The number of different chain isomers for C₇H₁₆ is __________.

Solution

Chemistry ma’am · 3 steps

Shrink the main chain one carbon at a time and place the leftover carbons every distinct way.

1. Method. Start with all 7 carbons in one straight chain. Then shorten the longest chain by one carbon at a time and attach the leftover carbons as branches. Number from the end that gives the lowest locants, so the same molecule is never counted twice.

   Longest chain	Carbons left as branches	Isomers	Count
   7 (heptane)	0	n-heptane	1
   6 (hexane)	1 methyl	2-methylhexane, 3-methylhexane	2
   5 (pentane)	2 methyls or 1 ethyl	2,2-, 2,3-, 2,4-, 3,3-dimethylpentane, 3-ethylpentane	5
   4 (butane)	3 methyls	2,2,3-trimethylbutane	1

2. Avoid repeats. On hexane, a methyl on C-4 is the same as 3-methylhexane read from the other end. An ethyl on C-2 of pentane makes a six-carbon chain, so only 3-ethylpentane is new. On butane, the three methyls fit only as 2,2,3, and a three-carbon chain cannot hold four branch carbons.
3. So. Total chain isomers = 1 + 2 + 5 + 1 = 9.

The common slip: 8. Missing 3-ethylpentane, the one isomer with an ethyl branch, gives 8 instead of 9.

The idea to keep. For chain isomers, work down from the longest straight chain. At each length, check that no branch secretly makes a longer chain, and count positions that match from the other end only once.

Answer from the NTA final answer key. Solution by PrepWiser.