Question

How many structural isomers of $C_6H_{12}$ may contain 3-membered ring?

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (A)

4

Answer 2

For a saturated C₆H₁₂ containing one ring, the degree‐of‐unsaturation is 1. Since a three‐membered ring (cyclopropane) accounts for that one ring, the remaining 3 carbons must appear as substituents on the cyclopropane. Write the substitution as a triple (a, b, c) where a + b + c = 3 (each “a”, “b”, “c” being the number of extra carbons attached to a ring carbon).

The possible partitions (up to the cyclopropane’s symmetry) are:

1. (3, 0, 0): A single substituent of 3 carbons attached to one ring carbon.

   • The C₃ group can be arranged in two ways:

     • n‑propyl (CH₂CH₂CH₃)
     • isopropyl (CH(CH₃)₂)

   This gives 2 isomers.

2. (2, 1, 0): Two substituents on different ring carbons; one is a C₂ group (only possible as ethyl, CH₂CH₃) and the other is a methyl group.

   This gives 1 isomer.

3. (1, 1, 1): Three methyl groups attached on all three ring carbons.

   This gives 1 isomer.

Adding these: 2 + 1 + 1 = 4 structural isomers.