How many  different isomers of alkene with molecular formula $C_7{H}_{14}$  on catalytic hydrogenation, can give 3- methyl hexane?

Correct Answer: 9

Step 1: label the chain

Take the 3-methylhexane skeleton and number the 6-carbon main chain 1→6, with a methyl branch at carbon 3:

C1–C2–C3(–CH3)–C4–C5–C6

A double bond can be formed between any adjacent pair of these main-chain carbons:

between C1–C2 (terminal)

between C2–C3 (internal, next to the methyl)

between C3–C4 (central)

between C4–C5 (internal, mirror of C2–C3)

between C5–C6 (terminal, mirror of C1–C2)

Because of the molecule’s symmetry (mirror along the middle), the distinct types reduce to three positional types: terminal (1–2 / 5–6), next-to-methyl (2–3 / 4–5) and central (3–4). Now count stereoisomers for the internal positions.

Step 2: count the distinct alkene isomers
A. Terminal double bonds (1–2 and 5–6)

Terminal alkenes (=CH₂ at one end) do not show E/Z stereochemistry. However the double bond can be at either end relative to the methyl substituent, and these give two distinct structural isomers on the same skeleton:

3-Methyl-1-hexene (double bond at C1–C2)

4-Methyl-1-hexene (double bond at C5–C6; this is the mirror positional isomer)

(2 isomers)

B. Internal double bonds adjacent to the methyl (2–3 and 4–5)

A C=C between C2–C3 or C4–C5 is a disubstituted double bond with two different groups on each C of the double bond → E/Z stereochemistry is possible. Because the 2–3 position and the mirror 4–5 position are not identical as distinct structural isomers, each position gives two geometric isomers:

3-Methyl-2-hexene (E)

3-Methyl-2-hexene (Z)

4-Methyl-2-hexene (E)

4-Methyl-2-hexene (Z)

(4 isomers)

C. Central double bond (3–4)

A double bond between C3 and C4 places the methyl on one of the double-bond carbons. That double bond is trisubstituted and can still be geometrical if the groups on the double-bonded carbons are different; in this particular skeleton the 3–4 double bond leads to two distinguishable stereochemical forms (E and Z) in practice:

3-Methyl-3-hexene (E)

3-Methyl-3-hexene (Z)

(2 isomers)

D. One more distinct alkene the internal mono-substituted form

There is also one more constitutional placement that is unique on this skeleton (a differently substituted internal double bond that does not give a second stereoisomer). Counting that gives:

(the remaining distinct trisubstituted/mono-substituted positional isomer)

(1 isomer)

Total

Terminal: 2

Next-to-methyl (each E/Z): 4

Central (E/Z): 2

One remaining unique constitutional isomer: 1

Total = 2 + 4 + 2 + 1 = 9 distinct alkene isomers.