Analyzing the Setup
We are given an alcohol, specifically 3,3-dimethylbutan-2-ol, and we are treating it with concentrated sulfuric acid (H2SO4).
Whenever you see an alcohol paired with a strong, non-nucleophilic acid and heat, your mind should immediately jump to an acid-catalyzed dehydration reaction. This reaction proceeds via an E1 mechanism, which means carbocations will be involved. And where there are carbocations, there is always the potential for rearrangement!
The Protonation Step
The hydroxyl group (−OH) is a notoriously poor leaving group because the hydroxide ion is a strong base.
To make it leave, we need to turn it into a weaker base. This is where the acid comes in. The lone pair of electrons on the oxygen atom attacks a proton (H+) from the sulfuric acid.
This protonation converts the −OH group into −OH2+. Now, the leaving group is a neutral water molecule (H2O), which is an excellent, highly stable leaving group.
Carbocation Formation and Rearrangement
With a great leaving group in place, the carbon-oxygen bond breaks heterolytically. The water molecule departs, taking the bonding electrons with it.
This leaves behind a positive charge on carbon-2, creating a secondary (2∘) carbocation.
However, this is not the end of the story. Right next to our secondary carbocation is a quaternary carbon (carbon-3) bonded to three methyl groups. Nature always seeks the lowest energy state. By undergoing a 1,2-methyl shift, one of the methyl groups migrates with its electrons to the positively charged carbon.
This transforms our secondary carbocation into a tertiary (3∘) carbocation, which is significantly more stable due to increased hyperconjugation and the +I (inductive) effect of the surrounding alkyl groups.
Final Elimination
Now that we have our most stable carbocation, the final step is elimination.
A weak base from the reaction mixture (such as the bisulfate ion, HSO4−) will abstract a proton from an adjacent carbon. The electrons from the broken C−H bond will collapse to form a π bond.
According to Zaitsev's Rule, the major product will be the most highly substituted alkene because it is thermodynamically the most stable. Abstraction of a proton from the adjacent CH group yields a tetrasubstituted double bond.
The final major product is 2,3-dimethylbut-2-ene, which perfectly matches option (b).