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The correct order of increasing reactivity of C–X bond towards nucleophile in the following compounds is
(I) $C_6H_5-X$, (II) 2,4-dinitrohalobenzene, (III) $(CH_3)_3C-X$, (IV) $(CH_3)_2CH-X$
(I) $C_6H_5-X$, (II) 2,4-dinitrohalobenzene, (III) $(CH_3)_3C-X$, (IV) $(CH_3)_2CH-X$
A
III < II < I < IV
B
I < II < IV < III
C
II < III < I < IV
D
IV < III < I < II
Detailed Solution
In aryl halides (I and II) the C–X bond has partial double bond character due to resonance and the carbon is $sp^2$ hybridised, so they are much less reactive towards nucleophiles than alkyl halides.
Among the aryl halides, the two electron-withdrawing $-NO_2$ groups at the ortho and para positions in (II) stabilise the intermediate carbanion, so (II) is more reactive than the unsubstituted halobenzene (I): I < II.
The alkyl halides (III and IV) react readily; taking the reaction through the carbocation ($S_N1$) pathway, the tertiary halide (III) forms the more stable tertiary carbocation and is more reactive than the secondary halide (IV): IV < III.
Combining these: I < II < IV < III
Among the aryl halides, the two electron-withdrawing $-NO_2$ groups at the ortho and para positions in (II) stabilise the intermediate carbanion, so (II) is more reactive than the unsubstituted halobenzene (I): I < II.
The alkyl halides (III and IV) react readily; taking the reaction through the carbocation ($S_N1$) pathway, the tertiary halide (III) forms the more stable tertiary carbocation and is more reactive than the secondary halide (IV): IV < III.
Combining these: I < II < IV < III