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In the acid catalysed hydration of allene, acetone is obtained as the major product. This is because of electrophilic addition of $\ce{H+}$ across a double bond to give a vinyl carbocation, and subsequent addition of water and then tautomerism to yield the ketone. What I'm confused about is that why does not an allyl carbocation form, which would be resonance stabilised?(leading to allyl alcohol?)

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Good question! As the following figure illustrates, there are 2 ways we can protonate an allene.

enter image description here

(image source)

The top line in the drawing starts by protonating at the central allene carbon. This generates a very unstable primary carbocation. Initially, this primary carbocation is not stabilized by the adjacent double bond. It is not until after this carbocation rotates 90° that its p orbital is lined up with the p orbitals in the double bond and allylic stabilization can occur. Since there is no immediate allylic stabilization when the carbocation is formed, and since it is a primary carbocation, the pathway leading to it is very high energy.

On the other hand, protonation at the terminal allene carbon (bottom line of figure) produces a relatively stabilized secondary carbocation. Formation of a secondary carbocation is a much lower energy process. Therefore, protonation at the terminal allene carbon is lower energy and is what will occur.

Edit: Response to OP's comment

I always thought that a positive charge appearing on sp3 carbon (which then becomes sp2) is more stable than a positive charge appearing on sp2 carbon

Generally we think of vinylic carbocations as high energy. That is true, but what is meant by "vinylic" carbocation is different from what we have here. Here there is an empty p orbital. In a vinylic carbocation the empty orbital is not a p orbital, but rather something like $\ce{sp^2}$ or $\ce{sp}$ hybridized.

is the secondary carbocation more stable because of inductive effect, the rotational barrier in the primary carbocation, or both

The secondary carbocation is more stable for the same reasons that we have the tertiary > secondary > primary carbocation stability order.

  • Inductive effects, $\ce{sp^3}$ and $\ce{sp^2}$ carbons are electron releasing towards an $\ce{sp}$ carbon due to electronegativity differences
  • Resonance effects from hyperconjugation involving hydrogens on the carbon next to the carbocation center.
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    $\begingroup$ OMG!! I had accepted the statement made by OP when I was told about this nature in allenes (long back). This is a wonderful explanation. +1000! $\endgroup$ – user223679 May 20 '15 at 17:26
  • $\begingroup$ @ron I always thought that a positive charge appearing on sp3 carbon(which then becomes sp2) is more stable than a positive charge appearing on sp2 carbon(which then becomes sp)(even though sp3 carbon may be primary.). In this case, is the secondary carbocation more stable because of inductive effect, the rotational barrier in the primary carbocation, or both? $\endgroup$ – Abhishek May 20 '15 at 17:41
  • $\begingroup$ @Abhishek I've edited my answer to address these points. $\endgroup$ – ron May 20 '15 at 17:57
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    $\begingroup$ @ron Understood it all perfectly well now, thanks $\endgroup$ – Abhishek May 20 '15 at 18:18

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