Primary alkyl halide `C_(4)H_(9)Br` (a) reacted with alcoholic KOH to give compound (b). Compound (b) is reacted with HBr to give (c) which is an isomer of (a). When (a) is reacted with sodium metal it gives compound (d), `C_(8)H_(18)` which is different from the compound formed when n-butyl bromide is reacted with sodium. Give the structural formula of (a) and write the equations for all the reactions.

Explanation

(i) Two primary alkyl halides having the molecular formula `C_(4)H_(9)Br` are possible. These are given below:
`underset("n-Butyl bromide")(CH_(3)CH_(2)CH_(2)CH_(2)Br)` `underset("Isobutyl bromide")(CH_(3)-underset(CH_(3))underset(|)CH-CH_(2)Br)`
(ii) When compound (a) was reacted with Na metal, it gave a compound (d) (`C_(8)H_(18)`) which was different from the compound obtained when n-butyl bromide was reacted with Na metal and hence the compound (a) must be isobutyl bromide and compound (d) must be 2,5-dimethylhexane.
`underset("n-Butyl bromide")(2CH_(3)CH_(2)CH_(2)CH_(2)Br)+2Na overset("Wurts reaction")to underset("n-Octane")(CH_(3)CH_(2)CH_(2)CH_(2)CH_(2)CH_(2)CH_(2)CH_(3))`
`underset("Isobutyl bromide")(2CH_(3)-underset(CH_(3))underset(|)CH-CH_(2)Br)+2Na overset("Wurts reaction")to underset("2,5-Dimethylhexane")(CH_(3)-underset(CH_(3))underset(|)CH-CH_(2)-CH_(2)-underset(CH_(3))underset(|)CH-CH_(3))`
(iii) If compound (a) is isobutyl hromide, then compound (b) obtained on treatment with alc. KOH must be 2-methyl prop-l-ene
`underset((a))(CH_(3)-underset(CH_(3))underset(|)CH-CH_(2)Br) overset(alc.KOH)to underset(underset((b))("2-Methylprep-l-ene"))(CH_(3)-underset(CH_(3))underset(|)C=CH_(2))`
(iv) Compound (b) on treatment with HBr gives compound (c) in accordance with Markovnikov.s rule
`underset("2-Methyl propane")(CH_(3)-underset(CH_(3))underset(|)C=CH_(3)) underset("Markovnikov rule")overset(HBr)to underset("tert-Butyl bromide (c)")(CH_(3)-underset(Br)underset(|)overset(CH_(3))overset(|)C-CH_(3))`
(c) is an isomer of compound (a).
Thus (a) = isobutyl bromide (b) = 2-Methylprop-1-ene te
(c) = tert-Butyl bromide (d) = 2,5-Dimethylhexane