3-chlorobutane.

2. Assigning R/S Configuration for Structure R: Structure R is also given as a Fischer projection.

  CH3
  |
Cl-C2-H
  |
H-C3-Br
  |
  CH3

  • For C2 (top chiral carbon):

    • Priorities of groups attached to C2: Cl (1), -CH(Br)CH3 (C3 carbon, 2), -CH3 (3), H (4).
    • H is on a horizontal line (coming out).
    • Path 1 -> 2 -> 3 (Cl -> C3 -> CH3) is counter-clockwise (S).
    • Since H is on a horizontal line, the actual configuration is the opposite.
    • Therefore, C2 is (R).

  • For C3 (bottom chiral carbon):

    • Priorities of groups attached to C3: Br (1), -CH(Cl)CH3 (C2 carbon, 2), -CH3 (3), H (4).
    • H is on a horizontal line (coming out).
    • Path 1 -> 2 -> 3 (Br -> C2 -> CH3) is counter-clockwise (S).
    • Since H is on a horizontal line, the actual configuration is the opposite.
    • Therefore, C3 is (R).

So, Structure R is (2R, 3R)-2-bromo-3-chlorobutane.

3. Assigning R/S Configuration for Structure Q: Structure Q is given as a Newman projection with wedge/dash bonds.

To convert this Newman projection to a Fischer projection:

  • Keep the CH3 groups vertical (anti-periplanar, as shown).
  • For the front carbon (C2): Br is left and wedge (coming out), H is right and dash (going in). In Fischer, horizontal lines are coming out. So, Br is on the left, H is on the right.
  • For the back carbon (C3): Cl is right and wedge (coming out), H is left and dash (going in). So, Cl is on the right, H is on the left.

The Fischer projection for Q is:

  CH3
  |
Br-C2-H
  |
H-C3-Cl
  |
  CH3

  • For C2 (top chiral carbon):

    • Priorities: Br (1), -CH(Cl)CH3 (C3 carbon, 2), -CH3 (3), H (4).
    • H is on a horizontal line (coming out).
    • Path 1 -> 2 -> 3 (Br -> C3 -> CH3) is counter-clockwise (S).
    • Since H is on a horizontal line, the actual configuration is the opposite.
    • Therefore, C2 is (R).

  • For C3 (bottom chiral carbon):

    • Priorities: Cl (1), -CH(Br)CH3 (C2 carbon, 2), -CH3 (3), H (4).
    • H is on a horizontal line (coming out).
    • Path 1 -> 2 -> 3 (Cl -> C2 -> CH3) is clockwise (R).
    • Since H is on a horizontal line, the actual configuration is the opposite.
    • Therefore, C3 is (S).

So, Structure Q is (2R, 3S)-2-bromo-3-chlorobutane.

Summary of Configurations:

  • P: (2S, 3S)
  • Q: (2R, 3S)
  • R: (2R, 3R)

4. Evaluating the Options:

  • A: P and Q are diastereomers

    • P: (2S, 3S)
    • Q: (2R, 3S)
    • They differ in configuration at one chiral center (C2: S vs R) and are the same at the other (C3: S vs S). Stereoisomers that are not mirror images and differ at at least one chiral center but not all are diastereomers. So, A is correct.

  • B: P and R are homomers

    • P: (2S, 3S)
    • R: (2R, 3R)
    • Homomers are identical molecules. P and R have opposite configurations at both chiral centers. They are non-superimposable mirror images. Thus, P and R are enantiomers, not homomers. So, B is incorrect.

  • C: Q and R are enantiomers

    • Q: (2R, 3S)
    • R: (2R, 3R)
    • They are the same at one chiral center (C2: R vs R) and opposite at the other (C3: S vs R). Thus, Q and R are diastereomers, not enantiomers. So, C is incorrect.

  • D: P and Q are enantiomers

    • P: (2S, 3S)
    • Q: (2R, 3S)
    • They are opposite at one chiral center (C2: S vs R) and the same at the other (C3: S vs S). Thus, P and Q are diastereomers, not enantiomers. So, D is incorrect.

Based on the detailed R/S analysis, option A is the correct statement.