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I am facing difficulty in the following problem:

Which of the following cations is the most stable?

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If we take the number of hyper conjugative structures into consideration then a) should be most stable. It is known that $\ce{-OH}$ is a $\ce{-I}$ group. So if it is present nearer to the carbonation it must destabilise it.Near the carbonation $\ce{-I}$ effect should be more effective than $\ce{+M}$ effect. However my textbook gives the answer as c). Is there something that I am missing out? Thanks.

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    $\begingroup$ @aniline think about the lone pairs on the oxygen atom and how they can contribute $\endgroup$ – getafix Dec 25 '16 at 22:38
  • $\begingroup$ @getafix Yes it's true that $OH$ group will also exert $+M$ effect.But since it is very close to the carbonation its inductive effect should dominate over the mesomeric effect.Moreover mesomeric effect should be neglected since it will bring about a positive charge on more electronegative oxygen. $\endgroup$ – Pink Dec 26 '16 at 1:28
  • $\begingroup$ That's what make (c) more stable $\endgroup$ – getafix Dec 26 '16 at 1:30
  • $\begingroup$ @getafix I couldn't follow.as I have pointed out in the comment above how can be judge that in a fight between inductive and mesomeric effect how can we say that mesomeric effect will win when it has a destabilising effect as well. $\endgroup$ – Pink Dec 26 '16 at 1:44
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    $\begingroup$ What does a carbocation look like? How is the p orbital positioned. How are the lone pairs on oxygen atom positioned? Can electrons transfer from oxygen to the vacant p orbital ? How does the inductive effect work? Think about these questions. I'm afraid I cannot write up a complete explanation right now $\endgroup$ – getafix Dec 26 '16 at 1:48
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It is difficult to arrive at a strict definition of a carbocation, and that is perhaps what makes their chemistry interesting!

I am of the opinion that (a) is the only bona-fide carbocation of all four - the rest have potential interactions, either through sigma framework or through pi electrons with -O atoms (nearby).

(c) looks like a protonated aldehyde in disguise - the protonated aldehyde resonance form (if you like) will be the greatest contributor primarily due to enthalpic considerations - you technically have a distorted C=O bond (think: why is it distorted?)

It is hard to find such an arrangement in any of the other structures, and hence (c) should be most stable. That effectively answers the question, but you may also want to note that (b) is a protonated epoxide in disguise (think bridged bromonium ions vs carbocations), whereas (d) looks like a substituted oxetane.

We could expect the chemistry of (b), (c) and (d) to be vastly different from (a), and also from each other.

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