Concept:

When alcohols react with nucleophiles (e.g., halide ions in the Lucas test), the reaction proceeds via the cleavage of the C-O bond (an \(\text{S}_N1\) mechanism for 2°/3°). The reactivity is governed entirely by the stability of the carbocation intermediate.

Formula:

$$ \text{Carbocation Stability: } 3^{\circ} > 2^{\circ} > 1^{\circ} $$

Solution:

• First, classify each alcohol:



• 2-methyl-1-pentanol has the -OH on C1. It is a Primary (1°) alcohol.



• 3-methyl-2-pentanol has the -OH on C2 (bonded to C1 and C3). It is a Secondary (2°) alcohol.



• 2-methyl-2-pentanol has both a methyl group and an -OH on C2. It is a Tertiary (3°) alcohol.



• Increasing order means lowest to highest. Therefore: Primary < Secondary < Tertiary.



• This matches the sequence: 2-methyl-1-pentanol < 3-methyl-2-pentanol < 2-methyl-2-pentanol.

Why other options are incorrect:

Option A is the decreasing order. Options B and D use incorrect mathematical signs or scrambled logic for the established carbocation stability trend.