Draw every stereoisomer for 1,2-difluoro-1,2-dimethylcyclopentane. Use wedge-and-dash bonds for the substituent groups and be sure that they are drawn on the outside of the ring, adjacent to each other. Clearly show stereochemistry by drawing the wedge-and-dashed bonds like the example. You should replace the X with the appropriate halide.
The Correct Answer and Explanation is:
C2.
* Carbon 1 (C1) is bonded to four different groups: a fluorine atom (-F), a methyl group (-CH3), the adjacent substituted carbon of the ring (C2), and the rest of the ring (via C5). Therefore, C1 is a stereogenic center.
* Carbon 2 (C2) is also bonded to four different groups: a fluorine atom (-F), a methyl group (-CH3), the adjacent substituted carbon of the ring (C1), and the rest of the ring (via C3). Therefore, C2 is also a stereogenic center.
- Determining the Number of Stereoisomers: With two stereogenic centers (n=2), the maximum possible number of stereoisomers is 2^n = 2^2 = 4. However, we must check for the existence of meso compounds, which are achiral molecules with stereogenic centers, possessing an internal plane of symmetry. This would reduce the total number of unique stereoisomers.
- Analyzing Stereochemical Possibilities: We can analyze the relative orientations of the substituents. Let’s consider the positions of the two fluorine atoms relative to the plane of the ring. They can be on the same side (cis) or on opposite sides (trans).
- Cis Isomer: In this configuration, both fluorine atoms are on the same side of the ring (e.g., both pointing up with wedge bonds), and consequently, both methyl groups are also on the same side (e.g., both pointing down with dash bonds).
- Let’s examine this structure for symmetry. A plane of symmetry can be drawn through the C4 carbon and the midpoint of the C1-C2 bond. This plane bisects the molecule into two mirror-image halves. The reflection of the fluorine on C1 is the fluorine on C2, and the reflection of the methyl group on C1 is the methyl group on C2.
- Because this molecule possesses an internal plane of symmetry, it is achiral, despite having two stereogenic centers. This is the definition of a meso compound. Since a meso compound is superimposable on its mirror image, there is only one such isomer.
- Trans Isomer: In this configuration, the two fluorine atoms are on opposite sides of the ring (e.g., one F on a wedge bond, the other on a dash bond). Consequently, the two methyl groups are also on opposite sides.
- Let’s examine this structure for symmetry. There is no internal plane of symmetry or center of inversion. The molecule is asymmetric.
- Since the trans isomer is chiral, it is not superimposable on its mirror image. Therefore, it exists as a pair of enantiomers.
- Cis Isomer: In this configuration, both fluorine atoms are on the same side of the ring (e.g., both pointing up with wedge bonds), and consequently, both methyl groups are also on the same side (e.g., both pointing down with dash bonds).
- Conclusion: In total, 1,2-difluoro-1,2-dimethylcyclopentane has three stereoisomers:
- One meso compound (the cis isomer).
- A pair of enantiomers (the trans isomers).
The three stereoisomers are drawn below:
1. The Meso Compound (cis): Both fluorine atoms are on the same side of the ring, and both methyl groups are on the same side. This molecule has an internal plane of symmetry and is achiral.
2. and 3. The Enantiomeric Pair (trans): The fluorine atoms are on opposite sides of the ring, as are the methyl groups. These two molecules are non-superimposable mirror images of each other and are therefore a pair of enantiomers.
