The compound \((CH_3)_2C=CHCH_2CH_3\) is an alkene with the structure:
- The molecule features a double bond between the \(C=C\) carbon atoms.
- Specifically, it has the structure of 3-hexene with two methyl groups on the second carbon (\(C_2\)) and a double bond between \(C_2\) and \(C_3\).
To determine if this compound exhibits cis-trans (geometric) isomerism, we need to evaluate the substituents around the double bond:
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Cis-Trans Isomerism Conditions:
- For a compound to exhibit cis-trans isomerism, each carbon involved in the double bond must have different substituents.
- In this case, the double bond is between \(C_2\) and \(C_3\).
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Examining the Double Bond:
- \(C_2\) has three substituents: two methyl groups \((-CH_3)\) and a hydrogen atom.
- \(C_3\) has two substituents: one hydrogen atom and another carbon chain (\(CH_2CH_3\)), i.e., it's connected to the ethyl group.
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Types of Substituents:
- Since both substituents on \(C_2\) (the two methyl groups) are the same, it does not satisfy the criteria for cis-trans isomerism.
- On the \(C_3\) carbon, there is one hydrogen and one ethyl group, which are different, but since \(C_2\) does not have different substituents, the overall double bond does not allow for cis-trans isomerism.
Conclusion:
The compound \((CH_3)_2C=CHCH_2CH_3\) does not exist as cis-trans isomers because one of the carbons in the double bond (\(C_2\)) does not have two different substituents. Therefore, it lacks the structural requirements for geometric isomerism.