Maximum Number of Monochlorination Isomers for Branched Alkane

To find the maximum number of isomers (including stereoisomers) formed by the monochlorination of 3-methylpentane, we analyze the different positions at which a hydrogen atom can be replaced by a chlorine atom ($\text{Cl}$).

The structure of the given compound is 3-methylpentane:
$\text{CH}_3-\text{CH}_2-\overset{\overset{\text{CH}_3}{\mid}}{\text{C}}\text{H}-\text{CH}_2-\text{CH}_3$

Due to the symmetry of the molecule, there are four distinct types of hydrogen atoms that can be substituted:

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1. Chlorination at the methyl group attached to C-3

Replacing a hydrogen on the branch methyl group yields:
$\text{CH}_3-\text{CH}_2-\overset{\overset{\text{CH}_2\text{Cl}}{\mid}}{\text{C}}\text{H}-\text{CH}_2-\text{CH}_3 \quad (\text{1-chloro-2-ethylbutane})$

• The central carbon (C-3) is bonded to:
  • $-\text{H}$
  • $-\text{CH}_2\text{Cl}$
  • Two identical ethyl groups ($-\text{CH}_2\text{CH}_3$)
• Since it has two identical groups, this molecule is achiral and has no stereocenters.
• Number of isomers = $1$

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2. Chlorination at the C-3 tertiary carbon

Replacing the tertiary hydrogen at C-3 yields:
$\text{CH}_3-\text{CH}_2-\overset{\overset{\text{CH}_3}{\mid}}{\underset{\underset{\text{Cl}}{\mid}}{\text{C}}}-\text{CH}_2-\text{CH}_3 \quad (\text{3-chloro-3-methylpentane})$

• The central carbon (C-3) is bonded to:
  • $-\text{Cl}$
  • $-\text{CH}_3$
  • Two identical ethyl groups ($-\text{CH}_2\text{CH}_3$)
• Due to the presence of two identical ethyl groups, this molecule is also achiral and optically inactive.
• Number of isomers = $1$

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3. Chlorination at C-2 (or the equivalent C-4 position)

Replacing a hydrogen at the secondary carbon C-2 yields:
$\text{CH}_3-\overset{*}{\text{C}}\text{H}(\text{Cl})-\overset{*}{\text{C}}\text{H}(\text{CH}_3)-\text{CH}_2-\text{CH}_3 \quad (\text{2-chloro-3-methylpentane})$

• C-2 is bonded to four different groups: $-\text{H}$, $-\text{Cl}$, $-\text{CH}_3$, and $-\text{CH}(\text{CH}_3)\text{CH}_2\text{CH}_3$ (chiral center).
• C-3 is bonded to four different groups: $-\text{H}$, $-\text{CH}_3$, $-\text{CH}_2\text{CH}_3$, and $-\text{CH}(\text{Cl})\text{CH}_3$ (chiral center).
• Since both C-2 and C-3 are distinct chiral centers and the molecule is not symmetrical, the total number of stereoisomers is:
  $2^n = 2^2 = 4 \text{ stereoisomers} \quad [(2R,3R), (2R,3S), (2S,3R), (2S,3S)]$
• Number of isomers = $4$

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4. Chlorination at C-1 (or the equivalent C-5 position)

Replacing a hydrogen at the terminal methyl carbon C-1 yields:
$\text{Cl}-\text{CH}_2-\text{CH}_2-\overset{*}{\text{C}}\text{H}(\text{CH}_3)-\text{CH}_2-\text{CH}_3 \quad (\text{1-chloro-3-methylpentane})$

• C-3 is bonded to four different groups:
  • $-\text{H}$
  • $-\text{CH}_3$
  • $-\text{CH}_2\text{CH}_3$ (ethyl group)
  • $-\text{CH}_2\text{CH}_2\text{Cl}$ (2-chloroethyl group)
• Since all four groups on C-3 are distinct, C-3 is a chiral center.
• This compound exists as a pair of enantiomers ($R$ and $S$).
• Number of isomers = $2$

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Total Number of Isomers:

$\text{Total} = 1 + 1 + 4 + 2 = 8$

Thus, the maximum number of isomers (including stereoisomers) is 8.