Determine Number of Alkenes Formed by Dehydrobromination of 3-Bromo-3-cyclopentylhexane

To determine the total number of alkenes formed by the dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic $\text{KOH}$, we analyze the structure of the substrate and the available $\beta$-hydrogens.

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1. Structure of 3-bromo-3-cyclopentylhexane

The substrate consists of a central carbon atom ($C_3$) attached to four different groups:

1. An ethyl group: $-\text{CH}_2\text{CH}_3$ (containing $C_2$)
2. A propyl group: $-\text{CH}_2\text{CH}_2\text{CH}_3$ (containing $C_4$)
3. A cyclopentyl ring: $-\text{C}_5\text{H}_9$ (attached at $C_{1'}$)
4. A bromine atom: $-\text{Br}$

$\text{Structure: } \text{CH}_3-\text{CH}_2-\underset{\substack{| \\ \text{C}_5\text{H}_9}}{\overset{\substack{\text{Br} \\ |}}{\text{C}}}-\text{CH}_2-\text{CH}_2-\text{CH}_3$

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2. Identification of $\beta$-Carbons and Possible Eliminations

Elimination ($\text{E}_2/\text{E}_1$) removes a proton ($\text{H}^+$) from a $\beta$-carbon and a bromide ion ($\text{Br}^-$) from $C_3$. There are three distinct $\beta$-carbons with available hydrogen atoms:

Pathway 1: Elimination at $C_2$ ($\beta_1$-carbon of the ethyl group)

• Reaction: Loss of $\text{H}$ from $C_2$ forms a double bond between $C_2$ and $C_3$.
• Product: 3-cyclopentylhex-2-ene
• Structure: $\text{CH}_3-\text{CH}=\text{C}(\text{C}_5\text{H}_9)(\text{CH}_2\text{CH}_2\text{CH}_3)$
• Geometrical Isomerism:
  • At $C_2$, the two groups are $-\text{H}$ and $-\text{CH}_3$ (different).
  • At $C_3$, the two groups are cyclopentyl and propyl (different).
  • Therefore, this alkene exists as 2 geometrical isomers ($E$ and $Z$).

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Pathway 2: Elimination at $C_4$ ($\beta_2$-carbon of the propyl group)

• Reaction: Loss of $\text{H}$ from $C_4$ forms a double bond between $C_3$ and $C_4$.
• Product: 3-cyclopentylhex-3-ene
• Structure: $\text{CH}_3\text{CH}_2-\text{CH}=\text{C}(\text{C}_5\text{H}_9)(\text{CH}_2\text{CH}_3)$
• Geometrical Isomerism:
  • At $C_4$, the two groups are $-\text{H}$ and $-\text{CH}_2\text{CH}_3$ (different).
  • At $C_3$, the two groups are cyclopentyl and ethyl (different).
  • Therefore, this alkene exists as 2 geometrical isomers ($E$ and $Z$).

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Pathway 3: Elimination at $C_{1'}$ ($\beta_3$-carbon of the cyclopentyl ring)

• Reaction: Loss of $\text{H}$ from $C_{1'}$ forms an exocyclic double bond between $C_3$ and $C_{1'}$.
• Product: 3-(cyclopentylidene)hexane
• Structure: $(\text{C}_4\text{H}_8\text{C}=)\text{C}(\text{CH}_2\text{CH}_3)(\text{CH}_2\text{CH}_2\text{CH}_3)$
• Geometrical Isomerism:
  • At $C_3$, the attached groups are ethyl and propyl (different).
  • At $C_{1'}$, both paths around the symmetric unsubstituted cyclopentyl ring are identical.
  • Since the two groups on $C_{1'}$ are identical, this alkene does not exhibit geometrical isomerism.
  • Total stereoisomers for this structure = 1 alkene.

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3. Total Number of Alkenes

$\text{Total alkenes} = 2 \text{ (from Pathway 1)} + 2 \text{ (from Pathway 2)} + 1 \text{ (from Pathway 3)} = 5$