Primary alkyl halide `C_4 H_9Br` :
(a) reacted with alcoholic KOH to give compound (b) is reacted with HBr to give : (c) which is an isomer of (a). When (a) is reacted with Na metal, it gives a compound (d), `C_8H_18` hich is different from the compound formed when n-butyl bromide is reacted with Na metal. Give the structural formula of (a) and write the equations for all the reactions.

Explanation

Possible primary alkyl halides having the molecular formula `C_4H_9Br` are :
(i) `underset("n - butyl bromide"(1^@)) (CH_3CH_2 CH_2 CH_2Br)` (ii) `underset("isobutyl bromide "(1^@))(CH_3 - overset(CH_3)overset(|)(CH) - CH_2 Br)`
Thus, compound (a) is either n-butyl bromide or isobutyl bromide. Since compound (a) on reaction with sodium metalgives a compound (d) with molecular formula C3H18 which is different from the compound obtained when n-butyl bromide is reacted with sodium metal, hence, (a) must be isobutyl bromide and compound (d) formed by its treatment with sodium metal must be 2,5-dimethylhexane.
Reactions involved are :
`underset("n-butyl bromide (1^@)")(2CH_3CH_2 CH_2CH_2Br) + 2Na underset("-2 NaBr")overset("Ether")tounderset("n-Octane")(CH_3CH_2CH_2CH_2CH_2CH_2 CH_2CH_3)`
`underset("Isobutyl bromide"(1^@)(a))(CH_3-overset(CH_3)overset(|)(CH) - CH_2 Br + 2Na ) underset(-2NaBr)overset("Ether")tounderset("2,5-Dimethylhexane(d)")(CH_3-overset(CH_3)overset(|)(CH) -CH_2 - CH_2 - overset(CH_3)overset(|)(CH) - CH_3)`
If compound (a) is isobutyl bromide, compound (b) obtained from (a) by treatment with alcoholic KOH must be 2-methylpropene.
`{:(underset("Isobutyle bromide")(CH_3-overset(CH_3)overset(|)(CH) - CH_2Br) underset(("Dehydrohalogenation"))overset(KOH(alc.)Delta)tounderset(2-"Methylpropene")(CH_3- overset(CH_3)overset(|)C = CH_2)),(" "(a)" "-HBr" "(b)):}`
The compound (b) on treatment with HBr gives compound (c) which is an isomer of (a), i.e., isobutyl bromide
`underset("2-Methylpropene")(CH_3 - overset(CH_3)overset(|)C = CH_2 + HBr) overset(("Mark addn."))tounderset((c))underset("tert-Butylbromide")(CH_3 - underset(Br)underset(|)overset(CH_3)overset(|)C - CH_3)`
Thus, a = isobutyl bromide
b = 2-Methylpropene
c =tert-Butylbromide
d=2,5-Dimethylhexane