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I faced a question

How many cyclic isomers are possible for $\ce{C4H6}$?

I and my friend found the following four. enter image description here

But the answer key says there are 5. So what's the other one?

Mesentery
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Mockingbird
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1 Answers1

9

You can answer such questions using D.U. (Degree of unsaturation)

The formula is $\mathrm{C + 1 - }\frac{H + X - N}{2}$

C = Carbon.
H = Hydrogen.
X = Halogen.
N = Nitrogen.

If you get D.U. to be one, then in the structure there could be:

  • 1 double bond.

  • 1 ring.

Let's take an example of $\ce{C4H8}$ which has D.U. equal to one.

  • It can have three structures of 1 double bond:

enter image description here

  • It can have two structures of 1 ring:

enter image description here

Now for D.U. equal to two, the possibilities are:

  • 2 double bond.

  • 2 ring.

  • 1 double bond and 1 ring.

  • 1 triple bond.

Let's take your example of $\ce{C4H6}$ which has D.U. equal to two:

  • It can have two structures of 2 double bond:

enter image description here

  • It can have one structure of 2 ring:

enter image description here

  • It can have four structures of 1 double bond + 1 ring:

enter image description here

  • It can have two structures of 1 triple bond:

enter image description here

So, the answer is 5 cyclic isomers as you can see above.

Mesentery
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  • How do you decide whether or not the cyclobutene has both cis and trans isomers? – DavePhD May 25 '17 at 15:44
  • @DavePhD It cannot show geometrical isomerism as far as I can see. – Mesentery May 25 '17 at 15:50
  • "Now for D.U. equal to two, the possibilities are: 
    2 double bond.

2 ring.

1 double bond and 1 ring.

1 triple bond." how do u know that?
    – Mockingbird May 25 '17 at 15:55
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    Drawing angled $sp$ carbons is a sin bordering on blasphemy. – Ivan Neretin May 25 '17 at 15:56
  • @Mesentery Hypothetically, with respect to the double bond, the two hydrogens could be on one side and the two carbons on the other (cis) or there could be one hydrogen on each side with the ring stretching diagonally across the double bond. But I don't think it is known to occur experimentally for a ring this small http://www.chemgapedia.de/vsengine/vlu/vsc/en/ch/12/oc/vlu_organik/stereochemie/cyclische_stereoisomere.vlu/Page/vsc/en/ch/2/oc/stoffklassen/systematik_struktur/cyclische_verbindungen/carbocyclisch/cycloalkene/physikalische_eigenschaften.vscml.html – DavePhD May 25 '17 at 15:59
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    @Mockingbird That I have studied. But you can also make out like D.U. Is 2 means there should be 2 double bonds that are removing the hydrogen from the formula. And it can have 2 rings that all that. You will have two check what are the possibilities that can remove hydrogen from an alkane – Mesentery May 25 '17 at 15:59
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    @DavePhD Thanks for the information. I have studied that cyclic alkenes does not show geometrical isomerism having carbon less than 8. – Mesentery May 25 '17 at 16:02
  • @IvanNeretin Apologies for committing the sin :) – Mesentery May 25 '17 at 16:03
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    @Mesentery well perhaps you will find this article interesting, concerning the limit supposedly being 8 http://pubs.acs.org/doi/abs/10.1021/ja055388i and also http://pubs.acs.org/doi/abs/10.1021/jo00389a067 – DavePhD May 25 '17 at 16:06
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    Now that's much better. But look, a carbon with two double bonds is also an $sp$ carbon. – Ivan Neretin May 25 '17 at 17:34
  • @IvanNeretin You are referring to the Allene. Ok Thanks. – Mesentery May 26 '17 at 03:19
  • @Mersentery Is the formula empirical? – Mockingbird May 26 '17 at 08:02
  • @Mockingbird You can have an idea how the formula is made from here. BTW I don't understand what you mean by empirical. – Mesentery May 26 '17 at 08:14