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How can we convert but-2-ene to but-1-ene? Is it even possible, since but-2-ene is the more stable one.

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You are right that a disubstituted alkene will be more stable than a monosubstituted. This tendency towards forming highly substituted alkenes is known as Zaitsev's rule, but it is not without exception. In simple elimination reactions, more sterically hindered bases cannot access the secondary hydrogen as well as the primary hydrogen, and the monosubstituted product will dominate. Hofmann elimination is another reaction that favors the formation of less substituted alkenes, also for steric reasons.

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Though but-2-ene is more stable than but-1-ene it's still possible to convert them into each other easily as follows:

  1. Add $\ce{HBr}$ into but-2-ene solution it will result in formation of 2-bromobutane.

    reaction equation of HBr addition to but-2-ene

  2. Now add $\ce{C(CH3)OK}$ to the obtained 2-bromobutane, as it is a bulky base, due to steric factors it forms the Hoffman product via a Hoffman elimination reaction

    enter image description here

Sorry that the second picture is not the perfect representation, but it still should aid understanding.

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