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Why is Vinyl carbocation unstable?

Answer
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Hint: A carbocation is an electron deficient species in which the carbon atom in a hydrocarbon contains a positive charge as one of its valencies remains unfulfilled by a covalent bond. A Vinyl carbocation is the one in which the positively charged carbon is part of a double bond.

Complete answer:
The stability of carbocations is associated with the type of hybridization, the number of hyperconjugative structures if possible, the presence or absence of lone pairs and the electron donating elements that are placed adjacent to the carbocation in hydrocarbon chains.
A Vinyl carbocation is the one in which one of the double bonded carbons loses a group and gains a positive charge.
Carbocation, being an electron deficient species, can only be stabilized by the presence of groups or molecules that can actually donate electrons to the vacant orbital of the carbocation. But a double bonded carbon has an \[s{p^2}\] hybridization with a higher s-character. A higher s-character further depletes the carbon atom and makes it more electron deficient that makes a carbocation highly unstable.
\[ \therefore \] Thus, vinyl carbocation is unstable because of its hybridization and presence of double bonds.

Note:
Do not confuse vinyl carbocations with allylic carbocations as allylic carbocations are placed adjacent to a double bond and the conjugation makes them quite stable but vinyl carbocations are part of the double bond and are actively attacked by nucleophiles.