The number of stereoisomers possible for 1,2-dimethyl cyclopropane is :
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For substituted cycloalkanes, always follow this two-step process:
1. Draw the possible geometrical isomers (cis and trans).
2. For each geometrical isomer, check for chirality by looking for planes of symmetry.
If a plane of symmetry exists, it's a meso compound (achiral).
If no plane of symmetry exists, it's chiral and will have an enantiomer.
Step 1: Understanding the Question
We need to find the total number of stereoisomers for the molecule 1,2-dimethylcyclopropane.
Stereoisomers include both geometrical isomers (cis/trans) and optical isomers
(enantiomers/diastereomers). Step 2: Identifying Geometrical Isomers
1,2-dimethylcyclopropane can exist as two different geometrical isomers based on the relative positions of the two methyl groups with respect to the plane of the cyclopropane ring. Cis isomer: Both methyl groups are on the same side of the ring (both pointing up or both pointing down). Trans isomer: The methyl groups are on opposite sides of the ring (one pointing up, one pointing down). Step 3: Analyzing for Chirality (Optical Isomerism)
Now, we need to check if these geometrical isomers are chiral. A molecule is chiral if it is non-superimposable on its mirror image. A quick way to check is to look for a plane of symmetry. Cis-1,2-dimethylcyclopropane:
This molecule has a plane of symmetry that passes through the C3 atom and bisects the C1-C2 bond. Due to this symmetry, the molecule is achiral, even though it has two chiral centers. Such a compound is called a meso compound. A meso compound is a single stereoisomer.
Number of stereoisomers from the cis form = 1. Trans-1,2-dimethylcyclopropane:
This molecule does not have any plane of symmetry. Therefore, it is chiral. A chiral molecule and its non-superimposable mirror image form a pair of enantiomers.
Number of stereoisomers from the trans form = 2 (the pair of enantiomers). Step 4: Calculating the Total Number of Stereoisomers
The total number of stereoisomers is the sum of all distinct forms.
Total isomers = (Isomers from cis form) + (Isomers from trans form)
Total isomers = 1 (meso compound) + 2 (enantiomeric pair) = 3.
