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Is benzene acidic? It has $sp^2$ hybridization so doen it mean that it is acidic in nature? Are alkenes acidic?

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A sp2-hybridized carbon is more electronegative than an sp3-hybridized carbon, and you would expect it to be more acidic.

Experiments support this prediction. Benzene has a pKa of ~ 43, compared to alkanes, which have a pKa of ~ 50. You can prepare lithioaromatics from bromo/iodoaromatics and butyllithium via metal-halogen exchange.

The situation with alkenes is slightly more complicated; the pKa of vinylic protons is in the same ballpark as of aromatic protons, but allylic protons are slighty more acidic.

Consult any of the usual pKa tables on the web.

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