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
`underset("n-Butyl bromide")(CH_(3)CH_(2)CH_(2)CH_(2)Br)" and "underset("Isobutyl bromide")((CH_(3)-overset(CH_(3))overset(|)(C)H-CH_(2)Br)`
Thus, compound (a) is either n-butyl bromide or isobutyl bromide.
(ii) Since compound (a) when reacted with Na metal gives a compound (d) with M.F. `C_(8)H_(18)` which is different from the compound obtained when n-butyl bromide is reacted with Na metal, therefore, (a) must be isobutyl bromide and compound (d) must be 2,5-dimethylhexane.
`underset("n-Butyl bromide "(1^(@)))(2CH_(3)CH_(2)CH_(2)CH_(2)Br)+2Na underset(-2NaBr)overset("Wurtz reaction")to underset("n-Octane")(CH_(3)CH_(2)CH_(2)CH_(2)CH_(2)CH_(2)CH_(2)CH_(3))`
`underset("Isobutyl bromide "(a)" "(1^(@)))(CH_(3)-overset(CH_(3))overset(|)(C)H-CH_(2)Br)+2Na underset(-2" "NaBr)overset("Wurtz reaction")to underset("2,5-Dimethylhexane (d), M.F. "C_(8)H_(18))(CH_(3)-overset(CH_(3))overset(|)(C)H-CH_(2)-CH_(2)-overset(CH_(3))overset(|)(C)H-CH_(3))`
(iii) If compound (a) is isobutyl bromide then compound (b) which it gives on treatment with alcoholic KOH must be 2-methyl-1-propene
`underset("Isobutyl chloride (a)")(CH_(3)-overset(CH_(3))overset(|)(C)H-CH_(2)Br) underset(("Dehydrohalogenation"))overset(KOH(alc),Delta)to underset("2-Methyl-1-propene (b)")(CH_(3)-overset(CH_(3))overset(|)(C)=CH_(2))`
(iv) The compound (b) on treatment with HBr gives compound (c) in accordance with Markovnikov's rule. therefore, compound (c) is tert-butyl bromide which is an isomer of compound (a), i.e., isobutyl bromide.
`underset("2-Methyl-1-propene")(CH_(3)-overset(CH_(3))overset(|)(C)=CH_(2)) underset(("Mark. addn."))overset(HBr)to underset("tert-Butyl bromide (c) (an isomer of compound (a)")(CH_(3)-underset(Br)underset(|)overset(CH_(3))overset(|)(C)-CH_(3))`
thus, (a) is isobutyl bromide, (b) is 2-methyl-1-propene, (c) is tert-butyl bromide and (d) is 2,5-dimethylhexane.