Arrange the compounds of each set in order of reactivity towards `S_(N)2` displacement:
(i) 2-Bromo-2-methylbutane, 1-Bromopentane, 2-Bromopentane
(ii) 1-Bromo-3-methylbutane, 2-Bromo-2-methylbutane, 2-Bromo-3-methylbutane
(iii) 1-Bromobutane, 1-Bromo-2,2-dimethylpropane, 1-Bromo-2-methylbutane, 1-Bromo-3-methylbutane.

Explanation

The reactivity in `S_(N)2` reactions depends upon steric hindrance , more the steric hindrance slower the reaction.
(i) `underset("2-Bromo-2-methylbutane "(3^(@)))(CH_(3)-underset(Br)underset(|)overset(CH_(3))overset(|)(C)-CH_(2)CH_(3))" "underset("1-Bromopentane "(1^(@)))(CH_(3)CH_(2)CH_(2)CH_(2)CH_(2)-Br)" "underset("2-Bromopentane "(2^(@)))(CH_(3)-underset(Br)underset(|)(C)H-CH_(2)CH_(2)CH_(3))`
Since due to steric reasons, the order of reactivity in `S_(N)2` reactions follows the order: `1^(@) gt 2^(@) gt 3^(@)`, therefore, order of reactivity of the given alkyl bromides is:
1-Bromopentanegt2-Bromopentanegt2-Bromo-2-methylbutane.
(ii) `underset("1-Bromo-3-methylbutane "(1^(@)))(CH_(3)-overset(CH_(3))overset(|)(.^(3)C)H-overset(2)(C)H_(2)overset(1)(C)H_(2)Br)" "underset("2-Bromo-2-methylbutane "(3^(@)))(overset(1)(C)H_(3)-underset(Br)underset(|)overset(CH_(3))overset(|)(.^(2)C)-overset(3)(C)H_(2)overset(4)(C)H_(3))" "underset("2-Bromo-3-methylbutane "(2^(@)))(overset(1)(C)H_(3)-underset(Br)underset(|)overset(2)(C)H-overset(CH_(3))overset(|)(.^(3)C)H-overset(4)(C)H_(3))`
Since due to steric reasons, the order of reactvity of alkyl halides in `S_(N)2` reactions follows the order:
`1^(@)gt2^(@)gt3^(@)`, therefore, the order of reactivity of the given alkyl bromides is:
1-Bromo-3-methylbutane `(1^(@))gt2-`Bromo-3-methylbutane `(2^(@))gt`2-Bromo-2-methylbutane `(3^(@))`
(iii) `underset("1-Bromobutane "(1^(@)" with no branching"))(CH_(3)CH_(2)CH_(2)CH_(2)Br)" "underset("1-Bromo-2,2-dimethylpropane "(1^(@)" with two "beta-"methyl groups"))(CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(.^(beta)C)-overset(alpha)(C)H_(2)Br)" "underset("1-Bromo-2-methylbutane "(1^(@)" with one "beta-"ethyl group"))(CH_(3)CH_(2)-overset(CH_(3))overset(|)(.^(beta)C)H-overset(alpha)(C)H_(2)Br)" "underset("1-Bromo-3-methylbutane "(1^(@)" with one methyl group "gamma-"position"))(CH_(3)-overset(CH_(3))overset(|)(.^(gamma)C)H-overset(beta)(C)H_(2)-overset(alpha)(C)H_(2)-Br)`
Since in case of `1^(@)` alkyl halides, steric hindrance increases in the order: n-alyl halides, alkyl halide with a substituent at any position other than the `beta`-position, one substituent at the `beta`-position, two substituents at the `beta`-position, therefore, the reactivity decreases in the same order. thus, the reactivity of the given akyl bromides decreases in the order:
1_bromobutanegt1-Bromo-3-methylbutanegt1-Bromo-2-methylbutanegt1-Bromo-2,2-dimethylpropane.