Explanation:

When HBr reacts with alcohols, it undergoes a nucleophilic substitution reaction, also known as an SN1 reaction. The rate of this reaction is dependent on the stability of the carbocation intermediate that forms during the reaction.

The stability of a carbocation is determined by the number of alkyl groups attached to the positively charged carbon. The more alkyl groups attached, the more stable the carbocation, and the faster the reaction.

Therefore, in this case, we need to determine which alcohol produces the most stable carbocation intermediate when it reacts with HBr.

The four alcohols given in the question are:

a) 2-Methylpropan-1-ol
b) 2-Methylpropan-2-ol
c) Propan-2-ol
d) Propan-1-ol

Out of these, 2-Methylpropan-2-ol (also known as tert-butanol) produces the most stable carbocation intermediate due to the presence of three alkyl groups on the carbon that forms the carbocation.

On the other hand, Propan-1-ol and Propan-2-ol produce less stable carbocation intermediates due to the presence of only one alkyl group on the carbon that forms the carbocation.

2-Methylpropan-1-ol also produces a less stable carbocation intermediate compared to 2-Methylpropan-2-ol, as it has only two alkyl groups attached to the carbon that forms the carbocation.

Therefore, HBr reacts fastest with 2-Methylpropan-2-ol, as it produces the most stable carbocation intermediate.