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Exercises · 7.33

Q.When 3-methylbutan-2-ol is treated with HBr, the following reaction takes place: CH3−CH∣CH3−CH∣OH−CH3 →HBr CH3−C∣CH3∣Br−CH2−CH3\mathrm{CH_3-\underset{\underset{\displaystyle CH_3}{|}}{CH}-\underset{\underset{\displaystyle OH}{|}}{CH}-CH_3\ \xrightarrow{HBr}\ CH_3-\overset{\overset{\displaystyle Br}{|}}{\underset{\underset{\displaystyle CH_3}{|}}{C}}-CH_2-CH_3} Give a mechanism for this reaction. (Hint : The secondary carbocation formed in step II rearranges to a more stable tertiary carbocation by a hydride ion shift from 3rd carbon atom.

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The reaction proceeds via an Sₙ1 mechanism where the initial secondary carbocation undergoes a 1,2-hydride shift to form a more stable tertiary carbocation, which is then attacked by Br⁻ to give the rearranged product.


Why this happens — the concept

The hint tells you the key: a hydride shift. But why does the carbocation bother to rearrange at all? The answer is carbocation stability. Tertiary carbocations are more stable than secondary ones because the three alkyl groups donate electron density via hyperconjugation and inductive effects, spreading the positive charge. The reaction is driven by the thermodynamic urge to form the most stable intermediate possible.

In Williamson ether synthesis, you'd use an alkoxide and an alkyl halide — but here we have an alcohol with HBr, which is a classic Sₙ1 or Sₙ2 situation. Because the alcohol is secondary and the acid provides a good leaving group (water), the reaction favours an Sₙ1 pathway, especially when rearrangement can lead to a more stable carbocation.


Step-by-step mechanism

1. Protonation of the hydroxyl group

The lone pair on oxygen of 3-methylbutan-2-ol attacks a proton from HBr, forming an oxonium ion. This makes the OH group a much better leaving group (water instead of hydroxide).

CHX3−CH(CHX3)−CH(OH)−CHX3+HBr→CHX3−CH(CHX3)−CH(OHX2X+)−CHX3+BrX−\ce{CH3-CH(CH3)-CH(OH)-CH3 + HBr -> CH3-CH(CH3)-CH(OH2+)-CH3 + Br-}

2. Loss of water to form a secondary carbocation

The C–O bond breaks heterolytically, ejecting a water molecule and leaving behind a secondary carbocation at the 2nd carbon.

CHX3−CH(CHX3)−CH(OHX2X+)−CHX3→CHX3−CH(CHX3)−CHX+ −CHX3+HX2O\ce{CH3-CH(CH3)-CH(OH2+)-CH3 -> CH3-CH(CH3)-CH+ -CH3 + H2O}

This carbocation is secondary — it has two alkyl groups attached to the positive carbon. It's reasonably stable, but not as stable as it could be.

Watch out

A common mistake is to stop here and attack Br⁻ directly. But if you do that, you'd get the unrearranged product (2-bromo-3-methylbutane), which is not what the question shows. The product given has the bromine on a tertiary carbon — so rearrangement must occur.

3. 1,2-Hydride shift

A hydride ion (H⁻) from the 3rd carbon (the one bearing the methyl group) shifts to the positively charged 2nd carbon. This moves the positive charge to the 3rd carbon, which is now tertiary (attached to three alkyl groups: two methyls and one ethyl group).

CHX3−CH(CHX3)−CHX+ −CHX3→H− shiftCHX3−CX+(CHX3)−CHX2−CHX3\ce{CH3-CH(CH3)-CH+ -CH3 ->[H⁻ shift] CH3-C+(CH3)-CH2-CH3}

The arrow-pushing: the C–H bond at C3 breaks, and the pair of electrons moves to the empty p-orbital at C2. The result is a tertiary carbocation at C3. …

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